VIBRONIC TRANSDUCER WITH ECCENTRIC EXCITATION

Description

[0001] The present invention relates to a vibronic sensor for mass flow and density measurement with eccentric excitation.

[0002] The density of a medium conveyed in a measuring tube is determined using a vibronic sensor based on the natural frequencies of vibration modes of the measuring tube. Ideally, the medium is incompressible, so that when the measuring tube vibrates, the medium follows the movement of the measuring tube. However, if the medium becomes compressible, for example due to gas loading in the medium, the mass flow measurement and the density measurement can be inaccurate because the medium begins to vibrate relative to the measuring tube. The influence of this so-called resonator effect can be corrected by detecting the natural frequencies of two vibration modes, essentially determining a speed of sound of the medium for which the two natural frequencies result in consistent density measurements for the medium. Details are disclosed, for example, in DE 10 2015 122 661 A1.Typically, the first and second symmetrical vibration modes, i.e., the f1 and f3 modes, are excited for this purpose. However, in some sensors, the natural frequency of the second symmetrical vibration mode, f3, can be so high that it lies in the range of the medium's resonance frequency, making stable excitation of the second symmetrical vibration mode unreliable. In this case, the first antisymmetrical vibration mode is an attractive alternative, as the natural frequency of this mode is lower, and thus a greater distance from the resonance frequency of the measuring tube can be expected.

[0003] US 2003 / 0131669 A1 discloses a vibronic measuring transducer with two eccentrically arranged exciter arrangements, positioned symmetrically with respect to the center of the measuring tube at a large distance from each other. The modes to be excited are selected based on the frequency and phase relationship of the excitation signals applied to the two exciters. Deviations in the phase relationship or unequal amplitudes of the excitation forces result in the excitation of other, undesired modes. This can lead to undetected measurement errors that cannot be compensated for. Furthermore, two exciters that must be controlled independently of each other require increased cabling and circuitry.

[0004] US 5,321,991 A1 and WO 2004 / 099734 A2 disclose Coriolis sensors with seismic exciters that can be mounted eccentrically in the longitudinal direction of a measuring tube using clamping devices in order to excite higher modes than the fundamental mode.

[0005] DE 3 650 535 T2 discloses a Coriolis sensor with two parallel, U-shaped measuring tubes, each of which has a bend between two parallel legs, and the two legs are connected to a support extending substantially perpendicularly to them. The Coriolis sensor further comprises an electrodynamic excitation arrangement and an inlet-side and an outlet-side electrodynamic vibration sensor arrangement, each of which has an assembly on the two support bodies. The excitation arrangement appears to be positioned centrally with respect to the longitudinal axis of the measuring tube in order to excite the fundamental bending vibration mode.

[0006] It is the object of the present invention to provide a vibronic measuring transducer which enables excitation of the first symmetrical vibration mode and the first antisymmetrical vibration mode without impairing the normal measuring operation which is based on the first symmetrical vibration mode.

[0007] The object is achieved according to the invention by the vibronic measuring sensor according to independent patent claim 1.

[0008] The sensor according to the invention comprises: an oscillator with at least one measuring tube for guiding a medium; only one excitation arrangement for exciting the oscillator to flexural vibrations of the at least one measuring tube; at least one inlet-side sensor arrangement for detecting the flexural vibrations of the at least one measuring tube; and at least one outlet-side sensor arrangement for detecting the flexural vibrations of the at least one measuring tube;and a measuring and operating circuit which is configured to apply an excitation signal to the excitation arrangement and to detect sensor signals from the inlet-side and outlet-side sensor arrangements, and to determine a density measurement value and / or a mass flow rate measurement value on the basis of the sensor signals, wherein the excitation arrangement has a first excitation assembly which is fastened to the at least one measuring tube, and a second excitation assembly with respect to which the at least one measuring tube is to be excited to oscillate, wherein the first excitation assembly has a center of gravity which, except for manufacturing tolerances, lies in a transverse measuring tube plane which runs perpendicular to the at least one measuring tube and with respect to which the at least one measuring tube has a substantially mirror-symmetrical profile;wherein the exciter arrangement comprises an electrodynamic exciter and a balancing mass, wherein the electrodynamic exciter is configured to exert an excitation force on the at least one measuring tube, which acts between the first and the second exciter assemblies, wherein an effective center of the excitation force is located outside the measuring tube transverse plane, wherein the second exciter assembly comprises a coil configured to generate an alternating magnetic field with which the magnet interacts in order to excite the vibrations of the measuring tube, wherein the first exciter assembly has a carrier body on which the magnet and the balancing mass are arranged, wherein the carrier body is designed symmetrically with respect to the measuring tube transverse plane, and wherein the first exciter assembly is fastened to the at least one measuring tube by means of a joint, and wherein the measuring tube transverse plane runs through the joint.

