Vibronial measuring system

Abstract

Vibronal measuring system, in particular a Coriolis mass flow meter or Coriolis mass flow / density meter, for measuring and / or monitoring at least one measured quantity, in particular a flow parameter, in particular a mass flow rate and / or a volume flow rate and / or a flow velocity, and / or a material parameter, in particular a density and / or a viscosity, of a fluid medium, in particular a gas, a liquid or a dispersion, which, in particular designed as an in-line measuring device and / or a compact measuring device, comprises: - a measuring transducer (10) -- with a pipe arrangement for guiding the flowing medium, -- mechanical power useful with an excitation arrangement for converting electrical power into the excitation and maintenance of forced mechanical vibrations of the pipe arrangement -- and with a sensor arrangement for detecting mechanical vibrations of the pipe arrangement and for providing vibration measurement signals representing the vibration movements of the pipe arrangement; - as well as a measuring system electronics (20) electrically coupled to the measuring transducer (10), namely both to its excitation arrangement and to its sensor arrangement, in particular by means of electrical connecting lines, in particular formed by means of at least one microprocessor and / or arranged in electronic protective housing, for controlling the measuring transducer and for evaluating vibration measurement signals supplied by the measuring transducer; - wherein the pipe arrangement comprises at least one, in particular at least partially curved and / or at least partially straight and / or first, pipe (111), -- which pipe extends from a first pipe end to a second pipe end with a pipe length, in particular more than 100 mm, and has a lumen enclosed by a pipe wall, in particular metallic, extending from the first pipe end to the second pipe end, -- and which pipe is set up to be flowed through by the measuring medium in at least one flow direction pointing from the first pipe end to the second pipe end and to be vibrated during this process, -- and wherein the tube possesses a plurality of vibration modes (natural modes) each having an associated resonance frequency (f1, f2, ... , fx), in which the tube can or does perform vibrational movements having one or more antinodes and two or more nodes, such that --- that the vibrational movements of the pipe in a fundamental vibration mode, namely a first-order vibration mode (f1-mode), in particular a first-order bending vibration mode, exhibit exactly one antinode and two nodes --- and that the vibrational movements of the pipe in a higher-order vibration mode, namely a second or higher order vibration mode (f2 mode, ... fx mode), in particular a second or higher order bending vibration mode, exhibit two or more antinodes and three or more nodes; - wherein the excitation arrangement includes a vibration exciter (31), in particular an electrodynamic one, -- mechanically connected to the pipe -- and is designed to convert electrical power into mechanical power using a time-varying electric current, such that a time-varying driving force acts on the pipe at a drive point formed by means of the vibration exciter on the pipe mechanically connected thereto, in particular such that a line of action of the driving force runs perpendicular to a normal of a driving cross-sectional area of ​​the pipe, -- wherein the vibration exciter (31) is positioned and aligned such that a drive offset (ΔE), namely a minimum distance between a drive cross-sectional area of ​​the tube enclosed by an imaginary circumferential line of the tube passing through the drive point and a predetermined reference cross-sectional area of ​​the at least one tube, determined in particular with an intact or original transducer, is no more than 3 mm, in particular less than 2 mm, and / or less than 0.5% of the tube length, in particular less than 0.2% of the tube length, in particular is zero with an intact or original transducer, wherein a vibration antinode formed between two antinodes of vibration movements of the at least one tube in a vibration mode (second or higher order) (deviating from the first order vibration mode), in particular(nominally) located at half a pipe length, vibration nodes of namely vibration movements lie within the reference cross-sectional area, . - and wherein the measuring system electronics (20) is configured to supply current to the vibration exciter (31), namely to supply electrical power to the vibration exciter (31) by means of an electrical driver signal (e1) having a time-varying electrical current, such that the tube performs forced mechanical vibrations, in particular bending vibrations, with one or more vibration frequencies specified by the driver signal (e1); - wherein the sensor arrangement includes a first vibration sensor, in particular an electrodynamic or optical one, -- which is positioned on the pipe, in particular at a distance of more than 10 mm and / or more than one fifth of the pipe length in the direction of flow, and in particular is at least partially mechanically connected to the pipe, is -- and which is equipped to detect vibrations of the pipe and to convert them into a first vibration measurement signal representing vibrations, in particular an electrical or optical signal, in particular such that the first vibration measurement signal contains one or more sinusoidal signal components, each with a frequency corresponding to a vibration frequency of vibrations of the pipe; - wherein the sensor arrangement includes at least one second vibration sensor, in particular an electrodynamic or optical one, -- which is positioned on the pipe, in particular more than 10 mm and / or more than one fifth of the pipe length away from the vibration exciter in the direction of flow and / or which is positioned away from the first vibration sensor in the direction of flow, in particular at least partially mechanically connected to the pipe, is -- and which is equipped to detect vibrations of the pipe and to convert them into a second vibration measurement signal representing the same vibrations, in particular an electrical or optical signal, in particular such that the second vibration measurement signal contains one or more sinusoidal signal components, each with a frequency corresponding to a vibration frequency of vibrations of the pipe; - and wherein the measuring system electronics are configured to receive and evaluate the first and second vibration measurement signals, in particular to determine and output the measured values ​​representing at least one measured quantity; - where the measuring system electronics are set up, -- to provide both the driver signal (e1) at least temporarily with a sinusoidal first (useful) current (eN1) having a first (alternating current) frequency, in such a way, --- that the tube performs at least partially, in particular predominantly, first useful vibrations, namely mechanical vibrations forced by the (energized) vibration exciter with a first useful frequency, namely a (vibration) frequency corresponding to the first (alternating current) frequency, in particular such that the first useful frequency deviates from a resonance frequency, f1, of the fundamental vibration mode by less than 1% of the same resonance frequency, f1, and / or by less than 1 Hz and / or that the first useful frequency deviates from a resonance frequency, f2, of the second-order vibration mode by more than 5% of the same resonance frequency, f2, and / or by more than 10 Hz and / or that the first useful vibrations are suitable to cause Coriolis forces in the flowing medium that depend on the mass flow rate, --- and that each of the first and second oscillation signals (s1; s2) has a first useful signal component (s1N1; s2N1), namely a sinusoidal signal component with a (signal) frequency corresponding to the first useful frequency, -- as well as on the basis of at least the first useful signal components (s1N1; s2N1), in particular on the basis of their (signal) frequency and / or on the basis of an amplitude of at least one of the first useful signal components (s1N1; s2N1) and / or on the basis of a phase angle of at least one of the first useful signal components (s1N1; s2N1), which represent at least one measured quantity, in particular mass flow values ​​representing the mass flow of the measured substance and / or density values ​​representing the density of the measured substance; - and where the measuring system electronics are set up, -- to provide both the driver signal (e1) at least temporarily, in particular during a test interval lasting more than 10 ms and / or limited in time and / or restarted repeatedly, with a sinusoidal second (useful) current (eN2) having a second (AC) frequency, in such a way, --- that the second (alternating current) frequency, in particular for two or more oscillation periods and / or a period of more than 10 ms, deviates from a resonance frequency, f2, of the second order oscillation mode by less than 1%, in particular by less than 0.1%, namely resonance frequency, f2, and / or by less than 1 Hz, in particular by less than 0.1 Hz, --- and that the pipe at least partially – in particular simultaneously with the first useful oscillations and / or stationary, namely for two or more oscillation periods and / or a period of more than 10 ms – performs second useful oscillations, namely mechanical oscillations forced by the (energized) vibration exciter with a second useful frequency, namely one corresponding to the second (alternating current) frequency, whereby each of the first and second oscillation signals has a second useful signal component (s1N2; s2N2), namely a sinusoidal signal component with a (signal) frequency corresponding to the second useful frequency, -- as well as on the basis of at least one of the second useful signal components (s1N2; s2N2), in particular on the basis of their (signal) frequency and / or on the basis of a (signal) amplitude of at least one of the second useful signal components (s1N2) and / or on the basis of a phase angle of at least one of the second useful signal component (s1N2), to carry out a (self-)diagnosis of the measuring system, in particular to check the functionality of the measuring system and / or to (re-)calibrate the measuring system and / or to determine whether there is a fault in the measuring system.

Description

[0001] The invention relates to a vibronic measuring system formed by means of a vibration-type transducer and electrically connected measuring system electronics, in particular a Coriolis mass flow meter or Coriolis mass flow / density meter, for measuring and / or monitoring at least one measured quantity of a flowing medium, in particular a gas, a liquid, or a dispersion. The measured quantity can be, for example, a time-varying flow parameter, such as a mass flow rate, a volume flow rate, or a flow velocity, and / or a time-varying material parameter, such as a density and / or a viscosity, of the respective medium. Such measuring systems—typically designed as compact in-line measuring devices—have long been known and have proven their worth in industrial applications.not least in the area of ​​regulating and monitoring automated process engineering processes or process plants, or in the area of ​​transfer points for goods transport, which may also be subject to calibration requirements. Examples of vibronic measuring systems of the type in question are, for example, in EP-A 317 340, EP-A 816 807, JP-A 8-136311, JP-A 9-015015, US-A 2005 / 0125167, US-A 2006 / 0000293, US-A 2006 / 0112774, US-A 2006 / 0266129, US-A 2007 / 0062308, US-A 2007 / 0113678, US-A 2007 / 0119264, US-A 2007 / 0119265, US-A 2007 / 0151370, US-A 2007 / 0151371, US-A 2007 / 0186685, US-A 2008 / 0034893, US-A 2008 / 0041168, US-A 2008 / 0141789, US-A 2010 / 0011882, US-A 2010 / 0050783, US-A 2010 / 0101333, US-A 2010 / 0139417, US-A 2010 / 0236338, US-A 2010 / 0242623, US-A 2010 / 0242624, US-A 2010 / 0251830, US-A 2011 / 0167907, US-A 2012 / 0123705, US-A 2014 / 0352454, US-A 2016 / 0033314, US-A 2016 / 0349091,US-A 2016 / 0123836, US-A 2016 / 0138997, US-A 2017 / 0030870, US-A 2017 / 0356777, US-A 2020 / 0132529, US-A 46 80 974, US-A 47 38 144, US-A 47 68 384, US-A 47 77 833, US-A 47 93 191, US-A 48 01 897, US-A 48 23 614, US-A 48 31 885, US-A 48 79 911, US-A 50 09 109, US-A 50 24 104, US-A 50 50 439, US-A 52 91 792, US-A 53 59 881, US-A 53 98 554, US-A 54 76 013, US-A 55 31 126, US-A 56 02 345, US-A 56 91 485, US-A 57 28 952, US-A 57 34 112, US-A 57 96 010, US-A 57 96 011, US-A 57 96 012, US-A 58 04 741, US-A 58 31 178, US-A 58 61 561, US-A 58 69 770, US-A 59 26 096, US-A 59 45 609, US-A 59 79 246, US-A 60 47 457, US-A 60 73 495, US-A 60 92 429, US-A 63 11 136, US-A 2010 / 0011882, US-A 2010 / 0139416, US-B 62 23 605, US-B 63 11 136, US-B 63 30 832, US-B 63 97 685, US-B 65 13 393, US-B 65 57 422, US-B 66 51 513,US-B 66 66 098, US-B 66 91 583, US-B 68 40 109, US-B 68 68 740, US-B 68 83 387, US-B 70 17 424, US-B 70 40 179, US-B 70 73 396, US-B 70 77 014, US-B 70 80 564, US-B 71 34 348, US-B 72 99 699, US-B 73 05 892, US-B 73 60 451, US-B 73 92 709, US-B 74 06 878, US-B 75 62 586, WO-A 00 / 14485, WO-A 01 / 02816, WO-A 03 / 021205, WO-A 2004 / 072588, WO-A 2005 / 040734, WO-A 2005 / 050145, WO-A 2006 / 036139, WO-A 2007 / 097760, WO-A 2008 / 013545, WO-A 2008 / 077574, WO-A 2009 / 136943, WO-A 2011 / 019345, WO-A 2013 / 002759, WO-A 2013 / 009307, WO-A 2017 / 019016, WO-A 2017 / 069749, WO-A 2019 / 017891, WO-A 2019 / 081169, WO-A 2019 / 081170, WO-A 87 / 06691, WO-A 93 / 01472, WO-A 95 / 16897, WO-A 95 / 29386, WO-A 96 / 05484, WO-A 96 / 08697, WO-A 97 / 26508, WO-A 99 / 39164, WO-A 99 / 40394,described in WO-A 99 / 44018 or in the applicant's own unpublished patent applications DE102019124709.8 and PCT / EP2019 / 082044, and are also manufactured and offered by the applicant itself for a long time as Coriolis mass flow meters or as Coriolis mass flow / density meters, for example under the trade names "PROMASS G 100", "PROMASS O 100", "PROMASS E 200", "PROMASS F 300", "PROMASS X 500", "CNGmass", "LPGmass" or "Dosimass" (https: / / www.endress.com / de / search?filter.text=promass).

[0002] Each of the transducers of the measuring systems shown therein comprises at least one pipe arrangement for guiding the flowing fluid, an excitation arrangement for converting electrical power into mechanical power useful for exciting and maintaining forced mechanical vibrations of the pipe arrangement, and a sensor arrangement for detecting mechanical vibrations of the pipe arrangement and for providing vibration measurement signals representing the vibration movements of the pipe arrangement. Both the excitation arrangement and the sensor arrangement are electrically coupled to the measuring system electronics, which in turn serve to control the transducer, in particular its excitation arrangement, and to receive and evaluate the measurement signals supplied by it, in particular the vibration measurement signals supplied by its sensor arrangement, specifically to determine the measured values ​​representing at least one measured quantity.To protect against external influences, the pipe assembly, together with the exciter and sensor assembly, is housed in a typically metallic transducer housing, and the measuring system electronics are housed in a separate, also metallic, electronics housing; the latter can, for example, form a compact Coriolis mass flow / density meter and be mounted directly on the aforementioned transducer housing. In the measuring systems shown in WO-A 96 / 08697 or WO-A 2019 / 017891, the transducer housing and the pipe assembly are specifically designed to be detachably connected, for example, to allow for subsequent insertion of the pipe assembly or the replacement of a defective or worn pipe assembly with an intact one on site.

[0003] The aforementioned pipe arrangements are each designed to be integrated into the course of a process line and each comprises at least one pipe – for example, exactly one pipe, exactly two pipes, or exactly four pipes – extending from a first pipe end to a second pipe end with a pipe length of [missing information] and having a lumen enclosed by a pipe wall – typically metallic – extending from the first pipe end to the second pipe end. The pipe, which is at least partially curved and / or at least partially straight, is – due to the measuring principle – configured to allow flow from the first pipe end to the second pipe end via the connected process line.The fluid being measured is then discharged and, during this process, vibrated—for example, to generate Coriolis forces dependent on the mass flow rate, inertial forces dependent on the density of the fluid, and / or frictional forces dependent on the viscosity of the fluid—to achieve a static equilibrium position. The tubes of commercially available (standard) measuring systems typically have at least two mutually orthogonal planes of symmetry and can, for example, have a U- or V-shape, or a rectangular or triangular shape, and less frequently an Ω- or helical shape. Furthermore, their respective tube walls are typically made of steel, such as stainless steel, duplex steel, or superduplex steel, a titanium alloy, a zirconium alloy, such as Zircaloy, and / or a tantalum alloy.The length of such tubes can range from approximately 100 mm to 2000 mm, and the caliber (inner diameter) of such tubes can range from approximately 0.1 mm to approximately 100 mm, typically such that the respective tube has a caliber-to-length ratio that lies between approximately 0.08 and 0.25.

[0004] In single-tube transducers, the transducer typically communicates with the aforementioned process line via an essentially straight connecting pipe section opening at the inlet and another essentially straight connecting pipe section opening at the outlet. Furthermore, the pipe arrangement of such single-tube transducers comprises at least one one-piece or multi-part, for example, tubular, box-shaped, or plate-shaped, counter-oscillator, which is coupled to the inlet of the tube, forming a first coupling zone, and to the outlet of the tube, forming a second coupling zone. During operation, the counter-oscillator is essentially stationary or oscillates in opposition to the tube, i.e., at the same frequency and out of phase.The tube assembly of such a transducer, formed by a tube and counter-oscillator, is usually mounted in the aforementioned transducer housing in a way that allows it to vibrate, solely by means of the two connecting tube sections through which the tube communicates with the process line during operation. In the (standard) transducers with a single, essentially straight tube, as shown, for example, in US-A 52 91 792, US-A 57 96 010, US-A 59 45 609, US-B 70 77 014, US-A 2007 / 0119264, WO-A 01 / 02816, or WO-A 99 / 40394, the latter and the counter-oscillator are, as is quite common in conventional transducers, essentially coaxially aligned with each other. The materials used for the counter-vibrators, especially when titanium, tantalum or zirconium are used for the tube, are usually relatively inexpensive types of steel, such as structural steel or free-cutting steel.In measuring transducers with two or more tubes, the respective tube arrangement typically has an inlet-side flow divider extending between the tubes and an inlet-side connection flange, as well as an outlet-side flow divider extending between the tubes and an outlet-side connection flange, via which the tube arrangement can be integrated into the process line. The pipe arrangements shown in US-A 2012 / 0123705, US-A 56 02 345, US-A 59 26 096, WO-A 2009 / 136943, WO-A 87 / 06691, WO-A 96 / 05484, WO-A 96 / 08697, WO-A 97 / 26508, WO-A 99 / 39164 or WO-A 2019 / 017891 each have two pipes, namely a first pipe and a second pipe of identical construction and parallel to it, as well as a first flow divider with exactly two flow openings (serving here as a pipe branch or inlet-side) and a second pipe of identical construction to the first flow divider (serving here as a pipe union).The outlet-side second flow divider with exactly two flow openings is shown, whereas in US-A 56 02 345, WO-A 96 / 08697, US-A 2017 / 0356777, WO-A 2019 / 081169, WO-A 2019 / 081170, or the aforementioned patent application PCT / EP2019 / 082044, the pipe arrangements shown each have a first flow divider with exactly two flow openings (serving here as a pipe branch or inlet-side), a second flow divider with exactly two flow openings (identical in construction to the first flow divider and serving here as a pipe junction or outlet-side), and two pipes, namely a first pipe and a second pipe. Furthermore, each of the two...Four pipes are connected to each of the first and second flow dividers, such that the first pipe opens with its first end into a first flow opening of the first flow divider and with its second end into a first flow opening of the second flow divider, and the second pipe opens with its first end into a second flow opening of the first flow divider and with its second end into a second flow opening of the second flow divider.that the first pipe, with its first end, opens into a first flow opening of the first flow divider and, with its second end, into a first flow opening of the second flow divider; the second pipe, with its first end, into a second flow opening of the first flow divider and, with its second end, into a second flow opening of the second flow divider; the third pipe, with its first end, into a third flow opening of the first flow divider and, with its second end, into a third flow opening of the second flow divider; and the fourth pipe, with its first end, into a fourth flow opening of the first flow divider and, with its second end, into a fourth flow opening of the second flow divider. The flow dividers of commercially available transducers are also typically designed as an integral component of the aforementioned transducer protective housing.

[0005] To generate vibration signals influenced by or corresponding to the respective measured quantity, the at least one tube of the transducer is actively excited to vibrations in a vibration mode suitable for measuring the respective measured quantity or generating the aforementioned Coriolis, inertial or frictional forces, occasionally also referred to as the drive or useful mode, by means of the excitation arrangement during operation of the measuring system, and the corresponding vibration responses, namely the resulting vibration movements of the at least one tube, are simultaneously detected by means of the sensor arrangement.

[0006] To excite mechanical vibrations in at least one pipe, the excitation arrangement comprises at least one electromechanical, typically electrodynamic, vibration exciter, which is partially mechanically connected to the pipe and configured to convert electrical power into mechanical power using a time-varying electric current, such that a time-varying driving force acts on the pipe at a drive point formed by the vibration exciter on the mechanically connected pipe. In the aforementioned case where the pipe arrangement comprises at least one further (second) pipe, the at least one vibration exciter can also be partially attached to it, such that the vibration exciter acts differentially on the two pipes.In the other case described above, where the pipe assembly has a counter-oscillator, the vibration exciter can be partially attached to it, such that the vibration exciter acts differentially on the pipe and the counter-oscillator. The vibration exciter can also, for example, be partially attached to the aforementioned transducer housing. In transducers of conventional (standard) measuring systems, the at least one vibration exciter is typically designed and arranged such that the driving force generated thereby acts practically only at a single point on the respective pipe, or that a line of action of the driving force generated thereby runs essentially perpendicular to a normal of a drive cross-sectional area, namely a cross-sectional area of ​​the pipe enclosed by an imaginary circumferential line passing through the aforementioned drive point.In (standard) transducers of commercially available (standard) measuring systems, the excitation arrangements, as shown, among others, in US-A 56 02 345, US-A 57 96 010, US-B 68 40 109, US-B 70 77 014 or US-B 70 17 424, US-A 2014 / 0352454, WO-A 93 / 01472, WO-A 2005 / 050145, WO-A 2013 / 002759, WO-A 2011 / 019345, are typically designed such that each of the tubes is (partially) connected to exactly one vibration exciter, such that the excitation arrangement does not connect any other vibration exciter to the respective tube besides the (one) vibration exciter. exhibits vibration exciters.Not least for this (standard) case, the vibration exciter is typically of the electrodynamic type, namely formed by means of a voice coil, for example in such a way that its magnetic armature is mechanically connected to the at least one tube, forming the drive point, and that its air coil, through which the magnetic field of the armature is permeated, is electrically connected to the measuring system electronics and mechanically connected to the other tube or the counter-vibrator of the tube arrangement or to the transducer protective housing.However, vibronic measuring systems are also known, for example from WO-A 2017 / 069749, WO-A 2017 / 019016, WO-A 2006 / 036139, US-A 59 26 096, WO-A 99 / 28708, WO-A 99 / 44018, WO-A 99 / 02945, US-A 2020 / 0132529, US-A 48 31 885, US-B 65 57 422, US-A 60 92 429 or US-A 48 23 614, in which the excitation arrangement has two or more vibration exciters connected to one and the same of the tubes of the respective tube arrangement and / or formed by means of one or more piezo elements.

[0007] To detect vibrations of at least one pipe, the sensor arrangement comprises at least two vibration sensors, for example, electrodynamic or optical. A first vibration sensor is positioned on the inlet side of the pipe, spaced apart from the vibration exciter in the direction of flow, and a second vibration sensor—typically identical in construction to the first—is positioned on the outlet side of the pipe, spaced apart from the vibration exciter in the direction of flow. Each of the at least two vibration sensors is also configured to detect vibrations of the pipe and convert them into a first or second vibration measurement signal representing these vibrations, in particular an electrical or optical signal, for example, with an electrical voltage that depends on the vibrations of the pipe.In the case of electrodynamic vibration sensors, these can, for example, each be formed by means of a moving coil electrically connected to the measuring system electronics, for example in such a way that its magnetic armature is mechanically connected to the at least one tube and that its air coil, through which the magnetic field of the armature is permeated, is electrically connected to the measuring system electronics and mechanically connected to the other tube or the counter-oscillator of the tube arrangement or to the transducer protection housing.

