CA2448377C - Vibratory transducer - Google Patents

Vibratory transducer Download PDF

Info

Publication number
CA2448377C
CA2448377C CA 2448377 CA2448377A CA2448377C CA 2448377 C CA2448377 C CA 2448377C CA 2448377 CA2448377 CA 2448377 CA 2448377 A CA2448377 A CA 2448377A CA 2448377 C CA2448377 C CA 2448377C
Authority
CA
Canada
Prior art keywords
side
inlet
transducer
outlet
flow tube
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CA 2448377
Other languages
French (fr)
Other versions
CA2448377A1 (en
Inventor
Wolfgang Drahm
Alfred Rieder
Ennio Bitto
Rainer Lorenz
Christian Schuetze
Alfred Wenger
Michael Fuchs
Martin Anklin
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Endress and Hauser Flowtec AG
Original Assignee
Endress and Hauser Flowtec AG
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Priority to EP01112546.5 priority Critical
Priority to EP20010112546 priority patent/EP1260798A1/en
Application filed by Endress and Hauser Flowtec AG filed Critical Endress and Hauser Flowtec AG
Priority to PCT/EP2002/005276 priority patent/WO2002099363A1/en
Publication of CA2448377A1 publication Critical patent/CA2448377A1/en
Application granted granted Critical
Publication of CA2448377C publication Critical patent/CA2448377C/en
Application status is Active legal-status Critical
Anticipated expiration legal-status Critical

Links

Classifications

    • GPHYSICS
    • G01MEASURING; TESTING
    • G01FMEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F1/00Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through the meter in a continuous flow
    • G01F1/76Devices for measuring mass flow of a fluid or a fluent solid material
    • G01F1/78Direct mass flowmeters
    • G01F1/80Direct mass flowmeters operating by measuring pressure, force, momentum, or frequency of a fluid flow to which a rotational movement has been imparted
    • G01F1/84Gyroscopic mass flowmeters
    • G01F1/8409Gyroscopic mass flowmeters constructional details
    • G01F1/8413Gyroscopic mass flowmeters constructional details means for influencing the flowmeter's motional or vibrational behaviour, e.g., conduit support or fixing means, or conduit attachments
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01FMEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F1/00Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through the meter in a continuous flow
    • G01F1/76Devices for measuring mass flow of a fluid or a fluent solid material
    • G01F1/78Direct mass flowmeters
    • G01F1/80Direct mass flowmeters operating by measuring pressure, force, momentum, or frequency of a fluid flow to which a rotational movement has been imparted
    • G01F1/84Gyroscopic mass flowmeters
    • G01F1/8409Gyroscopic mass flowmeters constructional details
    • G01F1/8413Gyroscopic mass flowmeters constructional details means for influencing the flowmeter's motional or vibrational behaviour, e.g., conduit support or fixing means, or conduit attachments
    • G01F1/8418Gyroscopic mass flowmeters constructional details means for influencing the flowmeter's motional or vibrational behaviour, e.g., conduit support or fixing means, or conduit attachments motion or vibration balancing means
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01FMEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F1/00Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through the meter in a continuous flow
    • G01F1/76Devices for measuring mass flow of a fluid or a fluent solid material
    • G01F1/78Direct mass flowmeters
    • G01F1/80Direct mass flowmeters operating by measuring pressure, force, momentum, or frequency of a fluid flow to which a rotational movement has been imparted
    • G01F1/84Gyroscopic mass flowmeters
    • G01F1/845Gyroscopic mass flowmeters arrangements of measuring means, e.g., of measuring conduits
    • G01F1/8468Gyroscopic mass flowmeters arrangements of measuring means, e.g., of measuring conduits vibrating measuring conduits
    • G01F1/8472Gyroscopic mass flowmeters arrangements of measuring means, e.g., of measuring conduits vibrating measuring conduits having curved measuring conduits, i.e. whereby the measuring conduits' curved center line lies within a plane

Abstract

A vibratory transducer for a fluid flowing in a pipe comprising a curved flow tube for conducting the fluid. The flow tube communicates with the pipe via an inlet-side tube section and an outlet-side tube section. An antivibrator is mechanically connected with the flow tube by means of a first coupler on the inlet side and by means of a second coupler on the outlet side. During operation of the transducer flow tube and antivibrator oscillates in opposition of phase. For driving flow tube and antivibrator the transducer comprising an excitation system and for sensing inlet-side and outlet-side vibrations of the flow tube the transducer comprising a sensor system. An internal system formed by at least said flow tube, said antivibrator, said excitation system, and said sensor system, oscillating about a longitudinal axis of the transducer which is essentially in alignment with the inlet-side tube sections, forces a torsion of the first and second couplers about the longitudinal axis and an essentially torsional elastic deformation of at least parts of the inlet--side and outlet-side tube sections. In order to achieve a torsionally soft oscillation of the internal system, at least the first coupler, tuned to a torsional rigidity of the inlet-side tube section, and at least the second coupler, tuned to a torsional rigidity of the outlet-side tube section, are so dimensioned that an inlet-side inherent torsion eigenmode of the first coupler and of the inlet-side tube section has a natural frequency approximately equal to the excitation frequency, and an outlet-side inherent torsion eigenmode of the second coupler and of the outlet-side tube section has a natural frequency essentially equal to the natural frequency of the inlet-side inherent torsion eigenmode.