[0009] In a further development of the invention, the at least one measuring tube has a free oscillation length which extends between an inlet-side fixing of the measuring tube and an outlet-side fixing of the measuring tube, wherein the center of the excitation force is spaced not less than 0.5% of the free oscillation length, in particular not more than 1% of the free oscillation length, and not more than 10% of the free oscillation length, in particular not more than 5%, from the transverse plane of the measuring tube.

[0010] For an exciter with a coaxial arrangement of a rotationally symmetric magnet and a rotationally symmetric coil, the center of the excitation force lies on the common axis of rotational symmetry. For other designs, the center of the excitation force for an electromagnetic exciter is determined as the center of gravity of the integral of the force density between the magnet and the coil.

[0011] In a further development of the invention, a principal axis of inertia of the first exciter assembly runs in the transverse plane of the measuring tube, with this principal axis of inertia running, in particular, perpendicular to the direction of vibration of the measuring tube in the transverse plane of the measuring tube. This means that the eccentric arrangement of the exciter, while affecting the excitation forces, does not introduce any inertia-induced angular momentum into the oscillating first measuring tube.

[0012] By mounting the excitation assembly in the center of the measuring tube, the same positioning and mounting methods can ultimately be used for the inventive sensors as for state-of-the-art sensors with purely symmetrical excitation. The eccentric excitation is made possible by the special design of the excitation assembly's components.

[0013] According to a further development of the invention, the sensor arrangements are each designed as electrodynamic sensor arrangements with a coil and a magnet.

[0014] According to a further development of the invention, the oscillator further comprises a second measuring tube, wherein the first measuring tube and the second measuring tube extend mirror-symmetrically to each other with respect to a longitudinal plane of the measuring sensor, wherein the longitudinal plane of the measuring sensor extends perpendicular to the transverse plane of the measuring tube. In this case, the free oscillation length is defined, for example, by coupler plates connecting the two measuring tubes on the inlet and outlet sides.

[0015] According to a further development of the invention, the second exciter assembly is fastened to the second measuring tube opposite the first exciter assembly, wherein the center of gravity of the second exciter assembly lies in the transverse plane of the measuring tube except for manufacturing tolerances.

[0016] According to a further development of the invention, a principal axis of inertia of the second exciter assembly runs in the transverse plane of the measuring tube, with this principal axis of inertia running, in particular, perpendicular to the direction of oscillation of the second measuring tube in the transverse plane of the measuring tube. This means that the eccentric arrangement of the exciter, while affecting the excitation forces, does not introduce any inertia-induced angular momentum into the oscillating second measuring tube.

[0017] According to a further development of the invention, the excitation signal comprises a periodic signal with the natural frequency of a symmetrical oscillation mode of the at least one measuring tube and / or the natural frequency of an antisymmetrical oscillation mode of the at least one measuring tube.

[0018] According to a further development of the invention, the measuring and operating circuit is configured to excite the first symmetrical oscillation mode and the first antisymmetrical oscillation mode, to determine the natural frequencies of the first symmetrical oscillation mode and the first antisymmetrical oscillation mode on the basis of the natural frequencies of the first symmetrical oscillation mode and the first antisymmetrical oscillation mode, a density measurement value or mass flow measurement value for a medium guided in the measuring tube, wherein the density measurement value or the mass flow measurement value is corrected with regard to a resonator effect due to a gas loading of the medium.

[0019] Since the first antisymmetric vibration mode usually has a significantly lower natural frequency than the second symmetric vibration mode, the described procedure can be used to determine the influence of the gas loading even for gas concentrations in which the second symmetric mode can no longer be reliably excited due to the resonator effect.

[0020] The invention will now be explained in more detail with reference to the embodiments shown in the drawings.

[0021] It shows: Fig. 1a : a representation of an embodiment of a measuring sensor according to the invention; Fig. 1b :a schematic side view of a first excitation assembly of the sensor from Fig. 1a ; Fig. 1c : a schematic side view of a second excitation assembly of the sensor from Fig. 1a ; Fig. 2 : a diagram of the vibration modes of a sensor; Fig. 3 : a flow diagram for determining the density of a compressible medium with the measuring sensor according to the invention; Fig. 4 : Measurement data for density measurement with the sensor according to the invention; and Fig. 5 : Measurement data for mass flow measurement with the sensor according to the invention.