[0008] The measuring system electronics of each of the aforementioned measuring systems are also designed to energize the at least one vibration exciter in operation according to the desired mode of excitation, namely by means of at least one time-varying electrical driver signal, e.g. with an electrical current controlled with respect to (alternating current) frequency, phase angle and amplitude, supplying electrical power to the at least vibration exciter, such that the tube performs forced mechanical vibrations, for example bending vibrations, with one or more vibration frequencies specified by the driver signal, typically corresponding to one or more resonant frequencies of the at least one tube; this can also be done, for example, with a constantly controlled vibration amplitude.The driver signal can be configured as a harmonic sine wave with precisely one (AC) frequency, or, for example, as a multi-frequency signal containing several signal components with differing (AC) frequencies. Consequently, each of the first and second vibration measurement signals supplied by the sensor arrangement contains one or more sinusoidal signal components, each with a frequency corresponding to a vibration frequency of the pipe's oscillations, such that each of the first and second vibration signals also includes at least one useful signal component, namely a sinusoidal signal component with a (signal) frequency corresponding to the first useful frequency.Accordingly, the measuring system electronics are also configured to provide the aforementioned driver signal for the vibration exciter at least temporarily with a sinusoidal (useful) current having an (alternating current) frequency, such that the at least one tube performs at least partially or predominantly useful vibrations, namely mechanical vibrations forced by the (energized) vibration exciter with a useful frequency, namely a (vibration) frequency corresponding to the aforementioned (alternating current) frequency.

[0009] In measuring systems of the type in question, the useful mode is typically one or more of the many natural vibration modes inherent in the tube, each with its own resonant frequency. In particular, one or more symmetrical vibration modes are used, in which the tube can and does exhibit an odd number of antinodes and a correspondingly even number of nodes. Due to their suitability for measuring mass flow, density, and viscosity of the fluid, such measuring systems, especially commercially available standard measuring systems, preferably utilize one or more natural symmetrical bending vibration modes as the useful mode. In transducers with a curved tube, or...For curved tubes, a symmetrical bending vibration mode is typically chosen as the operating mode, in which the respective tube oscillates around a static equilibrium position about an imaginary first axis of vibration connecting the first and second tube ends, similar to a cantilever clamped only at its ends (out-of-plane mode), whereas for transducers with a straight tube or straight tubes, a symmetrical bending vibration mode is usually chosen as the operating mode, in which the respective tube oscillates around a static equilibrium position about an imaginary axis of vibration that coincides with one of its principal axes of inertia (longitudinal axis) and connects the first and second tube ends, similar to a clamped string (in-plane mode).In commercially available measuring systems, the use of the first-order (bending) vibration mode, sometimes also referred to as the fundamental vibration mode or f1 mode, in which the vibrational movements of the tube each have exactly one antinode and two nodes, and are therefore symmetrical, has become particularly established as the useful mode; less frequently, the use of the third-order (bending) vibration mode, sometimes also referred to as the f3 mode, in which the vibrational movements of the tube each have exactly three antinodes and four nodes, has also become established.

[0010] In the aforementioned (standard) case where exactly one vibration exciter is provided per pipe (or per pair of pipes), it is accordingly always positioned and aligned in such a way that the aforementioned drive cross-sectional area is located as close as possible to half the pipe length, thus at a respective maximum vibration amplitude of each of the aforementioned symmetrical vibration modes or a maximum amplitude of the corresponding useful vibrations, but also at a vibration node of the asymmetrical vibration mode inherent in the pipe.To achieve the highest possible efficiency in exciting the desired vibration mode, but also to avoid unwanted excitation of vibrations in one or more of the aforementioned asymmetric vibration modes, the vibration exciter in commercially available (standard) measuring systems is specifically positioned such that the drive offset—namely, the smallest possible distance between the drive cross-sectional area of ​​the tube and a predetermined reference cross-sectional area of ​​the at least one tube located at a maximum amplitude of the vibration movements of the desired vibrations—is as small as possible, ideally zero. In commercially available (standard) measuring systems, a line of intersection of two mutually orthogonal planes of symmetry of the at least one tube, or a line perpendicular to the direction of vibration of the tube's vibration movements, typically lies in the second-order vibration mode.The principal axis of inertia of at least one tube within the aforementioned reference cross-sectional area, relative to the driving force. In commercially available (standard) measuring systems, the drive offset, due in no small part to the various tolerances of the transducers and the components and assemblies required for them, is indeed slightly different from zero, but typically amounts to less than 5 mm and less than 0.5% of the tube length, and usually even less than 2 mm and less than 0.2% of the tube length.

[0011] For the purpose of efficient excitation of the useful mode, the measuring system electronics are specifically designed to adjust the (alternating current) frequency determining the useful frequency so that it corresponds as closely as possible to a resonance frequency (f1) of the first-order oscillation mode or a resonance frequency (f3) of the third-order oscillation mode, or deviates from the respective resonance frequency to be set by less than 1% of that resonance frequency and / or by less than 1 Hz, and thus from the resonance frequency of each of the other natural oscillation modes of the tube by more than 5% of that resonance frequency and / or by more than 10 Hz.The measuring system electronics are configured to respond to changes in the resonant frequency, for example, due to a change in the density of the fluid in the tube, by adjusting the (AC) frequency of the driver signal, such that the excited vibrations are predominantly resonant vibrations of at least one tube. To adjust the (AC) frequency, the measuring system electronics of the respective measuring system can, as shown, among others, in US-A 2016 / 0349091, US-A 2017 / 0030870, US-A 5831178, and US-A 4801897, incorporate, for example, a phase-locked loop (PLL), possibly a digital one.

[0012] As a result of the useful vibrations of the at least one tube excited in the aforementioned manner, Coriolis forces, which depend on the mass flow rate, are also induced in the flowing medium, such that Coriolis vibrations, namely additionally forced vibrations with the useful frequency, are superimposed on the useful vibrations. These vibrations correspond to a natural vibration mode, occasionally also called a Coriolis mode, with an order increased by one compared to the order of the useful mode. The useful signal components of the vibration measurement signals follow a change in the mass flow rate of the medium guided in the tube with a change in the phase difference of the useful signal components, namely a difference between the phase angle of the useful signal component of the first vibration measurement signal and the phase angle of the useful signal component of the second vibration measurement signal.The electronics of each of the aforementioned measuring systems are also configured to generate mass flow rate measurements representing the mass flow rate based on the phase difference of the signal components caused by the pipe's vibrations in the Coriolis mode. In commercially available (standard) measuring systems, the antisymmetric second-order vibration mode typically serves as the Coriolis mode when the fundamental mode is used as the signal mode, and the antisymmetric fourth-order vibration mode typically serves as the Coriolis mode when the third-order vibration mode is used as the signal mode.Since the resonant frequency of the vibration mode used as the measurement mode is particularly dependent on the instantaneous density of the fluid being measured, commercially available Coriolis mass flow meters can be used to directly measure not only the mass flow rate but also the density of the fluid flowing through it, based on the (AC) frequency of the driver signal and / or the (signal) frequency of the useful signal components of the vibration measurement signals. Accordingly, the measurement system electronics of such systems are typically configured to generate density measurement values ​​representing the density based on the aforementioned (AC) frequency of the driver signal and / or the signal frequency of at least one of the vibration signals.Furthermore, it is also possible to directly measure the viscosity of the fluid flowing through the system using vibronic measuring systems of the type in question, for example, based on the excitation energy or power required to maintain the desired vibrations and / or based on the damping of the desired vibrations resulting from the dissipation of vibrational energy. In addition, further measured quantities, such as the Reynolds number, can be readily determined from the aforementioned flow and / or material parameters using such vibronic measuring systems.

[0013] As mentioned above, among others, in US-A 2007 / 0113678, US-A 2012 / 0123705, US-A 2016 / 0349091, US-A 2016 / 0123836, US-A 2016 / 0138997, US-B 73 92 709, US-B 75 62 586, WO-A 03 / 021205, WO-A 2005 / 050145, WO-A 2011 / 019345, WO-A 2013 / 002759, WO-A 2013 / 009307, WO-A 2017 / 069749, WO-A 93 / 01472, WO-A 99 / 39164 or the As discussed in German patent application 102019124709.8, vibration-type transducers, and thus the measuring systems formed by them, can be exposed to a multitude of stresses during their service life, which usually lasts several years. These stresses can cause significant deviations of the measuring system from a reference state determined beforehand, for example during calibration at the manufacturer's plant and / or during commissioning of the measuring system. Consequently, they can significantly reduce the measuring accuracy of the measuring system, with which it ultimately maps the measured quantity to be recorded, not least the mass flow and the density, into the corresponding measured values.Examples of such leading loads, which result in irreversible changes to the vibration properties of at least one pipe or the pipe arrangement formed with it, whether they occur once or repeatedly, are:Examples of factors that can occur permanently or only briefly include high (over)temperatures, temperature shocks, or other thermally induced overloads of the at least one tube; high pressure surges in the measured medium; excessive clamping forces and / or vibration forces exerted on the transducer by the process line, resulting in cracking and / or plastic deformation in the at least one tube; erosion of the at least one tube from the inside out, caused by the measured medium in the transducer, for example through corrosion and / or abrasion, thus reducing its wall thickness; the formation of deposits on the inner surface of the at least one tube in contact with the measured medium; material fatigue; or other signs of wear on the at least one tube. Furthermore, during the operation of the measuring system, the at least one vibration exciter as well as each of the vibration sensors can also be affected, for example, by thermally induced overload or...Aging may cause changes relevant to measurement accuracy, such as changes that result in an electrical impedance of the measuring transducer.

[0014] As a result of such (over-)loading of the transducer, it can regularly be assumed that one or more system functions (transfer functions) inherent to the transducer, each of which characterizes a vibration response of the pipe assembly—for example, a functional dependence of the useful vibrations or the vibration measurement signals on the driver signal, or one or more functional dependencies of the useful vibrations or the vibration measurement signals on the driver signal and the respective flow and / or material parameters of the measured medium—are altered compared to a (reference) system function inherent to the respective original transducer. Examples of such system functions of the transducer include, among others...to name a mass flow-to-phase-difference system function, according to which the aforementioned phase difference of the useful signal components of the vibration measurement signals depends on the mass flow, or a density-to-resonance-frequency system function of the measuring transducer, according to which one or more resonance frequencies of the pipe connection depend on the density of the measured material.The aforementioned system functions of the measuring system, which involve the measuring system, are equally affected by such (over-)loads of the measuring transducer. These include the measuring functions of the measuring system, according to which the measuring system as a whole converts the respective measured quantity to be recorded into the respective measured values. For example, a mass flow-to-phase difference system function of the measuring transducer, composed of the aforementioned mass flow-to-phase difference system function of the measuring transducer and a phase difference-to-mass flow measurement characteristic function, namely a characteristic function implemented in the measuring system electronics, according to which a determined phase difference is converted into mass flow measurement values. This mass flow-to-measurement measurement function of the measuring system is composed of the aforementioned mass flow-to-mass flow system function and is composed of a mass flow-to-measurement function of the measuring system, according to which the mass flow measurement values ​​determined in this way depend on the mass flow.The phase difference-to-mass flow rate characteristic function can, for example, be a (linear) parameter function with a (scale) zero point corresponding to the phase difference of the useful signal components measured with the sample at rest, and a (measurement) sensitivity that corresponds to a change in the phase difference of the useful signal components related to a change in the mass flow rate (slope of the characteristic function). Further examples of such system functions or measurement functions derived from them include, among others, a density-to-resonance frequency system function of the transducer, or a density-to-measurement (measurement) function of the measuring system involving this as well as a resonance frequency-to-density characteristic function of the measuring system electronics, and / or a viscosity-to-damping system function of the transducer.This can be called a viscosity-to-measurement (measurement) function of the measuring system, involving both a damping-to-viscosity characteristic curve function of the measuring system electronics. The change in the respective system function can accordingly manifest itself, for example, as a drift of one or more of the respective characteristic curve parameters of one or more of the aforementioned characteristic curve functions, in the case of a linear parameter function, for example, from the zero point and / or its slope.

[0015] The aforementioned change to one or more of the system functions of the transducer or one or more of the measurement functions of the measuring system can occasionally lead to the transducer or the measuring system formed by it malfunctioning to such an extent that the high measurement accuracy typically sought for such systems is no longer guaranteed. Consequently, the functionality of the measuring system is significantly impaired, possibly even suspended, or a corresponding malfunction of the affected measuring system occurs. Furthermore, such overloads, which also affect the overall structural integrity of the transducer, may even lead to damage to the pipe assembly or the transducer formed by it, potentially resulting in leakage or explosion.Such changes, which also affect the operational safety of measuring systems of the type in question, can have catastrophic consequences for the entire process plant and the people present therein, for example in the case of toxic and / or highly flammable measuring substances or in the case of gases under high pressure.

[0016] Accordingly, measuring systems of the type in question are typically subjected to recurring inspections, for example, as part of routine predictive maintenance, in order to initiate appropriate repair measures as quickly as possible if necessary, particularly upon detection of a malfunction in the measuring system. Such repair measures may, in the case of a permanent reduction in measurement accuracy, include reprogramming the measuring system electronics to recalibrate them, or, in the case of wear or mechanical damage to the transducer, replacing it or, as mentioned, among others, in WO-A 2019 / 017891, replacing the tube assembly. To detect such malfunctions in measuring systems of the type in question as early as possible, especially those caused by a permanent reduction in measurement accuracy and / or an impairment of operational safety, it is necessary, among other things, to...In US-A 2012 / 0123705, US-A 2010 / 0011882, WO-A 2005 / 050145, WO-A 2013 / 002759, WO-A 2017 / 069749, WO-A 2011 / 019345, WO-A 96 / 05484, WO-A 99 / 39164, US-A 46 80 974, US-A 57 96 010, US-A 57 28 952, US-A 59 26 096 or also DE102019124709.8, it is proposed to subject the respective measuring system to a corresponding diagnosis on a recurring basis on site, in particular namely the measuring system - additionally or exclusively - to a self-diagnosis. to be carried out using onboard means, namely solely by means of a measuring transducer and connected measuring system electronics. In order to determine the aforementioned changes in system functions or associated impairments of the functionality of the measuring system, the pipe can therefore, for example, also be actively stimulated by means of the excitation arrangement during a (self-)diagnosis, if necessary.Vibrations can also be excited multimodally and / or simultaneously with the useful vibrations, and the vibration measurement signals representing the resulting vibration responses can be evaluated accordingly in the measurement system electronics, namely examined for disturbances in the measurement system. For example, parameter values ​​can be determined from the vibration measurement signals that characterize the respective vibration response or one or more of the aforementioned system functions and compared with the corresponding predefined reference values, for example, to generate a system status or fault message, possibly also declared as an alarm, when a corresponding predefined threshold value representing a still acceptable tolerance level is exceeded, i.e., when a fault is diagnosed.Such parameters characterizing vibration responses can be, for example, vibration amplitude ratios or vibration frequency ratios. System parameters characterizing the system functions, in turn, can be, for example, one or more modal bending stiffnesses, one or more modal mass distributions, or one or more modal damping values ​​of at least one pipe. The corresponding reference values ​​can be determined in advance, for example, during initial calibration of the measuring system by the manufacturer at the factory or, if necessary, during commissioning of the measuring system on site, using the measuring system itself while still in its original (reference) state, and stored accordingly in the measuring system electronics.

[0017] Suitable vibration modes for (self-)diagnosis in measuring systems of the type in question, and especially in standard measuring systems, are those natural vibration modes of the pipe that are equally symmetrical as the respective established operating mode. For example, in the (standard) measuring systems shown in US-A 46 80 974, US-A 57 96 010, US-A 57 28 952, and WO-A 2017 / 069749, resonant vibrations of one or more symmetrical vibration modes, preferably resonant vibrations of first and / or third, and possibly also fifth order, vibration modes, are excited and evaluated for the respective self-diagnosis; this is also done, for example, by evaluating free vibrations, i.e., vibrations that have been allowed to decay after active excitation. Alternatively or additionally, as in US-A 2012 / 0123705 or DE102019124709.8. It is proposed that non-resonant vibrations, namely vibrations of the tube forced by means of a correspondingly energized vibration exciter with a vibration frequency deviating from any resonance frequency of the tube by more than 1 Hz or more than 1%, be used for (self-)diagnosis, for example, to minimize or eliminate the dependence of the system function of the measuring transducer under test on the medium carried within it. As in DE102019124709.8, however, due to the typically very low vibration amplitudes of non-resonant vibrations, this can lead to a very long observation period, namely more than 10,000, possibly even more than 10,000 vibration periods, accompanied by a high demand for computing power and storage capacity.

[0018] Based on the aforementioned prior art, one object of the invention is to improve vibronic measuring systems of the aforementioned type in such a way that the occurrence of any disturbances or defects of the measuring system, such as wear or aging of the respective transducer that reduces the measuring accuracy and / or the operational reliability of the measuring system, can be detected as early and reliably as possible, and possibly also signaled; this is particularly important when using the (standard) transducers or typical transducer designs established for conventional measuring systems, as well as while largely maintaining proven technologies and architectures of already established measuring system electronics.

[0019] To solve this problem, the invention comprises a vibronic measuring system, in particular a Coriolis mass flow meter or a Coriolis mass flow / density meter, for measuring and / or monitoring at least one measured quantity, in particular a flow parameter, in particular a mass flow rate and / or a volume flow rate and / or a flow velocity, and / or a material parameter, in particular a density and / or a viscosity, of a fluid medium, in particular a gas, a liquid or a dispersion.The measuring system according to the invention, designed, for example, as an in-line measuring device and / or a compact measuring device, comprises: a transducer with a pipe arrangement for guiding the flowing medium, an excitation arrangement for converting electrical power into mechanical power useful for exciting and maintaining forced mechanical vibrations of the pipe arrangement, and a sensor arrangement for detecting mechanical vibrations of the pipe arrangement and for providing vibration measurement signals representing the respective vibration movements of the pipe arrangement, as well as a connection to the transducer, namely both to its excitation arrangement and to its sensor arrangement, in particularelectrically coupled measuring system electronics, for example formed by means of at least one microprocessor and / or arranged in electronic protective housings, for controlling the measuring transducer and for evaluating vibration measurement signals supplied by the measuring transducer, by means of electrical connecting lines.

[0020] The measuring system according to the invention further provides that the pipe arrangement comprises at least one pipe, for example, at least partially curved and / or at least partially straight and / or a first pipe, which extends from a first pipe end to a second pipe end with a pipe length of, for example, more than 100 mm and has a lumen enclosed by a pipe wall, for example, made of metal, extending from the first pipe end to the second pipe end, and which pipe is configured to be permeated by a flow of the measured medium in at least one direction of flow from the first pipe end to the second pipe end and to be vibrated during this process. Naturally, the pipe possesses a plurality of resonant frequencies, each with an associated resonance frequency (f1, f2, ...)., fx) exhibiting modes of vibration (natural modes of vibration) in which the pipe can or does perform vibrational movements having one or more antinodes and two or more nodes, such that vibrational movements of the pipe in a fundamental mode of vibration, namely a first-order mode of vibration (f1-mode), for example a first-order bending mode, have exactly one antinode and two nodes, and that vibrational movements of the pipe in a higher-order mode of vibration, namely a second-order or higher-order mode of vibration (f2-mode, ... fx-mode), for example a second-order or higher-order bending mode, have two or more antinodes and three or more nodes.

[0021] In the measuring system according to the invention, it is further provided that the excitation arrangement includes a vibration exciter, for example an electrodynamic one, which is mechanically connected to the pipe and is configured to convert electrical power into mechanical power with a time-varying electrical current, such that a time-varying driving force acts on the pipe at a drive point formed on the pipe mechanically connected to it by means of the vibration exciter, for example such that a line of action of the driving force runs perpendicular to a normal of a drive cross-sectional area of ​​the pipe, wherein the vibration exciter is positioned and aligned such that a drive offset, namely a minimum distance between a drive cross-sectional area of ​​the pipe enclosed by an imaginary circumferential line of the pipe passing through the drive point and a predetermined, for example in the case of an intact orThe reference cross-sectional area of ​​the at least one pipe, determined by the original transducer, is no more than 3 mm, for example less than 2 mm, and / or less than 0.5% of the pipe length, for example less than 0.2% of the pipe length, for example zero with an intact or original transducer, wherein a node of vibration movements of the at least one pipe, formed between two antinodes of vibration movements in a vibration mode (second or higher order) (deviating from the first order vibration mode), and located (nominally) at half the pipe length, lies within the reference cross-sectional area.

[0022] In the measuring system according to the invention, it is also provided that the measuring system electronics are configured to supply current to the vibration exciter, namely to feed electrical power into the vibration exciter by means of an electrical driver signal having a time-varying electrical current, such that the pipe performs forced mechanical vibrations, for example bending vibrations, with one or more vibration frequencies specified by the driver signal.

[0023] The measuring system according to the invention further provides that the sensor arrangement comprises a first vibration sensor, for example electrodynamic or optical, which is positioned on the pipe, for example at a distance of more than 10 mm and / or more than one-fifth of the pipe length from the vibration exciter in the direction of flow, for example at least partially mechanically connected to the pipe, and which is configured to detect vibrational movements of the pipe and to convert them into a first vibration measurement signal representing such vibrational movements, for example electrical or optical, such that the first vibration measurement signal contains one or more sinusoidal signal components, each with a frequency corresponding to a vibration frequency of vibrational movements of the pipe, and that the sensor arrangement comprises at least one second vibration sensor, for example electrodynamic or optical, whichfor example, positioned at a distance of more than 10 mm and / or more than one-fifth of the pipe length from the vibration exciter in the direction of flow, and / or positioned at a distance from the first vibration sensor in the direction of flow, for example, being at least partially mechanically connected to the pipe, and being configured to detect vibrations of the pipe and convert them into a second vibration measurement signal representing the same vibrations, for example, an electrical or optical signal, such that the second vibration measurement signal contains one or more sinusoidal signal components, each with a frequency corresponding to a vibration frequency of the pipe's vibrations.

[0024] In the measuring system according to the invention, it is also provided that the measuring system electronics are configured to receive and evaluate the first and second vibration measurement signals, for example, to determine and output the measured values ​​representing at least one measured quantity.

[0025] Furthermore, the measuring system according to the invention is also provided that the measuring system electronics are configured to supply the driver signal, at least temporarily, with a sinusoidal first (useful) current having a first (AC) frequency, such that the tube performs first useful vibrations, namely mechanical vibrations forced by the (energized) vibration exciter, at least partially, for example predominantly, with a first useful frequency corresponding to the first (AC) frequency, for example, such that the first useful frequency deviates from a resonance frequency, f1, of the fundamental vibration mode by less than 1% of that resonance frequency, f1, and / or by less than 1 Hz, and / or that the first useful frequency deviates from a resonance frequency, f2, of the second-order vibration mode by more than 5% of that resonance frequency, f2.and / or deviates by more than 10 Hz and / or that the first useful oscillations are suitable for inducing Coriolis forces in the flowing medium that depend on the mass flow rate, and that each of the first and second oscillation signals has a first useful signal component, namely a sinusoidal signal component with a (signal) frequency corresponding to the first useful frequency, as well as determining, based on at least the first useful signal components, for example, based on their (signal) frequency and / or based on an amplitude of at least one of the first useful signal components and / or based on a phase angle of at least one of the first useful signal components, the measured values ​​representing at least one measured quantity, for example, mass flow values ​​representing the mass flow rate of the medium and / or density values ​​representing the density of the medium. Furthermore, the measuring system according to the invention also provides thatthat the measuring system electronics are configured to provide the driver signal, at least temporarily, for example during a test interval lasting more than 10 ms and / or limited in time and / or restarted repeatedly, with a sinusoidal second (useful) current having a second (AC) frequency, such that the second (AC) frequency deviates from a resonance frequency, f2, of the second-order oscillation mode by less than 1%, for example by less than 0.1%, and / or by less than 1 Hz, for example by less than 0.1 Hz, for two or more oscillation periods and / or a period of more than 10 ms, and that the tube exhibits a constant, at least partially - for example simultaneously with the first useful oscillations and / or stationary, namely for two or more oscillation periods and / or a period of more than 10 ms- second useful vibrations exhibiting a vibration amplitude other than zero - namely, mechanical vibrations forced by the (energized) vibration exciter with a second useful frequency, namely a (vibration) frequency corresponding to the second (AC) frequency, whereby each of the first and second vibration signals has a second useful signal component, namely a sinusoidal signal component with a (signal) frequency corresponding to the second useful frequency, as well as performing a (self-)diagnosis of the measuring system on the basis of at least one of the second useful signal components, for example on the basis of its (signal) frequency and / or on the basis of a (signal) amplitude of at least one of the second useful signal components and / or on the basis of a phase angle of at least one of the second useful signal component,For example, to check the functionality of the measuring system and / or to (re-)calibrate the measuring system and / or to determine whether there is a malfunction of the measuring system.

