VIBRONIC MEASURING SYSTEM

Description

[0001] The invention relates to a vibronic measuring system formed by a vibration-type measuring 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 variable of a flowing medium, in particular a gas, a liquid, or a dispersion. The measured variable can be, for example, a time-varying flow parameter, such as a mass flow, a volume flow, or a flow velocity, and / or a time-varying material parameter, such as a density and / or viscosity, of the respective medium. Such measuring systems—typically designed as an in-line measuring device with a compact design—have been known for a long time and have proven themselves in industrial use.not least in the field of control and monitoring of automated process engineering processes or process plants or in the area of transfer points of goods transport that may also be subject to legal metrology. 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, DE-A 10 2019 124709, 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 / 0116319, US-A 2016 / 0123836, US-A 2016 / 0138997, US-A 2017 / 0030870, US-A 2017 / 0356777, US-A 2019 / 0003875, US-A 2020 / 0132529, US-A 2020 / 0393278, 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 27 662, 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 2020 / 259762, WO-A 2020 / 126285, 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 or WO-A 99 / 44018 and have been manufactured by the applicant itself for a long time and are offered as Coriolis mass flowmeters 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 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 signals representing vibrational movements of the pipe arrangement. Both the excitation arrangement and the sensor arrangement are electrically coupled to the measuring system electronics, which in turn serves to control the transducer, in particular its excitation arrangement, and to receive and evaluate measurement signals supplied thereby, in particular vibration signals supplied by its sensor arrangement, in particular to determine measured values representing at least one measured variable.To protect against external influences, the tube assembly, together with the excitation and sensor assembly, is typically housed in a metallic transducer protective housing, and the measuring system electronics are housed in a protective electronics housing, also made of metal, for example. The latter can, for example, be mounted directly on the aforementioned transducer protective housing, forming a Coriolis mass flowmeter or a compact Coriolis mass flow / density meter. In the measuring systems shown in WO-A 96 / 08697 or WO-A 2019 / 017891, the transducer protective housing and the tube assembly are, in particular, detachably connected to one another, for example, to enable subsequent insertion of the tube assembly or replacement of a defective or worn tube assembly with an intact tube assembly on site.

[0003] The aforementioned pipe arrangements are each intended to be integrated into the course of a process line and each have at least one pipe - for example exactly one pipe or exactly two pipes or exactly four pipes - which extends from a respective first pipe end to a respective second pipe end with a pipe length and has a lumen enclosed by a - typically metallic - pipe wall and 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 - designed to flow in or out of the pipe connected via the process line, at least in a flow direction pointing from the first pipe end to the second pipe end.The medium is then discharged again and, during this time, is caused to vibrate, for example in order to generate Coriolis forces dependent on the mass flow, inertial forces dependent on the density of the medium and / or frictional forces dependent on the viscosity of the medium. For example, bending vibrations are used to create a static rest 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-shaped, V-shaped, rectangular, or triangular shape, and more rarely an Ω-shaped or helical shape. In addition, their respective tube walls are typically made of a steel, for example stainless steel, duplex steel or super duplex steel, a titanium alloy, a zirconium alloy, for example Zircaloy, and / or a tantalum alloy.The tube length of such tubes may be in a range between about 100 mm and about 2000 mm and a caliber (inner tube diameter) of such tubes may be in a range between about 0.1 mm and about 100 mm, typically such that the respective tube has a caliber-to-tube length ratio that is in the range between about 0.08 and about 0.25.

[0004] In single-tube transducers, this usually communicates with the aforementioned process line via a substantially straight connecting pipe section opening at the inlet side and a substantially straight connecting pipe section opening at the outlet side. Furthermore, the pipe arrangement of such single-tube transducers each comprises at least one single-piece or multi-piece counteroscillator, for example, tubular, box-shaped, or plate-shaped, which is coupled to the pipe on the inlet side to form a first coupling zone and which is coupled to the pipe on the outlet side to form a second coupling zone. During operation, the counteroscillator is essentially stationary or oscillates inversely to the pipe, i.e., at the same frequency and in antiphase.The tube arrangement of such a transducer, formed by a tube and counteroscillator, is usually mounted in the aforementioned protective housing for oscillation solely by means of the two connecting tubes through which the tube communicates with the process line during operation. In the (standard) transducers with a single, essentially straight tube, 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 tube and the counteroscillator are aligned essentially coaxially with each other, as is quite common with conventional transducers. The materials used for the counter-oscillators are usually comparatively inexpensive steel grades, such as structural steel or free-cutting steel, not least when titanium, tantalum or zirconium are used for the tube.In the case of 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. 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 thereto, as well as a first flow divider with exactly two flow openings - serving here as a line branch or on the inlet side - and a first flow divider with exactly two flow openings that is identical to the first flow divider - serving here as a line union oroutlet-side - second flow splitter with exactly two flow openings, whereas in US-A 56 02 345, WO-A 96 / 08697 or US-A 2017 / 0356777 or WO-A 2019 / 081169 or WO-A 2019 / 081170 or the aforementioned patent application PCT / EP2019 / 082044 the pipe arrangements shown each have a first flow splitter - serving here as a line branch or on the inlet side - with exactly two flow openings, a second flow splitter structurally identical to the first flow splitter - serving here as a line connection or on the outlet side - with exactly two flow openings and two pipes, namely a first pipe and a second pipe. In addition, each of the two orfour pipes are connected to each of the first and second flow dividers in such a way 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, 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 tube 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, the second tube 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, the third tube opens 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 tube opens 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 measuring transducers are also typically designed as an integral component of the aforementioned protective transducer housing.

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

[0006] To excite mechanical vibrations of the at least one tube, the exciter arrangement comprises at least one electromechanical, typically electrodynamic, vibration exciter, which is partially mechanically connected to the tube and configured to convert electrical power into mechanical power using a time-varying electrical current, such that a time-varying drive force acts on the tube at a drive point formed by the vibration exciter on the mechanically connected tube. For the aforementioned case in which the tube arrangement comprises at least one further (second) tube, the at least one vibration exciter can also be partially attached thereto, such that the vibration exciter acts differentially on the two tubes.For the other aforementioned case, in which the pipe arrangement has a counter-oscillator, the vibration exciter can be partially attached thereto in such a way that the vibration exciter acts differentially on the pipe and the counter-oscillator. However, the vibration exciter can also be partially attached to the aforementioned transducer protective housing, for example. In the case of 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 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 the case of (standard) measuring transducers of commercially available (standard) measuring systems, the excitation arrangements, as shown, inter alia, 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 also designed in such a way that each of the tubes is (proportionately) connected to exactly one vibration exciter, in such a way that the excitation arrangement, apart from the (one) vibration exciter, does not have any other vibration exciter connected to the respective tube. connected vibration exciter.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 to form the drive point and that its air coil, which is flooded by the magnetic field of the armature, 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 protective housing.Nevertheless, 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 2016 / 0116319, 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 comprises two or more excitation tubes connected to one and the same tube of the respective tube arrangement. and / or vibration exciters formed by one or more piezo elements.

[0007] To detect vibrations of the at least one pipe, the sensor arrangement comprises at least two vibration sensors, for example electrodynamic or optical, of which 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 vibration sensor—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 vibrational movements of the pipe and to convert them into a first or second vibration signal representing the same vibrational movements, in particular an electrical or optical one, for example, using an electrical voltage dependent 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, which is flooded by the magnetic field of the armature, 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 converter protection housing.

[0008] The measuring system electronics of each of the aforementioned measuring systems is also designed to energize the at least one vibration exciter during operation according to the useful mode to be excited, namely to feed electrical power into the at least one vibration exciter by means of at least one electrical drive signal having a time-varying electrical current, e.g., with an electrical current regulated with regard to (alternating current) frequency, phase angle, and amplitude, such that the pipe executes forced mechanical vibrations, for example, bending vibrations, with one or more vibration frequencies predetermined by the drive signal, typically corresponding to one or more resonance frequencies of the at least one pipe; this, for example, also with a constantly regulated vibration amplitude.In particular, the measuring system electronics are configured to provide the aforementioned drive 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 at least partially or predominantly executes useful vibrations, namely mechanical vibrations forced by the (energized) vibration exciter at a useful frequency, namely a (oscillation) frequency corresponding to the aforementioned (alternating current) frequency. The drive signal can be configured as a harmonic sinusoidal signal, namely having exactly the one (alternating current) frequency, thus containing no further spectral current component apart from the (useful) current, or, for example, as a multifrequency signal, namely containing several signal components with differing (alternating current) frequencies.As a result of the aforementioned excitation of useful vibrations of the at least one pipe, each of the first and second vibration signals supplied by the sensor arrangement also contains one or more sinusoidal signal components, each with a frequency corresponding to an vibration frequency of vibrational movements of the pipe, in such a way that each of the first and second vibration signals also has at least one useful signal component, namely a sinusoidal signal component with a (signal) frequency corresponding to the useful frequency.

[0009] In measuring systems of the type in question, the useful mode typically used is one or more of a plurality of natural vibration modes inherent in the pipe, each having an associated resonance frequency, in particular one or more symmetrical vibration modes in which the pipe can or does execute oscillation movements having an odd number of antinodes and a correspondingly even number of nodes. Not least because of their particular suitability for measuring both the mass flow and the density and viscosity of the flowing medium, in such measuring systems, in particular also in commercially available standard measuring systems, one or more natural symmetrical bending vibration modes are preferably used as the useful mode, in particular in such a way that the useful vibrations cause Coriolis forces in the medium flowing through the at least one pipe with a mass flow other than zero.In the case of transducers with a curved tube or curved tubes, a symmetrical bending vibration mode, i.e. a bending vibration mode of odd order, is typically selected as the useful mode, in which the respective tube oscillates around a static rest position about an imaginary first oscillation axis imaginarily connecting the first and second tube ends in the manner of a cantilever clamped only at the ends (out-of-plane mode), whereas in the case of transducers with a straight tube or straight tubes, a symmetrical bending vibration mode is typically selected as the useful mode, in which the respective tube oscillates around a static rest position about an imaginary oscillation axis coinciding with one of its principal axes of inertia (longitudinal axis) and imaginarily connecting the first and second tube ends in the manner of a clamped string (in-plane mode).In commercially available measuring systems, the use of the first-order (bending) vibration mode, occasionally referred to as the fundamental vibration mode or f1 mode, in which the vibrational movements of the pipe each exhibit exactly one antinode and two vibration nodes, and are thus symmetrical, has become established as the useful mode. More rarely, the use of higher-order (bending) vibration modes of odd orders, for example, the third-order (bending) vibration mode (f3 mode), in which the vibrational movements of the pipe each exhibit exactly three antinodes and four vibration nodes, has also been established. A (resonance) frequency spacing, namely a difference between the resonance frequencies of the f1 mode and the adjacent second-order (bending) vibration mode (f2 mode) or between the f2 mode and the f3 mode, is typically in the range of a few hundred Hz to a few thousand Hz in commercially available measuring systems.

[0010] Not least for the purpose of efficient excitation of the wanted mode, the measuring system electronics are also particularly designed to set the (alternating current) frequency determining the wanted frequency accordingly so that the wanted frequency ultimately corresponds as closely as possible to a resonance frequency of one of the (symmetrical) oscillation modes with an odd order, in particular the resonance frequency (f1) of the first order oscillation mode (f1 mode) or a resonance frequency (f3) of the third order oscillation mode (f3 mode) or deviates from the respective set resonance frequency by less than 1% of the same 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 the same resonance frequency and / or by more than 10 Hz.The measuring system electronics are also accordingly configured to follow a change in the resonance frequency, for example due to a change in the density of the medium conveyed in the pipe, with a change in the (alternating current) frequency of the driver signal, such that the excited useful oscillations are predominantly resonance oscillations of the at least one pipe. To adjust the (alternating current) frequency, the measuring system electronics of the respective measuring system can, for example, use a phase-locked loop (. PLL - phase locked loop ).

[0011] As a result of the useful vibrations of the at least one tube excited in the manner described above, Coriolis forces which are also dependent on the mass flow are known to be induced in the medium flowing through it, such that Coriolis vibrations, namely additional forced vibrations with a useful frequency, are superimposed on the useful vibrations, which correspond to a natural vibration mode, occasionally also referred to as a Coriolis mode, with an order increased by one compared to the order of the useful mode; this in particular such that the useful signal components of the vibration signals are also dependent on the mass flow of the medium due to the Coriolis vibrations, namely they each have a (measurement) phase angle which is dependent on a mass flow of the medium carried in the at least one tube.a change in the same mass flow with a change in a (measurement) phase difference of the wanted signal components, namely a difference (normalized to the wanted frequency) between the (measurement) phase angle of the wanted signal component of the first oscillation signal and the (measurement) phase angle of the wanted signal component of the second oscillation signal. In commercially available (standard) measuring systems, when the fundamental oscillation mode is used as the wanted mode, the second-order antisymmetric oscillation mode typically serves as the Coriolis mode, or when the third-order oscillation mode is used as the wanted mode.

[0012] The measuring system electronics of each of the aforementioned measuring systems is also set up accordingly to determine, on the basis of one or more of the aforementioned vibration signals, one or more measured values representing the respective flow parameter of the medium to be measured. In the case of a measuring system designed as a Coriolis mass flow meter or as a Coriolis mass flow / density meter, for example, to generate (mass flow) measured values representing the mass flow based on the aforementioned (measurement) phase difference of the useful signal components caused by the vibrations of the pipe in the Coriolis mode, as well as a phase difference-to-measured value characteristic function set up in the measuring system electronics. The phase difference-to-mass flow measured value characteristic function can, for example, be a (linear) parameter function with a (scale) zero point which corresponds to a flow parameter which occurs when the medium or mass flow is at rest.a mass flow of zero corresponds to a measurable (measurement) phase difference of the useful signal components, and with a gradient that corresponds to a (measurement) sensitivity or a change in the (measurement) phase difference of the useful signal components related to a change in the mass flow. Since the resonance frequency of the oscillation mode serving as the useful mode, as already mentioned, is particularly dependent on the instantaneous density of the medium being measured, such a measuring system will directly measure not only the mass flow but also the density of the medium flowing through it based on the (alternating current) frequency of the drive signal and / or the (signal) frequency of the useful signal components of the oscillation signals.Accordingly, the measuring system electronics of measuring systems of the type in question are typically also configured to generate (density) measured values representing the density based on the aforementioned (AC) frequency of the driver signal and / or based on the signal frequency of the aforementioned useful signal component of at least one of the vibration signals, for example using a useful frequency-to-measured value characteristic function correspondingly configured in the measuring system electronics. Furthermore, it is also possible to directly measure the viscosity of the medium flowing through using vibronic measuring systems of the type in question, for example based on the excitation energy or excitation power required to maintain the useful vibrations and / or based on the damping of the useful vibrations or damping resulting from the dissipation of vibration energy.using a damping-to-measured-value characteristic curve function appropriately configured in the measuring system electronics. Furthermore, other derived measured variables, such as the Reynolds number, can be easily determined from the aforementioned flow and / or material parameters using such vibronic measuring systems.

[0013] For the aforementioned (standard) case that one or more natural symmetrical (bending) vibration modes or (bending) vibration modes of odd order are (to be) used as the useful mode in the respective measuring system and that exactly one single vibration exciter is provided per pipe (or per pipe pair), this is typically positioned and aligned in such a way that the aforementioned drive cross-sectional area is (nominally) in the range of 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 antisymmetrical (bending) vibration modes (of even order) also inherent in the pipe.Due to various manufacturing tolerances during transducer production, for example during the positioning of the vibration exciter and / or the vibration sensors on the at least one pipe and / or during the manufacture of the at least one pipe itself, it can generally be assumed that a transducer provided in this way will have a drive offset, measured as the smallest distance between the drive cross-sectional area of the pipe and a predetermined reference cross-sectional area of the at least one pipe, namely one located at a maximum amplitude of the vibration movements of the useful vibrations, which is slightly different from zero. In the case of a perfectly symmetrical pipe, the reference cross-sectional area also corresponds to a plane of symmetry of the pipe or there is an intersection line between the same plane of symmetry and another plane of symmetry of the at least one pipe that is orthogonal to it.a principal axis of inertia of at least one tube within the aforementioned reference cross-sectional area, perpendicular to the direction of vibration of the tube's vibrational movements in the desired mode. In commercially available (standard) measuring systems, the drive offset can be in the order of magnitude of up to 5 mm or 0.5% of the tube length, but is typically less than 2 mm or less than 0.2% of the tube length.