Description

May 08, 2002 Vibratory Transducer FIELD OF THE INVENTION
This invention relates to a vibratory transducer which is particularly suited for use in a Coriolis mass flowmeter.
BACKGROUND OF THE INVENTION
To determine the mass flow rate of a fluid flowing in a pipe and particularly of a liquid, use is frequently made of measuring devices which induce Coriolis forces in the fluid and derive therefrom a measurement signal representative of mass flow rate by means of a vibratory transducer and control and evaluation electronics connected thereto.
Such transducers and particularly their use in Coriolis mass flow meters have been known and in industrial use for a long time. U.S. Patent 5,549,009, for example, discloses a Coriolis mass flowmeter incorporating a vibratory transducer which responds to the mass flow rate of a fluid flowing in a pipe and comprises:
- a curved flow tube for conducting the fluid which vibrates in operation and communicates with the pipe via an inlet-side tube section and an outlet-side tube section;
- an antivibrator which extends essentially parallel to and oscillates in a phase opposition to the flow tube and is mechanically connected with the flow tube -- by means of at least a first coupler on the inlet side and -- by means of at least a second coupler on the outlet side;

May 08, 2002 - an excitation system for driving the flow tube and the antivibrator at an excitation frequency; and - a sensor system for sensing inlet-side and outlet-side vibrations of the flow tube, - wherein a torsional rigidity of the inlet-side tube section and a torsional rigidity of the outlet-side tube section are adapted to one another and to an internal system supported by the two tube sections and formed by at least the flow tube, the antivibrator, the excitation system, and the sensor system such that the internal system is suspended essentially "torsionally soft", i.e., in a torsionally nonrigid manner.
As is well known, vibrating flow tubes, for example U-, V-, or S2-shaped tubes, if excited into cantilever vibrations in a first natural mode, can cause Coriolis farces in the fluid passing therethrough. In such transducers, the first natural vibration mode chosen for the flow tube is usually the mode in which the flow tube oscillates about a longitudinal axis of the transducer at a lowest natural resonance frequency.
The Coriolis forces thus produced in the fluid result in cantilever vibrations of an at least second natural mode being superimposed on the excited, pendulum-like cantilever vibrations of the so-called useful mode, the vibrations of the second mode being equal in frequency to those of the useful mode. In transducers of the kind described, these cantilever vibrations forced by Coriolis forces, the so-called Coriolis mode, commonly correspond to the natural mode in which the flow tube also performs torsional vibrations about a vertical axis that is perpendicular to the longitudinal axis. As a result of the superposition of the useful and Coriolis modes, the flow tube vibrations sensed on the inlet and outlet sides of the tube by means of the sensor system have a measurable phase difference, which is also dependent on mass flow rate.
Frequently, the flow tubes of such transducers, which are used in Coriolis mass flowmeters, for example, are excited in operation at an instantaneous May 08, 2002 resonance frequency of the first natural mode, particularly with the vibration amplitude maintained constant. As this resonance frequency is also dependent on the instantaneous density of the fluid in particular, commercially available Coriolis mass flowmeters can also be used to measure the density of moving fluids.
One advantage of a curved tube shape is that thermally induced expansion, particularly in flow tubes with a high expansion coefficient, produce virtually no or only very slight mechanical stresses in the flow tube itself andlor in the connected pipe. Another advantage of curved flow tubes is that the flow tube can be made relatively long, so that high sensitivity of the transducer to the mass flow rate to be measured can be achieved with a relatively short mounting length and relatively low excitation energy. These circumstances permit the flow tube to be made from materials having a high expansion coefficient andlor a high modules of elasticity, such as special steel.
In vibratory transducers with a straight flow tube, the latter is commonly made from a material having at least a lower expansion coefficient and possibly a lower modules of elasticity than special steel in order to avoid axial stresses and achieve sufficient measuring sensitivity. Therefore, such straight flow tubes are preferably made of titanium or zirconium, but because of the higher material cost and the generally higher machining cost, such tubes are far more expensive than those made of special steel.
Transducers of the kind disclosed in U.S. Patent 5,549,009, i.e., transducers With a single curved flow tube and with an antivibrator, particularly one extending parallel to the flow tube, have proved especially effective in applications where the fluid to be measured has an essentially constant or only very slightly varying density. For such applications, it is readily possible by means of the antivibrator oscillating in operation at the same frequency as, but in phase opposition to, the flow tube to nearly completely neutralize those transverse forces which were induced in the transducer as a result of May 08, 2002 alternating lateral motions of the oscillating flow tube, thus virtually keeping such transverse forces away from the connected pipe.