[0026] According to a first embodiment of the invention, it is further provided that the first useful frequency deviates from a resonance frequency, f1, of the fundamental vibration mode by less than 1% of that resonance frequency, f1, and / or by less than 1 Hz.

[0027] According to a second embodiment of the invention, it is further provided that the first operating frequency deviates from a resonance frequency, fr3, of a third-order vibration mode inherent in the at least one tube, for example, a third-order bending vibration mode, in which the vibrational movements of the tube exhibit exactly three antinodes and two nodes, by less than 1% and / or by less than 1 Hz, for example, by the resonance frequency, fr3. Further developing this embodiment of the invention, it is also provided that a first node of vibration of the vibrational movements of the at least one tube in the third-order vibration mode is located in the first tube end and a second node of vibration of the third-order vibration mode is located in the second tube end.

[0028] According to a third embodiment of the invention, it is further provided that the upper vibration mode corresponds to a second-order vibration mode (f2-mode), for example a second-order bending vibration mode, in which second-order vibration mode the vibrational movements of the tube have exactly two antinodes and three nodes.Further developing this embodiment of the invention, it is also provided that a node of vibration of the vibrational movements of the at least one tube in the second order vibration mode, formed between the two antinodes of the vibrational movements of the at least one tube in the second order vibration mode and located, for example (nominally), at half a tube length, lies within the reference cross-sectional area and / or that a principal axis of inertia of the at least one tube, perpendicular to the direction of vibration of the vibrational movements of the tube in the second order vibration mode, lies within the reference cross-sectional area of ​​the at least one tube.

[0029] According to a fourth embodiment of the invention, it is further provided that the drive offset corresponds to a distance between a centroid (center) of the drive cross-sectional area of ​​the tube and a centroid (center) of the reference cross-sectional area of ​​the at least one tube.

[0030] According to a fifth embodiment of the invention, it is further provided that a line of action of the driving force runs perpendicular to a normal of a drive cross-sectional area of ​​the tube.

[0031] According to a sixth embodiment of the invention, it is further provided that a line of intersection of two mutually orthogonal planes of symmetry of the at least one tube lies within the reference cross-sectional area.

[0032] According to a seventh embodiment of the invention, it is further provided that a principal axis of inertia of the at least one tube, perpendicular to the driving force, lies within the reference cross-sectional area of ​​the at least one tube.

[0033] According to an eighth embodiment of the invention, it is further provided that the measuring system electronics are configured to provide the second useful current of the driver signal at least temporarily simultaneously with the first (useful) current, for example in such a way that an amplitude of the first (useful) current is set not less than an amplitude of the second (useful) current and / or that an amplitude of the second (useful) current is set to more than 40%, for example not less than 50%, of an amplitude of the first (useful) current.

[0034] According to a ninth embodiment of the invention, it is further provided that the measuring system electronics are configured to adjust the second (AC) frequency depending on the first (AC) frequency, for example such that the second (AC) frequency lies within a frequency setting interval, of which an upper interval limit and / or a lower interval limit and / or a center frequency corresponds to a predetermined multiple of the first (AC) frequency, for example namely more than 230% of the first (AC) frequency and / or less than 300% of the first (AC) frequency.

[0035] According to a tenth embodiment of the invention, the measuring system electronics further provide that the measuring system electronics comprise a first phase-locked loop (PLL1), for example, a digital one, for setting the first (AC) frequency, and that the measuring system electronics comprise a second phase-locked loop (PLL2), for example, a digital one, for setting the second (AC) frequency. Further developing this embodiment of the invention, the measuring system electronics are also configured to set a capture range of the second phase-locked loop (PLL2) by means of at least one output signal of the first phase-locked loop (PLL1), for example, an output signal of a loop filter of the first phase-locked loop (PLL1), and / or based on the first (AC) frequency.

[0036] According to an eleventh embodiment of the invention, it is further provided that the measuring system electronics are configured to perform the (self-)diagnosis of the measuring system on the basis of at least one second useful signal component, for example on the basis of its (signal) frequency and / or on the basis of a (signal) amplitude of at least one of the second useful signal components and / or on the basis of a phase angle of at least one of the second useful signal component: to determine whether and / or to what extent a disturbance of the measuring system exists, for example, one that reduces the functionality of the measuring system and / or causes a malfunction of the measuring system and / or reduces the integrity of at least one of the first and second vibration measurement signals or measured values ​​obtained therefrom and / or provokes a measurement error in the measured values ​​obtained therefrom; and / or to determine whether or to what extent the pipe arrangement is altered compared to a previously determined reference state, for example, damaged, and / or to determine whether and / or to what extent a disturbance of the measuring system exists due to one or more vibration properties of the pipe arrangement that have changed compared to a reference state determined beforehand, for example as a result of damage to the pipe arrangement, - and / or to determine whether and / or to what extent damage to the pipe assembly is present, for example as a result of erosion on an inner surface of the pipe wall facing the lumen and / or as a result of deposit formation on an inner surface of the pipe wall facing the lumen, - and / or to determine whether and / or to what extent a measurement error exists in the determination of the measured values ​​due to damage to the measuring transducer, for example to the pipe arrangement.

[0037] According to a twelfth embodiment of the invention, it is further provided that the measuring system electronics are configured to perform (self-)diagnosis of the measuring system based on the second useful signal components, for example, based on their (signal) frequency and / or based on a (signal) amplitude of at least one of the second useful signal components and / or based on a phase angle of at least one of the second useful signal component, to determine whether an existing disturbance of the measuring system is attributable to a change, for example irreversible, in one or more flow properties of the pipe arrangement, for example due to a reduction of a flow cross-section of the pipe arrangement, for example as a result of a blockage of one or more of the pipes and / or as a result of a coating on an inner surface of the pipe wall of one or more of the pipes.

[0038] According to a thirteenth embodiment of the invention, it is further provided that the measuring system electronics are configured to perform (self-)diagnosis of the measuring system based on the second useful signal components, for example, based on their (signal) frequency and / or based on a (signal) amplitude of at least one of the second useful signal components and / or based on a phase angle of at least one of the second useful signal components, to determine whether an existing disturbance of the measuring system is due to a change, for example irreversible, in one or more vibration characteristics of the pipe arrangement, for example due to a reduction in the wall thickness of one or more of the pipes and / or due to plastic deformation of one or more of the pipes and / or due to a coating on the inside of one or more of the pipes and / or due to a crack in the pipe wall of one or more of the pipes.is due to this.

[0039] According to a fourteenth embodiment of the invention, it is further provided that the measuring system electronics are configured to determine a (signal) amplitude of one of the first useful signal components, for example a difference of the (signal) amplitudes of the first useful signal components, corresponding to a (modal) displacement of the first useful vibrations, for example namely to determine displacement values ​​representing the displacement of the first useful vibrations on the basis of at least one of the vibration measurement signals.

[0040] According to a fifteenth embodiment of the invention, it is further provided that the measuring system electronics are configured to determine a (signal) amplitude of one of the second useful signal components, for example a difference of the (signal) amplitudes of the second useful signal components, corresponding to a (modal) displacement of the first useful vibrations, for example namely to determine displacement values ​​representing the displacement of the second useful vibrations on the basis of at least one of the vibration measurement signals.

[0041] According to a sixteenth embodiment of the invention, it is further provided that the measuring system electronics are configured to determine a deflection ratio corresponding to a ratio of a (modal) deflection of the first useful vibrations and a (modal) deflection of the second useful vibrations, for example, by determining deflection ratio values ​​representing the deflection ratio on the basis of at least one of the vibration measurement signals.

[0042] According to a seventeenth embodiment of the invention, it is further provided that the measuring system electronics are configured to determine a (modal) damping of the first useful oscillations corresponding to a ratio of the (signal) amplitude of one of the first useful signal components, for example a sum or a difference of the (signal) amplitudes of the first useful signal components, and a (signal) amplitude of the first (useful) current, for example namely to determine damping values ​​representing the damping of the first useful oscillations on the basis of the driver signal and at least one of the oscillation measurement signals.

[0043] According to an eighteenth embodiment of the invention, it is further provided that the measuring system electronics are configured to determine a (modal) damping of the second useful oscillations corresponding to a ratio of the (signal) amplitude of one of the second useful signal components, for example a sum or a difference of the (signal) amplitudes of the second useful signal components, and a (signal) amplitude of the second (useful) current, for example namely to determine damping values ​​representing the damping of the second useful oscillations on the basis of the driver signal and at least one of the oscillation measurement signals.

[0044] According to a nineteenth embodiment of the invention, it is further provided that the measuring system electronics are configured to determine a damping ratio corresponding to the ratio of the (modal) damping of the first useful vibrations and the (modal) damping of the second useful vibrations, for example by determining damping ratio values ​​representing the damping ratio on the basis of the driver signal and / or at least one of the vibration measurement signals.

[0045] According to a twentieth embodiment of the invention, the measuring system electronics are further configured to determine damping values ​​representing a (modal) damping of the second useful vibrations based on the driver signal and at least one of the vibration measurement signals, for example, by comparing one or more of the damping values ​​with a reference value (damping reference value) determined beforehand. Further developing this embodiment of the invention, the measuring system electronics are further configured to compare one or more of the damping values ​​with at least one reference value (damping reference value) determined beforehand and / or by means of an intact measuring system in order to perform (self-)diagnosis of the measuring system, for example, by outputting a message representing a deviation of one or more of the damping values ​​from the reference value, for example, declared as a (fault) alarm.and / or that the measuring system electronics are configured to perform (self-)diagnosis of the measuring system based on several of the damping values ​​to determine a temporal change, for example, a change trend and / or a change rate and / or a change velocity, of the damping of the second useful vibrations, for example, to determine an increasing disturbance when the damping of the second useful vibrations decreases and / or to output a message representing an increase in a disturbance, for example, declared as a (disturbance) alarm, and / or that the measuring system electronics are configured to determine a measure of dispersion, for example, an empirical variance and / or a range, for the damping of the second useful vibrations of the at least one tube based on a multitude of damping values.for example, to output and / or to compare the same measure of dispersion with one or more predefined reference values ​​for carrying out the (self-)diagnosis of the measuring system.

[0046] According to a twenty-first embodiment of the invention, it is further provided that the measuring system electronics have a non-volatile electronic data storage device (EEPROM) which is configured to store digital data, for example even without an applied operating voltage, namely, to store one or more pre-determined reference values ​​for the measuring system identifier, wherein one or more reference values ​​for the measuring system identifier, for example, pre-determined by the manufacturer of the measuring system and / or during the manufacture of the measuring system and / or during the operation of the measuring system, are stored in the electronic data storage device, for example, namely one or more reference values ​​representing a reduced functionality of the measuring transducer and / or namely one or more reference values ​​representing a malfunction of the measuring transducer.Further developing this embodiment of the invention, it is also provided that the measuring system electronics are configured to compare one or more characteristic values ​​for the measuring system characteristic with one or more reference values ​​for the measuring system characteristic stored in the data memory.

[0047] According to a twenty-second embodiment of the invention, it is further provided that the measuring system electronics are configured to determine the resonance frequency f1 of the first oscillation mode of the at least one tube, for example by determining frequency values ​​representing the resonance frequency on the basis of the driver signal and / or at least one of the oscillation measurement signals.

[0048] According to a twenty-third embodiment of the invention, it is further provided that the measuring system electronics are configured to determine the resonance frequency f2 of the second mode of vibration of the at least one tube, for example by determining frequency values ​​representing the resonance frequency on the basis of the driver signal and / or at least one of the vibration measurement signals.

[0049] According to a twenty-fourth embodiment of the invention, it is further provided that the measuring system electronics are configured to determine a resonance frequency ratio corresponding to a ratio of the resonance frequency of the first vibration mode of the at least one tube and the resonance frequency of the second vibration mode of the at least one tube, for example, by determining frequency ratio values ​​representing the resonance frequency ratio based on the first and second (AC) frequencies of the driver signal and / or based on the signal frequencies of the first and second useful signal components of at least one of the vibration measurement signals.

[0050] According to a twenty-fifth embodiment of the invention, it is further provided that the measuring system electronics are configured to determine frequency values ​​representing the resonance frequency of the second vibration mode of the at least one tube on the basis of the driver signal and / or at least one of the vibration measurement signals, for example, to compare one or more of the frequency values ​​with one or more specified reference values ​​and / or to use several of the frequency values ​​to determine a measure of dispersion for the resonance frequency of the second vibration mode of the at least one tube.Further developing this embodiment of the invention, it is also provided that the measuring system electronics are configured to determine a dispersion measure for the resonance frequency of the second oscillation mode of the at least one tube based on a plurality of frequency values, for example also to output and / or to compare the same dispersion measure with a reference value specified for this purpose in order to carry out the (self-)diagnosis of the measuring system and, in the event of a deviation of the dispersion measure from the reference value, to output a message representing this.

[0051] According to a twenty-sixth embodiment of the invention, the measuring system electronics are further configured to determine frequency ratio values ​​representing the ratio of the resonance frequency of the first vibration mode of the at least one tube to the resonance frequency of the second vibration mode of the at least one tube, based on the driver signal and / or at least one of the vibration measurement signals. This includes, for example, comparing one or more of the frequency ratio values ​​with one or more predetermined reference values ​​and / or using several of the frequency ratio values ​​to determine a measure of dispersion for the resonance frequency ratio of the at least one tube. Further developing this embodiment of the invention, the measuring system electronics are further configured to...to perform (self-)diagnosis of the measuring system, to compare one or more of the frequency ratio values ​​with at least one pre-determined reference value (frequency ratio reference value), for example, to issue a message representing a deviation of one or more of the frequency ratio values ​​from the reference value, for example, declared as a (fault) alarm, and / or that the measuring system electronics are configured to determine a measure of dispersion, for example, an empirical variance and / or a range, for the resonance frequency ratio of the at least one tube based on a multitude of frequency ratio values, for example, also to output this measure, and / or to perform (self-)diagnosis of the measuring system, to compare this measure of dispersion with a predefined reference value and to issue a message representing a deviation of the measure of dispersion from the reference value.

[0052] According to a twenty-seventh embodiment of the invention, the measuring system electronics are further configured to determine, based on the vibration measurement signals, phase difference values ​​representing a phase difference of the second useful signal components, namely a difference between a phase angle of the second useful signal component of the first vibration measurement signal and a phase angle of the second useful signal component of the second vibration measurement signal. This determination can be made, for example, by comparing one or more of the phase difference values ​​with a previously determined reference value (phase difference reference value) and / or by using several of the phase difference values ​​to determine a measure of dispersion for the phase difference of the second useful signal components of the at least one tube. Further developing this embodiment of the invention, the measuring system electronics are further configured to...To perform (self-)diagnosis of the measuring system, to compare one or more of the phase difference values ​​with at least one pre-determined reference value (phase difference reference value), for example, to issue a message representing a deviation of one or more of the phase difference values ​​from the reference value, for example, declared as a (fault) alarm, and / or that the measuring system electronics are configured to determine a measure of dispersion, for example, an empirical variance and / or a range, for the phase difference of the second useful signal components based on a large number of phase difference values, for example, also to output this measure, and / or to perform (self-)diagnosis of the measuring system, to compare this measure of dispersion with a predefined reference value and to issue a message representing a deviation of the measure of dispersion from the reference value.

[0053] According to a twenty-eighth embodiment of the invention, the measuring system electronics are further configured to determine displacement ratio values ​​representing the ratio of a displacement (amplitude) of the first useful vibrations to a displacement (amplitude) of the second useful vibrations, based on at least one of the vibration measurement signals. This includes, for example, comparing one or more of the displacement ratio values ​​with one or more predetermined reference values ​​and / or using several of the displacement ratio values ​​to determine a measure of dispersion for the displacement ratio of the at least one tube. Further developing this embodiment of the invention, the measuring system electronics are also configured to compare one or more of the displacement ratio values ​​with at least one previously determined reference value (displacement ratio reference value) in order to perform (self-)diagnosis of the measuring system.For example, to issue a message representing a deviation of one or more of the deflection ratio values ​​from the reference value, for example, declared as a (fault) alarm, and / or that the measuring system electronics are configured to determine a measure of dispersion, for example, an empirical variance and / or a range, for the deflection ratio of at least one tube based on a large number of deflection ratio values, for example, also to output this measure, and / or to compare this measure of dispersion with a predefined reference value for the purpose of performing (self-)diagnosis of the measuring system, and to issue a message representing a deviation of the measure of dispersion from the reference value.

[0054] According to a twenty-ninth embodiment of the invention, it is further provided that the measuring system electronics are configured to provide the second (useful) current (eN2) with a predetermined (current) amplitude. Further developing this embodiment of the invention, it is also provided that the measuring system electronics are configured to perform (self-)diagnostics of the measuring system by repeatedly comparing the (signal) amplitude of at least one of the second useful signal components with a reference value (amplitude reference value) that depends on the (signal) amplitude of the second (useful) current and / or is predetermined for this purpose, for example, a (signal) amplitude of at least one second useful signal component determined with the predetermined (current) amplitude of the second (useful) current, for example, to determine whether or to what extent the (signal) amplitude deviates from the aforementioned reference value.

[0055] According to a thirtieth embodiment of the invention, it is further provided that the measuring system electronics are configured, for example, to perform the (self-)diagnosis of the measuring system, to calculate one or more characteristic values ​​for at least one measuring system characteristic value, which characterizes an operating state of the measuring system, based on the second useful signal components of at least one of the vibration measurement signals, for example, based on their (signal) frequency and / or based on a (signal) amplitude of at least one of the second useful signal components and / or based on a phase angle of at least one of the second useful signal components, for example, such that the same measuring system characteristic value depends on one or more parameters of a system function of the measuring system mediating between the second useful current component of the driver signal and the second useful signal component of the at least one vibration measurement signal.Further developing this embodiment of the invention, it is further provided that the measuring system electronics are configured to perform (self-)diagnosis of the measuring system by comparing one or more characteristic values ​​for the measuring system characteristic with one or more reference values ​​determined for the measuring system characteristic, for example, by the manufacturer of the measuring system and / or during the manufacture and / or commissioning of the measuring system and / or depending on the driver signal, for example, one or more reference values ​​representing reduced functionality of the measuring transducer and / or one or more reference values ​​representing a malfunction of the measuring transducer and / or one or more reference values ​​representing a defective measuring transducer, for example, to evaluate and / or quantify a deviation of one or more of the characteristic values ​​from one or more of the reference values.Furthermore, the measuring system electronics can also be configured to determine whether one or more key figure values ​​for the measuring system key figure are greater than at least one reference value for the measuring system key figure, for example, if one or more key figure values ​​for the measuring system key figure are greater than one or more reference values ​​representing reduced functionality of the measuring transducer and / or greater than one or more reference values ​​representing a malfunction of the measuring transducer and / or greater than one or more reference values ​​representing a no longer intact measuring transducer, to issue a message representing this, for example, declared as a (fault) alarm.

[0056] According to a thirty-first embodiment of the invention, it is further provided that the measuring system electronics are configured to follow a change in the density of the measured substance guided in the tube with a change in the first (alternating current) frequency of the driver signal, and that the measuring system electronics are configured to generate density measurement values ​​representing the density based on the first (alternating current) frequency of the driver signal and / or based on the signal frequency of the first useful signal component of at least one of the vibration signals.

[0057] According to a thirty-second embodiment of the invention, it is further provided that the first useful signal components of the first and second vibration measurement signals follow a change in the mass flow rate of the measured substance guided in the tube with a change in the phase difference of the first useful signal components, namely a difference between a phase angle of the first useful signal component of the first vibration measurement signal and a phase angle of the first useful signal component of the second vibration measurement signal, and that the measuring system electronics are configured to generate mass flow rate measurement values ​​representing the mass flow rate on the basis of the phase difference of the first useful signal components.Further developing this embodiment of the invention, it is further provided that the measuring system electronics are configured, for example, to perform (self-)diagnosis of the measuring system, to check or calibrate a (mass flow-to-phase-difference) characteristic curve of the measuring transducer, according to which the phase difference of the first useful signal components depends on the mass flow, and / or a (mass flow-to-measurement value) characteristic curve of the measuring system, according to which mass flow measurement values ​​determined on the basis of the phase difference of the first useful signal components depend on the mass flow, based on at least one of the vibration measurement signals, for example, based on a phase angle of at least one of the second useful signal components and / or based on a phase difference of the second useful signal components.Furthermore, the measurement system electronics can also be configured, for example, to perform (self-)diagnostics of the measurement system, to check the (mass flow-to-phase difference) characteristic curve function of the measuring transducer, for example, a (scale) zero point of that characteristic curve function and / or a (measurement) sensitivity of the measurement system, based on a phase difference of the second useful signal components, namely a difference between a phase angle of the second useful signal component (s1N2) of the first vibration measurement signal (s1) and a phase angle of the second useful signal component (s2N2) of the second vibration measurement signal (s2), for example, to determine whether or to what extent there is a drift of the characteristic curve function or an irreversible change of the (scale) zero point.

[0058] According to a thirty-third embodiment of the invention, it is further provided that the measuring system electronics have a non-volatile electronic data storage device which is designed to store digital data, for example even without an applied operating voltage, for example namely to store one or more pre-determined reference values ​​for the measuring system characteristic.

[0059] According to a thirty-fourth embodiment of the invention, it is further provided that the measuring system electronics are configured to provide the driver signal (e1) with the second (useful) current during a test interval lasting, for example, more than 10 ms and / or limited in time and / or restarted, with a sinusoidal waveform having a second (alternating current) frequency, for example, such that the second (useful) current (eN2) is non-volatile or stationary, namely, has a (substantially) constant, non-zero amplitude for two or more oscillation periods and / or a period of more than 10 ms (milliseconds).Further developing this embodiment of the invention, it is further provided that the measuring system electronics are configured to determine the measured values ​​representing at least one measured quantity during the test interval based on the second useful signal components, for example, based on their (signal) frequency and / or based on a (signal) amplitude of at least one of the second useful signal components (s1N2) and / or based on a phase angle of at least one of the second useful signal components (s1N2), and / or that the test interval lasts longer than 100 ms (milliseconds), for example, not less than 1 s (second), and / or that the measuring system electronics are configured to automatically start and / or end the test interval, for example, repeatedly, for example, in a time-controlled manner; and / or that the measuring system electronics are configured to receive and execute one or more commands that start the test interval.