[0014] Last but not least, the aforementioned drive offset also leads to the fact that, even when the pipe is not flowing through by fluid or when the mass flow in the pipe is zero, in addition to the useful vibrations, such disturbing vibrations of the same frequency are also forced in the pipe, which correspond to the second-order vibration mode (f2 mode), thus the aforementioned Coriolis mode. As a result, among other things,the useful signal components of the vibration signals also each have additional (interference) phase angles, such that between the useful signal components of the vibration signals, in addition to the respective (measurement) phase difference, there also exists a (interference) phase difference of the same frequency and independent of the mass flow, so that the vibration signals have a non-zero systematic phase or zero point error corresponding to the phase difference (normalized to the useful frequency) between the useful signal components of the two vibration signals at a mass flow of zero; this in particular also in the way that the phase error also depends on one or more material parameters of the measuring medium, in particular its viscosity. Compensation for the aforementioned phase error typically takes place during a (wet) calibration of the respective measuring system, for example with the aid of one or more predetermined, for example constant oroccasionally also zero, (reference) mass flows of one or more calibration fluids kept as stable as possible at a (reference) temperature and / or a (reference) pressure, such as water or air, possibly also oil at 20°C (room temperature) and 1 bar (atmospheric pressure), which are (sequentially) each passed through the measuring transducer, while at least one tube is excited to useful oscillations in the manner described above.On the basis of the oscillation signals, a respective reference phase difference, namely a difference between a (reference) phase angle of the useful signal component of each of the two oscillation signals at the respective reference mass flow, can be determined and then, using the reference phase difference values, a (damping) correction value compensating for the (interference) phase difference can be calculated, for example by means of compensation calculation; this can be done, for example, in such a way that the (damping) correction value corresponds to the previously designated (scale) zero point of the phase difference-to-measured-value characteristic function and / or that as a result the measuring system electronics can use the phase difference-to-measured-value characteristic function on the basis of the respective reference phase difference orthe respective reference phase difference value, mass flow measurement values representing the respective reference mass flow for at least one of the calibration fluids, for example water at 20°C and 1 bar, are determined, each of which has a measurement deviation of less than 0.1% of the same reference mass flow and / or less than 0.05 kg / h. Taking into account additional dependencies of the (interference) phase difference, for example on the aforementioned material parameters of the respective calibration fluid, not least its viscosity, requires further measurements under correspondingly varied reference conditions. For example, in the tests described in US-B 65 13 393, US-A 2020 / 0393278, US-A 20190003875 andIn the measuring systems shown in WO-A 2020 / 259762, the dependence of the (disturbance) phase difference on the viscosity of the medium is compensated on the basis of previously determined viscosity values, for example also using a data field for (damping) correction values which shows the dependence of the flow parameter on the viscosity and which is determined by complex individual measurements and interpolation methods.

[0015] There is therefore a need, on the one hand, for a further improvement in the measuring accuracy of vibronic measuring systems of the type in question and an improvement in the robustness or stability with which the measured values for the at least one flow parameter can be determined during operation of such a measuring system, even with fluctuating properties or material parameters of the respective measuring substance, in particular its viscosity, and, on the other hand, for a reduction in the technical effort for recording and taking into account further dependencies of the (disturbance) phase difference when determining the measured values, not least when determining (mass flow) measured values by means of the aforementioned phase difference-to-measured value characteristic function.

[0016] Taking this into account, one object of the present invention is to further improve vibronic measuring systems of the type in question by appropriately taking into account the drive offset and its temporal changes with regard to the achievable (measurement) accuracy and robustness with which the measured values are determined during operation; this not least in the case of an initial or recurring calibration of such a vibronic measuring system in situ, namely directly on site at the respective measuring point and / or in the case of a vibronic measuring system with a tube arrangement that can be replaced on site and / or in the case of the use of a (standard) measuring transducer established for conventional vibronic measuring systems and / or an equally extensive retention of proven technologies and architectures for the respective measuring system electronics.In addition, a further object of the invention is to provide a vibronic measuring system which allows the aforementioned drive offset to be taken into account during operation or calibration and in which, as a result, a (disturbance) phase angle caused by the drive offset or a corresponding cross-sensitivity of the measured values determined by the measuring system to changing material parameters of the measured material is reduced.

[0017] To achieve the object, the invention consists in a vibronic measuring system, for example a Coriolis mass flow meter or Coriolis mass flow / density meter, which measuring system, for example designed as an in-line measuring device and / or a compact measuring device, is designed to measure at least one flow parameter, for example a mass flow and / or a volume flow and / or a flow velocity, of a flowing fluid medium, for example a gas, a liquid or a dispersion, in a pipe and / or a hose line; and which measuring system: -- a measuring transducer (of the vibration type) --- with a pipe arrangement for guiding the flowing medium,--- with an excitation arrangement for converting electrical power into mechanical power useful for exciting and maintaining forced mechanical vibrations of the pipe arrangement --- and with a sensor arrangement for detecting mechanical vibrations of the pipe arrangement and for providing vibration signals representing vibration movements of the pipe arrangement; -- as well as a measuring system electronics electrically connected to the measuring transducer, for example both to its excitation arrangement and to its sensor arrangement and / or by means of electrical connecting lines, for example formed by at least one microprocessor and / or arranged in an electronics protective housing, wherein the measuring system electronics is configured to at least temporarily feed an electrical drive signal into the vibration exciter; wherein the pipe arrangement has at least one,for example, at least partially curved and / or at least partially straight and / or first tube (111), -- which tube extends from a first tube end to a second tube end with a tube length of, for example, more than 100 mm and has a lumen enclosed by a, for example, metallic, tube wall and extending from the first tube end to the second tube end, -- and which tube is designed to have measured material flowing through it at least in a flow direction pointing from the first tube end to the second tube end and to be allowed to vibrate during this flow, -- and wherein the tube arrangement has a plurality of vibration modes (natural vibration shapes), each having an associated (modal) damping and an associated resonance frequency (co-)determined thereby,in which the at least one pipe can execute or executes (damped) oscillation movements each having one or more antinodes and two or more nodes, such that --- that oscillation movements of the pipe in a fundamental oscillation mode, namely a first-order oscillation mode (f1 mode), for example a first-order flexural oscillation mode, have exactly one antinode and two nodes --- and that oscillation movements of the pipe in a higher oscillation mode, namely a second-order or higher-order oscillation mode (f2 mode, f3 mode,... fx mode), for example a second-order or higher-order flexural oscillation mode, have two or more antinodes and three or more nodes; wherein the exciter arrangement has at least one, for example a single and / or electrodynamic, oscillation exciter, -- which is mechanically connected to the at least one pipe -- and is configured,to convert electrical power into mechanical power using a time-varying electrical current, such that a time-varying drive force acts on the pipe at a drive point formed by the vibration exciter on the pipe mechanically connected thereto, for example such that a line of action of the drive 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 smallest 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 reference cross-sectional area of the at least one pipe, determined for example with an intact or original measuring transducer, is not 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, wherein a vibration node of said vibration movements, formed between two vibration antinodes of vibration movements of the at least one pipe in a vibration mode (second or higher order) (deviating from the first-order vibration mode), for example (nominally) located at half the pipe length, lies within the reference cross-sectional area; wherein the sensor arrangement comprises a first vibration sensor, for example an electrodynamic or opto-electrical one, -- 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 flow direction, for example at least partially mechanically connected to the pipe -- and which is configured to detect vibration movements of the at least one pipe and to convert them into a signal representing said vibration movements, for example an electrical or optical signal.to convert a first vibration signal, for example in such a way that the first vibration signal contains one or more sinusoidal signal components, each with a frequency corresponding to a vibration frequency of vibration movements of the pipe; and wherein the sensor arrangement comprises at least one, for example electrodynamic or opto-electrical, second vibration sensor, -- which, for example, is spaced from the vibration exciter by more than 10 mm and / or more than one fifth of the pipe length in the flow direction and / or which is spaced from the first vibration sensor in the flow direction, positioned on the pipe, for example, namely at least partially mechanically connected to the pipe -- and which is configured to detect vibration movements of the at least one pipe and to convert them into a second vibration signal representing the same vibration movements, for example electrical or optical, for example in such a way,that the second vibration signal contains one or more sinusoidal signal components, each with a frequency corresponding to an vibration frequency of vibrational movements of the pipe; wherein the measuring system electronics are configured to feed the electrical drive signal -- both at least temporarily with a sinusoidal first (useful) current component having a first (alternating current) frequency and a, for example, predetermined and / or variable, first (current) amplitude for exciting first useful vibrations, namely mechanical vibrations of the at least one pipe forced by the (energized) vibration exciter with a first useful frequency, namely an (oscillation) frequency corresponding to the first (alternating current) frequency, into the vibration exciter, in such a way that --- the first (alternating current) frequency is different from a resonance frequency of a (symmetrical) vibration mode of odd order,for example, namely the fundamental vibration mode (f1 mode), deviates by less than 1% of the same resonance frequency and / or by less than 1 Hz, for example, namely the resonance frequency of the odd-order vibration mode and / or such that the second useful vibrations are suitable for causing Coriolis forces in a medium flowing through the at least one pipe with a mass flow other than zero, wherein the resonance frequency corresponds to or is dependent on an associated first modal damping of the same odd-order vibration mode, --- and that the first and second vibration signals generated by the first and second vibration sensors each have a first useful signal component, namely a sinusoidal signal component with a (signal) frequency corresponding to the first useful frequency,for example, namely each with a phase angle dependent on the mass flow of the medium flowing through the at least one pipe, -- as well as at least temporarily with a sinusoidal second (useful) current component having a second (alternating current) frequency and a, for example, predetermined and / or variable, second (current) amplitude for generating second useful oscillations, namely mechanical oscillations of the pipe forced by the (energized) oscillation exciter with a second useful frequency, namely an (oscillation) frequency corresponding to the second (alternating current) frequency, for example simultaneously with the first (useful) current component, to be fed into the oscillation exciter, such that --- the second (alternating current) frequency deviates from a resonance frequency of an (antisymmetric) oscillation mode of even-order order, for example the second-order oscillation mode (f2 mode), by less than 1%,for example, by less than 0.1%, the same resonant frequency, and / or by less than 1 Hz, for example by less than 0.1 Hz, for example, namely the resonant frequency of the even-order oscillation mode, wherein the resonant frequency corresponds to or is dependent on an associated second modal damping of the same even-order oscillation mode, --- and that the first and second oscillation signals generated by the first and second oscillation sensors each have a second useful signal component, namely a sinusoidal signal component with a (signal) frequency corresponding to the second useful frequency, and wherein the measuring system electronics is set up, based on both the first useful signal components,for example, based on a difference between a phase angle of the first useful signal component of the first oscillation signal and a phase angle of the first useful signal component of the second oscillation signal, as well as at least one of the second useful signal components and / or the second (useful) current component, to determine the measured values representing at least one flow parameter of the medium, for example, namely mass flow measured values representing the mass flow of the medium.

[0018] According to a first embodiment of the invention, it is further provided that the first useful frequency deviates from a resonance frequency of the fundamental oscillation mode by less than 1% of the same resonance frequency and / or by less than 1 Hz, in particular corresponding to the resonance frequency of the first-order oscillation mode.

[0019] According to a second embodiment of the invention, it is further provided that the first useful frequency deviates from a resonance frequency of a third-order vibration mode inherent in the at least one pipe, in particular a third-order bending vibration mode, in which vibration mode the vibration movements of the pipe have exactly three antinodes and two vibration nodes, by less than 1% of the same resonance frequency and / or by less than 1 Hz, in particular corresponding to the resonance frequency of the third-order vibration mode; this, for example, in such a way that a first vibration node of vibration movements of the at least one pipe in the third-order vibration mode is located in the first pipe end and a second vibration node of the third-order vibration mode is located in the second pipe end.

[0020] According to a third embodiment of the invention, it is further provided that the second useful frequency deviates from a resonance frequency of a second-order vibration mode (f2 mode) inherent in the at least one pipe, in particular a second-order bending vibration mode, in which vibration mode the vibration movements of the pipe have exactly two vibration antinodes and three vibration nodes, by less than 1% of the same resonance frequency and / or by less than 1 Hz, in particular corresponds to the resonance frequency.

[0021] According to a fourth embodiment of the invention, it is further provided that the second useful frequency deviates from a resonance frequency of a second-order vibration mode (f2 mode) inherent in the at least one pipe, in particular a second-order bending vibration mode, in which vibration mode the vibration movements of the pipe have exactly two vibration antinodes and three vibration nodes, by less than 1% of the same resonance frequency and / or by less than 1 Hz, in particular corresponds to the resonance frequency, and that a first vibration node of vibration movements of the at least one pipe in the second-order vibration mode is located in the first pipe end and a second vibration node of vibration movements of the at least one pipe in the second-order vibration mode is located in the second pipe end.

[0022] According to a fifth embodiment of the invention, it is further provided that the second useful frequency deviates from a resonance frequency of a second-order vibration mode (f2 mode) inherent in the at least one pipe, in particular a second-order bending vibration mode, in which vibration mode the vibration movements of the pipe have exactly two antinodes and three nodes, by less than 1% of the same resonance frequency and / or by less than 1 Hz, in particular corresponds to the resonance frequency, and that a node of the same vibration movements formed between the two antinodes of the vibration movements of the at least one pipe in the second-order vibration mode, in particular located at half the pipe length, lies within the reference cross-sectional area.

[0023] According to a sixth embodiment of the invention, it is further provided that the second useful frequency deviates from a resonance frequency of a second-order vibration mode (f2 mode) inherent in the at least one tube, in particular a second-order bending vibration mode, in which vibration mode the vibration movements of the tube have exactly two antinodes and three nodes, by less than 1% of the same resonance frequency and / or by less than 1 Hz, in particular corresponds to the resonance frequency, and that a principal axis of inertia of the at least one tube, which is perpendicular to the direction of vibration of the vibration movements of the tube in the second-order vibration mode, lies within the reference cross-sectional area of the at least one tube.

[0024] According to a seventh embodiment of the invention, it is further provided that the drive offset corresponds to a distance between a center of gravity (center point) of the drive cross-sectional area of the pipe and a center of gravity (center point) of the reference cross-sectional area of the at least one pipe.

[0025] According to an eighth embodiment of the invention, it is further provided that a line of action of the driving force runs perpendicular to a normal of a driving cross-sectional area of the tube.

[0026] According to a ninth embodiment of the invention, it is further provided that an intersection line of two mutually orthogonal planes of symmetry of the at least one tube lies within the reference cross-sectional area.

[0027] According to a tenth embodiment of the invention, it is further provided that a main axis of inertia of the at least one tube, which is perpendicular to the driving force, lies within the reference cross-sectional area of the at least one tube.

[0028] According to an eleventh embodiment of the invention, it is further provided that the drive offset results from a manufacturing tolerance in the manufacture of the exciter arrangement, in particular from tolerances in the positioning of the vibration exciter on at least one tube and / or from tolerances in the positioning of the tube arrangement within a converter protective housing.

[0029] According to a twelfth embodiment of the invention, it is further provided that the drive offset results from a manufacturing tolerance in the manufacture of the pipe arrangement, in particular the manufacture of the at least one pipe.

[0030] According to a thirteenth 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 component, in particular such that an amplitude of the first (useful) current component is set to be not less than an amplitude of the second (useful) current component and / or that an amplitude of the second (useful) current component is set to be more than 40%, in particular not less than 50%, of an amplitude of the first (useful) current component.

[0031] According to a fourteenth embodiment of the invention, it is further provided that the measuring system electronics are configured to set the second (alternating current) frequency as a function of the first (alternating current) frequency, in particular such that the second (alternating current) 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 (alternating current) frequency, in particular namely more than 230% of the first (alternating current) frequency and / or less than 300% of the first (alternating current) frequency corresponding multiple of the first (alternating current) frequency.

[0032] According to a fifteenth embodiment of the invention, it is further provided that the measuring system electronics are configured to feed the first and second (useful) currents of the driver signal simultaneously into the vibration exciter, in particular for a time interval lasting not less than two oscillation periods of the first (useful) current component and / or more than 10 ms.

[0033] According to a sixteenth embodiment of the invention, it is further provided that the measuring system electronics are configured to switch on the second (useful) current component during the feeding of the first (useful) current component, in particular to switch off the second (useful) current component again after a time interval lasting not less than two oscillation periods of the first (useful) current component and / or more than 1 s.

[0034] According to a seventeenth embodiment of the invention, it is further provided that the measuring system electronics comprise a first phase-locked loop, in particular a digital one, used to set the first (AC) frequency, and a second phase-locked loop, in particular a digital one, used to set the second (AC) frequency. Furthermore, the measuring system electronics can be further 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 based on the first (AC) frequency.

[0035] According to an eighteenth embodiment of the invention, it is further provided that the measuring system further comprises a support frame, in particular a metallic one and / or designed as a protective housing for the transducer, wherein the support frame and the tube arrangement are fastened to one another, in particular detachably, and wherein the exciter arrangement, in particular the at least one vibration exciter, and / or the sensor arrangement, in particular the first and second vibration sensors, are mounted proportionally on the support frame.

[0036] According to a nineteenth embodiment of the invention, it is further provided that the measuring system further comprises an electronics protective housing for the measuring system electronics, in particular fastened to a support frame or a converter protective housing of the measuring converter and / or made of metal.

[0037] According to a twentieth embodiment of the invention, it is further provided that the measuring transducer does not have any further vibration exciter apart from the vibration exciter which is mechanically connected to the at least one tube.

[0038] According to a twenty-first embodiment of the invention, it is further provided that the measuring system electronics are set up to determine at least one, in particular digital, first quality value based on the first useful signal component of at least one of the first and second oscillation signals and / or the first (useful) current component of the driver signal, wherein the first quality value represents a measure of the first modal damping, in particular a quality of the first useful oscillations or a damping degree of the first useful oscillations, or is dependent on said first modal damping, and that the measuring system electronics are set up to determine at least one, in particular digital, second quality value based on the second useful signal component of at least one of the first and second oscillation signals and / or the second (useful) current component of the driver signal, wherein the second quality value represents a measure of the second modal damping, in particularnamely a quality of the second useful vibrations or a degree of damping of the second useful vibrations, represents or depends on the second modal damping.