If used for fluids with widely varying densities, such a transducer has practically the same disadvantage as a transducer without antivibrator, particularly as compared to transducers with two parallel flow tubes.
It turned out that the aforementioned forces produced in the transducer cannot be completely balanced with such an antivibrator. As a result, the above-mentioned internal system, oscillating as a whole about the transducer's longitudinal axis, may also start to vibrate laterally.
Accordingly, these lateral vibrations of the internal system force an additional elastic deformation of the inlet-side and outlet-side tube sections and consequently may cause flexural vibrations in the connected pipe. In addition, such lateral vibrations may cause cantilever vibrations very similar to, and thus practically indistinguishable from, the Coriolis mode to be excited in the empty flow tube, and this, in turn, would render the measurement signal that ought to represent the mass flow rate of the fluid unusable.
On the other hand, as is well known, a significant advantage of a single flow tube transducer over a transducer having two parallel flow tubes is that no manifolds are necessary to connect the flow tubes with the pipe. Such manifolds, on the one hand, are expensive to make and, on the other hand, represent flow bodies with a strong tendency to sedimentation or clogging.
One way of reducing density-dependent transverse forces is described, for example, in U.S. Patent 5,287,754 or in U.S. Patent 5,705,754. In the transducers disclosed therein, the transverse forces produced by the vibrating single flow tube, which oscillate at medium or high frequencies, are kept away from the pipe by means of an antivibrator that is heavy compared to the flow tube, and by coupling the flow tube to the pipe relatively loosely, i.e., practically by means of a mechanical low-pass filter. Unfortunately, however, this causes the antivibrator mass required to achieve sufficient May 08, 2002 damping of the transverse forces to increase disproportionately with the nominal diameter of the flow tube.
This represents a big disadvantage for such transducers, since the use of 5 such massive components always entails both increased assembly costs during manufacture and increased costs during installation of the measuring device in the pipe. In addition, it is difficult to ensure that the lowest natural frequency of the transducer, which decreases with increasing mass, is still far from the likewise rather low natural frequencies of the connected pipe.
Thus, use of such a transducer in industrial Coriolis mass flowmeters is limited to relatively small nominal flow tube diameters up to about 10 mm.
SUMMARY OF THE INVENTION
It is therefore an object of the invention to provide a transducer which is particularly suited for a Coriolis mass flowmeter and which in operation, even if it uses only a single straight flow tube, is well balanced dynamically over a wide fluid density range and nevertheless has comparatively little mass.
To attain this object, the invention provides a vibratory transducer for a fluid flowing in a pipe, said transducer comprising:
- a curved flow tube for conducting the fluid which vibrates in operation and communicates with the pipe via an inlet-side tube section and an outlet-side tube section;
- an antivibrator which in operation oscillates in a phase opposition to the flow tube and is mechanically connected with the flow tube -- by means of a first coupler on the inlet side and -- by means of a second coupler on the outlet side;
- an excitation system for vibrating the flow tube and the antivibrator at an excitation frequency; and - a sensor system for sensing inlet-side and outlet-side vibrations of the flow tube, May 08, 2002 - wherein an internal system formed by at least the flow tube, the antivibrator, the excitation system, and the sensor system, oscillating about a longitudinal axis of the transducer which is essentially in alignment with the inlet-side tube sections, forces -- a torsion of the first and second couplers about the longitudinal axis and -- an essentially torsional elastic deformation of at least parts of the inlet-side and outlet-side tube sections, and - wherein in order to achieve a torsionally soft oscillation of the internal system, -- at least the first coupler, tuned to a torsional rigidity of the inlet-side tube section, and -- at least the second coupler, tuned to a torsional rigidity of the outlet-side tube section, are so dimensioned that --- an inlet-side inherent torsion eigenmode of the first coupler and of the inlet-side tube section has a natural frequency approximately equal to the excitation frequency, and --- an outlet-side inherent torsion eigenmode of the second coupler and of the outlet-side tube section has a natural frequency essentially equal to the natural frequency of the inlet-side inherent torsion eigenmode.
In a first preferred embodiment of the invention, the natural frequency of the inlet-side inherent torsion eigenmode is lower than the excitation frequency.
In a second preferred embodiment of the invention, the antivibrator extends essentially parallel to the flow tube.
In a third preferred embodiment of the invention, the antivibrator has a mass distribution at least similar to that of the flow tube.
In a fourth preferred embodiment of the invention, the antivibrator is tubular in form.