[0022] The Fig. 1a The measuring sensor 1 shown for measuring mass flow and density comprises an oscillator 10 with two essentially parallel, curved measuring tubes 10.1, 10.2 and an excitation arrangement 11 which acts between the measuring tubes 10 in order to excite them to bending vibrations against each other. The excitation arrangement 11 is attached to the measuring tubes 10.1, 10.2 in such a way that the center of an excitation force generated by it lies outside a measuring tube transverse plane which intersects the measuring tubes perpendicularly and with respect to which each of the measuring tubes has a mirror-symmetrical course. The center of the excitation force is located in the longitudinal direction of the measuring tubes in the exemplary embodiment at a distance of approximately 2.5% of the length L of the measuring tubes 10.1, 10.2 from the measuring tube transverse plane.Thus, when the oscillator is excited by the excitation arrangement 11, a sufficient asymmetric excitation force component is exerted to also excite the first antisymmetric oscillation mode, the so-called f2 mode, to resonant oscillations if the excitation of the oscillator 10 occurs with a resonant frequency f2 of the first antisymmetric oscillation mode. Furthermore, the measuring sensor 1 has two sensor arrangements 12a, 12b, which are arranged symmetrically to the transverse plane of the measuring tube in order to detect the measuring tube oscillations as a relative movement of the mutually oscillating measuring tubes 10.1, 10.2. The measuring tubes 10.1, 10.2 extend between two (not shown) flow dividers, which fluidically combine the measuring tubes 10.1, 10.2 and are each connected to a flange 30a, 30b, which serves to install the measuring sensor 1 in a pipeline.A rigid support tube 60 extends between the flow dividers, connecting the flow dividers to one another to suppress vibrations of the flow dividers relative to one another in the frequency range of the flexural vibration modes of the oscillator 10. The support tube 60 further carries an electronics housing 80, shown only schematically here, which contains a measuring and operating circuit 70 configured to operate the measuring sensor.

[0023] The exciter arrangement 11 and the sensor arrangements 12a, 12b comprise, as usual, electrodynamic transducers, with a magnet arranged on one of the measuring tubes and a coil on the other. This principle is known per se and need not be explained in more detail here. The special feature of the measuring sensor according to the invention is that the exciter arrangement 11, in addition to the excitation of symmetrical bending vibration modes, also enables the excitation of antisymmetrical bending vibration modes of the oscillator, while still being balanced with regard to its mass distribution. The exciter arrangement 11 comprises a first exciter assembly 11.1 on a first measuring tube 10.1, as shown in Fig. 1b is shown, and a second exciter assembly 11.2, which is arranged opposite the first exciter assembly 11.1 on a second measuring tube 10.2, as Fig. 1c shows.

[0024] The Fig. 1b The first exciter assembly 11.1 shown comprises a first ring segment 14.1 which partially surrounds the first measuring tube 10.1 symmetrically to the measuring tube transverse plane and is joined to the first measuring tube 10.1 in a materially bonded manner, for example by brazing. The first ring segment 14.1 holds a particularly planar first carrier body 15.1 which runs essentially perpendicular to the measuring tube transverse plane and is designed symmetrically to the measuring tube transverse plane. The first carrier body 15.1 has a slotted first exciter component carrier 16.1 and a slotted first balancing mass carrier 17.1. The first exciter component carrier 16.1 carries an exciter magnet component 18.1 which is positioned by means of a pin which engages in a slot in the first exciter component carrier 16.1 and is fixed to the latter, for example by soldering, gluing or screwing. The first balancing mass carrier 17.1 carries a balancing mass body 19.1, which is positioned by means of a pin that engages in a slot of the first balancing mass carrier 17.1 and is fixed to the latter, for example, by soldering, gluing, or screwing. The first balancing mass body 19.1 is matched to the mass of the excitation magnet component 18.1 such that their common center of gravity lies in the transverse plane of the measuring tube. In particular, the first balancing mass body 19.1 and the excitation magnet component 18.1 have the same mass. A principal axis of inertia of the first excitation assembly 11.1 runs in the transverse plane of the measuring tube.