[0039] According to a twenty-second embodiment of the invention, it is further provided that the measuring system electronics is set up to determine the measured values that at least provisionally represent the at least one flow parameter of the medium to be measured, in particular mass flow measured values that at least provisionally represent the mass flow of the medium to be measured, on the basis of a measured phase difference, namely a difference between a phase angle of the first useful signal component of the first oscillation signal and a phase angle of the first useful signal component of the second oscillation signal, and that the measuring system electronics is set up, based on the first and second oscillation signals and / or the driver signal, in particular on the basis of at least one first useful signal component and at least one second useful signal component and / or on the basis of the first and second (useful) current components, at least one, in particulardigital (attenuation) correction value for the measured phase difference and / or to determine preliminary measured values based on the same measured phase difference.

[0040] According to a twenty-third embodiment of the invention, it is further provided that the measuring system electronics are set up to determine the measured values that at least provisionally represent the at least one flow parameter of the medium to be measured, in particular mass flow measured values that at least provisionally represent the mass flow of the medium to be measured, on the basis of a measured phase difference, namely a difference between a phase angle of the first useful signal component of the first oscillation signal and a phase angle of the first useful signal component of the second oscillation signal, and that the measuring system electronics are set up, based on the first and second oscillation signals and / or the driver signal, in particular on the basis of at least one first useful signal component and at least one second useful signal component and / or on the basis of the first and second (useful) current components, to determine at least one, in particular digital, (damping) correction value for the measured phase difference orto determine measured values provisionally determined on the basis of the same measured phase difference in such a way that the (damping) correction value corresponds to the first and second modal dampings or is a function of the same first and second modal dampings and / or that the (damping) correction value is subtracted from the measured phase difference or from measured values provisionally determined on the basis of the measured phase difference and / or that the (damping) correction value corresponds to the drive offset, in particular is dependent thereon and / or is a measure of the drive offset.

[0041] According to a twenty-fourth embodiment of the invention, it is further provided that the measuring system electronics is set up to determine the measured values that at least provisionally represent the at least one flow parameter of the medium to be measured, in particular mass flow measured values that at least provisionally represent the mass flow of the medium to be measured, on the basis of a measured phase difference, namely a difference between a phase angle of the first useful signal component of the first oscillation signal and a phase angle of the first useful signal component of the second oscillation signal, and that the measuring system electronics is set up, based on the first and second oscillation signals and / or the driver signal, in particular on the basis of at least one first useful signal component and at least one second useful signal component and / or on the basis of the first and second (useful) current components, at least one, in particulardigital, (damping) correction value for the measured phase difference and / or measured values provisionally determined on the basis of the same measured phase difference, in such a way that the (damping) correction value corresponds to the first and second modal dampings or is a function of the first and second modal dampings, in particular in such a way that the (damping) correction value corresponds to a function of a quality (1 / D2) of the second useful oscillations or of an inverse of a damping factor of the second useful oscillations and a second power of a damping factor of the first useful oscillations or of an inverse of a quality (1 / D1) of the first useful oscillations.

[0042] According to a twenty-fifth embodiment of the invention, it is further provided that the measuring system electronics are set up to determine the measured values that at least provisionally represent the at least one flow parameter of the medium to be measured, in particular mass flow measured values that at least provisionally represent the mass flow of the medium to be measured, on the basis of a measured phase difference, namely a difference between a phase angle of the first useful signal component of the first oscillation signal and a phase angle of the first useful signal component of the second oscillation signal, and that the measuring system electronics are set up, based on the first and second oscillation signals and / or the driver signal, in particular on the basis of at least one first useful signal component and at least one second useful signal component and / or on the basis of the first and second (useful) current components, to determine at least one, in particular digital, (damping) correction value for the measured phase difference orto determine provisionally determined measured values on the basis of the same measuring phase difference, such that the (damping) correction value corresponds to a function of a product of a quality (1 / D1) of the first useful oscillations and a second power of a quality (1 / D2) of the second useful oscillations or a product of an inverse of a damping degree of the first useful oscillations and a second power of an inverse of a damping degree of the second useful oscillations.

[0043] According to a twenty-sixth embodiment of the invention, it is further provided that the measuring system electronics are set up to determine the measured values that at least provisionally represent the at least one flow parameter of the medium to be measured, in particular mass flow measured values that at least provisionally represent the mass flow of the medium to be measured, on the basis of a measured phase difference, namely a difference between a phase angle of the first useful signal component of the first oscillation signal and a phase angle of the first useful signal component of the second oscillation signal, and that the measuring system electronics are set up, based on the first and second oscillation signals and / or the driver signal, in particular on the basis of at least one first useful signal component and at least one second useful signal component and / or on the basis of the first and second (useful) current components, to determine at least one, in particular digital, (damping) correction value for the measured phase difference orto determine provisionally determined measured values on the basis of the same measuring phase difference in such a way that an amount of the (damping) correction value becomes smaller with increasing first modal damping (D1) and / or larger with increasing second modal damping (D2).

[0044] According to a twenty-seventh embodiment of the invention, it is further provided that the measuring system electronics are set up to determine the measured values that at least provisionally represent the at least one flow parameter of the medium to be measured, in particular mass flow measured values that at least provisionally represent the mass flow of the medium to be measured, on the basis of a measured phase difference, namely a difference between a phase angle of the first useful signal component of the first oscillation signal and a phase angle of the first useful signal component of the second oscillation signal, and that the measuring system electronics are set up, based on the first and second oscillation signals and / or the driver signal, in particular on the basis of at least one first useful signal component and at least one second useful signal component and / or on the basis of the first and second (useful) current components, to determine at least one, in particular digital, (damping) correction value for the measured phase difference orto determine provisionally determined measured values on the basis of the same measuring phase difference, such that the (attenuation) correction value is proportional to a ratio (D1 2< / D2) of a second power (D1 2< ) of the first modal attenuation (D1) to the second modal attenuation (D2).

[0045] According to a twenty-eighth embodiment of the invention, it is further provided that the measuring system electronics are set up to determine the measured values that at least provisionally represent the at least one flow parameter of the medium to be measured, in particular mass flow measured values that at least provisionally represent the mass flow of the medium to be measured, on the basis of a measured phase difference, namely a difference between a phase angle of the first useful signal component of the first oscillation signal and a phase angle of the first useful signal component of the second oscillation signal, and that the measuring system electronics are set up, based on the first and second oscillation signals and / or the driver signal, in particular on the basis of at least one first useful signal component and at least one second useful signal component and / or on the basis of the first and second (useful) current components, to determine at least one, in particular digital, (damping) correction value for the measured phase difference orto determine provisionally determined measured values on the basis of the same measuring phase difference, in such a way that the measuring system electronics are set up to store the (damping) correction value, in particular in a non-volatile data memory and / or in such a way that the (damping) correction value is stored as a measuring system-specific reference value and / or is contained in a measuring function of the measuring system, according to which the measuring system converts the at least one flow parameter to be measured into the respective measured values.

[0046] According to a twenty-ninth embodiment of the invention, it is further provided that the measuring system electronics are set up to determine the measured values that at least provisionally represent the at least one flow parameter of the medium to be measured, in particular mass flow measured values that at least provisionally represent the mass flow of the medium to be measured, on the basis of a measured phase difference, namely a difference between a phase angle of the first useful signal component of the first oscillation signal and a phase angle of the first useful signal component of the second oscillation signal, and that the measuring system electronics are set up, based on the first and second oscillation signals and / or the driver signal, in particular on the basis of at least one first useful signal component and at least one second useful signal component and / or on the basis of the first and second (useful) current components, to determine at least one, in particular digital, (damping) correction value for the measured phase difference orto determine provisionally determined measured values on the basis of the same measuring phase difference in such a way that the measuring system electronics are set up to compare the (damping) correction value with an initial (damping) correction value determined beforehand, in particular under reference conditions and / or during commissioning of the measuring system and / or during (re-)calibration of the measuring system and / or with another measuring system of the same construction, in particular stored in the measuring system electronics and / or serving as a reference value.

[0047] According to a thirtieth embodiment of the invention, it is further provided that the measuring system electronics are set up to determine the measured values that at least provisionally represent the at least one flow parameter of the medium to be measured, in particular mass flow measured values that at least provisionally represent the mass flow of the medium to be measured, on the basis of a measured phase difference, namely a difference between a phase angle of the first useful signal component of the first oscillation signal and a phase angle of the first useful signal component of the second oscillation signal, and that the measuring system electronics are set up, based on the first and second oscillation signals and / or the driver signal, in particular on the basis of at least one first useful signal component and at least one second useful signal component and / or on the basis of the first and second (useful) current components, to determine at least one, in particular digital, (damping) correction value for the measured phase difference orto determine provisionally determined measured values on the basis of the same measuring phase difference, in such a way that the measuring system electronics are set up to compare the (damping) correction value with at least one threshold value predetermined for this purpose, in particular representing a measuring transducer which is outside of a specification and / or an inadmissibly large drive offset, and / or that the measuring system electronics are set up to determine an extent of the drive offset and / or to carry out a check of the measuring system by means of at least one of the first and second oscillation signals and / or the driver signal, in particular using the (damping) correction value.

[0048] According to a thirty-first embodiment of the invention, it is further provided that the measuring system electronics is set up to determine the measured values that at least provisionally represent the at least one flow parameter of the medium to be measured, in particular mass flow measured values that at least provisionally represent the mass flow of the medium to be measured, on the basis of a measured phase difference, namely a difference between a phase angle of the first useful signal component of the first oscillation signal and a phase angle of the first useful signal component of the second oscillation signal, and it is further provided that the measuring system electronics is set up to determine at least one, in particular digital, first quality value based on the first useful signal component of at least one of the first and second oscillation signals and / or the first (useful) current component of the driver signal, wherein the first quality value is a measure of the first modal damping, in particularnamely a quality of the first useful oscillations or a degree of damping of the first useful oscillations, or is dependent on the same first modal damping, and in that the measuring system electronics are set up to determine at least one, in particular digital, second quality value based on the second useful signal component of at least one of the first and second oscillation signals and / or the second (useful) current component of the driver signal, wherein the second quality value represents a measure of the second modal damping, in particular a quality of the second useful oscillations or a degree of damping of the second useful oscillations, or is dependent on the same second modal damping, wherein the measuring system electronics are set up to use the first and second quality values to determine at least one, in particular digital, (damping) correction value for the measuring phase difference orto determine provisionally determined measured values on the basis of the same measuring phase difference, for example in such a way that the (damping) correction value corresponds to a function of a quality (1 / D2) of the second useful oscillations or a reciprocal of a damping factor of the second useful oscillations and a second power of a damping factor of the first useful oscillations or a reciprocal of a quality (1 / D1) of the first useful oscillations.

[0049] 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 signals follow a change in a mass flow of the medium carried in the pipe with a change in a (measurement) 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 signal and a phase angle of the first useful signal component of the second vibration signal, and that the measuring system electronics are set up to generate mass flow measurement values representing the mass flow based on the (measurement) phase difference of the first useful signal components.

[0050] According to a thirty-third embodiment of the invention, it is further provided that a phase difference to measured value characteristic function is set up in the measuring system electronics, according to which the measuring system electronics can determine or determines the measured values representing at least one flow parameter of the medium, in particular mass flow measured values representing the mass flow of the medium, on the basis of the measured phase difference, in particular in such a way that the first and second modal dampings are taken into account in the phase difference to mass flow measured value characteristic function or that the (damping) correction value is contained in the phase difference to mass flow measured value characteristic function.

[0051] According to a thirty-fourth embodiment of the invention, it is further provided that a phase difference to measured value characteristic curve function is set up in the measuring system electronics, according to which the measuring system electronics can determine or determines the measured values representing at least one flow parameter of the medium, in particular mass flow measured values representing the mass flow of the medium, on the basis of the measured phase difference, in particular in such a way that the first and second modal dampings are taken into account in the phase difference to mass flow measured value characteristic curve function or that the (damping) correction value is contained in the phase difference to mass flow measured value characteristic curve function, in particular in such a way that the first and second modal dampings are taken into account in the phase difference to mass flow measured value characteristic curve function or that the (damping) correction value is contained in the phase difference to mass flow measured value characteristic curve function, in particular.such that the phase difference to mass flow measured value characteristic function takes into account a product of a second power of the first modal damping and a reciprocal of the second modal damping and / or a product of a second power of the reciprocal of the quality of the first useful oscillations and the quality of the second useful oscillations.

[0052] According to a thirty-fifth embodiment of the invention, it is further provided that a phase difference-to-measured value characteristic function is set up in the measuring system electronics, according to which the measuring system electronics can determine or determines the measured values representing at least one flow parameter of the medium, in particular mass flow measured values representing the mass flow of the medium, on the basis of the measured phase difference, in particular such that the first and second modal dampings are taken into account in the phase difference-to-mass flow measured value characteristic function or that the (damping) correction value is included in the phase difference-to-mass flow measured value characteristic function, in such a way that the measuring system electronics is set up to check the phase difference-to-measured value characteristic function by means of at least one of the first and second oscillation signals and / or the driver signal, in particular using the (damping) correction value.

[0053] According to a thirty-sixth embodiment of the invention, it is further provided that a phase difference to measured value characteristic curve function is set up in the measuring system electronics, according to which the measuring system electronics can determine or determines the measured values representing at least one flow parameter of the medium, in particular mass flow measured values representing the mass flow of the medium, on the basis of the measured phase difference, in particular in such a way that the first and second modal dampings are taken into account in the phase difference to mass flow measured value characteristic curve function or that the (damping) correction value is contained in the phase difference to mass flow measured value characteristic curve function, and that the measuring system electronics is further set up, using the (damping) correction value, a (self-)diagnosis and / or (re-)calibration of the measuring system, in particularwith a measuring transducer integrated into a piping system and / or by means of measuring system electronics electrically connected to the measuring transducer.

[0054] According to a thirty-seventh embodiment of the invention, it is further provided that the measuring system electronics is configured to determine, based on at least one of the first and second vibration signals, a first speed value representing a first vibration speed, namely a speed of the vibration movements of the at least one pipe executing the first useful vibrations, in particular to store it in a non-volatile data memory.

[0055] According to a thirty-eighth embodiment of the invention, it is further provided that the measuring system electronics are configured to determine at least one second speed value representing a second vibration speed, namely a speed of the vibration movements of the at least one pipe performing the second useful vibrations, in particular to store it in a non-volatile data memory.

[0056] According to a thirty-ninth embodiment of the invention, it is further provided that the measuring system electronics are configured to determine at least one, in particular digital, first current measurement value representing the first (useful) current component, in particular a (current) amplitude of the first (useful) current component or an effective value of the first (useful) current component, in particular to store it in a non-volatile data memory.

[0057] According to a fortieth embodiment of the invention, it is further provided that the measuring system electronics are configured to determine at least one, in particular digital, second current measurement value representing the second (useful) current component, in particular an amplitude of the second (useful) current component or an effective value of the second (useful) current component, in particular to store it in a non-volatile data memory.

[0058] According to a forty-first embodiment of the invention, it is further provided that a phase difference to measured value characteristic function is set up in the measuring system electronics, according to which the measuring system electronics can determine or determines the measured values representing at least one flow parameter of the medium, in particular the mass flow measured values representing the mass flow of the medium, based on the measured phase difference.In addition, the measuring system electronics is also set up to determine, in particular in a non-volatile data memory, a first speed value representing a first vibration speed, namely a speed of the vibration movements of the at least one pipe carrying out the first useful vibrations, and at least one second speed value representing a second vibration speed, namely a speed of the vibration movements of the at least one pipe carrying out the second useful vibrations, based on at least one of the first and second vibration signals, and to store this in a non-volatile data memory, and to use the driver signal to determine at least one, in particular digital, first current measurement value representing the first (useful) current component, in particular a (current) amplitude of the first (useful) current component or an effective value of the first (useful) current component, and at least one, in particularto determine a second current measurement value, in particular a digital one, representing an amplitude of the second (useful) current component or an effective value of the second (useful) current component, in particular to store it in a non-volatile data memory, and to determine at least one, in particular a digital, (damping) correction value for the measurement phase difference or measurement values provisionally determined on the basis of the same measurement phase difference by means of the first and second speed values and the first and second current measurement values, in particular as a function of the first oscillation speed, a second power of a (current) amplitude of the second (useful) current component (eN2), an inverse of a (current) amplitude of the first (useful) current component (eN1) and an inverse of a second power of the second oscillation speed.

[0059] According to a forty-second embodiment of the invention, it is further provided that the measuring system electronics has a non-volatile data memory (EEPROM) which is designed to store digital data, in particular the first quality value and / or the (attenuation) correction value, in particular even without an applied operating voltage.

[0060] According to a forty-third embodiment of the invention, it is further provided that the vibration exciter is formed by means of a voice coil, in particular having an air coil and an armature.

[0061] According to a forty-fourth embodiment of the invention, it is further provided that each of the first and second vibration sensors is formed by a plunger coil, in particular having an air coil and an armature.

[0062] According to a forty-fifth embodiment of the invention, it is further provided that the vibration exciter comprises a magnetic armature, in particular formed by a permanent magnet, and a coil, in particular an air-core coil, through which the magnetic field of the armature flows; this, for example, also in such a way 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 drive signal and to carry its first and second (useful) currents.