[0060] According to a thirty-fifth embodiment of the invention, it is further provided that the pipe wall consists of a steel, for example a stainless steel, duplex steel or superduplex steel, a titanium alloy and / or a zirconium alloy, for example a Zircaloy, and / or a tantalum alloy.

[0061] According to a thirty-sixth embodiment of the invention, it is further provided that the tube has a caliber (inner tube diameter) greater than 0.1 mm, for example, greater than 0.5 mm. Further developing this embodiment of the invention, it is further provided that the tube has a caliber-to-tube-length ratio greater than 0.08, for example, greater than 0.1, and / or less than 0.25, for example, less than 0.2, and / or that the tube length is greater than 200 mm, for example, greater than 500 mm, and / or less than 2000 mm, for example, less than 1500 mm, and / or that the tube has a caliber greater than 10 mm, for example, greater than 15 mm.

[0062] According to a thirty-seventh embodiment of the invention, it is further provided that the excitation arrangement has no further vibration exciter connected to the tube other than the vibration exciter.

[0063] According to a thirty-eighth embodiment of the invention, it is further provided that the vibration exciter is positioned and aligned such that the drive offset is less than 0.5 mm, for example, zero, or that the centroid of the drive cross-sectional area of ​​the tube corresponds to or coincides with the drive reference point.

[0064] According to a thirty-ninth embodiment of the invention, it is further provided that each of the first and second order vibration modes of the tube has a first vibration node located in the first tube end of the at least one tube and a second vibration node located in the second tube end of the at least one tube.

[0065] According to a fortieth embodiment of the invention, it is further provided that the tube is curved section by section, for example in a circular arc shape and / or a V shape, for example such that the tube has a central vertex arc segment and / or that exactly one principal axis of inertia of the at least one tube lies within the reference cross-sectional area of ​​the at least one tube.

[0066] According to a forty-first embodiment of the invention, it is further provided that the tube is straight in sections, for example over the entire tube length, for example such that the principal axis of inertia of the at least one tube lies within the reference cross-sectional area of ​​the at least one tube and / or a center of mass lies within the reference cross-sectional area of ​​the at least one tube.

[0067] According to a forty-second embodiment of the invention, it is further provided that the vibration exciter is formed by means of a voice coil, for example comprising an air coil and an armature.

[0068] According to a forty-third embodiment of the invention, it is further provided that each of the first and second vibration sensors is formed by means of a moving coil, for example comprising an air coil and an armature.

[0069] According to a forty-fourth embodiment of the invention, the vibration exciter further comprises a magnetic armature, formed, for example, by means of a permanent magnet, and a coil, for example an air-core coil, through which the magnetic field of the armature flows. Further developing this embodiment of the invention, it is also provided that the magnetic armature is mechanically connected to the at least one tube, forming the drive point, and / or that the coil is electrically connected to the measuring system electronics and configured to receive the driver signal and to carry its first and second (useful) currents.

[0070] According to a first further development of the invention, it is further provided that the pipe arrangement has at least one second pipe, for example, which is curved at least in sections and / or straight at least in sections and / or identical in construction to the first pipe and / or parallel to the first pipe at least in sections.

[0071] According to a first embodiment of the first further development, it is further provided that the second tube extends from a first tube end to a second tube end with a tube length and has a lumen enclosed by a tube wall, for example made of metal, extending from the first tube end to the second tube end, and that the second tube is arranged to be supplied with measuring fluid and vibrated at least in a flow direction pointing from the first tube end to the second tube end, for example simultaneously with the first tube.

[0072] According to a second embodiment of the first further development, it is further provided that the second tube possesses a plurality of vibration modes (natural modes) each having an associated resonance frequency, in which the second tube can or does perform vibrational movements with one or more antinodes and two or more nodes, for example such that vibrational movements of the second tube in the second-order vibration mode (f1-mode) are opposite to, for example, the vibrational movements of the first tube in the second-order vibration mode (f2-mode), and / or that vibrational movements of the second tube in the first-order vibration mode (f1-mode) are opposite to, for example, the vibrational movements of the first tube in the first-order vibration mode.Further developing this embodiment of the invention, it is also provided that a resonance frequency of the first order vibration mode of the first tube is equal to a resonance frequency of the first order vibration mode (f1 mode) of the second tube and that a resonance frequency of the second order vibration mode of the first tube is equal to a resonance frequency of the second order vibration mode of the second tube.

[0073] According to a third embodiment of the first further development, it is further provided that the first vibration sensor is positioned on both the first and second pipes, for example, that it is mechanically connected to both the first and second pipes in a proportionate manner, and that the first vibration sensor is configured to detect vibrational movements, for example, opposing vibrational movements, of both the first and second pipes, for example, differentially, and to convert them into the first vibration measurement signal, such that the vibration measurement signal represents, for example, opposing vibrational movements of the first and second pipes.

[0074] According to a fourth embodiment of the first further development, it is further provided that the second vibration sensor is positioned on both the first and second pipes, for example, that it is mechanically connected to both the first and second pipes in a proportionate manner, and that the second vibration sensor is configured to detect vibration movements, for example, opposing vibration movements, of both the first and second pipes, for example, differentially, and to convert them into the second vibration measurement signal, such that the vibration measurement signal represents, for example, opposing vibration movements of the first and second pipes.

[0075] According to a fifth embodiment of the first further development, it is further provided that the pipe arrangement has a first flow divider with at least two flow openings, for example serving as a pipe branch and / or on the inlet side, and that the pipe arrangement has a second flow divider with at least two flow openings, for example identical in construction to the first flow divider and / or serving as a pipe junction and / or on the outlet side.Further developing this embodiment of the invention, it is further provided that each of the first and second pipes of the pipe arrangement, for example by forming fluidically parallel flow channels, is connected to each of the first and second flow dividers, such that the first pipe opens with its first pipe end into a first flow opening of the first flow divider and with its second pipe end into a first flow opening of the second flow divider, and the second pipe opens with its first pipe end into a second flow opening of the first flow divider and with its second pipe end into a second flow opening of the second flow divider.

[0076] According to a sixth embodiment of the first further development, it is further provided that the vibration exciter is mechanically connected both proportionally to the first tube and proportionally to the second tube.

[0077] According to a seventh embodiment of the first further development, it is further provided that the vibration exciter is configured to act differentially on the first and second tubes, for example, such that the first and second tubes simultaneously perform forced mechanical vibrations of the same frequency but opposite frequency, and / or that the vibration exciter is configured to convert electrical power into mechanical power with a time-varying electrical current in such a way that a time-varying driving force acts on the second tube at a drive point formed by the vibration exciter on the mechanically connected second tube, for example, simultaneously and / or oppositely to the driving force acting on the first tube at the drive point formed by the vibration exciter on the mechanically connected first tube, and / or that the vibration exciter is configuredto convert electrical power supplied by means of the electrical driver signal simultaneously into forced mechanical vibrations of the first and second tubes, for example in such a way that the first and second tubes perform forced mechanical vibrations at the first operating frequency and / or at the second operating frequency simultaneously.

[0078] According to a second further development of the invention, the measuring system further comprises an electronics protective housing for the measuring system electronics, for example, attached to a converter protective housing of the measuring transducer and / or made of metal.

[0079] According to a third further development of the invention, the measuring system further comprises a transducer protective housing, for example made of metal, wherein the transducer protective housing and the pipe arrangement are attached to each other, for example in a releasable manner.

[0080] A fundamental concept of the invention is to actively, and in particular non-volatilely or statically, excite or attempt to excite, for example, bending vibrations, in vibronic measuring systems of the type in question for the purpose of (self-)diagnosis, using at least one vibration exciter, according to such a natural vibration mode of the at least one tube, which has a vibration node located at or in the immediate vicinity of the vibration exciter. In measuring systems, including commercially available (standard) measuring systems, with a single vibration exciter acting centrally on the tube, the aforementioned vibration mode corresponds to a second-order vibration mode, for example, a second-order bending vibration mode.Due to the resulting very small drive offset, the aforementioned useful vibrations exhibit only a very small or even no amplitude, even when excited at the respective resonance frequency of the vibration mode. On the other hand, any change in the drive offset associated with a shift of the aforementioned vibration node nearest to the vibration exciter—for example, due to changing geometric or mechanical properties of the tube or the transducer formed by it—relative to the original drive offset (e.g., the one used for the initial calibration of the measuring system) leads to a corresponding change in the amplitude for the same excitation compared to the initially measured amplitude. Specifically, as the drive offset increases, the amplitude also increases accordingly.For the purpose of (self-)diagnosis of the measuring system, for example, to check the functionality of the measuring system, the corresponding vibration responses generated by excitation of the second-order vibration mode, or the (system) parameters characterizing them, can be very easily and repeatedly determined during operation of the measuring system and compared with corresponding reference vibration responses ("fingerprint") or reference values, such that increased deviations from the corresponding reference values, or deviations exceeding a predetermined tolerance, can detect the presence of a fault in the measuring system and, if necessary, report it; this can advantageously be done simultaneously with the actual measurement operation without significantly affecting it or having to interrupt the measurement operation for an extended period.

[0081] A further advantage of the invention is that the (self-)diagnosis according to the invention can also be implemented using, or even exclusively using, the proven designs for conventional vibronic measuring systems, not least for the transducers used therein to date, as well as retaining proven technologies and architectures of established measuring system electronics to an equally large extent; for example, also in such a way that conventional, possibly already installed, measuring systems can be retrofitted by reprogramming the respective measuring system electronics accordingly.

[0082] The invention and advantageous embodiments thereof are explained in more detail below with reference to exemplary embodiments illustrated in the figures of the drawing. Identical, equivalent, or similarly functioning parts are designated with the same reference numerals in all figures; where clarity requires it or it otherwise appears appropriate, previously mentioned reference numerals are omitted in subsequent figures. Further advantageous embodiments or developments, in particular combinations of aspects of the invention initially described only individually, will also become apparent from the figures of the drawing and / or from the claims themselves.

[0083] Specifically, we show: Fig. 1 in a perspective side view an embodiment of a vibronic measuring system; Fig. 2 schematically depicts an embodiment of a vibronic measuring system according to the type of a block diagram. Fig. 1 suitable vibration-type measuring transducer and electrically coupled measuring system electronics; Fig. 3 schematically depicts a further embodiment of a vibronic measuring system according to a block diagram Fig. 1 suitable vibration-type measuring transducer and thus electrically coupled measuring system electronics; Fig. 4a schematically a pipe arrangement of a vibronic measuring system according to Fig. 1 suitable vibration-type transducer with a tube excited to first useful vibrations; Fig. 4b schematically for a pipe arrangement according to Fig. 4 Coriolis vibrations of the pipe, excited by useful vibrations and dependent on mass flow; Fig. 5 schematically a diagram of a pipe of a pipe arrangement according to Fig. 4 inherent vibration modes of the first, second or third order; Fig. 6, Fig. 7 schematically the pipe arrangement according to Fig. 4 with a tube excited to second useful vibrations;

[0084] In Fig. 1 or 2 and Fig. 3. Exemplary embodiments and configurations of a vibronic measuring system for measuring and / or monitoring at least one, in particular time-varying, measured quantity of a fluid, for example, at least intermittently flowing and / or at least intermittently two-phase or multi-phase or inhomogeneous, measured substance FL, are schematically depicted. The measured quantity can be, for example, a flow parameter such as a mass flow rate ṁ, a volume flow rate, and / or a flow velocity, or, for example, a material parameter such as a density ρ and / or a viscosity η of the measured substance FL. The measuring system is specifically designed and configured to be integrated into a process line carrying a fluid FL serving as the measured substance—for example, a gas, a liquid, or a dispersion—and, during operation, is controlled by the fluid supplied via the process line.The system is designed to allow the fluid FL, which is subsequently discharged, to flow through it at least temporarily. Furthermore, the measuring system is intended to quantify at least one physical measurement quantity (sequentially), possibly also digital measurement values ​​X. M to determine, in particular to calculate and / or output. The process line can be, for example, a pipeline, such as a pipeline of a filling plant, a refueling device, or another industrial plant.

[0085] As in Fig. 1, Fig. As shown in Figures 2 and 3 respectively, or as can be readily seen from their combination, the measuring system comprises a vibration transducer 10, namely a transducer with a pipe arrangement formed by means of at least one (first) or more pipes for guiding the measured substance, an excitation arrangement (31) for converting electrical power into the excitation and maintenance of forced mechanical vibrations of the at least one pipe, and a sensor arrangement (41, 42) for detecting mechanical vibrations of the pipe arrangement and for providing vibration measurement signals (s1, s2) representing, for example, electrical or optical vibration movements of the pipe arrangement, in particular of one or more of its pipes.Furthermore, the measuring system comprises measuring system electronics 20 for controlling the measuring transducer, in particular for causing the aforementioned mechanical vibrations of the at least one tube, and for evaluating vibration measurement signals supplied by the measuring transducer, for example by means of appropriate electrical connecting lines, formed in particular by means of at least one microprocessor (µC) and / or arranged in an electronic protective housing (200) and / or serving as a transmitter.

[0086] According to a further embodiment of the invention, the measuring system also comprises a support frame 100, which is in particular rigid against bending and / or torsion, wherein – as also in Fig. 1, Fig. Figures 2 and 3 are shown schematically – the aforementioned support frame 100 and the pipe assembly are attached to one another, for example, by a material bond or in a releasable manner. To protect the transducer or its components from harmful environmental influences, to prevent unwanted noise emissions from the vibrating pipes, or to collect any measuring fluid that has escaped from a leaking pipe assembly, the aforementioned support frame 100 can, as is quite common in vibronic measuring systems of the type in question, also be designed as a transducer protective housing enclosing the pipe assembly together with the exciter and sensor assembly, for example, such that the transducer protective housing is metallic and / or has a pressure resistance that is greater than the maximum pressure resistance of at least one pipe of the pipe assembly and / or that is more than 50 bar.Furthermore, the measuring system electronics 20, as is quite common with measuring systems of the type in question, can also be housed within an electronics protective housing 200, for example attached to the aforementioned support frame or converter protective housing of the measuring transducer and / or made of metal.

[0087] The at least one tube of the tube arrangement can be at least partially straight, in particular hollow cylindrical, and / or at least partially curved, for example such that the tube has a central apex arc segment, in particular is essentially V-shaped or has a V-shaped silhouette, and / or that the tube ultimately has a tube shape lying in a single (tube) plane. As in Fig. As indicated in Figure 2, the at least one tube extends from a first tube end to a second tube end with a tube length corresponding to the length of an imaginary center line of the tube, for example, more than 100 mm, and the tube has a lumen enclosed by a tube wall extending from the first tube end to the second tube end. According to a further embodiment of the invention, the tube length is more than 200 mm, for example, also more than 500 mm, and / or less than 2000 mm, for example, also less than 1500 mm. In the case of a tube that is at least partially curved, the aforementioned tube length corresponds to a stretched or unwound length of the tube, and the tube can be manufactured by bending a tubular semi-finished product. According to a further embodiment of the invention, the tube wall of the at least one tube consists of a metal, for example, a steel, in particular...a stainless steel, duplex steel or superduplex steel, a titanium alloy and / or a zirconium alloy, in particular a Zircaloy, and / or a tantalum alloy and / or a nickel-based alloy. Furthermore, the at least one tube of the tube assembly can be formed in one piece, for example, such that the tube is seamless or (at least in the case of a metal tube wall) manufactured with a single welded seam. According to a further embodiment of the invention, the at least one tube of the tube assembly has a caliber (inner tube diameter) that is greater than 0.1 mm, for example, also greater than 0.5 mm, and / or the tube wall of the at least one tube has a minimum wall thickness that is not less than 0.5 mm, for example, also greater than 1.5 mm, in particular such that the wall thickness of the tube wall is essentially uniform.According to a further embodiment of the invention, the tube has a caliber-to-tube-length ratio that is greater than 0.08, in particular greater than 0.1, and / or less than 0.25, in particular less than 0.2. Furthermore, the at least one tube, or each of the tubes of the tube arrangement, can also assume any other geometric shape and / or dimensions customary in conventional vibronic (standard) measuring systems, for example, dimensions of 1 mm, 2 mm, 5 mm, 10 mm, 15 mm or more, and / or be made of other materials commonly used for this purpose.

[0088] According to a further embodiment of the invention, the pipe arrangement of the measuring transducer 10 - as in Fig. Figure 3 schematically shows at least one second pipe 112. The pipe 112 can be curved at least in sections and / or straight at least in sections. In addition, the pipe 112 can be - as in Fig. 3 indicated - for example, also identical in construction to pipe 111 and / or arranged at least partially parallel to pipe 111. Pipe 112 extends from a first pipe end to a second pipe end with a pipe length in the same way as pipe 111 and, like pipe 111, has a lumen enclosed by a pipe wall, for example, made of metal, extending from the first pipe end to the second pipe end. In addition, pipe 112 is also configured to be permeated by the medium or a partial volume thereof, at least in a flow direction pointing from the first pipe end to the second pipe end, in particular simultaneously with the first pipe, and to be vibrated during this process. Furthermore, the pipe arrangement can also include a first flow divider 21, serving here, for example, as a pipe branch and / or on the inlet side, with at least two flow openings, as well as aFor example, the aforementioned flow divider 21 may have a second flow divider 22, identical in construction and / or serving as a conduit junction and / or located on the outlet side, also with at least two flow openings, and each of the pipes 111, 112 of the pipe arrangement may then be connected to each of the first and second flow dividers, forming two fluidically parallel flow channels, for example, such that the first end of pipe 111 opens into a first flow opening 21a of flow divider 21 and the second end of pipe 22 opens into a first flow opening 22a of flow divider 22, and that the first end of pipe 112 opens into a second flow opening 21b of flow divider 21 and the second end of pipe 22 opens into a second flow opening 22b of flow divider 22. The pipe length of pipe 111 may, for example, be equal to the pipe length of pipe 112. Furthermore, the pipe arrangement can accommodate additional pipes,For example, two further pipes, thus, as also shown in the aforementioned US-A 56 02 345, WO-A 96 / 08697, US-A 2017 / 0356777, WO-A 2019 / 081169 or WO-A 2019 / 081170, a total of four pipes. Accordingly, both the flow divider 21 and the flow divider 22 can each have, in particular, exactly four flow openings, and each of the pipes of the pipe arrangement can be connected to each of the flow dividers 21, 22, forming four fluidically parallel flow paths. In the aforementioned case, where the pipe arrangement has four pipes, the pipes can, for example, also be designed such that they are only identical in pairs, for example, that the pipe lengths are only chosen to be the same in pairs. Furthermore, in the aforementioned case where the pipe arrangement has two or more pipes,The wall of each of the tubes – as is quite common in tube arrangements of the type in question or in measuring transducers or measuring systems formed therewith – consists, for example, of the same material; this is also the case, for example, that the tube wall of each of the tubes in the tube arrangement has a wall thickness equal to the wall thickness of the other tube(s) and / or that each of the tubes in the tube arrangement has a caliber, namely an inner diameter, equal to the caliber of the other tube(s).

[0089] The pipe assembly, or the measuring transducer MW formed therewith, is, as already indicated, specifically designed to be connected to the aforementioned process line via an inlet end 10+ of the pipe assembly or measuring transducer MW, which may, for example, be enclosed by a first connecting flange, and a corresponding outlet end 10#, which may, for example, be enclosed by a second connecting flange, and through which the measuring fluid FL flows during operation. A sealing surface may also be formed on each of the aforementioned connecting flanges.In the aforementioned case, where the pipe arrangement comprises at least two pipes and the two flow dividers connected thereto, the inlet end 10+ of the pipe arrangement is formed by means of the flow divider 21 and the outlet end 10# of the pipe arrangement is formed by means of the flow divider 22, and accordingly, the flow divider 21 can have the aforementioned first connection flange and the flow divider 22 the aforementioned second connection flange. Furthermore, the at least one pipe of the pipe arrangement is also configured to carry measuring fluid FL or a partial volume thereof into its lumen and to vibrate it during this process, for example, in particular...To perform forced mechanical vibrations around a corresponding static equilibrium position, producing a measurement effect corresponding to at least one measured quantity and / or excited by means of the excitation arrangement; this is done in particular by allowing the at least one tube of the tube arrangement to vibrate while, starting from its first tube end and moving towards its second tube end (flow direction), the measured medium flows through it. The aforementioned forced mechanical vibrations can, as is quite common with transducers of the type in question, be at least partially forced bending vibrations of the at least one tube around an imaginary axis of vibration of the tube arrangement, for example, an axis of vibration imaginarily connecting the first and second tube ends.

[0090] The aforementioned excitation arrangement of the measuring transducer 10 is specifically designed and configured to convert electrical power fed into it (by the measuring system electronics 20) into mechanical power, such that – as in Fig. 4a indicated or also from a summary of the Fig. 2 and Fig. 4a is readily apparent - that at least one pipe 111 of the pipe arrangement and / or each of its pipes performs at least temporarily forced mechanical vibrations around a respective static equilibrium position, while the sensor arrangement is provided or configured to detect mechanical vibrations of the pipe arrangement, not least mechanical vibrations forced by means of the excitation arrangement and / or bending vibrations of the at least one pipe, and to provide a first vibration measurement signal s1 and a second vibration measurement signal s2, of which - for example, electrical - vibration measurement signals s1, s2 each represent at least partially vibrational movements of one or more of the pipes of the pipe arrangement, for example, each by means of a respective vibrational movement (X). s1 , X s2 ) of the variable electrical voltage corresponding to at least one tube; this in particular in such a way that - as in Fig. 4b schematically represented - the vibration measurement signals s1, s2 (or each a spectral signal component s1N1 or s2N1 thereof) follow a change in the mass flow rate of the measured substance guided in the pipe arrangement with a change in a first phase difference (Δφ12), namely a change in the difference between a phase angle of the vibration measurement signal s1 and a phase angle of the vibration measurement signal s2, and / or in such a way that each of the aforementioned vibration measurement signals s1, s2 follows a change in the density of the measured substance guided in the pipe arrangement with a change in the respective signal frequency of at least one spectral signal component.

[0091] The excitation arrangement of the measuring system according to the invention comprises a vibration exciter 31, for example an electrodynamic one, which is mechanically connected to the at least one tube and is also configured to convert electrical power into mechanical power with a time-varying electrical current, such that – as in Fig. 2 indicated or from a summary of Fig. 2 and Fig. 4a is readily apparent - at a drive point formed by means of the same vibration exciter 31 on the mechanically connected pipe, a time-varying driving force F exc1 the vibration exciter acts on the pipe. An imaginary circumferential line of the pipe, passing through the aforementioned drive point, encloses a cross-sectional area of ​​the pipe, which is hereinafter also referred to as the drive cross-sectional area of ​​the pipe. According to a further embodiment of the invention, the vibration exciter 31 is positioned such that – as in Fig. 4a indicated - a line of action of the aforementioned driving force F exc1 perpendicular to a normal of the drive cross-sectional area of ​​the tube. According to a further embodiment of the invention, the vibration exciter 31 is of the electrodynamic type, namely formed by means of a voice coil, for example comprising an air coil and an armature, or the vibration exciter 31 has a magnetic armature, for example formed by means of a permanent magnet, and a coil, for example an air coil, through which the magnetic field of the armature permeates. The magnetic armature can, for example, be mechanically connected to the at least one tube 111, forming the drive point, and / or the coil can, for example, be electrically connected to the measuring system electronics 20.