[0025] The Fig. 1c The second exciter assembly 11.2 shown comprises a second ring segment 14.2 which partially surrounds the second measuring tube 10.2 symmetrically to the measuring tube transverse plane and is joined to the second measuring tube 10.2 in a materially bonded manner, for example by brazing. The second ring segment 14.2 holds a particularly planar second carrier body 15.2 which runs essentially perpendicular to the measuring tube transverse plane and is designed symmetrically to the measuring tube transverse plane. The second carrier body 15.2 has a slotted second exciter component carrier 16.2 and a slotted second balancing mass carrier 17.2. The second exciter component carrier 16.2 carries an exciter coil component 18.2 which is positioned by means of a pin which engages in a slot in the second exciter component carrier 16.2 and is fixed to the latter, for example by soldering, gluing or screwing. The excitation coil component 18.2 and the excitation magnet component 18.1 are aligned with one another in relation to the longitudinal direction of the measuring tubes. The second balancing mass carrier 17.2 carries a balancing mass body 19.1, which is positioned by means of a pin that engages in a slot in the second balancing mass carrier 17.2 and is fixed to the latter, for example, by soldering, gluing, or screwing. The second balancing mass body 19.2 is matched to the mass of the excitation coil component 18.2 such that the common center of gravity lies in the transverse plane of the measuring tube. In particular, the second balancing mass body 19.2 and the excitation coil component 18.2 have the same mass. A main axis of inertia of the second excitation assembly 11.2 runs in the transverse plane of the measuring tube. The second ring segment 14.2 is, in particular, identical in construction to the first ring segment 14.1, and the second carrier body 15.2 is, in particular, identical in construction to the first carrier body 15.1.

[0026] The main axes of inertia of the first exciter assembly 11.1 and the second exciter assembly 11.2 in the transverse plane of the measuring tube run parallel to each other and in particular mirror-symmetrically to each other with respect to a measuring sensor longitudinal plane which runs between the two measuring tubes 10.1, 10.2, wherein the two measuring tubes are arranged mirror-symmetrically to each other with respect to the measuring sensor longitudinal plane.

[0027] The excitation coil component 18.2 is configured to be supplied by the measuring and operating circuit 70 with an alternating current signal whose frequency corresponds to the instantaneous natural frequency of a bending vibration mode to be excited. Of course, alternating current signals of different frequencies can also be superimposed, for example, with the instantaneous natural frequencies of the first symmetrical and the first antisymmetrical bending vibration mode. The resulting magnetic field exerts an alternating attractive and repulsive force on the excitation magnet component 18.1, causing the two measuring tubes 10.1, 10.2 of the oscillator to oscillate relative to each other.

[0028] The excitation magnet component 18.1, the excitation coil component 18.2, and the two balancing mass bodies 19.1, 19.2 are preferably designed to be rotationally symmetrical, with the axis of rotation running essentially in the direction of the vibrations of the measuring tubes. In particular, the excitation magnet component 18.1, the excitation coil component 18.2, and the two balancing mass bodies 19.1, 19.2 exhibit cylindrical symmetry, at least in sections.

[0029] The mode-dependent deflection of a measuring tube is Fig. 2 shown schematically. Here, the curve a(f 1 ) shows the bending line of a measuring tube for the first symmetrical oscillation mode, which is also called the drive mode or f 1 mode. The curve a(f 2 ) shows the bending line of the measuring tube for the first antisymmetrical oscillation mode, in which the measuring tube is deflected by the Coriolis forces when a mass flow flows through the measuring tube oscillating with the first symmetrical oscillation mode. The first antisymmetrical oscillation mode has an oscillation node in the longitudinal direction of the measuring tube in the middle of the tube at z = 0. An exciter at this position would not be able to excite an oscillation of the first antisymmetrical oscillation mode. Therefore, the exciter arrangement 11 is positioned here such that the excitation force FE acts between the measuring tubes offset by approximately 2.5% of the measuring tube length, i.e. approximately 5% of half the measuring tube length, compared to the transverse plane of the measuring tube.The measuring tube length is the length of a measuring tube centerline following the curved course of a measuring tube between the inlet-side and outlet-side flow dividers, in which the measuring tubes 10 are fixed at their ends. In the offset position, the exciter can excite the first antisymmetric oscillation mode by applying an excitation force FE with the resonance frequency of the first antisymmetric oscillation mode.

[0030] The positions of the sensor arrangements 12a, 12b are selected in the longitudinal direction z symmetrically to the center of the measuring tubes so that deflections of the vibration sensors produce a sufficient measurement signal both during vibrations in the drive mode and in the first antisymmetric vibration mode.