[0063] According to a forty-sixth embodiment of the invention, it is further provided that the measuring system electronics are configured to follow a change in the density of the medium conveyed in the pipe 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 oscillation signals.

[0064] According to a forty-seventh 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 component (eN2) during a test interval, in particular one lasting more than 10 ms and / or limited in time and / or started repeatedly, with a sinusoidal signal having a second (alternating current) frequency; this, for example, also in such a way that the test interval lasts longer than 100 ms (milliseconds), in particular not less than 1 s (second), and / or that the measuring system electronics are configured to start and / or end the test interval, in particular recurringly, automatically, in particular 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.

[0065] According to a forty-eighth embodiment of the invention, it is further provided that the pipe wall consists of a steel, in particular a stainless steel, duplex steel or super duplex steel, of a titanium alloy and / or a zirconium alloy, in particular a Zircaloy, and / or a tantalum alloy.

[0066] According to a forty-ninth embodiment of the invention, it is further provided that the tube has a caliber (inner tube diameter) that is more than 0.1 mm, in particular more than 0.5 mm; this, for example, also such that the tube has a caliber-to-tube length ratio that is more than 0.08, in particular more than 0.1, and / or less than 0.25, in particular less than 0.2, and / or that the tube length of the tube 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 that the tube has a caliber that is more than 10 mm, in particular more than 15 mm.

[0067] According to a fiftieth embodiment of the invention, it is further provided that the exciter arrangement does not have any further vibration exciter connected to the pipe apart from the vibration exciter.

[0068] According to a fifty-first 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, in particular zero, or that the center of gravity of the drive cross-sectional area of the tube corresponds to or coincides with the drive reference point.

[0069] According to a fifty-second 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.

[0070] According to a fifty-third embodiment of the invention, it is further provided that the tube is curved in sections, in particular in a circular arc and / or V-shaped manner, in particular such that the tube has a central vertex arc segment and / or that exactly one main axis of inertia of the at least one tube lies within the reference cross-sectional area of the at least one tube.

[0071] According to a fifty-fourth embodiment of the invention, it is further provided that the pipe is straight in sections, in particular over the entire pipe length, in particular such that a center of mass lies within the reference cross-sectional area of the at least one pipe.

[0072] According to a fifty-fifth embodiment of the invention, it is further provided that the pipe arrangement has at least one second pipe, in particular one that is at least partially curved and / or at least partially straight and / or structurally identical to the first pipe and / or at least partially parallel to the first pipe. Further developing this embodiment of the invention, it is further provided that the vibration exciter is mechanically connected both partially to the first pipe and partially to the second pipe, and / or that the vibration exciter is configured to act differentially on the first and second pipes, in particularsuch that the first and second tubes simultaneously carry out forced mechanical oscillations of the same frequency and opposite frequencies, and / or that the oscillation exciter is set up to convert electrical power into mechanical power using 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 oscillation exciter on the second tube mechanically connected thereto, in particular at the same time and / or opposite to the driving force acting on the first tube at the drive point formed by the oscillation exciter on the first tube mechanically connected thereto, and / or that the oscillation exciter is set up to convert electrical power fed in by the electrical drive signal simultaneously into forced mechanical oscillations of the first and second tubes, in particularsuch that the first and second tubes perform forced mechanical vibrations at the first useful frequency and / or at the second useful frequency simultaneously.

[0073] A basic idea of the invention is to actively excite, during the operation of vibronic measuring systems of the type in question, not least for the purpose of compensating for measurement errors dependent on variable material parameters of the respective measured material, by means of the at least one vibration exciter (arranged centrally of the at least one tube), in addition to the typically excited useful vibrations according to an odd-order (bending) vibration mode, at least temporarily also useful vibrations, for example bending vibrations, according to an even-order vibration mode, thus a natural vibration mode of the at least one tube which (nominally) has a vibration node located at the vibration exciter or in its immediate vicinity, for example a second-order (bending) vibration mode (f2 mode) and / or a fourth-order (bending) vibration mode (f4 mode).

[0074] The invention is based, among other things, on the surprising discovery that, due to the drive offset being typically very small but regularly different from zero even in the case of an original or undamaged measuring transducer, the aforementioned useful oscillations corresponding to the even-order oscillation mode, when actively excited at the respective resonance frequency of the same oscillation mode, for example the resonance frequency (f2) of the second-order (bending) oscillation mode (f2 mode), have an amplitude which is, admittedly, rather small but nevertheless regularly sufficiently well measurable and, accordingly, also a well-measurable (modal) damping; this is particularly true to the extent that, based on the respective modal damping of both excited useful oscillations, the aforementioned drive offset orthe resulting influence of one or more material parameters of the measured substance on the respective measurement error can be determined with a measuring system according to the invention during operation, for example, during a (self-)adjustment of the measuring system ("autozero") and / or in such a way that the influence of the drive offset is taken into account accordingly when determining the measured values. Furthermore, it has also been recognized that it is also possible, based on one or more such actively excited (bending) vibration modes of an even order, for example the f2 mode, in combination with one or more simultaneously actively excited vibration modes of an odd order, for example a typically excited (bending) vibration mode of the first order (f1 mode) or a (bending) vibration mode of the third order (f3 mode), respectively.Based on the respective driver signal and at least one of the corresponding oscillation signals, the aforementioned phase error, which typically occurs in conventional measuring systems as a systematic (measurement) deviation dependent on one or more material parameters of the measuring medium, can also be quantitatively determined "on-the-fly", namely during ongoing operation of the respective measuring system, at least approximately in the form of a (damping) correction value; this can also be used, for example, in order to adjust the (damping) correction value accordingly in the event of a change in the phase error, for example as a result of changing material parameters of the measuring medium, not least the viscosity.

[0075] Furthermore, it has been recognized that, conversely, a change in the drive offset during use of the respective measuring system, which is accompanied by a displacement of the aforementioned vibration node closest to the vibration exciter, for example due to changing geometric or mechanical properties of the pipe or the measuring transducer formed therewith relative to the original drive offset, which is effective, for example, for the (initial) calibration of the measuring system, can also lead to, among other things, the modal damping of the useful vibrations for the same excitation in comparison to the damping initially measured; this in particular in the way that with increasing drive offset the modal damping of the (bending) vibration mode of odd order (f1 mode) becomes greater and the modal damping of the (bending) vibration mode of even order (f2 mode) becomes smaller.Thus, based on the useful vibrations according to the even-order vibration mode, a (self-)diagnosis can also be carried out very easily, for example in the sense of checking the functionality of the measuring system or verifying the measuring system ("pass / fail"). For the purpose of such a (self-)diagnosis of the measuring system, the vibration responses generated by the active excitation of useful vibrations according to the even-order vibration mode or the (system) parameters characterizing them, if necessary also together with the vibration responses generated by the useful vibrations according to the odd-order vibration mode, can advantageously be determined very easily and repeatedly during operation of the measuring system and compared with corresponding reference vibration responses ("fingerprint") or reference values for them, for example in such a way that at increased orDeviations from the corresponding reference values that exceed a specified tolerance level are used to detect and, if necessary, report a fault in the measuring system; this can advantageously be done simultaneously with the actual measuring operation without significantly affecting it or without having to interrupt the measuring operation for any lengthy period.

[0076] A further advantage of the invention is that both the compensation or correction of the phase error according to the invention and the aforementioned (self-)diagnosis can be realized by extensively, if necessary even exclusively, using the designs proven for conventional vibronic measuring systems, not least for the transducers previously installed therein, as well as by equally extensively retaining proven technologies and architectures of established measuring system electronics; for example, even in such a way that conventional, possibly already installed, measuring systems can be retrofitted by appropriately reprogramming the respective measuring system electronics.

[0077] The invention is defined by the subject matter of the independent claim. The dependent claims relate to advantageous embodiments.

[0078] The invention and advantageous embodiments thereof are explained in more detail below using exemplary embodiments illustrated in the figures of the drawing. Identical or similarly acting or functioning parts are provided with the same reference numerals in all figures; where clarity requires it or it otherwise seems appropriate, previously mentioned reference numerals have been omitted in subsequent figures.

[0079] In detail: Fig. 1 shows a perspective side view of an embodiment of a vibronic measuring system; Fig. 2 shows a block diagram of an embodiment of a vibronic measuring system according to Fig. 1 suitable vibration type measuring transducer and a measuring system electronics electrically coupled thereto; Fig. 3 schematically shows in the form of a block diagram a further embodiment of a vibronic measuring system according to Fig. 1 suitable vibration type measuring transducer and electrically coupled measuring system electronics; Fig. 4a schematically shows a tube 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 with a tube arrangement according to Fig. 4 Mass flow dependent Coriolis oscillations of the tube, excited by useful oscillations; Fig. 5 schematically shows a diagram of a tube of a tube arrangement according to Fig. 4 immanent vibration modes of first, second and third order, respectively; Fig. 6, 7 schematically the tube arrangement according to Fig. 4 with tube excited to second useful vibrations;

[0080] In Fig. 1 or 2 and 3, exemplary embodiments or design variants for a vibronic measuring system suitable for measuring and / or monitoring at least one, in particular time-varying, measured variable of a fluid, for example at least temporarily flowing and / or at least temporarily two- or multi-phase or inhomogeneous, medium FL are shown schematically, wherein the measured variable can be, for example, a flow parameter, such as a mass flow ṁ, a volume flow and / or a flow velocity, or for example a material parameter, such as a density ρ and / or a viscosity η, of the medium FL. The measuring system is particularly intended or set up to be integrated into the course of a process line carrying a fluid FL serving as a medium - for example a gas, a liquid or a dispersion - and, during operation, from the fluid supplied to or discharged via the process line.The fluid FL is then discharged again and flows through it at least temporarily. Furthermore, the measuring system is designed to determine, in particular calculate, and / or output the measured values XM that quantify at least one physical measured variable (sequentially in time), possibly also digitally. The process line can, for example, be part of a possibly extensive and / or branched line system and / or a pipe or hose line, for example a pipe of a filling plant or a refueling device, or, for example, a hose line in a biotechnological plant.

[0081] As in Fig. 1 , 2or 3 respectively or as is readily apparent from their combination, the measuring system comprises a measuring transducer 10 of the vibration type, namely a measuring transducer with a tube arrangement formed by at least one (first) or more tubes for guiding the measuring medium, an excitation arrangement (31) for converting electrical power in the excitation and maintenance of forced mechanical vibrations of the at least one tube and a sensor arrangement (41, 42) for detecting mechanical vibrations of the tube arrangement and for providing vibration signals (s1, s2), for example electrical or optical, representing vibration movements of the tube arrangement, in particular of its one or more tubes.In addition, the measuring system further comprises a measuring system electronics 20 which is electrically coupled to the measuring transducer 10, namely both to the aforementioned excitation arrangement of the measuring transducer and to the aforementioned sensor arrangement of the measuring transducer, for example by means of corresponding electrical connecting lines, in particular formed by means of at least one microprocessor (µC) and / or arranged in an electronics protective housing (200) and / or serving as a transmitter, for controlling the measuring transducer, in particular namely for causing the aforementioned mechanical vibrations of the at least one pipe, and for evaluating vibration signals supplied by the measuring transducer, for example namely for determining the aforementioned measured values.The measuring system electronics 20 can, for example, be designed to be programmable and / or remotely parameterizable, 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 module (FPGA) and / or by means of a customer-specific programmed logic module (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 from the measuring system electronics 20 via a connecting cable. The electrical coupling or connection of the measuring transducer 10 to the measuring system electronics 20 can be achieved by means of corresponding electrical connecting cables and corresponding cable bushings. The connecting cables can be designed at least partially as electrical conductors, at least partially enclosed in electrical insulation, e.g.Inform of twisted-pair cables, ribbon cables, and / or coaxial cables. Alternatively or in addition, the connecting lines can also be formed, at least in sections, by conductor tracks on a printed circuit board, especially a flexible one, possibly coated.

[0082] The measuring system electronics 20 can also - as in Fig. 1 schematically shown - for example, in a corresponding, in particular impact- and / or explosion-proof and / or at least splash-proof, dedicated electronics protective housing 200 and also be designed so that, during operation of the measuring system, it can exchange measurement and / or other operating data, for example also status messages, with a higher-level (not shown here) electronic (measurement) data processing system, for example a programmable logic controller (PLC), a process control system (PCS), a remote control terminal (RTU), or a monitoring control and data acquisition system (SCADA) 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, such as current measured values or setting and / or diagnostic values used to control the measuring system ( Fig. 2 or 3). Accordingly, the measuring system electronics 20 can, for example, have such a transmitting and receiving circuit COM, which is powered during operation by a (central) evaluation and supply unit provided in the aforementioned data processing system and remote 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 is electrically connectable to the aforementioned external electronic data processing system via a two-wire connection 2L, possibly also configured as a 4-20 mA current loop, and can thereby draw 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,digitized measured values can be transmitted to the data processing system, for example by (load) modulation of a direct current supply fed by the evaluation and supply unit. In addition, the measuring system electronics 20 can also be designed such that it can be nominally operated with a maximum power of 1 W or less and / or is intrinsically safe. The measuring system electronics 20 can also be constructed in a modular manner, for example, such that various electronic components of the measuring system electronics 20, such as a measuring and evaluation circuit DSV, formed for example by one or more microprocessors and / or by one or more digital signal processors, for processing and evaluating the measurement signals provided by the measuring transducer 10, not least the vibration signals, a driver circuit Exc for controlling the measuring transducer 10 orwhose excitation arrangement, an internal power supply circuit VS for providing one or more internal operating voltages and / or the aforementioned transmitting and receiving circuit COM serving for communication with the aforementioned higher-level (measurement) data processing system or the aforementioned external field bus, are each arranged on one or more separate printed circuit boards and / or are each formed by means of one or more separate microprocessors.

[0083] As from the Fig. 2 or 3, the aforementioned transmitting and receiving circuit COM can, for example, also be provided for the output (xm) of measured values (X m ), for example determined internally by the aforementioned measuring and control circuit DSV, measuring system. Accordingly, the transmitting and receiving circuit COM can also be configured to convert received measured values XM into an output signal xm providing the same measured values XM, for example, conforming to 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).For the on-site visualization of measured values (XM ) and / or status messages generated internally by the measuring system, such as an error message or an alarm, the measuring system can further comprise a display and operating element HMI that communicates at least temporarily with the measuring system electronics 20, such as an LCD, OLED or TFT display placed in the aforementioned electronics housing 200 behind a window provided therein, as well as a corresponding input keyboard and / or a touchscreen.

[0084] 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 stored persistently, for example, in one or more non-volatile data memories (EEPROMs) of the measuring system electronics 20, which digital data can be retained even without an applied operating voltage, and can be loaded when the same is started into a volatile data memory (RAM) provided in the measuring system electronics 20 or the aforementioned measuring and evaluation circuit DSV, for example, integrated in the microprocessor. The oscillation signals s1, s2 are intended for processing in the microprocessor orin the digital signal processor by means of corresponding analog-to-digital converters (A / D), of course first to be converted into corresponding digital signals, for example by digitizing the respective signal voltage of each of the - here electrical - oscillation signals s1, s2 in a suitable manner, cf. for example the US-B 63 11 136 mentioned at the beginning. Accordingly, in the measuring system electronics 20, for example in the aforementioned measuring and evaluation circuit DSV, corresponding analog-to-digital converters for the oscillation signals s1, s2 and / or at least one non-volatile electronic data memory EEPROM can be provided, which is set up to hold digital data, for example even without an applied operating voltage.

[0085] According to a further embodiment of the invention, the measuring system further comprises a support frame 100, in particular a support frame which is rigid and / or torsion-resistant, wherein - as in Fig. 1 , 2or 3 schematically shown - namely support frame 100 and the pipe arrangement are fastened to one another, for example materially or - as shown in, among other things, the aforementioned WO-A 2019 / 017891 - also detachably. To protect the measuring transducer or its components from harmful environmental influences, to avoid unwanted sound emissions from the vibrating pipes or to collect medium escaping from a leaking pipe arrangement, as is quite common in vibronic measuring systems of the type in question, the aforementioned support frame 100 can also be designed as a transducer protective housing enclosing the pipe arrangement together with the excitation and sensor arrangement, for example also in such a way that the transducer protective housing is metallic and / or has a compressive strength that is greater than a maximum compressive strength of at least one pipe of the pipe arrangement and / or that is more than 50 bar.The excitation arrangement and / or the sensor arrangement can also be partially mounted on the support frame or on the converter's protective housing. In the aforementioned case where the measuring system electronics 20 is housed within an electronics protective housing 200, the latter can be mounted on a support frame, as shown in FIG. Fig. 1 , 2 and 3 each shown schematically or readily apparent from their combination and, as is quite usual with measuring systems of the type in question, for example, also be attached to the aforementioned support frame or to the outside of the protective housing of the measuring transducer.