[0092] In the aforementioned case where the pipe arrangement comprises two pipes, according to a further embodiment of the invention, the vibration exciter 31 is configured to simultaneously excite mechanical vibrations of both pipes 111, 112; specifically, in such a way that the vibration exciter 31 acts differentially on the two pipes 111, 112, namely, it can introduce, or does introduce, only opposite excitation forces into the two pipes 111, 112, for example, such that the first and second pipes 111, 112 simultaneously perform forced mechanical vibrations of the same frequency but opposite frequency. Accordingly, the vibration exciter 31 can, for example, be mechanically connected to both pipe 111 and pipe 112, for example, in such a way that the aforementioned driving force acts on both pipe 111 and pipe 112.According to a further embodiment of the invention, the vibration exciter 31 is configured to convert electrical power into mechanical power using a time-varying electric current such that a time-varying driving force acts on the second tube at a drive point formed by the vibration exciter 31 on the second tube mechanically connected to it, in particular simultaneously and / or oppositely to the driving force acting on the tube 111 at the drive point formed by the same vibration exciter 31 on the tube 111 mechanically connected to it. According to a further embodiment of the invention, it is also provided that the exciter arrangement, as is common, for example, in conventional vibronic (standard) measuring systems, has no other vibration exciter connected to the tube besides the vibration exciter 31.

[0093] The sensor arrangement of the measuring system according to the invention, in turn, features – as also in Fig. Figure 2 schematically depicts a first vibration sensor 41, in particular electrodynamic or optical, and a second vibration sensor 42, in particular electrodynamic or optical. Each of the vibration sensors 41, 42, which may be identical in construction, is positioned on the tube, in particular at least partially mechanically connected to the tube, and is also configured to detect vibrations of the tube and to convert them into a first or second vibration measurement signal representing these vibrations, for example, an electrical or optical signal; in particular, each of the first and second vibration measurement signals contains one or more sinusoidal signal components, each with a frequency corresponding to a vibration frequency of the tube.According to a further embodiment of the invention, it is further provided that each of the vibration sensors 41, 42 is positioned on the pipe at a distance from the vibration exciter 31 in the direction of flow, in particular more than 10 mm and / or more than one-fifth of the pipe length and / or at the same distance; specifically, such that the vibration sensors 41, 42 are positioned at a distance from each other in the direction of flow, as is also customary in conventional vibronic (standard) measuring systems. According to a further embodiment of the invention, each of the first and second vibration sensors 41, 42 is formed by means of a moving coil, for example, comprising an air coil and an armature. In the aforementioned case, where the pipe arrangement has at least two pipes, each of the vibration sensors 41, 42 can be positioned on both the first pipe 111 and the second pipe 112, in particular,namely be mechanically connected both proportionally to the first tube and proportionally to the second tube, and each of the vibration sensors 41, 42 can also be configured to detect vibration movements, in particular opposing vibration movements, of both the first tube and the second tube, in particular differentially, and to convert them into the first or second vibration measurement signal, such that each of the vibration measurement signals, in particular opposing vibration movements, represents vibration movements of the first and second tubes 111, 112 (. Fig. 3); this applies in particular to the aforementioned case where the vibration sensors 41, 42 are electrodynamic vibration sensors constructed in the manner of a moving coil. In the aforementioned case where the pipe arrangement comprises two pipes, according to a further embodiment of the invention, each of the first and second vibration sensors is positioned on both the first and second pipes, for example, being mechanically connected to both the first and second pipes. Furthermore, each of the first and second vibration sensors is configured to detect vibrations, for example, opposing vibrations, of both the first and second pipes and to convert them into the respective first and second vibration measurement signals, such that each of the first and second vibration measurement signals represents vibrations of the first and second pipes.The vibration sensors can be designed in such a way that vibration movements, including opposing vibration movements of the pipes, are detected differentially and / or that each of the first and second vibration measurement signals represents opposing vibration movements of the first and second pipes.

[0094] Each of the pipes in the pipe arrangement naturally possesses a multitude of vibration modes (natural modes), each exhibiting a corresponding resonant frequency (f1, f2, ... , fx). In these modes, the pipe can and does exhibit one or more antinodes (SB) and two or more nodes (SK), such that the number of nodes is always exactly one greater than the number of corresponding antinodes. Vibrations of the respective pipe in a fundamental vibration mode, namely a first-order mode (f1 mode), for example, a first-order bending mode, exhibit—as also in Fig. 5 indicated - exactly one antinode and accordingly two nodes (f1 mode: 1SB, 2SK), while vibrational movements of the respective pipe in a (different from the basic vibration mode) higher vibration mode, namely a second or higher order vibration mode (f2 mode, f3 mode, f4 mode, ... fx mode), for example a bending vibration mode of the second, third, fourth or higher order, accordingly two or more antinodes and accordingly three or more nodes (f2 mode: 2SB, 3SK, f3 mode: 3SB, 4SK, f4 mode: 4SB, 5SK,..., fx mode: x·SB, [x+1]·SK). Each of the aforementioned vibration modes of the tube, including the first, second and third order vibration modes (f1 mode, f2 mode, f3 mode), has a first vibration node located in the first tube end of the at least one tube and a second vibration node located in the second tube end of the at least one tube ( Fig. 5) In the aforementioned case that the pipe arrangement has two (or more) pipes, the second pipe 112 also possesses a plurality of vibration modes, each with an associated resonant frequency, in which the second pipe (like the pipe 111) can perform vibrational movements with one or more antinodes and two or more nodes.executes; for example, also in such a way that – upon appropriate excitation – the vibrational movements of the tube 112 in the first-order vibration mode (f1-mode) are opposite to, or even opposite to, the vibrational movements of the tube 111 in its first-order vibration mode (f1-mode), and / or that – upon appropriate excitation – the vibrational movements of the tube 112 in the second-order vibration mode (f2-mode) are opposite to, or even opposite to, the vibrational movements of the tube 111 in its second-order vibration mode. According to a further embodiment of the invention, the tube arrangement is further designed such that – at least with the original or intact measuring transducer – a resonance frequency f1 of the first-order vibration mode of the tube 111 is equal to a resonance frequency of the first-order vibration mode (f1-mode) of the tube 112, and / or that – at least nominally, namely with the original or intact measuring transducer –With an intact measuring transducer, a resonance frequency f2 of the second-order vibration mode of tube 111 is equal to a resonance frequency of the second-order vibration mode of tube 112. Furthermore, in the aforementioned case where the tube arrangement has two or more tubes, and as is quite common with conventional vibronic (standard) measuring systems, the tube arrangement can also include coupling elements useful for adjusting the vibration characteristics of the tube arrangement, and not least for tuning one or more resonance frequencies of its tubes; this is done in particular in such a way that, as also in . Fig. 3 indicated, a first coupler element 23, for example plate-shaped, is mechanically connected to each of the tubes and is positioned further away from the flow divider 22 than from the flow divider 21, and that at least one second coupler element 24, for example plate-shaped and / or identical in construction to the coupler element 23, is mechanically connected to each of their tubes and is positioned further away from the flow divider 21 than from the flow divider 22.

[0095] In the measuring system according to the invention, the vibration exciter 31 is positioned and aligned such that – as also in Fig. 4a or 6 schematically depicted and also quite common in conventional vibronic (standard) measuring systems - a drive offset ΔE, namely a minimum distance between the aforementioned drive cross-sectional area of ​​the tube 111 and a predetermined reference cross-sectional area of ​​the at least one tube is no more than 3° mm and / or less than 0.5% of the tube length, wherein the reference cross-sectional area is again chosen or defined in such a way, for example, with an intact or original transducer, that a vibration node of the same vibration movements formed between two antinodes of vibration movements of the at least one tube in a higher vibration mode, for example, the second order vibration mode, and / or (nominally) located at half a tube length, lies within the reference cross-sectional area.The drive offset ΔE thus practically corresponds to a distance between a centroid (center) of the drive cross-sectional area of ​​the tube and a centroid (center) of the reference cross-sectional area of ​​the at least one tube. According to a further embodiment of the invention, the reference cross-sectional area of ​​the at least one tube is also selected such that a principal axis of inertia of the tube perpendicular to the aforementioned drive force and / or a line of intersection of two mutually orthogonal planes of symmetry of the tube lies within the reference cross-sectional area. Furthermore, according to a further embodiment of the invention, the tube arrangement and excitation arrangement are designed such that the drive offset ΔE – at least nominally or initially, i.e., with an intact or original transducer and as described, among other things – isThis is also quite common with conventional vibronic (standard) measuring systems - only slightly larger than zero, namely less than 2 mm, for example also less than 1 mm, and / or less than 0.2% of the pipe length; in the case of ideal or completely symmetrical pipe and sensor arrangements, also such that the drive offset is zero (ΔE = 0), thus the centroid of the drive cross-sectional area of ​​the pipe corresponds as closely as possible to the centroid of the reference cross-sectional area or coincides with it.In the aforementioned case where the at least one pipe is curved at least in sections, for example, at least in sections circular arcs and / or substantially V-shaped, the at least one pipe 111 can furthermore be designed and the aforementioned reference cross-sectional area can be selected such that exactly one principal axis of inertia of the at least one pipe lies within the reference cross-sectional area of ​​that pipe. In the other case where the at least one pipe is straight over its entire length, the aforementioned reference cross-sectional area can again be selected such that each of the three principal axes of inertia of the at least one pipe lies within the reference cross-sectional area of ​​the at least one pipe, or that a center of mass lies within the reference cross-sectional area of ​​the at least one pipe.According to a further embodiment of the invention, the reference cross-sectional area is selected such that a node of vibration formed between the two antinodes of the vibrational movements of the at least one tube in the aforementioned second-order vibration mode, in particular the second-order bending vibration mode, and / or a principal axis of inertia of the at least one tube perpendicular to the direction of vibration of the vibrational movements of the tube in the same second-order vibration mode lies within the reference cross-sectional area of ​​the at least one tube.

[0096] As already mentioned, in addition to the measuring transducer 10, the measuring system comprises measuring system electronics 20 that are electrically coupled to it, in particular to both its excitation arrangement and its sensor arrangement. The measuring system electronics 20 can, for example, be programmable and / or remotely configurable, for example, by means of at least one microprocessor and / or at least one digital signal processor (DSP) and / or by means of a programmable logic gate (FPGA) and / or by means of a customer-specific programmed logic gate (ASIC). Furthermore, the measuring system electronics 20 can be supplied with the electrical energy required during operation by means of internal energy storage devices and / or externally via a connecting cable. The electrical coupling orConnecting the measuring transducer 10 to the measuring system electronics 20 can be accomplished using appropriate electrical connecting cables and cable glands. The connecting cables can be designed, at least partially, as electrical conductors, or at least partially as conductors sheathed in electrical insulation, e.g., in the form of twisted-pair cables, ribbon cables, and / or coaxial cables. Alternatively or additionally, the connecting cables can also be formed, at least partially, by conductor tracks on a printed circuit board, particularly a flexible one, which may be coated. The measuring system electronics 20 can also be – as in . Fig. 1 schematically represented - for example, housed in a suitable, in particular impact- and / or explosion-proof and / or at least splash-proof, dedicated electronic protective housing 200 and also designed so that, during operation of the measuring system, it can exchange measurement and / or other operating data, such as status messages, such as current measured values ​​or setting and / or diagnostic values ​​used for controlling the measuring system, with a higher-level (not shown here) electronic (measurement) data processing system, for example, a programmable logic controller (PLC), a process control system (PLC), a remote control unit (RTU), or a monitoring control and data acquisition (SCADA) system running on a personal computer (PC) and / or a workstation, via a data transmission system, for example, a fieldbus system and / or wirelessly via radio, with a higher-level (not shown here) electronic (measurement) data processing system, for example, a remote control unit (RTU), or a monitoring control and data acquisition (SCADA) system running on a personal computer (PC) and / or a workstation, via a data transmission system, for example, a fieldbus system and / or wirelessly via radio. Fig. 2 or 3). Accordingly, the measuring system electronics 20 can, for example, have such a transmitting and receiving circuit COM, which in operation is powered by a (central) evaluation and supply unit provided in the aforementioned data processing system and located remotely from the measuring system. For example, the measuring system electronics 20 (or its aforementioned transmitting and receiving circuit COM) can also be designed such that it can be electrically connected to the aforementioned external electronic data processing system via a two-wire connection 2L, which may also be configured as a 4-20 mA current loop, and thereby obtain both the electrical power required for the operation of the measuring system from the aforementioned evaluation and supply unit of the data processing system and, if necessary,The measurement system electronics 20 can transmit digitized measured values ​​to the data processing system, for example, by (load) modulation of a DC supply current fed by the evaluation and supply unit. Furthermore, the measurement system electronics 20 can also be designed to operate nominally with a maximum power of 1 W or less and / or be intrinsically safe. The measurement system electronics 20 can also be modularly designed, for example, such that various electronic components of the measurement system electronics 20, such as a measurement and evaluation circuit DSV (for example, formed by one or more microprocessors and / or by one or more digital signal processors) for processing and evaluating the measurement signals provided by the transducer 10, including the vibration measurement signals, and a driver circuit Exc for controlling the transducer 10, can be integrated.whose excitation arrangement, an internal power supply circuit VS for providing one or more internal operating voltages, and / or the aforementioned transmit and receive circuit COM, which serves for communication with the aforementioned higher-level (measurement) data processing system or the aforementioned external fieldbus, are each arranged on one or more separate circuit boards and / or each are formed by means of one or more separate microprocessors. As shown in the... Fig. As can be seen in 2 and 3 respectively, the aforementioned transmit and receive circuit COM can also be used, for example, for one of the outputs (x m ) of, for example, the aforementioned measuring and control circuit DSV, internally determined measurement values ​​(X) M ) be provided. Accordingly, the COM transmitting and receiving circuit can also be configured to receive measured values ​​X. M into a single measured value X Mproviding an output signal compliant with an industry standard, for example DIN IEC 60381-1:1985-11, IEC 61784-1 CPF1 (Foundation Fieldbus), IEC 61784-1 CPF3 (Profibus), IEC 61158 or IEC 61784-1 CPF9 (HART). m to convert. To visualize measurement values ​​generated internally by the measurement system (X). MIn addition to internally generated status messages from the measuring system, such as an error message or an alarm, the measuring system may also have a display and control element (HMI) that communicates, at least temporarily, with the measuring system electronics 20. This HMI may include an LCD, OLED, or TFT display placed behind a window provided in the aforementioned electronics housing 200, as well as a corresponding keypad and / or touchscreen. If the measuring system has the aforementioned support frame 100, which is designed as a converter protective housing, the electronics protective housing 200 can be used, as also in Fig. 1, Fig. 2 and Fig. 3 each are shown schematically or can be readily seen from their combination, for example, attached to the same support structure.

[0097] In the measuring system according to the invention, the measuring system electronics 20 are specifically configured to energize the vibration exciter 31, namely to supply electrical power to the vibration exciter 31 by means of an electrical driver signal e1 having a time-varying electrical current, such that the at least one tube performs forced mechanical vibrations, for example bending vibrations, with one or more vibration frequencies specified by the driver signal e1. Furthermore, the measuring system electronics 20 are configured to modulate the driver signal e1 at least temporarily, for example, during normal measuring operation or during a measuring interval, with a first (alternating current) frequency f. eN1to provide the sinusoidal first (useful) current eN1, such that the at least one tube generates at least partially, for example also predominantly, first useful vibrations, namely through the vibration exciter 31 (energized with the (useful) current eN1) or a first driving force (component) F generated therewith exc1 forced mechanical vibrations with a first useful frequency f N1 , namely one of the first (alternating current) frequencies f eN1 (f N1 = f eN1 ) corresponding (oscillation) frequency and that as a result the oscillation signal s1 has a first useful signal component s1N1 and the oscillation signal s2 has a first useful signal component s2N1, namely each a sinusoidal signal component with one of the first useful frequencies f N1 corresponding (signal) frequency f s1N1 or f s2N1 (f s1N1 = f s2N1 = f N1) exhibits; this in particular in such a way that the first useful frequency f N1 from a resonance frequency f2 of the second order oscillation mode (f2-mode) by more than 5% of the same resonance frequency f2 (|f2 - f N1 | > 0.05 f2) and / or by more than 10 Hz (|f2 - f N1 | > 10 Hz deviates and / or in such a way that the first useful oscillations are suitable to measure Coriolis forces F in the measuring medium flowing through the at least one tube or the tube arrangement formed therewith, which depend on the mass flow rate cto effect this. Accordingly, the measuring system electronics can further be configured to adjust the first (useful) current eN1 of the driver signal, as is quite common in vibronic measuring systems of the type in question, in such a way that, due to the first useful oscillations thereby excited, Coriolis oscillations dependent on the mass flow rate are also forced, and as a result, the useful signal components s1N1; s2N1 of the vibration measurement signals s1, s2 follow a change in the mass flow rate of the measured substance, which is guided in at least one tube, with a change in the phase difference of the first useful signal components of the vibration measurement signals s1, s2, namely a difference between a phase angle of the first useful signal component s1N1 and a phase angle of the first useful signal component s2N1.In the aforementioned case where the pipe arrangement has at least two pipes, the vibration exciter 31 can also be configured to simultaneously convert electrical power supplied by means of the electrical driver signal e1 into forced mechanical vibrations of the first and second pipes 111, 112; this is particularly possible in such a way that the first and second pipes 111, 112 produce forced mechanical vibrations at the first operating frequency f. N1 simultaneously, for example, by performing opposing oscillations. In the aforementioned case, where the vibration exciter 31 is formed by means of a coil electrically connected to the measuring system electronics, energizing the vibration exciter 31 means that the coil receives the driver signal e1, i.e., carries its current.

[0098] The aforementioned (alternating current) frequency f eN1 of the useful current components eN1, thus the first useful frequency f N1This can, for example, correspond to a resonance frequency of the tube arrangement that also depends on the density of the measuring medium FL guided in the tube arrangement – ​​for example, namely a lowest resonance frequency of the tube 111 or the resonance frequency f1 of the fundamental oscillation mode (f1 mode). Accordingly, according to a further embodiment of the invention, the measuring system electronics 20 are further configured to measure the first (alternating current) frequency f eN1 so that the same (alternating current) frequency f eN1 or the operating frequency f N1 from the resonance frequency f1 of the fundamental vibration mode by less than 1% of the same resonance frequency f1 (|f1 - f N1 | < 0.01 f1) and / or by less than 1 Hz (|f1 - f N1| < 1 Hz), for example, that it corresponds to the resonance frequency f1 of the fundamental oscillation mode (f1 mode), or that, as a result, the oscillatory movements of the first useful oscillations correspond to those of the fundamental oscillation mode (f1 mode) of the at least one tube 111. According to another embodiment of the invention, the measuring system electronics are configured to determine the first (alternating current) frequency f eN1 so that the same (alternating current) frequency f eN1 or the operating frequency f N1 from a resonance frequency f3 of the third order vibration mode (f3 mode) by less than 1% of the same resonance frequency f3 (|f3 - f N1 | < 0.01 f3) and / or by less than 1 Hz (|f3 -f N1| < 1 Hz) deviates, for example, namely corresponds to the resonance frequency f3 of the third order vibration mode (f3 mode), or that as a result the vibrational movements of the first useful vibrations correspond to those of the third order vibration mode (f3 mode) of the at least one tube 111.

[0099] To generate the driver signal e1, the measuring system electronics 20 can – as is quite common in such measuring systems – have a corresponding driver circuit Exc, for example formed by means of one or more phase-locked loops (PLL) which serve to determine a resonance frequency or to set the currently required (AC) frequency.

[0100] As already indicated, the measuring system electronics 20 are also specifically designed to receive and evaluate the vibration measurement signals s1, s2 generated by the measuring transducer 10, in particular the measured values ​​X representing at least one measured quantity. Mto determine and output. In particular, the measuring system electronics 20 are configured to determine, based on at least the first useful signal components s1N1, s2N1, for example, based on their (signal) frequency and / or based on an amplitude of at least one of the useful signal components s1N1, s2N1 and / or based on a phase angle of at least one of the useful signal components s1N1 or s2N1.s2N1, to determine measured values ​​representing at least one measured quantity, for example, to generate mass flow value measurements representing the mass flow rate of the measured substance and / or density value measurements representing the density of the measured substance; This also applies, for example, to measuring systems of the type in question, not least also to those derived from the aforementioned US-A 2006 / 0266129, US-A 2007 / 0113678, US-A 2010 / 0011882, US-A 2012 / 0123705, US-A 2017 / 0356777, US-A 56 02 345, US-A 59 26 096, WO-A 2009 / 136943, WO-A 2019 / 017891, WO-A 2019 / 081169, WO-A 2019 / 081170, WO-A 87 / 06691, WO-A 96 / 05484, the WO-A 96 / 08697, WO-A 97 / 26508, WO-A 99 / 39164 or its own unpublished international patent application PCT / EP2019 / 082044 known measuring systems in a typical manner.According to a further embodiment of the invention, the measuring system electronics 20 is accordingly further configured to generate mass flow measurement values ​​representing the mass flow based on the aforementioned phase difference of the first useful signal components s1N1; s2N1, for example by means of a phase difference-to-mass flow measurement characteristic function programmed into the measuring system electronics, namely a characteristic function of the measuring system electronics, which may also be designed as a (linear) parameter function, according to which a determined phase difference is thereby converted into mass flow measurement values ​​X. mto be converted. According to a further embodiment of the invention, the measuring system electronics 20 are also configured to determine the resonance frequency f1 of the first vibration mode (f1 mode) of the at least one tube, for example, on the basis of the driver signal e1 and / or at least one of the vibration measurement signals s1, s2, frequency values ​​X representing the resonance frequency f1. f1 to determine; for example, also to use such frequency values ​​to calculate density measurements X representing the density ρto calculate, for example according to a corresponding resonance frequency-to-density measurement characteristic function of the measuring system electronics. Alternatively or additionally, the measuring system electronics 20 can also be designed or configured to generate viscosity measurements, namely measurements representing the viscosity of the measured substance FL, based on at least one of the vibration measurement signals s1, s2, and / or the driver signal e1, for example according to a damping-to-viscosity measurement characteristic function of the measuring system electronics. The processing of the vibration measurement signals s1, s2, and possibly also the control of the aforementioned driver circuit(s) Exc, which is quite common in such measuring systems, can be carried out – as also in Fig. 2 and 3 respectively are shown schematically - for example, also using the aforementioned measuring and evaluation circuit DSV.

[0101] The program codes executed during operation of the measuring system in the measuring system electronics 20, for example, in one or more of the aforementioned microprocessors or digital signal processors of the measuring system electronics 20, can each be persistently stored, for example, in one or more non-volatile data storage devices (EEPROM) of the measuring system electronics 20, which can retain digital data even without an applied operating voltage. Upon startup, these programs can be loaded into a volatile data storage device (RAM) provided in the measuring system electronics 20 or the aforementioned measurement and evaluation circuit DSV, for example, integrated into the microprocessor. The vibration measurement signals s1, s2 are available for processing in the microprocessor or...In the digital signal processor, the signals must first be converted into corresponding digital signals using appropriate analog-to-digital converters (A / D), for example, by digitizing the respective signal voltage of each of the (here electrical) vibration measurement signals s1, s2 in a suitable manner; see, for example, the aforementioned US-B 63 11 136. Accordingly, the measurement system electronics 20, for example, the aforementioned measurement and evaluation circuit DSV, can include appropriate analog-to-digital converters for the vibration measurement signals s1, s2 and / or at least a non-volatile electronic data storage device (EEPROM) designed to retain digital data, for example, even without an applied operating voltage. To further improve the accuracy with which the measured values ​​X are measured... M The measuring transducer can ultimately be determined – as is also the case in… Fig. 2 and 3 are each shown schematically and, as is quite common with such measuring systems, also include temperature sensors 71 (71, 72) that are useful for detecting temperatures within the pipe arrangement and providing one or more corresponding temperature measurement signals θ1 (θ1, θ2), for example, directly attached to at least one pipe of the pipe arrangement, and / or strain sensors that are useful for detecting mechanical stresses within the pipe arrangement and providing one or more corresponding strain measurement signals, for example, directly attached to one of the pipes of the pipe arrangement, and the measuring system electronics can also be configured to receive and process the temperature or strain measurement signals, in particular to use them in determining the measured values.