[0031] The measuring and operating circuit is configured to excite the first symmetrical oscillation mode and the first antisymmetrical oscillation mode, to determine a density measurement value or mass flow measurement value for a medium conveyed in the measuring tube based on the natural frequencies of the first symmetrical oscillation mode and the first antisymmetrical oscillation mode, wherein the density measurement value or the mass flow measurement value is corrected for a resonator effect due to a gas loading of the medium. The influence of this so-called resonator effect can be corrected by detecting the natural frequencies of two oscillation modes, essentially determining a speed of sound of the medium, for which matching density measurements for the medium result from the two natural frequencies.Details are disclosed, for example, in DE 10 2015 122 661 A1, wherein, according to the teaching described therein, the first and second symmetrical vibration modes are to be evaluated. Based on . Fig. 3 The method 100 for which the measuring and operating circuit is designed is now explained. In a first step 110, the first symmetric and the first antisymmetric oscillation mode, i.e. the f 1 mode and the f 2 mode, are excited. In a second step 120, a preliminary density measurement value ρ 1 , ρ 2 is determined based on the natural frequencies of the excited modes. For incompressible media, the two density measurements essentially agree. If deviations exist, a correction factor is determined in the next step 130, which depends on the speed of sound of the compressible medium. Accordingly, as disclosed in DE 10 2015 122 661 A1, the speed of sound is first determined, which leads to the observed ratio of the preliminary density measurements.Based on the speed of sound and one of the natural frequencies, a density error and a correction factor can then be determined, with which a corrected density measurement value ρ corr is then determined in the next step 140.

[0032] To provide a correct mass flow rate measurement, a preliminary mass flow rate measurement is first determined 150. In a next step 160, a flow correction factor is determined based on the density error or density correction factor, as also disclosed in DE 10 2015 122 661 A1. In a final step 170, a correct mass flow rate measurement is determined by correcting the preliminary mass flow rate measurement with the correction factor.

[0033] The effect of the correction function is derived from the data in Fign. 4 und 5 which show measurement results of density and mass flow measurements with the measuring sensor according to the invention, wherein the gas loading of a liquid medium flowing through the measuring sensor was slowly increased during the measurement.

[0034] The dotted curve in Fig 4 , shows uncorrected density measurements based on the natural frequency of the first symmetric bending vibration mode, i.e., the f 1 mode. These also correspond to one of the preliminary density measurements according to step 120 in the above procedure. The solid line, on the other hand, shows the actual course of the density values. The dotted line shows the course of the corrected density measurements after step 140 based on the first symmetric and the first antisymmetric bending vibration mode. The improvement is obvious, and the agreement with the actual density values ​​is satisfactory.

[0035] The dotted curve in Fig 5, shows uncorrected flow rate measurements. The solid line, on the other hand, shows the actual flow rate curve. The dotted line shows the curve of the corrected flow rate measurements according to step 170 of the above method based on the first symmetric and first antisymmetric bending vibration modes. Here, too, the improvement is evident, and the agreement with the actual flow rate measurements is satisfactory.

[0036] Since the eccentrically arranged exciter also proportionally causes a deflection in the eigenmode of the first antisymmetric oscillation mode at the frequency of the first symmetric oscillation mode, and this deflection could also be caused by flow-dependent Coriolis forces, the exciter causes a zero-point error in the flow measurement. However, this error is easily corrected because the excitation of the first symmetric oscillation mode and the first antisymmetric oscillation mode always occurs with the same excitation force at a constant excitation position. This zero-point error can be determined and corrected by performing an intermittent flow measurement during a decaying excitation oscillation compared to a flow measurement with the exciter running.