[0086] The at least one tube of the tube arrangement can be straight at least in sections, in particular hollow-cylindrical, and / or curved at least in sections, 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 as a result has a tube shape lying in a single (tube) plane. As in Fig. 2 As indicated, the at least one pipe extends from a first pipe end to a second pipe end with a pipe length corresponding to a length of an imaginary center line of the pipe, for example more than 100 mm, and the pipe has a lumen enclosed by a pipe wall and extending from the first pipe end to the second pipe end. According to a further embodiment of the invention, the pipe length of the pipe is more than 200 mm, for example more than 500 mm, and / or less than 2000 mm, for example less than 1500 mm. In the case of a pipe that is curved at least in sections, the aforementioned pipe length corresponds to a stretched or unwound length of the pipe and the pipe can be manufactured by bending a tubular semi-finished product. According to a further embodiment of the invention, the pipe wall of the at least one pipe consists of a metal, for example namely a steel, in particular.a stainless steel, duplex steel or super duplex steel, a titanium alloy and / or a zirconium alloy, in particular a Zircaloy, and / or a tantalum alloy and / or a nickel-based alloy. In addition, the at least one tube of the tube arrangement can be formed in one piece, for example in such a way that the tube is seamless or (at least in the case of a tube wall made of metal) with a single welded seam. According to a further embodiment of the invention, the at least one tube of the tube arrangement has a caliber (inner tube diameter) that is more than 0.1 mm, for example even more 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 even more than 1.5 mm, in particular in such a way 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 of more than 0.08, in particular more than 0.1, and / or less than 0.25, in particular less than 0.2. The at least one tube or each of the tubes of the tube arrangement can also assume any other of the geometric shapes and / or dimensions customary in conventional (standard) vibronic measuring systems, for example, 1 mm, 2 mm, 5 mm, 10 mm, 15 mm, or even more, and / or be made of other materials customary for this purpose.

[0087] According to a further embodiment of the invention, the tube arrangement of the measuring transducer 10 - as in Fig. 3 schematically shown - at least one second tube 112. The tube 112 can be curved at least in sections and / or straight at least in sections. In addition, the tube 112 - as in Fig. 3 indicated - for example, also be constructed identically to tube 111 and / or arranged at least partially parallel to tube 111. Tube 112 extends, like tube 111, from a first tube end to a second tube end with a tube length and, like tube 111, has a lumen enclosed by a, for example, metallic, tube wall and extending from the first tube end to the second tube end. In addition, tube 112 is also designed to be flowed through by the measuring medium or a partial volume thereof, at least in a flow direction pointing from the first tube end to the second tube end, in particular simultaneously with the first tube, and to be caused to vibrate during this flow. In addition, the tube arrangement can further comprise a first flow divider 21, which serves here, for example, as a line branch and / or is on the inlet side, with at least two flow openings and a,for example, the aforementioned flow divider 21 can have a second flow divider 22 which is structurally identical and / or serves as a line connection and / or is on the outlet side and also has at least two flow openings, and each of the tubes 111, 112 of the tube arrangement can then be connected to each of the first and second flow dividers to form two fluidically parallel flow channels, for example in such a way that the first end of the tube 111 opens into a first flow opening 21a of the flow divider 21 and the second end of the tube opens into a first flow opening 22a of the flow divider 22, and that the first end of the tube 112 opens into a second flow opening 21b of the flow divider 21 and the second end of the tube opens into a second flow opening 22b of the flow divider 22. The length of the tube 111 can, for example, be equal to the length of the tube 112. Furthermore, the pipe arrangement can include additional pipes,for example, namely two further tubes, thus, as shown, among other things, 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 tubes. Accordingly, both the flow divider 21 and the flow divider 22 can each have, in particular exactly, four flow openings, and each of the tubes of the tube arrangement can be connected to each of the flow dividers 21, 22 to form four fluidically parallel flow paths. For the aforementioned case in which the tube arrangement has four tubes, the tubes can, for example, also be designed such that they are only structurally identical in pairs, for example the tube lengths are only selected to be the same in pairs. In addition, in the case described above that the pipe arrangement comprises two or more pipes,the wall of each of the tubes - as is quite common with tube arrangements of the type in question or with measuring transducers or measuring systems formed thereby - may, for example, be made of the same material; this may, for example, also be such 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 or each of the other tubes 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 or each of the other tubes.

[0088] The pipe arrangement or the measuring transducer MW formed thereby is, as already indicated, specifically intended to be connected to the aforementioned process line via an inlet end 10+ of the pipe arrangement or the measuring transducer MW, for example, enclosed by a first connecting flange, and a corresponding outlet end 10#, for example, enclosed by a second connecting flange, and to be flowed through by the medium FL during operation. A sealing surface can also be formed on each of the aforementioned connecting flanges.In the aforementioned case that the pipe arrangement has 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 can have the aforementioned second connection flange. In addition, the at least one pipe of the pipe arrangement is further configured to carry the measured substance FL or a partial volume thereof in its lumen and to be vibrated during this process, for example, namely - in particularForced mechanical oscillations, which cause a measuring effect corresponding to the at least one measured variable and / or are excited by the excitation arrangement, in order to execute a corresponding static rest position; this is done in particular by vibrating the at least one tube of the tube arrangement and, during this time, flowing medium from its first tube end towards its second tube end (flow direction). The aforementioned forced mechanical oscillations can, as is quite common with measuring transducers of the type in question, be at least partially forced bending oscillations of the at least one tube about an imaginary oscillation axis of the tube arrangement, for example an oscillation axis imaginarily connecting the first and second tube ends.

[0089] The aforementioned excitation arrangement of the measuring transducer 10 is in turn particularly intended or arranged to convert electrical power fed thereto (from the measuring system electronics 20) into mechanical power in such a way that - as in Fig. 4a indicated or also from a summary of the Fig. 2 and 4aimmediately apparent - the at least one pipe 111 of the pipe arrangement and / or each of its pipes carries out at least temporarily forced mechanical oscillations about a respective static rest position, while the sensor arrangement is provided or set up to detect mechanical oscillations of the pipe arrangement, not least mechanical oscillations and / or bending oscillations of the at least one pipe forced by the excitation arrangement, and to provide a first oscillation signal s1 and a second oscillation signal s2, of which - for example electrical - oscillation signals s1, s2 each at least partially represents oscillatory movements of one or more of the pipes of the pipe arrangement, for example in each case by means of a respective variable electrical voltage corresponding to oscillatory movements (X s1 , X s2 ) of the at least one pipe.

[0090] The excitation arrangement of the measuring system has a vibration exciter 31, for example an electrodynamic one, which is mechanically connected to the at least one tube and is also designed 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 the Fig. 2 and 4aimmediately apparent - a time-varying drive force F exc1 acts on the pipe at a drive point formed by the same vibration exciter 31 on the pipe mechanically connected thereto. An imaginary circumferential line of the pipe passing through the aforementioned drive point encloses a cross-sectional area of the pipe, which is also referred to below as the drive cross-sectional area of the pipe. The measuring system electronics 20, in turn, is accordingly also designed, among other things, to energize the vibration exciter 31, namely to feed electrical power into the vibration exciter 31 by means of an electrical drive signal e1 having a time-varying electrical current, such that the at least one pipe executes forced mechanical vibrations, for example bending vibrations, at one or more vibration frequencies predetermined by the drive signal e1.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 drive force F exc1 runs 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 a voice coil, for example, having an air coil and an armature, or the vibration exciter 31 has a magnetic armature, for example, formed by a permanent magnet, and a coil through which the magnetic field of the armature flows, for example, namely an air coil. The magnetic armature can, for example, be mechanically connected to the at least one tube 111 to form the drive point, and / or the coil can, for example, be electrically connected to the measuring system electronics 20.According to a further embodiment of the invention, it is further provided that the exciter arrangement, as is also usual, for example, in conventional (standard) vibronic measuring systems, has no further vibration exciter connected to the tube 111 apart from the vibration exciter 31. For the aforementioned case in which the tube arrangement has at least two tubes, the vibration exciter 31 can also be correspondingly configured to simultaneously convert electrical power fed in by means of the electrical drive signal e1 into forced mechanical vibrations of the first and second tubes 111, 112; this in particular in such a way that the vibration exciter 31 acts differentially on the two tubes 111, 112, namely can and does introduce only opposing excitation forces into the two tubes 111, 112, for example in such a way that the first and second tubes 111, 112 simultaneously have the same, yet opposite, frequency, in particularnamely, execute counter-symmetrical, forced mechanical vibrations. The vibration exciter 31 can accordingly, for example, be mechanically connected to both the tube 111 and the tube 112, for example, in such a way that the aforementioned drive force acts on both the tube 111 and the tube 112. In addition, the vibration exciter 31 can also be configured to convert electrical power into mechanical power using a time-varying electrical current such that a time-varying drive force acts on the second tube at a drive point formed by the vibration exciter 31 on the second tube 112 mechanically connected thereto, for example, simultaneously and / or oppositely to the drive force acting on the tube 111 at the drive point formed by the vibration exciter 31 on the second tube 111 mechanically connected thereto.For the aforementioned case that 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 drive signal e1, namely carries its current.

[0091] The sensor arrangement of the measuring system, in turn, has - as in Fig. 2 schematically shown - a first vibration sensor 41, in particular an electrodynamic or optical one, and a second vibration sensor 42, in particular an electrodynamic or optical one. Each of the vibration sensors 41, 42, which may also be of identical construction, is positioned on the pipe, in particular at least partially mechanically connected to the pipe, and is also configured to detect vibrational movements (Xs1; Xs2) of the at least one pipe (pointwise) and to convert them into a first vibration signal s1, for example an electrical or optical one, and a second vibration signal s2 representing the same vibrational movements; this is done in particular in such a way that each of the first and second vibration signals (s1, s2) each contains one or more sinusoidal signal components, each with a frequency corresponding to an vibration frequency of vibrational movements of the pipe.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 by more than 10 mm and / or more than one fifth of the pipe length and / or the same distance; this in particular in such a way that the vibration sensors 41, 42 are positioned on the pipe at a distance from one another in the direction of flow, as is usual with conventional vibronic (standard) measuring systems. According to a further embodiment of the invention, each of the first and second vibration sensors 41, 42 is each formed by a moving coil, for example having an air coil and an armature. For the aforementioned case in which 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 bynamely, be mechanically connected both proportionally to the first pipe and proportionally to the second pipe, 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 pipe and the second pipe, in particular differentially, and to convert them into the first or second vibration signal, such that each of the vibration signals, in particular opposing vibration movements, represents the first and second pipes 111, 112 (. Fig. 3 ); this also applies in particular to the aforementioned case in which the vibration sensors 41, 42 are each electrodynamic vibration sensors constructed in the manner of a moving coil. For the aforementioned case in which the pipe arrangement has two pipes, according to a further embodiment of the invention, each of the first and second vibration sensors is positioned on both the first pipe and the second pipe, for example, namely, it is mechanically connected both partially to the first pipe and partially to the second pipe. In addition, each of the first and second vibration sensors is configured to detect vibrational movements, for example, namely, opposing vibrational movements, of both the first pipe and the second pipe and to convert them into the respective first or second vibration signal, such that each of the first and second vibration signals represents vibrational movements of the first and second pipes.The vibration sensors can be designed in particular in such a way that vibration movements, not least also opposing vibration movements of the pipes, are detected differentially and / or that each of the first and second vibration signals represents opposing vibration movements of the first and second pipes.

[0092] The at least one tube 111 or the tube arrangement formed thereby naturally contains a plurality of vibration modes (natural vibration shapes), each having an associated (modal) damping (D1, D2,..., Dx) as well as an associated resonance frequency (f1, f2, ..., fx) determined thereby, in which the at least one tube 111 can execute or executes vibration movements having one or more vibration nodes (SB) and two or more vibration nodes (SK), such that the number of vibration nodes is exactly one greater than the number of associated vibration nodes. Vibration movements of the at least one tube 111 in a fundamental vibration mode, namely a first-order vibration mode (f1 mode), for example a first-order bending vibration mode, have - as also in Fig. 5 indicated - exactly one vibration antinode and accordingly two vibration nodes (f1 mode: 1SB, 2SK), while vibration movements of the tube 111 in a higher vibration mode (deviating from the fundamental vibration mode), namely a vibration mode of the second or higher order (f2 mode, f3 mode, f4 mode, ... fx mode), for example namely a bending vibration mode of the second, third, fourth or higher order, accordingly have two or more vibration antinodes and correspondingly three or more vibration 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, 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 ). For the aforementioned case that the tube arrangement comprises two or more tubes, the tube arrangement can, as is quite common with conventional vibronic (standard) measuring systems, also comprise coupler elements which are useful for adjusting the vibration properties of the tube arrangement, not least for tuning one or more of the aforementioned resonance frequencies; this in particular in such a way that, as also in Fig. 3 As indicated, a first coupler element 23, for example plate-shaped, is mechanically connected to each of the tubes and 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 structurally identical to the coupler element 23, is mechanically connected to each of the tubes and positioned further away from the flow divider 21 than from the flow divider 22. According to a further embodiment of the invention, the tube arrangement is further designed such that the resonance frequency f2 of the second-order oscillation mode (f2 mode), in particular the second-order flexural oscillation mode, deviates from the resonance frequency f1 of the fundamental oscillation mode (f1 mode), in particular the first-order flexural oscillation mode, nominally, namely with the original or intact transducer, by more than 10% of the resonance frequency f1 and / or by more than 100 Hz.

[0093] In the measuring system according to the invention, the vibration exciter 31 is positioned and aligned so that - as in Fig. 4a or 6 and is also quite common in conventional vibronic (standard) measuring systems - a drive offset ΔE, namely a smallest 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 not more than 3°mm and / or less than 0.5% of the tube length, wherein the reference cross-sectional area is in turn selected or determined in such a way, for example, namely with an intact or original measuring transducer, that a vibration node of the said vibration movements formed between two vibration antinodes of vibration movements of the at least one tube in a higher vibration mode, for example, namely the second order vibration mode, and / or located (nominally) at half the tube length, lies within the reference cross-sectional area.The drive offset ΔE thus practically also corresponds to a distance between a center of gravity (center point) of the drive cross-sectional area of the tube and a center of gravity (center point) of the reference cross-sectional area of the at least one tube. The drive offset ΔE can, for example, result from a manufacturing tolerance in the manufacture of the exciter arrangement, not least from tolerances in the positioning of the vibration exciter on the at least one tube and / or from tolerances in the positioning of the tube arrangement within a transducer protective housing, and / or from a manufacturing tolerance in the manufacture of the tube arrangement, not least also in the manufacture of the at least one tube. Furthermore, the drive offset ΔE can also be subject to change over time, for example due to asymmetric or uneven changes in the mechanical properties of the tube arrangement caused by wear.According to a further embodiment of the invention, the reference cross-sectional area of the at least one tube is further selected such that a principal axis of inertia of the same tube, perpendicular to the aforementioned drive force, and / or a line of intersection between two mutually orthogonal symmetry planes of the same 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, thus with an intact or original measuring transducer and as is also quite common in conventional vibronic (standard) measuring systems—is only slightly greater than zero, namely less than 2 mm, for example even less than 1 mm, and / or less than 0.2% of the tube length.For the aforementioned case that the at least one pipe is curved at least in sections, for example namely at least in sections in the shape of a circular arc and / or essentially V-shaped, the at least one pipe 111 can also be designed and the aforementioned reference cross-sectional area can be selected such that exactly one main axis of inertia of the at least one pipe lies within the reference cross-sectional area of the same pipe. For the other case, that the at least one pipe is straight over the entire pipe length, the aforementioned reference cross-sectional area can in turn be selected such 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 an area between the two oscillation antinodes of the oscillation movements of the at least one pipe in the aforementioned second-order oscillation mode, in particularnamely the second-order bending vibration mode, formed vibration nodes of said vibration movements and / or a principal axis of inertia of the at least one tube perpendicular to the direction of vibration of the vibration movements of the tube in said second-order vibration mode lies within the reference cross-sectional area of the at least one tube.

[0094] The measuring system electronics 20 of the measuring system according to the invention is furthermore particularly designed to feed in the driver signal e1 with a sinusoidal first (useful) current component eN1 having a first (alternating current) frequency f eN1 and a, for example, predetermined and / or variable, first (current) amplitude, at least temporarily, for example during normal measuring operation or during a measuring interval, in order to thereby generate first useful oscillations in the manner described above, namely by the oscillation exciters or oscillators (energized with the useful current component eN1).to excite a thus generated first driving force (component) F exc1 forced mechanical vibrations of the at least one pipe with a first useful frequency f N1, namely a (vibration) frequency corresponding to the (alternating current) frequency f eN1 (f N1 = f eN1 ), and as a result to provide the vibration signals s1, s2 each with a first useful signal component s1N1, s2N1, namely a sinusoidal signal component with a (signal) frequency f s1N1 or f s2N1 (f s1N1 = f s2N1 = f N1 ) corresponding to the first useful frequency f N1.In addition, the measuring system electronics 20 of the measuring system according to the invention is also designed to feed the drive signal e1 with a second (AC) frequency f eN2 and a, for example, predetermined and / or variable, second (current) amplitude, sinusoidal second (useful) current component eN2 to the vibration exciter 31 for generating second useful oscillations, namely mechanical oscillations of the pipe forced by the (energized) oscillation exciter 31 or a second driving force (component) F exc2 generated thereby, with a second useful frequency f eN2 , namely a (oscillation) frequency corresponding to the (AC) frequency f eN2 (f N2 = f eN2 ), for example also simultaneously with the (useful) current component eN1, in order to thereby generate second useful oscillations, namely by the (with the (useful) current component eN2 energized) vibration exciter orto excite a thus generated second driving force (component) F exc2 forced mechanical vibrations of the at least one pipe with a second useful frequency f N2, namely a (vibration) frequency corresponding to the (alternating current) frequency f eN1 (f N1 = f eN1 ), and as a result to provide the vibration signals s1, s2 each with a second useful signal component s1N2, s2N2, namely a sinusoidal signal component with a (signal) frequency f s1N2 or f s2N2 (f s1N2 = f s2N2 = f N2 ) corresponding to the second useful frequency f N2. 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 formed, for example, by one or more phase locked loops (PLL) serving to determine a resonance frequency or to set the currently required (AC) frequency.In addition, the measuring system electronics 20 can further be configured to set a capture range of a phase-locked loop (PLL2) adjusting the second (AC) frequency based on the first (AC) frequency f eN1 or by means of at least one output signal of a phase-locked loop (PLL1) adjusting the same (AC) frequency f eN1, for example, namely an output signal of a loop filter of the same phase-locked loop (PLL1).Furthermore, the measuring system electronics 20 can advantageously also be configured to feed the first and second (useful) current components at least temporarily simultaneously into the vibration exciter 31, for example for a time interval lasting no less than two oscillation periods of the first (useful) current component and / or more than 10 ms (milliseconds); this, for example, in such a way that the measuring system electronics (20) is configured to switch on or off the (useful) current component e1N2 while the (useful) current component eN1 is being fed in.to switch off the (useful) current component e1N2 again after a time interval lasting not less than two oscillation periods of the (useful) current component e1N1 and / or more than 1 s, and / or also in such a way that the first (current) amplitude of the (useful) current component e1N1 is not set smaller than the second (current) amplitude of the (useful) current component e1N2 and / or that the second (current) amplitude is at least temporarily set to more than 40%, for example not less than 50%, of the first (current) amplitude.