[0102] As already mentioned, vibration-type transducers, and thus the vibronic measuring systems formed with them, can be subjected to a multitude of stresses during their service life, which can cause significant deviations of the transducer or the measuring system from a previously determined reference state, for example, an initial delivery state and / or a state during the commissioning of the measuring system on site; this can particularly occur in such a way that the pipe assembly, for example due to overloading, suffers damage that changes the vibration characteristics of at least one pipe, or that the transducer as a whole is damaged because, among other things, one or more system functions (transfer functions) inherent in the transducer or corresponding measurement functions formed in the measuring system are no longer correct compared to a respective (reference) system function of the original transducer.The (reference) measurement function of the measuring system is accordingly altered. Changes in the vibration characteristics of at least one tube can, for example, be attributed to changes in one or more modal parameters, namely bending stiffness, mass, and / or damping, each determining one of the aforementioned vibration modes. This results in one or more (natural) modes of vibration deviating from their respective counterparts when the transducer is in the reference state. This regularly occurs in such a way that an original—typically essentially homogeneous or uniform—distribution of the aforementioned (system) parameters (modal) bending stiffness, (modal) mass, and (modal) damping is altered, becoming increasingly uneven. Consequently, such loads not only lead to changes in the natural orThe resonance frequency of one or more of the aforementioned vibration modes, and in particular the shape of the vibrational motions of the respective vibration modes, are subject to changes such that the position of one or more of the vibration nodes located between two antinodes of the vibrational motions of the at least one tube in one or more of its upper vibration modes, and thus also the position of the aforementioned reference cross-sectional area, is changed compared to its respective original position. Accordingly, the drive offset determined relative to the reference cross-sectional area also undergoes changes, for example, such that the drive offset increases compared to the drive offset ΔE determined with the original or intact transducer.Furthermore, during the operation of the measuring system, at least one vibration exciter, as well as each of the vibration sensors, can be subject to changes relevant to measurement accuracy, for example, due to thermally induced (over-)stressing or aging. These changes can result in alterations to the electrical impedance of the transducer. (Over-)stresses that can lead to damage to the pipe assembly or the transducer as a whole can include, for example, high (over-)temperatures or temperature shocks, excessively high pressures or pressure surges in the fluid being measured, excessive clamping forces and / or excessive vibration forces exerted on the transducer by the process control, detrimental properties of the fluid being measured in the transducer, or material fatigue, among other factors.a significant reduction in the wall thickness of the pipe wall, for example due to corrosion and / or abrasion of the pipe wall of at least one pipe caused by the measuring medium, or a significant reduction in the flow cross-section of the pipe arrangement, for example due to at least partial clogging of the pipe arrangement and / or due to a solid coating on the inside of the pipe wall in contact with the measuring medium, a plastic deformation of the at least one pipe or even a crack formation within the pipe arrangement, for example namely the pipe wall, may result, and thus even lead to the transducer no longer being safe.

[0103] System functions affected by such damage to the transducer can, for example, correspond to one or more (modal) vibration responses of the pipe assembly relevant for measuring at least one measurand, such as a functional dependence of the amplitude of the aforementioned useful vibrations on the driver signal or a functional dependence of the amplitude of the aforementioned Coriolis vibrations on the driver signal and mass flow, or characterize a measurement function involving one or more of the aforementioned vibration responses, according to which the measuring system ultimately converts the respective measured quantity to be acquired into the respective measured values. Examples of such system functions of the transducer could therefore include, for instance, a mass flow-to-phase-difference system function, namely a system function of the transducer,According to which the aforementioned phase difference of the first useful signal components of the vibration measurement signals depends on the mass flow rate, system functions containing one or more resonance frequencies of the pipe arrangement as (system) parameters, such as a density-to-resonance-frequency system function, for example, a system function of the transducer according to which the aforementioned resonance frequency f1 depends on the density, or damping of vibrations as (system) parameters, such as a viscosity-to-damping function, for example, a system function of the transducer according to which damping of the first useful vibrations depends on the viscosity, are listed. Accordingly, those measurement functions of the measuring system that are based on one or more of the aforementioned system functions of the transducer can also be affected.for example, a mass flow-to-measurement function involving the mass flow-to-phase difference system function and the aforementioned phase difference-to-mass flow measurement characteristic function of the measuring system electronics, namely a measurement function of the measuring system according to which the mass flow measurements determined thereby are dependent on the mass flow, and / or a density-to-measurement function of the measuring system involving the aforementioned density-to-resonance frequency system function of the measuring transducer and the aforementioned resonance frequency-to-density measurement characteristic function of the measuring system electronics, and / or also a viscosity-to-measurement characteristic function of the measuring system involving the aforementioned viscosity-to-damping system function of the measuring transducer and the aforementioned damping-to-viscosity measurement characteristic function of the measuring system electronics.

[0104] Damage to the transducer or its tube assembly can, in particular, lead to one or more system functions or a corresponding measurement function being subject to corresponding changes over time, specifically drift. This includes parameters such as a (scale) zero point and / or a change in the phase difference of the first useful signal components related to a change in mass flow rate, as well as the measurement sensitivity (slope of the characteristic curve) of the aforementioned phase difference-to-mass flow measurement characteristic curve. As a result of such (over-)stressing of the transducer, which may occur repeatedly and / or over a longer period, it can be damaged to such an extent during its operating life that its functionality, or the functionality of the measurement system as a whole, is significantly impaired.is completely restricted; this may also result in a disturbance or a malfunction of the measuring system, possibly leading to measurement errors in the determination of the measured values, for example because the integrity of at least one of the vibration measurement signals or the measured values ​​obtained from them is significantly reduced, thus significantly reducing the measurement accuracy of the measuring system with which it ultimately maps the measured quantity to be recorded into the corresponding measured values ​​compared to an initial or nominal measurement accuracy of the original or intact measuring system.

[0105] In order to detect and, if necessary, report any changes to the measuring transducer, for example, to its mechanical and / or electrical properties, or to any resulting defects in the measuring transducer or the measuring system formed by it, as early and reliably as possible, it is further provided that, for example, during a self-diagnosis of the measuring system, the pipe arrangement is actively excited to mechanical vibrations by means of the excitation arrangement, such that at least one pipe performs vibrations which – as in Fig. 6 or 7 are shown schematically, or from their combination with Fig. 5 is readily apparent - corresponding to the aforementioned second-order vibration mode (f2 mode), and the resulting vibration measurement signals are evaluated accordingly by means of the measuring system electronics 20, in particular by examining them for disturbances of the measuring system; this is done in such a way that the vibrations corresponding to the second-order vibration mode (f2 mode) are non-volatile or stationary, namely exhibit a (substantially) constant, non-zero vibration amplitude for two or more vibration periods and / or a period of more than 10 ms (milliseconds). For this purpose, the measuring system electronics 20 of the measuring system according to the invention is further configured to at least temporarily measure the driver signal e1 - as also in Fig. 6 and 7 respectively indicated - with a - from the first (alternating current) frequency f eN1 for example, a second (alternating current) frequency that deviates by more than 10 Hz. eN2to provide the sinusoidal second (useful) current eN2, such that the at least one tube 111 generates at least partial second useful oscillations (different from the first useful oscillations), namely through the vibration exciter 31 (energized with the (useful) current eN2) or a second driving force (component) F generated therewith. exc2 energized vibration exciter 31 forced mechanical vibrations with a second operating frequency f N2 , namely one of the second (alternating current) frequencies f eN2 executes at the corresponding (oscillation) frequency (f N2 = f eN2 ), whereby each of the first and second oscillation signals s1, s2, generates a second useful signal component s1N2 and s2N2 ​​respectively, namely a sinusoidal signal component with one of the second useful frequencies f N2 corresponding (signal) frequency f s1N2 or f s2N2 (f s1N2 = f s2N2 = f N2). According to a further embodiment of the invention, the measuring system electronics 20 are further configured to provide the aforementioned second (useful) current (eN2) with a predetermined (current) amplitude.

[0106] In the measuring system according to the invention, the measuring system electronics 20 are also specifically designed to measure the second (alternating current) frequency f eN2 to adjust so that they deviate from a resonance frequency f2 of the second order vibration mode (f2-mode) of the at least one tube 111 by less than 1% (|f2 - f N2 | < 0.01 f2), for example also by less than 0.1%, namely resonance frequency f2, and / or by less than 1 Hz (|f1 - f N2 | < 1 Hz), for example also by less than 0.1 Hz; this also applies in particular to the (alternating current) frequency f eN2 the resonance frequency f2 of the second order oscillation mode (f2 mode) corresponds to (f eN2= f2). Only in the aforementioned, and therefore uncritical (ideal) case, which can only be expected with an original or a completely intact measuring transducer or measuring system, that the drive offset ΔE is actually zero, would the second useful oscillations not be excited in this way; consequently, the oscillation signals s1, s2, the second useful signal component s1N2 or s2N2 ​​would not be present or would have an amplitude of zero; otherwise, however (ΔE <> 0), as a result of such current flow to the vibration exciter 31 with the second (useful) current eN2, the second useful oscillations are indeed excited, and their oscillation movements correspond to those of the second-order oscillation mode (f2-mode) of the at least one tube 111.In the aforementioned case where the pipe arrangement has at least two pipes, the vibration exciter 31 can also be configured to convert electrical power supplied by means of the electrical driver signal e1 into forced mechanical vibrations of the first and second pipes 111, 112, such that the first and second pipes 111, 112 produce forced mechanical vibrations with the second useful frequency, for example, forced mechanical vibrations with the first useful frequency f. N1 and with the second usable frequency f N2, simultaneously. Accordingly, the measuring system electronics 20, according to a further embodiment of the invention, is also configured to provide the second useful current e1N2 of the driver signal e1 at least temporarily simultaneously with the first (useful) current e1N1; for example, also such that the (current) amplitude of the first (useful) current e1N1 is set not less than the (current) amplitude of the second (useful) current e1N2 and / or that the (current) amplitude of the second (useful) current e1N2 is set to more than 40%, for example, not less than 50%, of the (current) amplitude of the first (useful) current e1N1.

[0107] Alternatively or additionally, the measuring system electronics are further configured to measure the second (alternating current) frequency f eN2 depending on the first (alternating current) frequency f eN1 or to adjust depending on the resonance frequency f1; for example, by adjusting the second (alternating current) frequency feN2 within a frequency adjustment interval, of which an upper interval limit and / or a lower interval limit and / or a center frequency is a predetermined multiple of the first (AC) frequency f eN1 corresponds, for example, to a frequency greater than 230% of the first (alternating current) frequency f eN1 and / or less than 300% of the first (AC) frequency f eN1 corresponding multiples of the first (alternating current) frequency f eN1 According to a further embodiment of the invention, the measuring system electronics also feature a function for setting the (alternating current) frequency f. eN1 useful, for example also digital, first phase-locked loop (PLL1) as well as one for setting the (AC) frequency f eN2A useful, for example digital, second phase-locked loop (PLL2) is used. Furthermore, the measuring system electronics 20 can also be configured to define a capture range for the second phase-locked loop (PLL2) based on the first (AC) frequency f. eN1 or by means of at least one output signal of the first phase-locked loop (PLL1), for example an output signal of a loop filter of the first phase-locked loop (PLL1).

[0108] The measuring system electronics 20 of the measuring system according to the invention is also designed to evaluate at least one of the second useful signal components s1N2, s2N2, for example based on their (signal) frequency and / or based on a - in the case of an electrodynamic vibration sensor possibly also with the (alternating current) frequency f eN2normalized - (signal) amplitude of at least one of the second useful signal components s1N2, s2N2 ​​and / or based on a phase angle of at least one of the second useful signal components s1N2, s2N2, to perform a (self-)diagnosis of the measuring system, for example, to check the functionality of the measuring system and / or to (re-)calibrate the measuring system and / or to determine whether a disturbance of the measuring system exists, for example, such that the functionality of the measuring system is reduced and / or that a malfunction of the measuring system exists and / or a measurement error exists in the determination of the measured values, for example because the integrity of at least one of the vibration measurement signals s1, s2 is reduced.The measuring system electronics can, for example, also be configured to determine, in the course of the aforementioned (self-)diagnosis, for example on the basis of the (signal) frequency of the second useful signal components and / or on the basis of a (signal) amplitude of at least one of the second useful signal components s1N2 and / or on the basis of a phase angle of at least one of the second useful signal components s1N2, whether and / or to what extent a disturbance of the measuring system (☹) is due to one or more vibration properties of the pipe arrangement that have changed compared to a reference state (☺) determined beforehand. Fig.7), for example as a result of damage to the pipe assembly, if necessary also to determine to what extent damage to the pipe assembly is due to erosion (corrosion, abrasion) on an inner side of the pipe wall facing the lumen or a corresponding reduction in the wall thickness of the pipe wall of at least one pipe and / or due to deposit formation on an inner side of the pipe wall facing the lumen and / or due to a crack in the pipe wall of one or more of the pipes and / or due to plastic deformation of one or more of the pipes, and / or to what extent a measurement error is due to damage to the pipe assembly when determining the measured values.The aforementioned reference state of the transducer can, for example, correspond to its respective state upon delivery from the manufacturer, and thus be determined accordingly during calibration at the manufacturer's plant and / or during commissioning of the measuring system, and stored in the measuring system electronics in the form of corresponding reference values ​​for one or more system functions of the transducer, specifying (system) parameters.

[0109] The aforementioned evaluation of at least one of the second useful signal components s1N2, s2N2 ​​can, for example, be a simple examination of at least one of the vibration measurement signals s1, s2 for the second useful signal component, or a detection of said second useful signal components in the vibration measurement signals s1, s2 above a predetermined (minimum) signal level; however, it can also include a dedicated measurement of one or more of the second useful signal components s1N2, s2N2 ​​with regard to their respective (signal) amplitudes or temporal amplitude profiles and / or their respective phase angles or temporal phase angle profiles and / or their respective (signal) frequency or temporal frequency profiles.For example, using the vibration measurement signals s1, s2, parameter values ​​can be repeatedly determined by the measurement system electronics. These values ​​characterize the respective vibration response or one or more of the aforementioned system functions and can be compared with correspondingly defined reference values. Alternatively or additionally, using the vibration measurement signals s1, s2, one or more characteristic values ​​for at least one measurement system parameter can also be repeatedly calculated by the measurement system electronics. These parameters characterize an operating state of the measurement system, for example, such that each characteristic value corresponds to a combination of two or more of the aforementioned parameter values ​​or depends on several such parameter values.Furthermore, a measurement system parameter to be determined can also be chosen to represent a measure of drive offset, such that the measurement system parameter indicates whether or to what extent the drive offset deviates from an originally existing (initial) drive offset, for example, due to a change in the position of the centroid of the reference cross-sectional area or a corresponding displacement of the reference cross-sectional area. Alternatively, the parameter can be defined, for example, as a measure of how quickly the drive offset changes over time.If a predefined threshold is exceeded—for example, an acceptable tolerance for a deviation between a determined parameter and / or characteristic value and a predefined reference value, or an unacceptably high deviation—the measuring system electronics 20 can diagnose a fault quickly and easily. This allows for the generation and output of a corresponding system status or fault message, possibly declared as an alarm. System parameters characterizing vibration responses or system functions can include, for example, vibration amplitude ratios or frequency ratios, bending stiffnesses, ratios of modal bending stiffnesses, damping, or ratios of modal damping of at least one pipe.The corresponding reference values ​​for the parameter and / or key figure values, as well as the respective threshold values, can be determined in advance, for example, during initial calibration of the measuring system by the manufacturer at the factory or, if applicable, during commissioning of the measuring system on site, using the measuring system itself while still in its original (reference) state and / or based on laboratory measurements with identical measuring systems, and stored accordingly in advance in the measuring system electronics 20, for example, in its non-volatile EEPROM data storage. The parameter values ​​determined by the measuring system electronics 20 can also be output, for example, displayed on site and / or forwarded to the aforementioned (measurement) data processing system.

[0110] Taking into account the respective first and second operating frequencies, a corresponding resonance frequency ratio of the respective vibration modes can, for example, be determined and used as a (system) parameter specifying a system function of the transducer for (self-)diagnosis, for example, such that a time-varying, for example, continuously increasing or continuously decreasing, ratio of the resonance frequency f2 to the resonance frequency f1 is used as an indicator of the presence of a fault in the transducer. According to a further embodiment of the invention, the measuring system electronics 20 are configured accordingly, and the resonance frequency f2 of the second vibration mode (f2 mode) of the at least one tube 111 is determined, for example, based on the driver signal e1 and / or at least one of the vibration measurement signals s1, s2, by frequency values ​​X representing the resonance frequency f2. f2, to determine and / or to determine a resonance frequency ratio f1 / f2 corresponding to a ratio of the resonance frequency f1 of the first oscillation mode (f1 mode) and the resonance frequency f2 of the second oscillation mode (f2 mode), for example, based on the first and second (alternating current) frequencies f eN1 , f eN2 of the driver signal e1 and / or based on the signal frequencies f s1N1 , f s2N1 , f s1N2 , f s2N2 of the useful signal components s1N1, s1N2, s2N1, s2N2 ​​at least one of the vibration measurement signals representing the resonance frequency ratio f1 / f2 frequency ratio values ​​X f12 (X f12 = f eN1 / f eN2 ; X f12 = f s1N1 / f s1N2 ; X f12 = f s2N1 f s2N2 to determine. The recurring frequency ratio values ​​X f12Furthermore, for the purpose of performing (self-)diagnosis of the measuring system using the measuring system electronics 20, the values ​​can be compared, for example, with a specified reference value, in particular to determine whether or to what extent the resonance frequency ratio f1 / f2 deviates from the same reference value.

[0111] Taking into account the displacements (amplitude) of the second useful vibrations, a change in the natural mode of the second-order vibration can also be determined, for example, and used as a (system) parameter specifying a system function of the transducer for (self-)diagnosis. According to a further embodiment of the invention, the measuring system electronics 20 are therefore also configured to determine, based on the vibration measurement signals s1, s2, at least one phase difference of the second useful signal components, namely a difference between a phase angle of the second useful signal component s1N2 of the vibration measurement signal s1 and a phase angle of the second useful signal component s2N2 ​​of the vibration measurement signal s2.The repeatedly determined phase difference values ​​can be compared with one or more predefined reference values ​​for (self-)diagnosis of the measuring system using the measuring system electronics 20. This comparison can be used, for example, to determine whether or to what extent the phase difference of the second useful signal component, or an underlying modal displacement of the second useful oscillations of at least one pipe, deviates from the respective reference value. For example, an excessively high and / or continuously increasing phase difference of the second useful signal component can be used as an indicator of a fault. One or more of the aforementioned reference values ​​for the phase difference of the second useful signal component can also be used, for example, as a function of a current value X used to determine the mass flow measurement values. mThe phase difference of the first useful oscillations, which has already been determined, can be used as a basis. Alternatively or additionally, the phase difference values ​​determined for the second useful oscillations can also be used to perform the (self-)diagnosis of the measuring system using the measuring system electronics 20, in order to establish a ratio between the aforementioned phase difference of the second useful oscillations and the values ​​used to determine the mass flow measurement values ​​X. m The phase difference ratio corresponding to the phase difference of the first useful vibrations is to be determined. According to another embodiment of the invention, the measuring system electronics 20 are further configured to determine, on the basis of the vibration measurement signals s1, s2, at least one of the, in the case of an electrodynamic vibration sensor optionally also with the (alternating current) frequency f. eN1normalized, (signal) amplitudes of the first useful signal components s1N1, s2N1, thus representing amplitude values ​​x1 of the first useful oscillations, in particular amplitude values ​​X representing the (signal) amplitudes of the useful signal components s1N1 s1N1 as well as the (signal) amplitudes of the useful signal components s2N1 representing amplitude values ​​X s2N1 to determine, and / or the measuring system electronics 20 is set up to represent at least one of the (signal) amplitudes of the second useful signal components s1N2, s2N2, thus representing amplitude values ​​x2 of the second useful oscillations, in particular both the (signal) amplitudes of the useful signal components s1N2 representing amplitude values ​​X s1N2 as well as the (signal) amplitudes of the useful signal components s2N2 ​​representing amplitude values ​​X s2N2to determine, for example by forming a respective moving average for the (signal) amplitudes of the useful signal components s1N1, s1N2, s1N2 and s2N2 ​​using FIR filters and / or by numerical integration of the amplitude values ​​X s1N1 , X s2N1 , X s1N2 , or X s2N2 Alternatively or additionally, the measuring system electronics are further configured to determine a displacement ratio x1 / x2 corresponding to the ratio of the (modal) displacement (amplitude) of the first useful vibrations and the (modal) displacement of the second useful vibrations, for example, by determining displacement ratio values ​​representing the displacement ratio x1 / x2 based on at least one of the vibration measurement signals s1, s2, possibly using the aforementioned displacement values ​​X s1N1 , X s1N2 and / or the aforementioned deflection values ​​X s2N1 , X s2N2The recurring amplitude values, in particular the amplitude values ​​X s1N2 , X s2N2 , and / or the correspondingly determined displacement ratio values ​​can, for example, be compared with one or more predefined reference values ​​for the purpose of performing (self-)diagnosis of the measuring system using the measuring system electronics 20, to determine, for instance, whether or to what extent one and / or more of the (signal) amplitudes or one or more of the modal displacements of the vibrations of the at least one tube, in particular the displacements of the second useful vibrations, deviate from the respective reference value. One or more of the aforementioned reference values ​​for the amplitude values ​​X s1N2 , X s2N2(or the modal deflections of the vibrations of at least one tube) can, for example, also depend on a currently set (current) amplitude of the second (useful) current eN2 and / or on one of the current deflection values ​​X s1N1 and / or X s2N1 be set.

[0112] Taking into account both the displacements of the first and second useful vibrations and the driving force causing them, a corresponding modal spring stiffness of the respective useful vibrations or vibration modes can also be determined and used as a system parameter specifying a system function of the transducer for (self-)diagnosis. For example, a (modal) spring stiffness of the second useful vibration that is too low and / or steadily decreasing over time, or a time-varying ratio of a (modal) spring stiffness c2 of the second useful vibration to a (modal) spring stiffness c1 of the first useful vibration, which is steadily increasing or decreasing over time, can be used as an indicator of a fault. Alternatively or additionally, taking into account both the displacement velocities of the first and second useful vibrations, the modal spring stiffness c1 of the second useful vibration can be determined.In addition to the second useful vibrations and the driving force causing them, the (modal) damping of the respective useful vibrations or the corresponding vibration mode is also determined and used as a (system) parameter specifying system functions of the transducer for (self-)diagnosis, for example, such that an excessively high and / or continuously increasing damping of the second useful vibrations or a time-changing, for example continuously increasing or continuously decreasing, ratio of a (modal) damping d2 of the second useful vibrations to a (modal) damping d1 of the first useful vibrations is used as an indicator of the presence of a disturbance.