Claims

1. Measuring sensor (1), comprising: an oscillator (10) with at least one measuring tube (10.1, 10,2) for guiding a medium; only one exciter arrangement (11) for exciting the oscillator (10) to bending oscillations of the at least one measuring tube (10.1, 10, 2); at least one sensor arrangement (12a) on the inlet side for detecting the bending vibrations of the at least one measuring tube (10.1, 10, 2); and at least one sensor arrangement (12b) on the outlet side for detecting the Bending vibrations of the at least one measuring tube; and a measuring and operating circuit (70) which set up to control the exciter arrangement (11) with an excitation signal, and to detect sensor signals from the inlet-side and outlet-side sensor arrangements (12a, 12b), and to determine a measured density value and / or a measured mass flow rate value on the basis of the sensor signals, the exciter arrangement having a first exciter assembly (11.1), which is fastened to the at least one measuring tube (10.1), and a second exciter assembly (11.2), with respect to which the at least one measuring tube is to be excited to oscillate, the first exciter assembly (11.1) having a center of gravity which, apart from manufacturing tolerances, lies in a measuring tube transverse plane (EQ) which extends perpendicularly to the at least one measuring tube (10.1, 10.2), and with respect to the second exciter assembly (11.2) the at least one measuring tube (10.1, 10.2) is to be excited to oscillate. in which the at least one measuring tube (10.1, 10.2) has a substantially mirror-symmetrical course; wherein the exciter arrangement (11) comprises an electrodynamic exciter (18) and at least one equalizing mass body (19.1, 19.2), wherein the electrodynamic exciter is arranged to exert an excitation force (FE) on the at least one measuring tube (10.1, 10.2), the between the first and second exciter assemblies (11.1, 11.2), whereby an effective center of the excitation force is located outside the transverse plane of the measuring tube (EQ), wherein the first exciter assembly (11.1) comprises a magnet, the second exciter assembly (11.2) comprising a coil (18.2) arranged to generate an alternating magnetic field with which the magnet (18.1) interacts to generate the oscillations of the first exciter assembly (11.1). measuring tube (10.1, 10.2); characterized in that the first exciter assembly (11.1) has a carrier body (15.1) on which the magnet (18.1) and the compensating mass (18.2) are arranged, the carrier body (15.1) being designed symmetrically with respect to the transverse plane (EQ) of the measuring tube; and the first exciter assembly (11.1) by means of a joint at the at least one measuring tube (10.1) is attached, with the transverse plane of the measuring tube (EQ) running through the joint.

2. Measuring sensor (1) according to claim 1, wherein the at least one measuring tube (10.1, 10.2) has a free oscillation length which extends between an inlet-side fixation of the measuring tube and an outlet-side fixation of the measuring tube (10.1, 10.2), wherein the center of the excitation force is not less than 0.5% of the free oscillation length and not more than 10% of the free oscillation length away from the transverse plane of the measuring tube (EQ).

3. Measuring sensor (1) according to one of the preceding claims, wherein a main axis of inertia of the first exciter assembly (11.1) extends in the transverse plane (EQ) of the measuring tube.

4. Measuring sensor (1) according to one of the preceding claims, wherein the sensor arrangements (12a, 12b) are each designed as electrodynamic sensor arrangements.

5. Measuring transducer (1) according to one of the preceding claims, wherein the oscillator (10) further comprises a second measuring tube (10.2), wherein the first measuring tube (10.1) and the second measuring tube (10.2) extend mirror-symmetrically to one another with respect to a longitudinal plane of the measuring sensor, wherein the longitudinal plane of the measuring sensor extends perpendicular to the transverse plane (EQ) of the measuring tube.

6. Measuring sensor (1) according to claim 5, wherein the second exciter assembly (11.2) is connected to the second measuring tube (10.2) is fixed opposite the first exciter assembly (11.1), with the center of gravity of the second exciter assembly (11.2) lying in the measuring tube transverse plane (EQ) except for manufacturing tolerances.

7. Measuring sensor (1) according to claim 5 or 6, wherein a main axis of inertia of the second exciter assembly (11.2) extends in the transverse plane (EQ) of the measuring tube.

8. Measuring transducer (1) according to one of the preceding claims, wherein the energizing signal comprises a periodic signal with the natural frequency of a symmetrical oscillation mode of the at least one measuring tube and / or the natural frequency of an antisymmetrical oscillation mode of the at least one measuring tube (10.1, 10.2).

9. Measuring transducer (1) according to one of the preceding claims, wherein the measuring and operating circuit (70) is arranged to excite the first symmetrical oscillation mode and the first antisymmetrical oscillation mode, to determine the natural frequencies of the first symmetrical oscillation mode and the first antisymmetrical oscillation mode on the basis of the natural frequencies of the first symmetrical oscillation mode and the first antisymmetrical oscillation mode a density measurement value or mass flow rate measurement value for a medium flowing in the measuring tube, and to determine the natural frequencies of the first symmetrical oscillation mode and the first antisymmetrical oscillation mode. medium, whereby the density measured value or the mass flow rate measured value is corrected with regard to a resonator effect due to gas loading of the medium.