[0095] The measuring system electronics 20 of the measuring system according to the invention is further configured to adjust the (AC) frequencies f eN1 , f eN2 such that the (AC) frequencies f eN1 deviate from a resonance frequency f 2n+1 (n=0; 1; 2;... → f1; f3; ..) of a symmetrical oscillation mode, thus an odd-order oscillation mode, in particular the aforementioned fundamental oscillation mode (f1 mode), by less than 1% of the same resonance frequency f 2n+1 and / or by less than 1 Hz, and that the (AC) frequencies f eN2 deviate from a resonance frequency f 2n+2 (n=0; 1; 2;... → f2; f4; ..) of an antisymmetrical oscillation mode, thus an even-order oscillation mode, in particularnamely the aforementioned second-order oscillation mode (f2 mode), by less than 1% of the same resonance frequency f 2n+2 (f2; f4) and / or by less than 1 Hz; this, for example, in such a way that the (alternating current) frequency f eN1 corresponds to the resonance frequency f 2n+1 of the excited oscillation mode of odd order and / or the (alternating current) frequency f eN2 corresponds to the resonance frequency f 2n+2 of the excited oscillation mode of even order and / or in such a way that the first useful oscillations are suitable for causing Coriolis forces F c in a medium flowing through the at least one pipe with a mass flow other than zero and the useful signal components s1N1, s2N1 each have a phase angle which is dependent on the mass flow ora change in the mass flow with a change in a (measurement) phase difference Δφ12, namely a change in a difference between the phase angle of the useful signal component s1N1 and a phase angle of the useful signal component s2N1, and / or in such a way that the drive signal e1, and thus the oscillation signals s1, s2, follow a change in the density of the medium conveyed in the pipe arrangement, each with a change in the (alternating current) frequency f eN1, f eN2 of at least one of the useful current components eN1, eN2 or the (signal) frequency of the respective useful signal components. The aforementioned resonance frequency f 2n+1, and thus the (alternating current) frequency f eN1, corresponds to an associated first modal damping D1, namely a damping of the (excited) oscillation mode of odd order or of the first useful oscillations ordepends on it and the resonance frequency f 2n+2 , thus the (alternating current) frequency f eN2 corresponds to an associated second modal damping D2, namely a damping of the (excited) oscillation mode of even order or the second useful oscillations corresponds to or depends on it. The (alternating current) frequency f eN1 of the useful current components eN1, thus the first useful frequency f N1 can, for example, correspond to a resonant frequency of the tube arrangement that is measurably dependent on the density of the medium FL carried in the tube arrangement - for example, namely a lowest resonant frequency of the tube 111 or the resonant frequency f1 of the fundamental oscillation mode (f1 mode) - and the aforementioned (alternating current) frequency f eN2 of the useful current components eN2, thus the second useful frequency f N2 can, for example, correspond to the resonant frequency f2 of the second-order oscillation mode (f2 mode).Accordingly, according to a further embodiment of the invention, the measuring system electronics 20 is further configured to set the (AC) frequency f eN1 such that this or the useful frequency f N1 deviates from the resonance frequency f1 of the fundamental oscillation 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) or corresponds to the resonance frequency f1 of the fundamental oscillation mode (f1 mode), and that as a result the oscillation movements of the first useful oscillations correspond to those of the fundamental oscillation mode (f1 mode) of the at least one tube 111. Alternatively, the measuring system electronics can, for example, also be configured to set the first (AC) frequency f eN1 such that the same (AC) frequency f eN1 orthe useful frequency f N1 deviates 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), for example corresponding to the resonance frequency f3 of the third-order vibration mode (f3 mode), or that as a result the vibration movements of the first useful vibrations correspond to those of the third-order vibration mode (f3 mode) of the at least one tube 111. According to a further embodiment of the invention, the measuring system electronics 20 is additionally configured to set the (alternating current) frequency f eN2 such that the same (alternating current) frequency f eN2 or the useful frequency f N2 deviates from the resonance frequency f2 of the second-order oscillation mode (f2 mode) by less than 1% of the same resonance frequency f2 (| f2 - f N2 | < 0.01 f1) and / or by less than 1 Hz (| f2 - f N2 | < 1 Hz).the same resonance frequency f2, and that as a result the oscillation movements of the second useful oscillations correspond to those of the second order oscillation mode (f2 mode) of the at least one tube 111.

[0096] The aforementioned (system) parameters, in particular the resonance frequencies (f 2n+1 , f 2n+2 ) as well as the respective associated (modal) dampings can be directly determined during operation by means of the measuring system electronics 20, for example, namely calculated based on the vibration signals s1, s2 and / or the driver signal e1, and stored in the form of corresponding digital measurement data for further calculations, for example to be carried out in the measuring system electronics.Accordingly, according to a further embodiment of the invention, the measuring system electronics is further configured, for example, also for the purpose of determining viscosity measurement values X η representing the viscosity of the medium and / or density measurement values X ρ representing the density of the medium, based on the first useful signal component (s1N1; s2N1) of at least one of the oscillation signals (s1, s2) and / or the (useful) current component eN1 of the driver signal e1, to determine at least one, for example digital, first quality value XD1 and based on the second useful signal component (s1N2; s2N2) of at least one of the oscillation signals s1, s2 and / or the (useful) current component eN2 of the driver signal e1, to determine at least one, for example digital, second quality value XD2, such that the quality value XD1 depends on the (modal) damping D1 and the quality value XD2 depends on the (modal) damping D2 orthat the quality value XD1 represents a measure of the modal damping D1, for example, namely a quality (1 / D1) of the first useful oscillations or a damping degree of the first useful oscillations, and the quality value XD2 represents a measure of the (modal) damping D2, for example, namely a quality (1 / D2) of the second useful oscillations or a damping degree of the second useful oscillations, in particular quantifies it. The (modal) qualities or dampings can, as is known, be readily determined during operation of the measuring system based on a speed of the respective (modal) oscillatory movements and a useful current component of the drive signal e1 driving them, and can be represented, for example, in the form of corresponding digital measured values.For this purpose, the measuring system electronics 20 can further advantageously also be set up, on the basis of at least one of the vibration signals (s1, s2), to determine a (digital) first speed value which represents a first vibration speed, namely a speed of the vibration movements of the at least one pipe carrying out the first useful vibrations, at least one (digital) second speed value which represents a second vibration speed, namely a speed of the vibration movements of the at least one pipe carrying out the second useful vibrations, at least one the (useful) current component eN1, in particularto determine a (digital) first current measured value representing a (current) amplitude of the (useful) current component eN1 or an effective value of the (useful) current component eN1 and / or at least one (digital) second current measured value representing the (useful) current component eN2, for example an amplitude of the (useful) current component eN2 or an effective value of the (useful) current component eN2, for example also to store it in the aforementioned non-volatile data memory EEPROM. Furthermore, the measuring system electronics can also be configured to use at least one of the oscillation signals (s1, s2) and / or the drive signal e1 to determine at least one (digital) first frequency measured value X f1 representing the useful frequency fN1 or the resonance frequency f1, as well as at least one (digital) second frequency measured value X f1 representing the useful frequency fN2 or the resonance frequency f1.to determine the (digital) second frequency measured value X f2 representing the resonant frequency f2 and to keep it available for further calculations in the measuring system electronics, for example, also to store it in the EEPROM data memory; this also applies, for example, to calculate density measured values X ρ representing the density ρ of the medium based on such frequency values, for example according to a corresponding resonant frequency-to-density measured value characteristic function of the measuring system electronics. Alternatively or additionally, the measuring system electronics 20 can also be provided orbe configured to generate viscosity measurement values Xη, namely measurement values representing the viscosity η of the medium FL, based on at least one of the vibration signals s1, s2, and / or the driver signal e1, for example also based on the aforementioned first and / or second quality values (XD1, XD2), for example according to a damping(s)-to-viscosity measurement value characteristic function of the measuring system electronics. The processing of the vibration signals s1, s2, and possibly also a control of the aforementioned driver circuit(s) Exc, which is quite common in such measuring systems, can - as in . Fig. 2 or 3, respectively, can be carried out, for example, using the aforementioned measuring and evaluation circuit DSV. To further improve the accuracy with which the measured values XM are ultimately determined, the measuring transducer can be used, as in Fig. 2 or 3, respectively, are each shown schematically and, as is quite common with such measuring systems, furthermore also have temperature sensors 71 (71, 72) which are used to record temperatures within the pipe arrangement and to provide one or more corresponding temperature measuring signals θ1 (θ1, θ2), for example each mounted directly on at least one pipe of the pipe arrangement, and / or have strain sensors which are used to record mechanical stresses within the pipe arrangement and to provide one or more corresponding strain measuring signals, for example each mounted directly on one of the pipes of the pipe arrangement, and the measuring system electronics can furthermore be set up to receive and process the temperature or strain measuring signals, in particular to use them in determining the measured values.

[0097] As already indicated, the measuring system electronics 20 is further provided or designed, among other things, to receive and evaluate the vibration signals s1, s2 generated by the measuring transducer 10, in particular to determine and output the measured values XM representing at least one measured variable, wherein, as already mentioned, the first useful signal components s1N1, s2N1 of the vibration signals s1, s2, not least due to the aforementioned drive offset ΔE, can each have additional (interference) phase angles; this in particular in such a way that between the useful signal components s1N1, s2N1, in addition to the respective (measurement) phase difference Δφ12, there is also an error of the same frequency which is determined by one or more material parameters of the measuring material, in particularthe viscosity of the medium, which also determines the aforementioned modal dampings (D1, D2), also exists, but is nevertheless independent of the mass flow, so that the oscillation signals s1, s2 exhibit a non-vanishing systematic phase or zero-point error corresponding to the phase difference between the useful signal components of the two oscillation signals at a mass flow of zero. To minimize the aforementioned phase error, which is also dependent on the first and second (modal) dampings (D1, D2),the resulting (interference) phase difference, the measuring system electronics of the measuring system according to the invention is therefore particularly also set up on the basis of both the first (useful) current component eN1 and / or the first useful signal components s1N1, s2N1, for example namely on the basis of their (signal) frequency and / or on the basis of an amplitude of at least one of the useful signal components s1N1, s2N1 and / or on the basis of a phase angle of at least one of the useful signal components s1N1 ors2N1, as well as the second (useful) current component eN2 and / or at least one of the second useful signal components s1N2, s2N2, to determine the measured values X m representing the at least one flow parameter of the medium, for example namely based on the aforementioned (measurement) phase difference Δφ12 of the first useful signal components s1N1, s2N1 and based on both an amplitude of at least one of the first useful signal components s1N1, s2N1 and an amplitude of at least one of the second useful signal components s1N2, s2N2 and / or based on the first and second useful current components (e1N1, e1N2), in particular namely based on the first and second current amplitudes, the mass flow measured values X m representing the mass flow of the medium. For this purpose, according to a further embodiment of the invention, at least one phase difference to measured value characteristic function, in particulara phase difference to mass flow measured value characteristic function (X m = f{Δφ12, D1, D2}), set up, for example namely programmed, according to which the measuring system electronics can determine the measured values XM representing at least one flow parameter of the medium, in particular the mass flow measured values X m representing the mass flow of the medium, based on the measured phase difference Δφ12 (Δφ12 ∼ fN1·Δφ12*) - if necessary, not least in the case of electrodynamic vibration sensors also normalized to the useful frequency fN1.determined, wherein the aforementioned first and second modal attenuations (D1, D2) are taken into account in the at least one phase difference to (mass flow) measured value characteristic function; this, for example, also in such a way that a product of a second power D1 2< of the first modal attenuation D1 and an inverse 1 / D2 of the second modal attenuation D2 is taken into account in the phase difference to (mass flow) measured value characteristic function and / or in such a way that the phase difference to mass flow measured value characteristic function of a calculation rule: . Xm = k 11 ⋅ Δφ 12 2 π ⋅ fN 1 − k 12 − k 2 D 1 2 D 2 = k 11 ⋅ Δφ 12 * − k 12 − k 2 D 1 2 D 2 corresponds to, or the mass flow measured values X m determined by means of the measuring system electronics satisfy the aforementioned calculation rule. Each of the first and second modal dampings can be determined during operation, in particular numerically calculated or digitally measured, using the measuring system electronics, just like the (mass flow) measured values, based on the respective first or second current amplitude and at least one of the first or second useful signal components, if necessary also in real time.The coefficients k11, k12, and k2 in the calculation specification are each measuring system-specific (calibration) constants that can be determined in advance for the respective measuring system, for example, using computer-based (simulation) calculations and / or laboratory measurements carried out on a few examples of a measuring system series and / or by individually calibrating the respective measuring system under reference conditions, for example, during a (wet) calibration of the respective measuring system at the manufacturer's and / or a (re-)calibration of the measuring system on site.Coefficient k11, which is also implemented in conventional vibronic measuring systems, corresponds to a change in the phase difference of the first useful signal components (s1N1, s2N1) slope of the characteristic function of the aforementioned phase difference to mass flow measured value characteristic function or a (measurement) sensitivity of the measuring system, related to a change in the (reference) mass flow of a calibration fluid carried in the measuring transducer, for example water having a temperature of 25°C, and the coefficient k12, which is also implemented in conventional vibronic measuring systems, corresponds to a (scale) zero point, for example a static zero point, namely a calibration constant corresponding to a (measurement) phase difference determined at a zero (reference) mass flow of the calibration fluid, or a dynamic zero point. The coefficients k11, k12 can, for example, also be chosen in such a way that with just a shortened calculation rule: . Xm * = k 11 ⋅ Δφ 12 2 π ⋅ fN 1 − k 12 For a reference mass flow, the preliminary mass flow measured values Xm* each have a measurement deviation of less than 0.2% of the reference mass flow and / or less than 0.05 kg / h. Alternatively or in addition to water, air, oil, and / or alcohol, e.g., glycerol, can also be used as one of several calibration fluids. Accordingly, the measuring system electronics 20 can also be configured, in particular, to initially determine preliminary mass flow measured values Xm* during operation based on the measured phase difference Δφ12 (or the standardized measured phase difference Δφ12*), but without taking into account the second useful oscillations or the second (useful) signal components, and then to calculate the respective mass flow measured values Xm* accordingly with the currently determined first and second modal dampings (D1, D2), for example, based on a correspondingly modified calculation rule: Xm = X m * − k 2 D 1 2 D 2 .

[0098] The aforementioned preliminary mass flow measurement values Xm* can, for example, also correspond to those obtained in a conventional manner, namely in a manner suitable for conventional measuring systems of the type in question, not least those 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, US-B 63 11 136, WO-A 2009 / 136943, WO-A 2019 / 017891, WO-A 2019 / 081169, WO-A 2019 / 081170, WO-A 87 / 06691, WO-A 96 / 05484, WO-A 96 / 08697, WO-A 97 / 26508 or WO-A 99 / 39164, or can therefore also be easily determined based on the phase difference to mass flow measured value characteristic function already implemented in conventional measuring systems.