[0113] According to a further embodiment of the invention, the measuring system electronics 20 are therefore further configured to determine a (modal) damping of the second useful oscillations corresponding to a ratio of the (signal) amplitude of one of the second useful signal components s1N2, for example also a sum or a difference of the (signal) amplitudes of the second useful signal components, and a (signal) amplitude of the second (useful) current eN2, for example namely, to determine damping values ​​representing the damping d2 of the second useful oscillations based on the second (useful) current e1N2 and a second useful signal component of at least one of the oscillation measurement signals s1, s2. The repeatedly determined damping values ​​can further be compared with one or more predefined reference values, for example, to perform (self-)diagnosis of the measuring system using the measuring system electronics 20, in particular.namely, to determine whether or to what extent the damping of the second useful vibrations of the at least one tube deviates from a predetermined reference value (damping reference value). Alternatively or additionally, the measuring system electronics can also be configured to determine a damping ratio d1 / d2 corresponding to the ratio of the (modal) damping of the first useful vibrations and the (modal) damping d2 of the second useful vibrations, for example, by determining damping ratio values ​​representing the damping ratio d1 / d2 based on the first and second (useful) currents of the driver signal and / or at least the first and second useful signal components of at least one of the vibration measurement signals.Accordingly, the measuring system electronics 20 can also be configured to determine both the aforementioned (modal) damping of the second useful oscillations and a (modal) damping d1 of the first useful oscillations corresponding to a ratio of the (signal) amplitude of one of the first useful signal components s1N1, for example also a sum or a difference of the (signal) amplitudes of the useful signal components s1N1, s2N1, and a (signal) amplitude of the first (useful) current eN1, for example namely to determine damping values ​​representing the damping of the first useful oscillations on the basis of the driver signal and at least one of the oscillation measurement signals.According to a further embodiment of the invention, the measuring system electronics 20 is further configured to perform the (self-)diagnosis of the measuring system by comparing one or more of the aforementioned damping values ​​representing the damping of the second useful oscillations and / or one or more of the aforementioned damping ratio values ​​with at least one reference value determined beforehand and / or by means of an intact measuring system, for example, also by issuing a message representing a deviation of one or more of the damping values ​​from the respective reference value (damping reference value) or a deviation of one or more of the damping ratio values ​​from the respective reference value (damping ratio reference value), in particular declared as a (fault) alarm.According to another embodiment of the invention, the measuring system electronics 20 are further configured to determine, on the basis of the second (useful) current e1N2 and a second signal component, at least one of the vibration measurement signals s1, s2, representing the spring stiffness c2 of the second useful vibrations. The repeatedly determined spring stiffness values ​​can also be compared, for example, with one or more predefined reference values ​​for the purpose of performing (self-)diagnosis of the measuring system using the measuring system electronics 20, in particular to determine whether or to what extent the spring stiffness c2 of the second useful vibrations of the at least one tube deviates from a predefined reference value (spring stiffness reference value).Alternatively or additionally, the measuring system electronics can also be configured to determine a spring stiffness ratio c1 / c2 corresponding to a ratio of the (modal) spring stiffness c1 of the first useful vibrations and the (modal) spring stiffness c2 of the second useful vibrations, for example by determining spring stiffness ratio values ​​representing the spring stiffness ratio c1 / c2 based on the first and second (useful) currents and / or the first and two useful signal components of at least one of the vibration measurement signals.Accordingly, the measuring system electronics 20 can also be configured to determine both the aforementioned (modal) spring stiffness c2 of the second useful oscillations and a (modal) spring stiffness of the first useful oscillations corresponding to a ratio of the (signal) amplitude of one of the first useful signal components s1N1, for example also a sum or a difference of the (signal) amplitudes of the useful signal components s1N1, s2N1, and a (signal) amplitude of the first (useful) current eN1, for example namely to determine spring stiffness values ​​representing the spring stiffness c1 of the first useful oscillations on the basis of the first (useful) current e1N1 and the first useful signal component of at least one of the oscillation measurement signals.According to a further embodiment of the invention, the measuring system electronics 20 is further configured to perform the (self-)diagnosis of the measuring system by comparing one or more of the aforementioned spring stiffness values ​​representing the spring stiffness c2 of the second useful vibrations and / or one or more of the aforementioned spring stiffness ratio values ​​with at least one reference value determined beforehand and / or by means of an intact measuring system, for example, also by issuing a message representing a deviation of one or more of the spring stiffness values ​​from the respective reference value (spring stiffness reference value) or a deviation of one or more of the spring stiffness ratio values ​​from the respective reference value (spring stiffness ratio reference value), in particular declared as a (fault) alarm.

[0114] The parameters for one or more of the aforementioned (system) parameters, for example, the resonance frequency ratio f1 / f2 of the at least one tube, the displacement ratio x1 / x2 of the first and second useful vibrations, the (modal) damping d2 of the second useful vibrations, the damping ratio d1 / d2 of the first and second useful vibrations, the (modal) spring stiffness d2 of the second useful vibrations, the spring stiffness ratio c1 / c2 of the first and second useful vibrations, etc.The determined parameter values, such as the (modal) spring stiffness c2 (representing spring stiffness values), the spring stiffness ratio c1 / c2 (representing spring stiffness ratio values), the (modal) damping d2 (representing damping values), the damping ratio d1 / d2 (representing damping ratio values), the displacement ratio x1 / x2 (representing displacement ratio values), the phase difference of the second useful signal components (representing phase difference values), etc., can also be used to repeatedly determine a measure of dispersion for the respective system parameter. Such a measure of dispersion can, for example, be an empirical variance or a range for the respective (system) parameter or the parameter values ​​determined for it.The determined measure of dispersion can also be used for (self-)diagnosis, for example, by only concluding that a fault in the measuring system is present if the respective (system) parameter has a low measure of dispersion, i.e., below a correspondingly predefined threshold, and / or that a (system) parameter with a measure of dispersion above a correspondingly predefined threshold does not trigger a fault message, even if a comparison of its parameter values ​​with the respective reference value would initially indicate this. Alternatively or additionally, the measure of dispersion determined by the measuring system electronics 20 can also be output, for example, displayed on-site and / or forwarded to the aforementioned (measurement) data processing system.Alternatively or additionally, the parameter values ​​determined for one or more of the aforementioned (system) parameters, for example, the resonance frequency ratio f1 / f2 of the at least one tube, the displacement ratio x1 / x2 of the first and second useful vibrations, the damping of the second useful vibrations, the damping ratio d1 / d2 of the first and second useful vibrations, etc., can also be used to repeatedly determine a change over time, for example, a change trend and / or a rate of change and / or a rate of change, of the respective (system) parameter.The determined temporal change can also be used for (self-)diagnosis, for example, by detecting an increasing disturbance in the transducer if the damping of the second useful oscillation decreases or if the resonant frequency ratio f1 / f2 and / or damping ratio d1 / d2 changes at a rate of change within a predefined measuring range. This can then be done by issuing a message representing an increase in the disturbance, particularly one declared as a (fault) alarm. The temporal change, rate of change, or rate of change determined by the measuring system electronics 20 can also be output, for example, displayed locally and / or forwarded to the aforementioned (measurement) data processing system.

[0115] The (self-)diagnosis of the measuring system according to the invention can be performed, for example, during a test interval reserved for this purpose, which may be repeated occasionally or last more than 10 ms (milliseconds), advantageously more than 100 ms, and in particular not less than 1 s (second). The test interval can be limited in time, for example to less than 1 minute, but can nevertheless be restarted repeatedly, for example by an external command from the measuring system and / or automatically, namely time- and / or event-controlled by the measuring system electronics themselves. For example, the measuring system electronics can be configured to start the test interval when the measured substance FL is detected as flowing at a steady rate and / or to end it when the measured substance FL is flowing at a transient rate or when measuring conditions and / or measured variables are changing rapidly.Accordingly, according to a further embodiment of the invention, the measuring system electronics are capable of automatically starting and / or ending the test interval, and / or of receiving and executing one or more commands that start the test interval. According to a further embodiment of the invention, the measuring system electronics are also configured to start the test interval during normal measurement operation or during the excitation of the first useful oscillations, such that at least the driver signal e1 is provided with the second (useful) current eN2; this can also be done, for example, such that the driver signal e1 contains the first (useful) current eN1 at least temporarily, so that the second useful oscillations are excited simultaneously with the first useful oscillations, and thus the first and second useful oscillations are at least temporarily superimposed on each other during the test interval.According to a further embodiment of the invention, the measuring system electronics are also configured to determine, during the test interval, the measured values ​​representing at least one measured quantity based on the second useful signal components s1N2; s2N2, in particular based on their (signal) frequency and / or based on a (signal) amplitude of at least one of the second useful signal components s1N2 and / or based on a phase angle of at least one of the second useful signal component s1N2. QUOTES INCLUDED IN THE DESCRIPTION

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[0001]