[0099] According to a further embodiment of the invention, the measuring system electronics 20 is further configured, based on both the first (useful) current component eN1 and / or the first useful signal components s1N1, s2N1, for example, namely based on their (signal) frequency and / or based on an amplitude of at least one of the useful signal components s1N1, s2N1, as well as the second (useful) current component eN2 and / or at least one of the second useful signal components s1N2, s2N2, for example, namely based on their (signal) frequency and / or based on an amplitude of at least one of the useful signal components s1N2, s2N2, at least one (attenuation) correction value ΔD12, for example, which is useful for taking into account the contributions of the first and second modal attenuations (D1, D2) to the at least one preliminary mass flow measurement value X* m and / or digital, for the (Measurement) phase difference Δφ12 orfor preliminary mass flow measured values (Xm*) determined thereby, in such a way that the (damping) correction value ΔD12 corresponds to the first and second modal dampings (D1, D2) or is a function of the first and second modal dampings (D1, D2), thus the first and second modal dampings (D1, D2) are taken into account in the (damping) correction value ΔD12; this in particular in such a way that an amount of the (damping) correction value increases with increasing modal damping D1 and / or decreases with increasing modal damping D2 and / or the (damping) correction value ΔD12 contains a product of a second power of the inverse of a quality (1 / D1) of the first useful oscillations and a quality (1 / D2) of the second useful oscillations, and / or also in such a way that the at least one (damping) correction value ΔD12 is proportional to a ratio (D1 2< / D2) or a calculation rule: . ΔD 12 = k 2 ⋅ D 1 2 D 2 fulfilled and / or such that the at least one mass flow measured value X m a calculation rule: Xm = k 11 ⋅ Δφ 12 2 π ⋅ fN 1 − k 12 − ΔD 12 fulfilled. It has also surprisingly been shown that the coefficient k2 contained in the aforementioned calculation rules for calculating the mass flow measured value Xm or the (damping) correction value ΔD12 can advantageously also be designed as a calibration constant specific to the measuring transducer type or measuring system series, for example in such a way that the coefficient k2 is determined in advance on the basis of laboratory measurements carried out using one or a few examples of a measuring transducer type or a measuring system series and is reused accordingly in further measuring systems, each formed using a measuring transducer of the same type or belonging to the same (measuring system) series, or is contained in the respective phase difference to mass flow measured value characteristic function of the same measuring system.The (damping) correction value ΔD12 can, for example, also be calculated based on the previously designated quality values XD1, XD2 in the measuring system electronics 20, for example in such a way that the (damping) correction value ΔD12 is formed by means of a product of the quality value XD2 and a second power of the inverse of the quality value XD1 (ΔD12 ∼ 1 / XD1 2< XD2). Alternatively or in addition, the (damping) correction value ΔD12 can also be determined as a function of the second oscillation velocity, a second power of the (current) amplitude of the (useful) current component eN1, a reciprocal of the (current) amplitude of the (useful) current component eN2 and a reciprocal of a second power of the first oscillation velocity, for example using the aforementioned first and second velocity values and the aforementioned first and second current measured values.

[0100] According to a further embodiment, the measuring system electronics are also configured to store the at least one (damping) correction value ΔD12 or also several (damping) correction values determined sequentially, for example, in the aforementioned non-volatile data memory EEPROM and / or in such a way that at least one initially determined (damping) correction value is stored as a measuring system-specific reference value. Since the first and second modal dampings (D1, D2) or the (damping) correction value ΔD12 each correspond to the aforementioned drive offset ΔE or are dependent thereon, the first and second modal dampings (D1, D2) or the (damping) correction value ΔD12 can each also serve as a measure of the drive offset ΔE or can be used to calculate the drive offset ΔE.For example, the (damping) correction value ΔD12 can be determined initially or in advance under the aforementioned reference conditions using calibration fluid, for example by the manufacturer of the measuring system, and stored in the measuring system electronics 20, for example in the aforementioned non-volatile data memory (EEPROM), in order to be used later, for example when commissioning the measuring system and / or during (re-)calibration of the measuring system, as a reference value representing an intact measuring system, which can be compared with one or more (damping) correction values currently determined using calibration fluid. Any, among othersChanges in the measuring transducer resulting from a change in the drive offset ΔE, for example due to overloads such as high (over)temperatures or temperature shocks, excessive pressures or pressure surges in the medium being measured, excessive clamping forces and / or excessive vibration forces exerted on the measuring transducer by the process line, properties of the medium being measured in the measuring transducer that are harmful to at least one pipe, in particular corrosive or abrasive properties, or even material fatigue, can thus be detected at an early stage in the course of a (self-)diagnosis carried out on the measuring system - time-controlled and / or on request - and, if necessary, reported accordingly by the measuring system electronics 20 itself, for example to the aforementioned (measurement) data processing system and / or in the form of a system status or fault message declared as an alarm on site.Accordingly, according to a further embodiment of the invention, the measuring system electronics 20 is further configured to carry out a (self-)diagnosis of the measuring system based on the oscillation signals s1, s2 and / or the driver signal e1, for example, namely based on at least one first useful signal component (s1N1, s2N1) and at least one second useful signal component (s1N2, s2N2) and / or based on the first and second (useful) current components (eN1, eN2) or using the (damping) correction value ΔD12, for example, even when the measuring transducer is integrated into the aforementioned process line on site, namely at a measuring point formed by the measuring transducer or by the measuring system, and / or immediately after the measuring transducer has been inserted into the protective transducer housing, which may also already be mechanically connected to the line system. The aforementioned (self-)diagnosis can be used, for example, during commissioning of the measuring system orthe measuring point thus formed, in the course of a (re-)calibration and / or intermittently during (normal) measuring operation. For example, a (modal) damping D2 that increases too quickly and / or continuously over time while the (modal) damping D1 remains essentially constant or decreases and / or a ratio D1 / D2 (D1 / D2 ∼ XD2 / XD1 = ΔD12 / XD1) of the first and second (modal) dampings (D1, D2) or of the (damping) correction value ΔD12 that changes significantly over time, for example constantly increasing or decreasing, while the material parameters of the medium (density ρ, viscosity η, pressure, temperature,...) remain essentially the same can serve as an indicator for the presence of a fault in the measuring transducer and / or aA significantly scattered (damping) correction value ΔD12 serves as an indicator for the presence of a disturbance caused by the medium itself, for example, by foreign matter or bubbles entrained in the medium. The (parameter) measured values determined for one or more of the aforementioned (system) parameters, in particular the resonance frequencies (f 2n+1 , f 2n+2 ) of the at least one pipe and the associated (modal) damping, for example, the quality values (XD1, XD2) representing the (modal) damping (D1, D2) or the (damping) correction values ΔD12, 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 respectively determined first and second quality values and / or the (damping) correction values ΔD12.The determined degree of dispersion can also be used for (self-)diagnosis, for example, in such a way that a (mechanical) fault in the measuring transducer can only be concluded if the respective (system) parameter has a low degree of dispersion, namely below a correspondingly predetermined threshold value, and / or that a (system) parameter having a degree of dispersion above a correspondingly predetermined threshold value does not trigger such a fault message, even if a comparison of its parameter values with the respective reference value would initially indicate this. In addition, a (system) parameter having a degree of dispersion above a correspondingly predetermined threshold value can serve as an indicator for strongly fluctuating material parameters, for example due to foreign substances and / or bubbles in the medium. The degree of dispersion determined in each case using the measuring system electronics 20 can, if necessary,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 can also be used to repeatedly determine a change over time, for example a change trend and / or a change rate and / or a change speed, of the respective (system) parameter. The determined change over time can also be used for (self-)diagnosis, for example in such a way that when the attenuation D2 decreases or when the (attenuation) correction values ΔD12 change at a rate of change within a predetermined measuring range, an increasing fault in the measuring transducer is determined and / or a message representing an increase in a fault, in particular declared as a (fault) alarm, is output.The temporal change or rate of change or speed 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. Accordingly, the measuring system electronics 20 can further be configured to provide at least one currently determined (damping) correction value ΔD12 and / or at least one current rate of change (Δ / Δt) or-speed (d / dt) of the (damping) correction value ΔD12 and / or at least one parameter value representing a current (temporal) dispersion of the (damping) correction value ΔD12 with one or more threshold values predetermined for this purpose, for example calculated on the basis of one or more initially determined (damping) correction values, of which at least one represents a measuring transducer lying outside a specification and / or an impermissibly large drive offset ΔE. Alternatively or additionally, the measuring system electronics 20 can also be configured to use at least one of the oscillation signals s1, s2 and / or the driver signal e1, for example also using the (damping) correction value. ΔD12,to determine the extent of the drive offset ΔE at least qualitatively and / or to carry out a check of the measuring system, for example in the course of a self-diagnosis on site.

[0101] The aforementioned (self-)diagnosis of the measuring system can, for example, be carried out during a test interval reserved for this purpose, for example, one that can also be occasionally repeated 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 each, but can nevertheless be started repeatedly, for example by command from outside the measuring system and / or automatically, namely time- and / or event-controlled by the measuring system electronics itself. For example, the measuring system electronics can be configured to start the test interval when the medium FL is detected as flowing at a steady state and / or to end it when the medium FL is flowing at an unsteady state or when measuring conditions and / or measured variables are changing rapidly.Accordingly, according to a further embodiment of the invention, the measuring system electronics is capable of automatically starting and / or ending the test interval and / or receiving and executing one or more commands that start the test interval. According to a further embodiment of the invention, the measuring system electronics is further configured to start the test interval during normal measuring 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 component eN2; this can also be done, for example, such that the driver signal e1 simultaneously contains the first (useful) current component 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 one another during the test interval.

Claims

1. A vibronic measuring system, in particular a Coriolis mass flow meter or Coriolis mass flow / density meter, - said measuring system, in particular a measuring system configured as an in-line measuring device and / or measuring device with a compact design, being configured to measure at least one flow parameter, that is to say, in particular a mass flow and / or a volume flow and / or a flow velocity, of a flowing fluid measured substance, in particular in a pipeline and / or a hose line, in particular a gas, a liquid or a dispersion; - and said measuring system comprising: • a measuring transducer (10) ∘ with a tube arrangement for conveying the flowing measured substance, ∘ with an exciter arrangement for converting electrical power into mechanical power serving to excite and maintain forced mechanical oscillations of the tube arrangement, ∘ and with a sensor arrangement for registering mechanical oscillations of the tube arrangement and for providing oscillation signals each representing oscillatory movements of the tube arrangement; • and measuring system electronics (20) electrically connected to the measuring transducer, that is to say, in particular both to its exciter arrangement and to its sensor arrangement and / or by means of electrical connecting cables, and formed, in particular, by means of at least one microprocessor and / or arranged in an electronics protective housing, wherein the measuring system electronics (20) are configured to supply the oscillation exciter at least temporarily with an electrical driver signal (e1); - wherein the tube arrangement has at least one tube (111), in particular curved at least in sections and / or straight at least in sections and / or a first tube, • said tube extending from a first tube end to a second tube end with a tube length, in particular more than 100 mm, and having a lumen surrounded by an, in particular metal, tube wall extending from the first tube end to the second tube end, • and said tube being configured to have the measured substance flow through it, at least in a flow direction going from the first tube end to the second tube end, and during that to be caused to oscillate, • and wherein a number of oscillation modes (natural modes) each with an associated (modal) damping (D1, D2, ... , Dx) as well as a (co-)determined associated resonant frequency (f1, f2, ... , fx) are inherent in the tube arrangement, in which the at least one tube can execute or executes (damped) oscillatory movements with in each case one or more antinodes and in each case two or more nodes in such a way ∘ that oscillatory movements of the tube in a basic oscillation mode, that is to say an oscillation mode of the first order (f1-Mode), that is to say, in particular a bending oscillation mode of the first order, have exactly one antinode and two nodes, ∘ and in such a way that oscillatory movements of the tube in a higher-level oscillation mode, that is to say an oscillation mode of the second order or higher (f2-Mode, f3-Mode, f4-Mode, ... fx-Mode), that is to say, in particular a bending oscillation mode of the second order or higher, have two or more antinodes and three or more nodes; - wherein the exciter arrangement has at least one, in particular a single and / or electrodynamic, oscillation exciter (31) • which is mechanically connected to the at least one tube • and is configured to convert electrical power of a time-variable electrical current into mechanical power in such a way that a time-variable driving force acts on the tube at a drive point formed by means of the oscillation exciter on the tube mechanically connected to it, in particular in such a way that an effective line of the driving force runs perpendicular to a normal of a drive cross-sectional area of the tube, • wherein the oscillation exciter (31) is positioned and aligned in such a way that a drive offset (L1E), that is to say a smallest distance between a drive cross-sectional area of the tube enclosed by an imaginary perimeter of the tube leading through the drive point and a specified reference cross-sectional area of the at least one tube, in particular ascertained with an intact measuring transducer or the original measuring transducer, is not more than 3°mm, in particular less than 2 mm, and / or less than 0.5% of the tube length, that is to say, in particular less than 0.2% of the tube length, wherein a node of oscillatory movements formed between two antinodes of said oscillatory movements of the at least one tube in an oscillation mode (of the second order or higher) (different from the oscillation mode of the first order), in particular (nominally) located at a half tube length, is inside the reference cross-sectional area, - wherein the sensor arrangement has an, in particular electrodynamic or optoelectronic, first oscillation sensor • which is positioned on the tube, in particular in the flow direction spaced more than 10 mm and / or more than one fifth of the tube length away from the oscillation exciter, that is to say, in particular is at least partially mechanically connected to the tube, • and which is configured to detect oscillatory movements of the at least one tube and to convert them into an, in particular electrical or optical, first oscillation signal representing said oscillatory movements, in particular in such a way that the first oscillation signal contains one or more sinusoidal signal components each with a frequency corresponding to an oscillation frequency of oscillatory movements of the tube; - and wherein the sensor arrangement has at least an, in particular electrodynamic or optoelectronic, second oscillation sensor • which is positioned on the tube, in particular in the flow direction spaced more than 10 mm and / or more than one fifth of the tube length away from the oscillation exciter and / or away from the first oscillation sensor in the flow direction, that is to say, in particular is at least partially mechanically connected to the tube, • and which is configured to detect oscillatory movements of the at least one tube and to convert them into an, in particular electrical or optical, second oscillation signal representing said oscillatory movements, in particular in such a way that the second oscillation signal contains one or more sinusoidal signal components each with a frequency corresponding to an oscillation frequency of oscillatory movements of the tube; - wherein the measuring system electronics (20) are configured to supply the oscillation exciter (31) with the electrical driver signal (e1) • both at least temporarily with a sinusoidal first (useful) current component (eN1) having a first (alternating current) frequency (feN1) and an, in particular specified and / or changing, first (current) amplitude for initiating first useful oscillations, that is to say mechanical oscillations of the at least one tube forced by the oscillation exciter (supplied with current) with a first useful frequency (fN1), that is to say an (oscillation) frequency corresponding to the first (alternating current) frequency in such a way ∘ that the first (alternating current) frequency (feN1) differs from a resonant frequency (fan+1) of an oscillation mode of an odd order, that is to say, in particular the basic oscillation mode (f1-Mode), by less than 1% of said resonant frequency (fan+1) and / or by less than 1 Hz, that is to say, in particular corresponds to the resonant frequency (f1) of the oscillation mode of an odd order and / or in such a way that the second useful oscillations are suitable for effecting Coriolis forces in a measured substance flowing through the at least one tube with a mass flow that is not zero, wherein the resonant frequency (fan+1) corresponds to an associated first modal damping (D1) of said oscillation mode of an odd order or is dependent thereon, ∘ and that the first and second oscillation signals generated by means of the first and second oscillation sensors have in each case a first useful signal component (s1N1; s2N1), that is to say a sinusoidal signal component with a (signal) frequency corresponding to the first useful frequency (fN1), that is to say, in particular also in each case with a phase angle dependent on the mass flow of the measured substance flowing through the at least one tube, • and also to supply the oscillation exciter (31) at least temporarily with a sinusoidal second (useful) current component (eN2) having a second (alternating current) frequency (feN2) and an, in particular specified and / or changing, second (current) amplitude for initiating second useful oscillations, that is to say mechanical oscillations of the tube forced by the oscillation exciter (supplied with current) with a second useful frequency (fN2), that is to say an (oscillation) frequency corresponding to the second (alternating current) frequency, in particular simultaneously with the first (useful) current component (eN1) in such a way ∘ that the second (alternating current) frequency (feN2) differs from a resonant frequency (fan+2) of an oscillation mode of an even order, that is to say, in particular the oscillation mode of the second order (f2-Mode), by less than 1%, in particular by less than 0.1%, of said resonant frequency (fan+2), and / or by less than 1 Hz, in particular by less than 0.1 Hz, that is to say, in particular corresponds to the resonant frequency (fan+2) of the oscillation mode of an even order, wherein the resonant frequency (fan+2) corresponds to an associated second modal damping (D2) of said oscillation mode of an even order or is dependent thereon, ∘ and that the first and second oscillation signals generated by means of the first and second oscillation sensors have in each case a second useful signal component (s1N2; s2N2), that is to say a sinusoidal signal component with a (signal) frequency corresponding to the second useful frequency (fN2), - and wherein the measuring system electronics (20) are configured, based on both the first useful signal components (s1N1, s2N1), in particular based on a difference between a phase angle of the first useful signal component (s1N1) of the first oscillation signal (s1) and a phase angle of the first useful signal component (s2N1) of the second oscillation signal (s2), and also at least one of the second useful signal components (s1N2, s2N2) and / or the second (useful) current component (eN2), to determine measured values representing the at least one flow parameter of the measured substance, that is to say, in particular mass flow measured values representing the mass flow of the measured substance.

2. The measuring system as claimed in claim 1, wherein the first useful frequency differs from a resonant frequency, f1, of the basic oscillation mode (f1-Mode), that is to say, in particular a bending oscillation mode of the first order, by less than 1% of said resonant frequency, f1, and / or by less than 1 Hz.

3. The measuring system as claimed in claim 1, wherein the first useful frequency differs from a resonant frequency, f3, of an oscillation mode of the third order (f3-Mode) inherent in the at least one tube, that is to say, in particular a bending oscillation mode of the third order, in which oscillation mode the oscillatory movements of the tube have exactly three antinodes and four nodes, by less than 1% of said resonant frequency, f3, and / or by less than 1 Hz, that is to say, in particular corresponds to the resonant frequency, f3.

4. The measuring system as claimed in the preceding claim, wherein a first node of oscillatory movements of the at least one tube is located in the first tube end in the oscillation mode of the third order and a second node of oscillatory movements of the at least one tube is located in the second tube end in the oscillation mode of the third order.

5. The measuring system as claimed in one of the preceding claims, wherein the second useful frequency differs from a resonant frequency, f2, of an oscillation mode of the second order (f2-Mode) inherent in the at least one tube, that is to say, in particular a bending oscillation mode of the second order, in which oscillation mode the oscillatory movements of the tube have exactly two antinodes and three nodes, by less than 1% of said resonant frequency, f2, and / or by less than 1 Hz, that is to say, in particular corresponds to the resonant frequency, f2.

6. The measuring system as claimed in the preceding claim, - wherein a first node of oscillatory movements of the at least one tube is located in the first tube end in the oscillation mode of the second order and a second node of oscillatory movements of the at least one tube is located in the second tube end in the oscillation mode of the second order; and / or - wherein a node of the oscillatory movements formed between the two antinodes of said oscillatory movements of the at least one tube in the oscillation mode of the second order, in particular located at a half tube length, is inside the reference cross-sectional area; - and / or wherein a main axis of inertia of the at least one tube located perpendicular to the direction of oscillation of the oscillatory movements of the tube in the oscillation mode of the second order is inside the reference cross-sectional area of the at least one tube.

7. The measuring system as claimed in one of the preceding claims, - wherein the drive offset (L1E) corresponds to a distance between a centroid of an area (center point) of the drive cross-sectional area of the tube and a centroid of an area (center point) of the reference cross-sectional area of the at least one tube; and / or - wherein an effective line of the driving force runs perpendicular to a normal of a drive cross-sectional area of the tube; and / or - wherein an intersection line between two planes of symmetry which are orthogonal relative to one another of the at least one tube is inside the reference cross-sectional area; and / or - wherein a main axis of inertia of the at least one tube located perpendicular to the driving force is inside the reference cross-sectional area of the at least one tube; and / or - wherein the drive offset (L1E) is the result of a production tolerance when manufacturing the exciter arrangement, that is to say, in particular of tolerances when positioning the oscillation exciter on the at least one tube and / or of tolerances when positioning the tube arrangement inside a transducer protective housing; and / or - wherein the drive offset (L1E) is the result of a production tolerance when manufacturing the tube arrangement, that is to say, in particular when manufacturing the at least one tube.

8. The measuring system as claimed in one of the preceding claims, - wherein the measuring system electronics are configured to supply the second useful current of the driver signal (e1) at least sometimes simultaneously with the first (useful) current component, in particular in such a way that an amplitude of the first (useful) current component is not set to be less than an amplitude of the second (useful) current component and / or in such a way that an amplitude of the second (useful) current component is set to more than 40%, in particular not less than 50%, of an amplitude of the first (useful) current component; and / or - wherein the measuring system electronics (20) are configured to supply the oscillation exciter with the first and second (useful) currents of the driver signal simultaneously, in particular for a time interval lasting not less than two oscillation periods of the first (useful) current component and / or for more than 10 ms; and / or - wherein the measuring system electronics (20) are configured to activate the second (useful) current component while supplying the first (useful) current component, that is to say, in particular to deactivate the second (useful) current component again after a time interval lasting not less than two oscillation periods of the first (useful) current component and / or for more than 1 s; and / or - wherein the measuring system electronics are configured to set the second (alternating current) frequency as a function of the first (alternating current) frequency, in particular in such a way that the second (alternating current) frequency is within a frequency setting interval of which an upper interval limit and / or a lower interval limit and / or a center frequency correspond to a specified multiple of the first (alternating current) frequency, that is to say, in particular correspond to a multiple of the first (alternating current) frequency corresponding to more than 230% of the first (alternating current) frequency and / or less than 300% of the first (alternating current) frequency; and / or - wherein the measuring system electronics (20) are configured, based on the first and second oscillation signals (s1, s2) and / or the driver signal (e1), in particular based on at least a first useful signal component (s1N1, s2N1) and at least a second useful signal component (s1N2, s2N2) and / or based on the first and second (useful) current components (eN1, eN2), to perform a (self-)diagnostics and / or re(calibration of the measuring system, in particular in the case of a measuring transducer incorporated into a pipeline system and / or by means of measuring system electronics electrically connected to the measuring transducer; and / or - wherein the measuring system electronics are configured to follow a change in a density of the measured substance conducted 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 measured 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).

9. The measuring system as claimed in one of the preceding claims, - wherein the measuring system further comprises a support structure (100), in particular metal and / or configured as a transducer protective housing, wherein the support structure and the tube arrangement are secured to one another, in particular in such a way that they can be separated again, and wherein the exciter arrangement, that is to say, in particular the at least one oscillation exciter, and / or the sensor arrangement, that is to say, in particular the first and second oscillation sensors, is / are partially attached to the support structure; and / or - wherein the measuring system further comprises an electronics protective housing (200) for the measuring system electronics (20), in particular secured to a support structure or a transducer protective housing of the measuring transducer and / or metal.

10. The measuring system as claimed in one of the preceding claims, - wherein the measuring system electronics are configured, based on the first useful signal component (s1N1; s2N1) of at least one of the first and second oscillation signals and / or the first (useful) current component (eN1) of the driver signal, to determine at least one, in particular digital, first quality value, wherein the first quality value represents a measure of the first modal damping (D1), that is to say, in particular a quality (1 / D1) of the first useful oscillations or a degree of damping of the first useful oscillations, or is dependent on said first modal damping (D1), and - wherein the measuring system electronics are configured, based on the second useful signal component (s1N2; s2N2) of at least one of the first and second oscillation signals and / or the second (useful) current component (eN1) of the driver signal, to determine at least one, in particular digital, second quality value, wherein the second quality value represents a measure of the second modal damping (D2), that is to say, in particular a quality (1 / D2) of the second useful oscillations or a degree of damping of the second useful oscillations, or is dependent on said second modal damping (D2).

11. The measuring system as claimed in one of the preceding claims, - wherein the measuring system electronics are configured to determine measured values at least provisionally representing the at least one flow parameter of the measured substance, that is to say, in particular mass flow measured values at least provisionally representing the mass flow of the measured substance, based on a measured phase difference, that is to say a difference between a phase angle of the first useful signal component (s1N1) of the first oscillation signal (s1) and a phase angle of the first useful signal component (s2N1) of the second oscillation signal (s2), - and wherein the measuring system electronics are configured, based on the first and second oscillation signals (s1, s2) and / or the driver signal (e1), in particular based on at least a first useful signal component (s1N1, s2N1) and at least a second useful signal component (s1N2, s2N2) and / or based on the first and second (useful) current components (eN1, eN2), to determine at least one, in particular digital, (damping) correction value for the measured phase difference and / or measured values provisionally determined based on said measured phase difference, in particular in such a way that the (damping) correction value corresponds to the first and second modal dampings or is a function of said first and second modal dampings and / or in such a way that the (damping) correction value is subtracted from the measured phase difference and / or measured values provisionally determined based on the measured phase difference.

12. The measuring system as claimed in claims 10 and 11, wherein the measuring system electronics are configured, by means of the first and second quality values, to determine the (damping) correction value, in particular in such a way that the (damping) correction value corresponds to a function of a quality (1 / D2) of the second useful oscillations or a square of a degree of damping of the second useful oscillations as well as a second power of a degree of damping of the first useful oscillations or a square of a quality (1 / D1) of the first useful oscillations.

13. The measuring system as claimed in one of claims 11 to 12, - wherein the (damping) correction value corresponds to the drive offset (L1E), that is to say, in particular is dependent thereon and / or is a measure of the drive offset (L1E); and / or - wherein the (damping) correction value corresponds to the first and second modal dampings or is a function of the first and second modal dampings, in particular in such a way that the (damping) correction value corresponds to a function of a quality (1 / D2) of the second useful oscillations or a square of a degree of damping of the second useful oscillations as well as a second power of a degree of damping of the first useful oscillations or a square of a quality (1 / D1) of the first useful oscillations; and / or - wherein the (damping) correction value corresponds to a function of a product of a quality (1 / D1) of the first useful oscillations and a second power of a quality (1 / D2) of the second useful oscillations or a product of a square of a degree of damping of the first useful oscillations and a second power of a square of a degree of damping of the second useful oscillations; and / or - wherein an amount of the (damping) correction value decreases as the first modal damping (D1) increases and / or increases as the second modal damping (D2) increases; and / or - wherein the (damping) correction value is proportional to a ratio (D12 / D2) of a second power (D12) of the first modal damping (D1) to the second modal damping (D2); and / or - wherein the measuring system electronics are configured to save the (damping) correction value, in particular in a non-volatile memory and / or in such a way that the (damping) correction value is saved as a measuring system-specific reference value and / or is contained in a measuring function of the measuring system, according to which the measuring system converts the at least one flow parameter to be measured into the respective measured values; and / or - wherein the measuring system electronics are configured to compare the (damping) correction value with an initial (damping) correction value determined in advance, in particular under reference conditions and / or during a start-up of the measuring system and / or during a (re)calibration of the measuring system and / or with a different measuring system that is identical in design, in particular saved in the measuring system electronics and / or serving as a reference value; and / or - wherein the measuring system electronics are configured to compare the (damping) correction value with at least one threshold value specified for this, in particular representing a measuring transducer outside a specification and / or an impermissibly large drive offset (L1E); and / or - wherein the measuring system electronics are configured to determine an extent of the drive offset (L1E) and / or to perform a check on the measuring system by means of at least one of the first and second oscillation signals and / or the driver signal, in particular using the (damping) correction value; and / or - wherein the measuring system electronics (20) are configured to perform a (self-)diagnostics and / or (re)calibration of the measuring system using the (damping) correction value, in particular in the case of a measuring transducer incorporated into a pipeline system and / or by means of measuring system electronics electrically connected to the measuring transducer.

14. The measuring system as claimed in one of the preceding claims, - wherein the measuring system electronics (20) are configured to determine, based on at least one of the first and second oscillation signals, a first speed value which represents a first oscillation speed, that is to say a speed of the oscillatory movements of the at least one tube performing the first useful oscillations, in particular to save this in a non-volatile memory; and / or - wherein the measuring system electronics (20) are configured to determine, based on at least one of the first and second oscillation signals, at least a second speed value which represents a second oscillation speed, that is to say a speed of the oscillatory movements of the at least one tube performing the second useful oscillations, in particular to save this in a non-volatile memory; and / or - wherein the measuring system electronics (20) are configured to determine, based on the driver signal (e1), at least an, in particular digital, first current measured value representing the first (useful) current component (eN1), in particular a (current) amplitude of the first (useful) current component (eN1) or an effective value of the first (useful) current component (eN1), in particular to save this in a non-volatile memory; and / or - wherein the measuring system electronics (20) are configured to determine, based on the driver signal (e1), at least an, in particular digital, second current measured value representing the second (useful) current component (eN2), in particular an amplitude of the second (useful) current component (eN2) or an effective value of the second (useful) current component (eN2), in particular to save this in a non-volatile memory.

15. The measuring system as claimed in the preceding claim in conjunction with one of claims 13 to 14, - wherein the measuring system electronics (20) are configured to determine the (damping) correction value by means of the first and second speed values as well as the first and second current measured values, in particular as a function of the first oscillation speed, a second power of a (current) amplitude of the second (useful) current component (eN2), a square of a (current) amplitude of the first (useful) current component (eN1) as well as a square of a second power of the second oscillation speed; and / or - wherein the measuring system electronics (20) are configured to determine the (damping) correction value as a function of the first oscillation speed, a second power of a (current) amplitude of the second (useful) current component (eN2), a square of a (current) amplitude of the first (useful) current component (eN1) as well as a square of a second power of the second oscillation speed, in particular using the first and second speed values as well as the first and second current measured values.

16. The measuring system as claimed in one of the preceding claims, - wherein the first useful signal components (s1N1; s2N1) of the first and second oscillation signals follow a change in a mass flow of the measured substance conducted in the tube with a change in a (measured) phase difference between the first useful signal components, that is to say a difference between a phase angle of the first useful signal component (s1N1) of the first oscillation signal (s1) and a phase angle of the first useful signal component (s2N1) of the second oscillation signal (s2); - and wherein the measuring system electronics are configured to generate mass flow measured values representing the mass flow based on the (measured) phase difference between the first useful signal components (s1N1; s2N1).

17. The measuring system as claimed in the preceding claim, wherein in the measuring system electronics a phase difference-to-measured value characteristic curve function is configured, according to which the measuring system electronics can determine or determine measured values representing the at least one flow parameter of the measured substance based on the measured phase difference, that is to say, in particular mass flow measured values representing the mass flow of the measured substance, in particular in such a way that the first and second modal dampings are considered in the phase difference-to-mass flow measured value characteristic curve function or in such a way that the (damping) correction value is contained in the phase difference-to-mass flow measured value characteristic curve function.

18. The measuring system as claimed in the preceding claim, - wherein the first and second modal dampings are considered in the phase difference-to-mass flow measured value characteristic curve function or the (damping) correction value is contained in the phase difference-to-mass flow measured value characteristic curve function, in particular in such a way that the phase difference-to-mass flow measured value characteristic curve function considers a product of a second power of the first modal damping (D1) and a square of the second modal damping (D2) and / or contains a product of a second power of the square of the quality (1 / 01) of the first useful oscillations and the quality (1 / D2) of the second useful oscillations; and / or - wherein the measuring system electronics are configured to check the phase difference-to-measured value characteristic curve function by means of at least one of the first and second oscillation signals and / or the driver signal, in particular using the (damping) correction value.

19. The measuring system as claimed in one of the preceding claims, - wherein the measuring system electronics (20) have a non-volatile memory (EEPROM) which is configured to store digital data, that is to say, in particular first and second quality values and / or a (damping) correction value, in particular even when there is no operating voltage; and / or - wherein the measuring transducer, with the exception of the oscillation exciter, does not have any other oscillation exciters that are mechanically connected to the at least one tube (111); and / or - wherein the oscillation exciter (31) is formed by a moving coil, in particular one having an air coil and an anchor; and / or - wherein both of the first and second oscillation sensors are formed in each case by a plunger coil, in particular one with an air coil and an anchor.

20. The measuring system as claimed in one of the preceding claims, wherein the measuring system electronics are configured to supply the driver signal (e1) with the second (useful) current component (eN2) during a test interval, in particular one that lasts for more than 10 ms and / or is temporary and / or is restarted repeatedly.

21. The measuring system as claimed in the preceding claim, - wherein each test interval lasts for more than 100 ms (milliseconds), in particular not less than 1 s (second); and / or - wherein the measuring system electronics are configured to start and / or to end the test interval automatically, in particular in a time-controlled manner, in particular on a recurring basis; and / or - wherein the measuring system electronics are configured to receive and execute one or more commands which start the test interval.

22. The measuring system as claimed in one of the preceding claims, - wherein the exciter arrangement, with the exception of the oscillation exciter (31), does not have any other oscillation exciters that are connected to the tube; and / or - wherein the oscillation exciter (31) is positioned and aligned in such a way that the drive offset is less than 0.5 mm, that is to say, in particular is zero, or in such a way that the centroid of an area of the drive cross-sectional area of the tube corresponds to the drive reference point or coincides with it; and / or - wherein both of the oscillation modes of the first and of the second order of the tube have in each case a first node located in the first tube end of the at least one tube and a second node located in the second tube end of the at least one tube; and / or - wherein the tube is curved in sections, in particular is in the shape of an arc and / or a V, in particular in such a way that the tube has a central crown segment and / or in such a way that precisely one main axis of inertia of the at least one tube is inside the reference cross-sectional area of the at least one tube; and / or - wherein the tube is straight in sections, in particular over the entire tube length, in particular in such a way that a center of mass is inside the reference cross-sectional area of the at least one tube.

23. The measuring system as claimed in one of the preceding claims, wherein the tube arrangement has at least one second tube (112), in particular curved at least in sections and / or straight at least in sections and / or identical in design to the first tube and / or parallel to the first tube at least in sections.

24. The measuring system as claimed in the preceding claim, - wherein the oscillation exciter (31) is partially mechanically connected to the first tube and also partially mechanically connected to the second tube; and / or - wherein the oscillation exciter (31) is configured to act differentially on the first and second tubes, in particular in such a way that the first and second tubes simultaneously execute forced mechanical oscillations in opposite directions at the same frequency; and / or - wherein the oscillation exciter (31) is configured to convert electrical power of a time-variable electrical current into mechanical power in such a way that a time-variable driving force acts on the second tube at a drive point formed by means of the oscillation exciter on the second tube mechanically connected to it, in particular at the same time as and / or in the opposite direction to the driving force acting on the first tube at the drive point formed by means of the oscillation exciter on the first tube mechanically connected to it; and / or - wherein the oscillation exciter (31) is configured to convert electrical power supplied by means of the electrical driver signal (e1) simultaneously into forced mechanical oscillations of the first and second tubes, in particular in such a way that the first and second tubes simultaneously execute forced mechanical oscillations with the first useful frequency and / or with the second useful frequency.