Claims

[1] Vibronal measuring system, in particular a Coriolis mass flow meter or Coriolis mass flow / density meter, for measuring and / or monitoring at least one measured quantity, in particular a flow parameter, in particular a mass flow rate and / or a volume flow rate and / or a flow velocity, and / or a material parameter, in particular a density and / or a viscosity, of a fluid medium, in particular a gas, a liquid or a dispersion, which includes, in particular, a measuring system designed as an in-line measuring device and / or a compact measuring device: - a measuring transducer (10) -- with a pipe arrangement for guiding the flowing medium, -- mechanical power useful with an excitation arrangement for converting electrical power into the excitation and maintenance of forced mechanical vibrations of the pipe arrangement -- and with a sensor arrangement for detecting mechanical vibrations of the pipe arrangement and for providing vibration measurement signals representing the vibration movements of the pipe arrangement; - as well as a measuring system electronics (20) electrically coupled to the measuring transducer (10), namely both to its excitation arrangement and to its sensor arrangement, in particular by means of electrical connecting lines, in particular formed by means of at least one microprocessor and / or arranged in electronic protective housing, for controlling the measuring transducer and for evaluating vibration measurement signals supplied by the measuring transducer; - wherein the pipe arrangement comprises at least one, in particular at least partially curved and / or at least partially straight and / or first, pipe (111), -- which pipe extends from a first pipe end to a second pipe end with a pipe length, in particular more than 100 mm, and has a lumen enclosed by a pipe wall, in particular metallic, extending from the first pipe end to the second pipe end, -- and which pipe is set up to be flowed through by the measuring medium in at least one flow direction pointing from the first pipe end to the second pipe end and to be vibrated during this process, -- and wherein the tube possesses a plurality of vibration modes (natural modes) each having an associated resonance frequency (f1, f2, ... , fx), in which the tube can or does perform vibrational movements having one or more antinodes and two or more nodes, such that --- that the vibrational movements of the pipe in a fundamental vibration mode, namely a first-order vibration mode (f1-mode), in particular a first-order bending vibration mode, exhibit exactly one antinode and two nodes --- and that the vibrational movements of the pipe in a higher-order vibration mode, namely a second or higher order vibration mode (f2 mode, ... fx mode), in particular a second or higher order bending vibration mode, exhibit two or more antinodes and three or more nodes; - wherein the excitation arrangement includes a vibration exciter (31), in particular an electrodynamic one, -- mechanically connected to the pipe -- and is designed to convert electrical power into mechanical power using a time-varying electric current, such that a time-varying driving force acts on the pipe at a drive point formed by means of the vibration exciter on the pipe mechanically connected thereto, in particular such that a line of action of the driving force runs perpendicular to a normal of a driving cross-sectional area of ​​the pipe, -- wherein the vibration exciter (31) is positioned and aligned such that a drive offset (ΔE), namely a minimum distance between a drive cross-sectional area of ​​the tube enclosed by an imaginary circumferential line of the tube passing through the drive point and a predetermined reference cross-sectional area of ​​the at least one tube, determined in particular with an intact or original transducer, is no more than 3 mm, in particular less than 2 mm, and / or less than 0.5% of the tube length, in particular less than 0.2% of the tube length, in particular is zero with an intact or original transducer, wherein a vibration antinode formed between two antinodes of vibration movements of the at least one tube in a vibration mode (second or higher order) (deviating from the first order vibration mode), in particular(nominal) vibration nodes located at half a pipe length, namely vibration movements within the reference cross-sectional area. - and wherein the measuring system electronics (20) is configured to supply current to the vibration exciter (31), namely to supply electrical power to the vibration exciter (31) by means of an electrical driver signal (e1) having a time-varying electrical current, such that the tube performs forced mechanical vibrations, in particular bending vibrations, with one or more vibration frequencies specified by the driver signal (e1); - wherein the sensor arrangement includes a first vibration sensor, in particular an electrodynamic or optical one, -- which is positioned on the pipe, in particular at a distance of more than 10 mm and / or more than one fifth of the pipe length in the direction of flow, and in particular is at least partially mechanically connected to the pipe, is -- and which is equipped to detect vibrations of the pipe and to convert them into a first vibration measurement signal representing vibrations, in particular an electrical or optical signal, in particular such that the first vibration measurement signal contains one or more sinusoidal signal components, each with a frequency corresponding to a vibration frequency of vibrations of the pipe; - wherein the sensor arrangement includes at least one second vibration sensor, in particular an electrodynamic or optical one, -- which is positioned on the pipe, in particular more than 10 mm and / or more than one fifth of the pipe length away from the vibration exciter in the direction of flow and / or which is positioned away from the first vibration sensor in the direction of flow, in particular at least partially mechanically connected to the pipe, is -- and which is equipped to detect vibrations of the pipe and to convert them into a second vibration measurement signal representing the same vibrations, in particular an electrical or optical signal, in particular such that the second vibration measurement signal contains one or more sinusoidal signal components, each with a frequency corresponding to a vibration frequency of vibrations of the pipe; - and wherein the measuring system electronics are configured to receive and evaluate the first and second vibration measurement signals, in particular to determine and output the measured values ​​representing at least one measured quantity; - where the measuring system electronics are set up, -- to provide both the driver signal (e1) at least temporarily with a sinusoidal first (useful) current (eN1) having a first (alternating current) frequency, in such a way, --- that the tube performs at least partially, in particular predominantly, first useful vibrations, namely mechanical vibrations forced by the (energized) vibration exciter with a first useful frequency, namely a (vibration) frequency corresponding to the first (alternating current) frequency, in particular such that the first useful frequency deviates from a resonance frequency, f1, of the fundamental vibration mode by less than 1% of the same resonance frequency, f1, and / or by less than 1 Hz and / or that the first useful frequency deviates from a resonance frequency, f2, of the second-order vibration mode by more than 5% of the same resonance frequency, f2, and / or by more than 10 Hz and / or that the first useful vibrations are suitable to cause Coriolis forces in the flowing medium that depend on the mass flow rate, --- and that each of the first and second oscillation signals (s1; s2) has a first useful signal component (s1N1; s2N1), namely a sinusoidal signal component with a (signal) frequency corresponding to the first useful frequency, -- as well as on the basis of at least the first useful signal components (s1N1; s2N1), in particular on the basis of their (signal) frequency and / or on the basis of an amplitude of at least one of the first useful signal components (s1N1; s2N1) and / or on the basis of a phase angle of at least one of the first useful signal components (s1N1; s2N1), which represent at least one measured quantity, in particular mass flow values ​​representing the mass flow of the measured substance and / or density values ​​representing the density of the measured substance; - and where the measuring system electronics are set up, -- to provide both the driver signal (e1) at least temporarily, in particular during a test interval lasting more than 10 ms and / or limited in time and / or restarted repeatedly, with a sinusoidal second (useful) current (eN2) having a second (AC) frequency, in such a way, --- that the second (alternating current) frequency, in particular for two or more oscillation periods and / or a period of more than 10 ms, deviates from a resonance frequency, f2, of the second order oscillation mode by less than 1%, in particular by less than 0.1%, namely resonance frequency, f2, and / or by less than 1 Hz, in particular by less than 0.1 Hz, --- and that the pipe at least partially – in particular simultaneously with the first useful oscillations and / or stationary, namely for two or more oscillation periods and / or a period of more than 10 ms – performs second useful oscillations, namely mechanical oscillations forced by the (energized) vibration exciter with a second useful frequency, namely one corresponding to the second (alternating current) frequency, whereby each of the first and second oscillation signals has a second useful signal component (s1N2; s2N2), namely a sinusoidal signal component with a (signal) frequency corresponding to the second useful frequency, -- as well as on the basis of at least one of the second useful signal components (s1N2; s2N2), in particular on the basis of their (signal) frequency and / or on the basis of a (signal) amplitude of at least one of the second useful signal components (s1N2) and / or on the basis of a phase angle of at least one of the second useful signal component (s1N2), to carry out a (self-)diagnosis of the measuring system, in particular to check the functionality of the measuring system and / or to (re-)calibrate the measuring system and / or to determine whether there is a fault in the measuring system. [2] Measuring system according to claim 1, wherein the first useful frequency deviates from a resonance frequency, f1, of the fundamental vibration mode by less than 1% of that resonance frequency, f1, and / or by less than 1 Hz. [3] Measuring system according to claim 1, wherein the first useful frequency deviates from a resonance frequency, fr3, of a third-order vibration mode inherent in the at least one tube, in particular a third-order bending vibration mode, in which vibration mode the vibration movements of the tube have exactly three antinodes and two nodes, by less than 1% of said resonance frequency, fr3, and / or by less than 1 Hz, in particular the resonance frequency, fr3. [4] Measuring system according to the previous claim, wherein a first vibration node of vibration movements of the at least one tube in the third order vibration mode is located in the first tube end and a second vibration node of the third order vibration mode is located in the second tube end. [5] Measuring system according to one of the preceding claims, wherein the upper vibration mode corresponds to a second-order vibration mode (f2-mode), in particular a second-order bending vibration mode, in which second-order vibration mode the vibrational movements of the tube have exactly two antinodes and three nodes. [6] Measuring system according to the previous claim, - wherein a node of the vibration movements of the at least one tube in the second order vibration mode, formed between the two antinodes of the vibration movements of the at least one tube, and located (nominally) at half a tube length, lies within the reference cross-sectional area; - and / or wherein a principal axis of inertia of the at least one tube, perpendicular to the direction of vibration of the oscillatory movements of the tube in the second order vibration mode, lies within the reference cross-sectional area of ​​the at least one tube. [7] Measuring system according to any one of the preceding claims, - wherein the drive offset corresponds to a distance between a centroid (center) of the drive cross-sectional area of ​​the tube and a centroid (center) of the reference cross-sectional area of ​​the at least one tube; and / or - wherein a line of action of the driving force runs perpendicular to a normal of a driving cross-sectional area of ​​the pipe; and / or - wherein a line of intersection of two mutually orthogonal planes of symmetry of the at least one tube lies within the reference cross-sectional area; and / or - wherein a principal axis of inertia of the at least one tube, perpendicular to the driving force, lies within the reference cross-sectional area of ​​the at least one tube. [8] Measuring system according to any one of the preceding claims, - wherein the measuring system electronics are configured to provide the second useful current of the driver signal (e1) at least temporarily simultaneously with the first (useful) current, in particular such that the amplitude of the first (useful) current is set to be not less than the amplitude of the second (useful) current and / or that the amplitude of the second (useful) current is set to be more than 40%, in particular not less than 50%, of the amplitude of the first (useful) current; and / or - wherein the measuring system electronics are configured to adjust the second (AC) frequency depending on the first (AC) frequency, in particular such that the second (AC) frequency lies within a frequency setting interval, of which an upper interval limit and / or a lower interval limit and / or a center frequency corresponds to a predetermined multiple of the first (AC) frequency, in particular, more than 230% of the first (AC) frequency and / or less than 300% of the first (AC) frequency corresponding to multiples of the first (AC) frequency. [9] Measuring system according to any one of the preceding claims, - wherein the measuring system electronics have a first phase-controlled loop, in particular a digital one, which is useful for setting the first (alternating current) frequency - and wherein the measuring system electronics have a second phase-controlled loop, in particular a digital one, which is useful for setting the second (alternating current) frequency. [10] Measuring system according to the previous claim, wherein the measuring system electronics are configured to set a capture range of the second phase-locked loop by means of at least one output signal of the first phase-locked loop, in particular an output signal of a loop filter of the first phase-locked loop, and / or on the basis of the first (AC) frequency. [11] Measuring system according to one of the preceding claims, wherein the measuring system electronics are configured to perform the (self-)diagnosis of the measuring system on the basis of at least one second useful signal component (s1N2; s2N2), in particular on the basis of their (signal) frequency and / or on the basis of a (signal) amplitude of at least one of the second useful signal component (s1N2) and / or on the basis of a phase angle of at least one of the second useful signal component (s1N2): - to determine whether and / or to what extent a disturbance of the measuring system exists, in particular one that reduces the functionality of the measuring system and / or causes a malfunction of the measuring system and / or reduces the integrity of at least one of the first and second vibration measurement signals or measured values ​​obtained therefrom and / or provokes a measurement error in the measured values ​​obtained therefrom; and / or - to determine whether or to what extent the pipe arrangement has changed, in particular is damaged, compared to a previously determined reference state, - and / or to determine whether and / or to what extent a disturbance of the measuring system exists due to one or more vibration properties of the pipe arrangement that have changed compared to a reference state determined beforehand, in particular as a result of damage to the pipe arrangement, - and / or to determine whether and / or to what extent damage to the pipe assembly is present, in particular as a result of erosion on an inner surface of the pipe wall facing the lumen and / or as a result of deposit formation on an inner surface of the pipe wall facing the lumen, - and / or to determine whether and / or to what extent a measurement error exists in the determination of the measured values ​​due to damage to the measuring transducer, in particular to the pipe arrangement. [12] Measuring system according to any one of the preceding claims, - wherein the measuring system electronics are configured to perform (self-)diagnosis of the measuring system based on the second useful signal components (s1N2; s2N2), in particular based on their (signal) frequency and / or based on a (signal) amplitude of at least one of the second useful signal components (s1N2) and / or based on a phase angle of at least one of the second useful signal component (s1N2), to determine whether an existing disturbance of the measuring system is attributable to a change, in particular irreversible, in one or more flow properties of the pipe arrangement, in particular due to a reduction of a flow cross-section of the pipe arrangement, in particular as a result of a blockage of one or more of the pipes and / or as a result of a deposit on an inner surface of the pipe wall of one or more of the pipes; and / or - wherein the measuring system electronics are configured to perform (self-)diagnosis of the measuring system based on the second useful signal components (s1N2; s2N2), in particular based on their (signal) frequency and / or based on a (signal) amplitude of at least one of the second useful signal components (s1N2) and / or based on a phase angle of at least one of the second useful signal component (s1N2), to determine whether an existing disturbance of the measuring system is due to a change, in particular irreversible, of one or more vibration characteristics of the pipe arrangement, in particular due to a reduction in the wall thickness of the pipe wall of one or more of the pipes and / or due to plastic deformation of one or more of the pipes and / or due to a coating on the inside of the pipe wall of one or more of the pipes and / or due to a crack in the pipe wall of one or more of the pipes. [13] Measuring system according to any one of the preceding claims, - wherein the measuring system electronics are configured to determine a (signal) amplitude of one of the first useful signal components (s1N1), in particular a difference between the (signal) amplitudes of the first useful signal components (s1N1; s2N1), corresponding to a (modal) displacement of the first useful vibrations, in particular namely to determine displacement values ​​representing the displacement of the first useful vibrations on the basis of at least one of the vibration measurement signals; and / or - wherein the measuring system electronics are configured to determine a (signal) amplitude of one of the second useful signal components (s1N1), in particular a difference between the (signal) amplitudes of the second useful signal components (s1N1; s2N1), corresponding to a (modal) displacement of the first useful vibrations, in particular namely to determine displacement values ​​representing the displacement of the second useful vibrations on the basis of at least one of the vibration measurement signals; and / or - wherein the measuring system electronics are configured to determine a displacement ratio, x1 / x2, corresponding to a ratio of the (modal) displacement of the first useful vibrations and the (modal) displacement of the second useful vibrations, in particular to determine displacement ratio values ​​representing the displacement ratio, x1 / x2, on the basis of at least one of the vibration measurement signals. [14] Measuring system according to any one of the preceding claims, - wherein the measuring system electronics are configured to determine a (modal) damping, d1, of the first useful oscillations corresponding to a ratio of a (signal) amplitude of one of the first useful signal components (s1N1), in particular a sum or a difference of the (signal) amplitudes of the first useful signal components (s1N1; s2N1), and a (signal) amplitude of the first (useful) current (eN1), in particular namely to determine damping values ​​representing the damping of the first useful oscillations on the basis of the driver signal and at least one of the oscillation measurement signals; and / or - wherein the measuring system electronics are configured to determine a (modal) damping, d2, of the second useful oscillations corresponding to a ratio of a (signal) amplitude of one of the second useful signal components (s1N2), in particular a sum or a difference of the (signal) amplitudes of the second useful signal components (s1N2, s2N2), and a (signal) amplitude of the second (useful) current (eN2), in particular namely to determine damping values ​​representing the damping of the second useful oscillations on the basis of the driver signal and at least one of the oscillation measurement signals; and / or - wherein the measuring system electronics are configured to determine a damping ratio, d1 / d2, corresponding to a ratio of a (modal) damping, d1, of the first useful vibrations and a (modal) damping, d2, of the second useful vibrations, in particular to determine damping ratio values ​​representing the damping ratio, d1 / d2, on the basis of the driver signal and / or at least one of the vibration measurement signals. [15] Measuring system according to one of the preceding claims, wherein the measuring system electronics are configured to determine damping values ​​representing a (modal) damping of the second useful vibrations on the basis of the driver signal and at least one of the vibration measurement signals, in particular to compare one or more of the damping values ​​with a reference value (damping reference value) determined beforehand. [16] Measuring system according to the previous claim, - wherein the measuring system electronics are configured to perform (self-)diagnosis of the measuring system by comparing one or more of the attenuation values ​​with at least one reference value (attenuation reference value) determined beforehand and / or by means of an intact measuring system, in particular also by issuing a message representing a deviation of one or more of the attenuation values ​​from the reference value, in particular declared as a (fault) alarm; and / or - wherein the measuring system electronics are configured to perform (self-)diagnosis of the measuring system based on several of the damping values, to determine a temporal change, in particular a change trend and / or a change rate and / or a change velocity, in the damping of the second useful oscillations, in particular to determine an increasing disturbance when the damping of the second useful oscillations decreases, and / or to output a message representing an increase in a disturbance, in particular declared as a (disturbance) alarm; and / or - wherein the measuring system electronics are set up to determine a measure of dispersion, in particular an empirical variance and / or a range, for the damping of the second useful vibrations of the at least one tube, based on a multitude of damping values, in particular also to output and / or to compare the same measure of dispersion with one or more specified reference values ​​for carrying out the (self-)diagnosis of the measuring system. [17] Measuring system according to any one of the preceding claims, - wherein the measuring system electronics are configured to determine the resonance frequency f1 of the first mode of vibration of the at least one tube, in particular by determining frequency values ​​representing the resonance frequency f1 based on the driver signal and / or at least one of the vibration measurement signals; and / or - wherein the measuring system electronics are configured to determine the resonance frequency f2 of the second mode of vibration of the at least one tube, in particular by determining frequency values ​​representing the resonance frequency f2 based on the driver signal and / or at least one of the vibration measurement signals; and / or - wherein the measuring system electronics are configured to determine a resonance frequency ratio f1 / f2 corresponding to a ratio of the resonance frequency f1 of the first oscillation mode of the at least one tube and the resonance frequency f2 of the second oscillation mode of the at least one tube, in particular by determining frequency ratio values ​​representing the resonance frequency ratio f1 / f2 based on the first and second (AC) frequencies of the driver signal and / or based on the signal frequencies of the first and second useful signal components (s1N1, s1N2; s2N1, s2N2) of at least one of the oscillation measurement signals. [18] Measuring system according to one of the preceding claims, wherein the measuring system electronics are configured to determine frequency values ​​representing the resonance frequency f2 of the second mode of vibration of the at least one tube on the basis of the driver signal and / or at least one of the vibration measurement signals, in particular to compare one or more of the frequency values ​​with one or more specified reference values ​​and / or to use several of the frequency values ​​to determine a measure of dispersion for the resonance frequency f2 of the second mode of vibration of the at least one tube. [19] Measuring system according to the preceding claim, wherein the measuring system electronics are configured to determine a dispersion measure for the resonance frequency f2 of the second mode of vibration of the at least one tube on the basis of a plurality of frequency values, in particular also to output and / or to compare the same dispersion measure with a reference value specified for this purpose in order to carry out the (self-)diagnosis of the measuring system and to output a message representing a deviation of the dispersion measure from the reference value. [20] Measuring system according to one of the preceding claims, wherein the measuring system electronics are configured to determine frequency ratio values ​​representing a ratio of the resonance frequency f1 of the first vibration mode of the at least one tube and the resonance frequency f2 of the second vibration mode of the at least one tube, based on the driver signal and / or at least one of the vibration measurement signals, in particular to compare one or more of the frequency ratio values ​​with one or more specified reference values ​​and / or to use several of the frequency ratio values ​​to determine a measure of dispersion for the resonance frequency ratio f1 / f2 of the at least one tube. [21] Measuring system according to the preceding claim, - wherein the measuring system electronics are configured to perform (self-)diagnosis of the measuring system by comparing one or more of the frequency ratio values ​​with at least one previously determined reference value (frequency ratio reference value), in particular by issuing a message representing a deviation of one or more of the frequency ratio values ​​from the reference value, especially if this is declared as a (fault) alarm; and / or - wherein the measuring system electronics are configured to determine, in particular an empirical variance and / or a range, for the resonance frequency ratio f1 / f2 of the at least one tube based on a multitude of frequency ratio values, in particular also to output and / or to compare the same measure of dispersion with a specified reference value for carrying out the (self-)diagnosis of the measuring system and, in the event of a deviation of the measure of dispersion from the reference value, to output a message representing this. [22] Measuring system according to one of the preceding claims, wherein the measuring system electronics are configured to determine, on the basis of the vibration measurement signals, a phase difference of the second useful signal components, namely a difference between a phase angle of the second useful signal component (s1N2) of the first vibration measurement signal (s1) and a phase angle of the second useful signal component (s2N2) of the second vibration measurement signal (s2), in particular to compare one or more of the phase difference values ​​with a reference value determined beforehand (phase difference reference value) and / or to use several of the phase difference values ​​to determine a measure of dispersion for the phase difference of the second useful signal components of the at least one tube. [23] Measuring system according to the previous claim, - wherein the measuring system electronics are configured to perform (self-)diagnosis of the measuring system by comparing one or more of the phase difference values ​​with at least one previously determined reference value (phase difference reference value), in particular by issuing a message representing a deviation of one or more of the phase difference values ​​from the reference value, especially one declared as a (fault) alarm; and / or - wherein the measuring system electronics are configured to determine a measure of dispersion, in particular an empirical variance and / or a range, for the phase difference of the second useful signal components based on a large number of phase difference values, in particular also to output and / or to compare the same measure of dispersion with a specified reference value for carrying out the (self-)diagnosis of the measuring system and, in the event of a deviation of the measure of dispersion from the reference value, to output a message representing this. [24] Measuring system according to one of the preceding claims, wherein the measuring system electronics are configured to determine displacement ratio values ​​representing a ratio of the displacements, x1, of the first useful vibrations and the displacements, x2, of the second useful vibrations, on the basis of at least one of the vibration measurement signals, in particular to compare one or more of the displacement ratio values ​​with one or more specified reference values ​​and / or to use several of the displacement ratio values ​​to determine a measure of dispersion for the displacement ratio, x1 / x2, of the at least one tube. [25] Measuring system according to the preceding claim, - wherein the measuring system electronics are configured to perform (self-)diagnosis of the measuring system by comparing one or more of the deflection ratio values ​​with at least one previously determined reference value (deflection ratio reference value), in particular by issuing a message representing a deviation of one or more of the deflection ratio values ​​from the reference value, especially as a (fault) alarm; and / or - wherein the measuring system electronics are configured to determine, in particular an empirical variance and / or a range, for the deflection ratio x1 / x2 of the at least one pipe based on a large number of deflection ratio values, in particular also to output and / or to compare the same measure of dispersion with a specified reference value for carrying out the (self-)diagnosis of the measuring system and, in the event of a deviation of the measure of dispersion from the reference value, to output a message representing this. [26] Measuring system according to one of the preceding claims, wherein the measuring system electronics are configured to provide the second (useful) current (eN2) with a predetermined (current) amplitude. [27] Measuring system according to the previous claim, wherein the measuring system electronics are configured to perform the (self-)diagnosis of the measuring system by repeatedly measuring the (signal) amplitude of at least one of the second useful signal components (s1N2) with a value dependent on the (signal) amplitude of the second (useful) current (eN2) and / or predetermined for this purpose, in particular namely a value corresponding to the predetermined (current) amplitude of the second (useful) current (eN2). to compare the determined (signal) amplitude with the reference value (amplitude reference value) corresponding to at least one second useful signal component (s1N2), in particular to determine whether or to what extent the (signal) amplitude deviates from the same reference value. [28] Measuring system according to any one of the preceding claims, - wherein the first useful signal components (s1N1; s2N1) of the first and second vibration measurement signals follow a change in the mass flow rate of the measured substance guided in the pipe with a change in the phase difference of the first useful signal components, namely a difference between a phase angle of the first useful signal component (s1N1) of the first vibration measurement signal (s1) and a phase angle of the first useful signal component (s2N1) of the second vibration measurement signal (s2); - and wherein the measuring system electronics are set up to generate mass flow measurement values ​​representing the mass flow based on the phase difference of the first useful signal components (s1N1; s2N1). [29] Measuring system according to claims 22 and 28, wherein the measuring system electronics are configured, in particular for performing (self-)diagnosis of the measuring system, on the basis of the second useful signal components (s1N2; s2N2) at least one of the vibration measurement signals, in particular on the basis of a phase angle of at least one of the second useful signal components and / or on the basis of a phase difference of the second useful signal components, to check or calibrate a (mass flow-to-phase difference) characteristic function of the measuring transducer, according to which the phase difference of the first useful signal components depends on the mass flow, and / or a (mass flow-to-measurement value) characteristic function of the measuring system, according to which mass flow measurement values ​​determined on the basis of the phase difference of the first useful signal components depend on the mass flow. [30] Measuring system according to the preceding claim, wherein the measuring system electronics are configured, in particular for performing the (self-)diagnosis of the measuring system, to check the (mass flow-to-phase difference) characteristic curve function of the measuring transducer, in particular a (scale) zero point of said characteristic curve function, on the basis of a phase difference of the second useful signal components, namely a difference between a phase angle of the second useful signal component (s1N2) of the first vibration measurement signal (s1) and a phase angle of the second useful signal component (s2N2) of the second vibration measurement signal (s2), in particular to determine whether or to what extent a drift of the characteristic curve function is present. [31] Measuring system according to the preceding claim, in particular for performing the (self-)diagnosis of the measuring system, to check a (scale) zero point of the (mass flow-to-phase-difference) characteristic function of the measuring transducer, which corresponds to a phase difference of the first useful signal components measured with the sample at rest or to a mass flow measurement value determined with the sample at rest, and / or a (measuring) sensitivity of the measuring system, which corresponds to a change in the phase difference of the first useful signal components related to a change in the mass flow, in particular to determine whether or to what extent an irreversible change of the (scale) zero point is present. [32] Measuring system according to any one of the preceding claims, - wherein the measuring system electronics are configured to follow a change in the density of the medium guided in the tube with a change in the first (alternating current) frequency of the driver signal, - and wherein the measuring system electronics are configured to generate density measurement values ​​representing the density based on the first (alternating current) frequency of the driver signal and / or based on the signal frequency of the first useful signal component of at least one of the oscillation signals (s1N1; s2N1). [33] Measuring system according to one of the preceding claims, wherein the measuring system electronics are configured, in particular for performing the (self-)diagnosis of the measuring system, to calculate one or more characteristic values ​​for at least one measuring system characteristic (MK1) that characterizes an operating state of the measuring system, based on the second useful signal components (s1N2; s2N2) of at least one of the vibration measurement signals, in particular based on their (signal) frequency and / or based on a (signal) amplitude of at least one of the second useful signal components (s1N2) and / or based on a phase angle of at least one of the second useful signal component (s1N2), based on the second useful signal component (s1N2). [34] Measuring system according to the previous claim, wherein the measuring system electronics (20) is configured to perform (self-)diagnosis of the measuring system by comparing one or more characteristic values ​​for the measuring system characteristic with one or more reference values ​​determined for the measuring system characteristic, in particular by the manufacturer of the measuring system and / or during the manufacture and / or commissioning of the measuring system and / or depending on the driver signal, in particular by comparing one or more reference values ​​representing reduced functionality of the transducer and / or by comparing one or more reference values ​​representing a malfunction of the transducer and / or by comparing one or more reference values ​​representing a defective transducer, in particular by evaluating and / or quantifying a deviation of one or more of the characteristic values ​​from one or more of the reference values. [35] Measuring system according to the preceding claim, wherein the measuring system electronics (20) is configured to determine whether one or more key figure values ​​for the measuring system key figure (MK1) are greater than the at least one reference value for the measuring system key figure, in particular, if one or more key figure values ​​for the measuring system key figure are greater than one or more reference values ​​representing reduced functionality of the measuring transducer and / or greater than one or more reference values ​​representing a malfunction of the measuring transducer and / or greater than one or more reference values ​​representing a measuring transducer that is no longer intact, to output a message representing this, in particular declared as a (fault) alarm. [36] Measuring system according to one of the preceding claims, wherein the measuring system electronics (20) comprises a non-volatile electronic data storage device (EEPROM) which is configured to retain digital data, in particular even without an applied operating voltage, in particular to store one or more pre-determined reference values ​​for the measuring system identifier. [37] Measuring system according to claim 36 in conjunction with one of claims 33 to 35, wherein one or more reference values ​​for the measuring system characteristic value, in particular determined in advance by the manufacturer of the measuring system and / or during the manufacture of the measuring system and / or during the operation of the measuring system, are stored in the electronic data storage device, in particular namely one or more reference values ​​representing a reduced functionality of the measuring transducer and / or namely one or more reference values ​​representing a malfunction of the measuring transducer. [38] Measuring system according to the previous claim, wherein the measuring system electronics (20) is configured to compare one or more characteristic values ​​for the measuring system characteristic with one or more reference values ​​for the measuring system characteristic stored in the data storage. [39] Measuring system according to one of the preceding claims, wherein the measuring system electronics are configured to provide the driver signal (e1) with the second (useful) current (eN2) during a test interval, in particular lasting more than 10 ms and / or limited in time and / or restarted periodically, in particular such that the second (useful) current (eN2) is non-volatile or stationary, namely having a (substantially) constant, non-zero amplitude for two or more oscillation periods and / or a period of more than 10 ms (milliseconds). [40] Measuring system according to the preceding claim, - wherein the measuring system electronics are set up, during the test interval based on the second useful signal components (s1N2; s2N2), in particular based on their (signal) frequency and / or based on a (signal) amplitude of at least one of the second to determine measured values ​​representing at least one measured quantity based on a phase angle of at least one of the second useful signal components (s1N2); and / or - where each test interval lasts longer than 100 ms (milliseconds), in particular not less than 1 s (second); and / or - wherein the measuring system electronics are configured to automatically, in particular on a time-controlled basis, start and / or end the test interval, in particular recurringly; and / or - wherein the measuring system electronics are configured to receive and execute one or more commands that start the test interval. [41] Measuring system according to one of the preceding claims, wherein the tube wall consists of a steel, in particular a stainless steel, duplex steel or superduplex steel, a titanium alloy and / or a zirconium alloy, in particular a Zircaloy, and / or a tantalum alloy. [42] Measuring system according to one of the preceding claims, wherein the tube has a caliber (inner diameter of the tube) that is greater than 0.1 mm, in particular greater than 0.5 mm. [43] Measuring system according to the previous claim, - wherein the tube has a caliber-to-tube-length ratio that is greater than 0.08, in particular greater than 0.1, and / or less than 0.25, in particular less than 0.2; - and / or where the pipe length is more than 200 mm, in particular more than 500 mm, and / or less than 2000 mm, in particular less than 1500 mm; - and / or where the tube has a caliber greater than 10 mm, in particular greater than 15 mm. [44] Measuring system according to any one of the preceding claims, - wherein the excitation arrangement, apart from the vibration exciter (31), does not include any other vibration exciter connected to the pipe; and / or - wherein the vibration exciter (31) is positioned and aligned such that the drive offset is less than 0.5 mm, in particular zero, or that the centroid of the drive cross-sectional area of ​​the tube corresponds to or coincides with the drive reference point, and / or - wherein each of the first and second order vibration modes of the tube has a first node located at the first end of the at least one tube and a second node located at the second end of the at least one tube; and / or - wherein the tube is curved section by section, in particular in a circular arc and / or V-shape, in particular such that the tube has a central apex arc segment and / or that exactly one principal axis of inertia of the at least one tube lies within the reference cross-sectional area of ​​the at least one tube; and / or - wherein the pipe is straight in sections, in particular over the entire pipe length, in particular such that the principal axis of inertia of the at least one pipe lies within the reference cross-sectional area of ​​the at least one pipe and / or a center of mass lies within the reference cross-sectional area of ​​the at least one pipe. [45] Measuring system according to one of the preceding claims, wherein the pipe arrangement comprises at least one second pipe (112), in particular at least partially curved and / or at least partially straight and / or identical in construction to the first pipe and / or parallel to the first pipe at least partially. [46] Measuring system according to the previous claim, - wherein the second tube extends from a first tube end to a second tube end with a tube length and has a lumen enclosed by a tube wall, in particular metallic, extending from the first tube end to the second tube end, - and wherein the second tube is arranged to be supplied with fluid and vibrated at least in a flow direction from the first tube end to the second tube end, in particular simultaneously with the first tube. [47] Measuring system according to one of claims 45 to 46, wherein the second tube has a plurality of vibration modes (natural modes) each having an associated resonance frequency, in which the second tube can or does perform vibrational movements having one or more antinodes and two or more nodes, in particular such that vibrational movements of the second tube in the second-order vibration mode (f1-mode) are opposite to, in particular opposite to, the vibrational movements of the first tube in the second-order vibration mode (f2-mode) and / or that vibrational movements of the second tube in the first-order vibration mode (f1-mode) are opposite to, in particular opposite to, the vibrational movements of the first tube in the first-order vibration mode. [48] ​​Measuring system according to claim 47, - where a resonance frequency of the first-order vibration mode of the first tube is equal to a resonance frequency of the first-order vibration mode (f1-mode) of the second tube - and where a resonance frequency of the second order vibration mode of the first tube is equal to a resonance frequency of the second order vibration mode of the second tube. [49] Measuring system according to any one of claims 45 to 48, - wherein the first vibration sensor is positioned on both the first and second pipes, in particular being mechanically connected to both the first and second pipes proportionally, - and wherein a first vibration sensor is set up to detect vibrational movements, in particular opposing vibrational movements, of both the first pipe and the second pipe, in particular differentially, and to convert them into the first vibration measurement signal, such that the vibration measurement signal represents, in particular opposing, vibrational movements of the first and second pipes. [50] Measuring system according to any one of claims 45 to 49, - wherein the second vibration sensor is positioned on both the first and second pipes, in particular being mechanically connected to both the first and second pipes in part, - and wherein a second vibration sensor is set up to detect vibration movements, in particular opposing vibration movements, of both the first tube and the second tube, in particular differentially, and to convert them into the second vibration measurement signal, such that the vibration measurement signal represents, in particular opposing, vibration movements of the first and second tubes. [51] Measuring system according to any one of claims 45 to 50, - wherein the pipe arrangement has a first flow divider (21) with at least two flow openings, which serves in particular as a pipe branch and / or inlet-side, - and wherein the pipe arrangement includes a second flow divider (22) with at least two flow openings, in particular identical in construction to the first flow divider (21) and / or serving as a pipe junction and / or on the outlet side. [52] Measuring system according to claim 51, wherein each of the first and second tubes of the tube arrangement, in particular forming fluidically parallel flow channels, is connected to each of the first and second flow dividers, such that - the first pipe with its first pipe end into a first flow opening of the first flow divider (21) and with its second pipe end into a first flow opening of the second flow divider (22) - and the second pipe with its first pipe end into a second flow opening of the first flow divider (21) and with its second pipe end into a second flow opening of the second flow divider (22). [53] Measuring system according to one of claims 45 to 52, wherein the vibration exciter (31) is mechanically connected both proportionally to the first tube and proportionally to the second tube. [54] Measuring system according to any one of claims 45 to 53, - wherein the vibration exciter (31) is configured to act differentially on the first and second tubes, in particular such that the first and second tubes simultaneously perform forced mechanical vibrations of the same frequency but opposite frequency; and / or - wherein the vibration exciter (31) is configured to convert electrical power into mechanical power with a time-varying electric current in such a way that a time-varying driving force acts on the second tube at a driving point formed by the vibration exciter on the second tube mechanically connected thereto, in particular simultaneously and / or oppositely to the driving force acting on the first tube at the driving point formed by the vibration exciter on the first tube mechanically connected thereto; and / or - wherein the vibration exciter (31) is configured to convert electrical power supplied by means of the electrical driver signal (e1) simultaneously into forced mechanical vibrations of the first and second tubes, in particular such that the first and second tubes perform forced mechanical vibrations with the first useful frequency and / or with the second useful frequency simultaneously. [55] Measuring system according to any one of the preceding claims, - wherein the vibration exciter (31) is formed by means of a voice coil, in particular comprising an air coil and an armature; and / or - wherein each of the first and second vibration sensors is formed by means of a moving coil, in particular having an air coil and an armature. [56] Measuring system according to one of the preceding claims, wherein the vibration exciter (31) comprises a magnetic armature, in particular formed by means of a permanent magnet, and a coil through which the magnetic field of the armature flows, in particular an air coil. [57] Measuring system according to the previous claim, - wherein the magnetic armature is mechanically connected to the at least one tube, forming the drive point; and / or - wherein the coil is electrically connected to the measuring system electronics and is set up to receive the driver signal (e1) and to carry its first and second (useful) currents (eN1, eN2). [58] Measuring system according to one of the preceding claims, further comprising: an electronics protective housing (200) for the measuring system electronics (20), in particular attached to a transducer protective housing of the measuring transducer and / or made of metal. [59] Measuring system according to one of the preceding claims, further comprising: a transducer protective housing, in particular metallic, wherein the transducer protective housing and the pipe arrangement are attached to one another, in particular releasably.

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