May 08, 2002 In a fifth preferred embodiment of the invention, the antivibrator is essentially coaxial with the flow tube.
In a sixth preferred embodiment of the invention, the antivibrator is essentially identical in shape to the flow tube.
In a seventh preferred embodiment of the invention, counterbalance bodies are attached to the antivibrator for adjusting the mass distribution of the antivibrator.
In an eighth preferred embodiment of the invention, the antivibrator is heavier than the flow tube.
In a ninth preferred embodiment of the invention, a first rotating-mass counterbalance body is rigidly fixed to the inlet-side tube section to adjust the inlet-side torsion eigenmode, and a second rotating-mass counterbalance body is rigidly fixed to the outlet-side tube section to adjust the outlet-side torsion eigenmode.
In a tenth preferred embodiment of the invention, the transducer comprises a first torsion absorber, which is essentially coaxial with the inlet-side tube section, and a second torsion absorber, which is essentially coaxial with the outlet-side tube section.
In an eleventh preferred embodiment of the invention, the transducer comprises a transducer case fixed to the inlet-side tube section and to the outlet-side tube section and having a lowest natural frequency which is at least 20% above the excitation frequency.
The invention further provides a Coriolis mass flowmeter incorporating a transducer as mentioned above.

May 08, 2002 A fundamental idea of the invention is to use such torsional vibrations of the internal system suspended in the aforementioned manner, which are rather uncritical for the Coriolis mode and, consequently, for the mass flow rate measurement, and which are caused essentially by in-phase oscillating motions of the flow tube and the multivibrator, to neutralize lateral transverse forces, which are extremely detrimental to the development of the Coriolis mode and, consequently, to the measurement of the mass flow rate. This means that these hitherto undesired torsional vibrations are not merely not damped out but, by being selectively adjusted for their mechanical coupling to the pipe, produced in such a way as to achieve a reduction of interfering effects on the transducer and, thus, an improvement in the transducer's measuring properties.
To accomplish this, according to the invention, an inlet-side torsion vibrator, formed by the inlet-side coupler and the inlet-side tube section, and an outlet-side torsion vibrator, formed by the outlet-side coupler and the outlet-side tube section, are mechanically tuned so as to oscillate practically at resonance with the oscillating internal system. This serves to oscillate the internal system free from external reaction torques if possible, so that the internal system is practically perfectly isolated from the inlet-side and outlet-side tube sections. As a result of this isolation, a total angular momentum of the internal system is practically zero. To the same degree as the total angular momentum, a total lateral momentum of the internal system, and thus transverse forces derived therefrom and transmissible to the outside, are reduced to zero by this isolation.
One advantage of the invention is that the transducer is very well balanced with a relatively small additional amount of mechanical complexity, particularly over a wide fluid density range, regardless of operational variations of an internal total mass.
The transducer according to the invention is further characterized by the fact that the inlet-side and outlet-side tube sections can be kept short, so that the May 08, 2002 mounting length of the transducer can be substantially reduced while the high quality of the dynamic vibration isolation remains essentially unchanged.
Despite its short mounting length, the transducer can be made very light.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention and further advantages will become more apparent by reference to the following description of an embodiment taken in conjunction with the accompanying drawings. Like reference characters have been used to designate like parts throughout the various figures; reference characters already allotted have been omitted in subsequent figures if this contributes to clarity. In the drawings:
Fig. 1a is a perspective side view of a vibratory transducer;
Fig. 1 b is a axial front side view of the transducer of Fig. 1 a;
Fig. 2 is a first graphical plot for the transducer of Fig. 1a1, b;
Fig. 3 is a second graphical plot for the transducer of Fig. 1a, 1b; and Fig. 4 shows a torsion absorber for the transducer.
DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS
While the invention is susceptible to various modifications and alternative forms, exemplary embodiments thereof have been shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that there is no intent to limit the invention to the the particular forms diclosed, but on the contrary, the intention is to cover all May 08, 2002 modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the intended claims.
Fig. 1 a and 1 b show schematically a meter for moving fluids with a vibratory 5 transducer. The transducer serves to produce in a fluid passing therethrough mechanical reaction forces, such as mass-flow-rate dependent Coriolis forces, density-dependent inertial forces, andlor viscosity-dependent friction forces, which react on the transducer and are measurable, particularly with sensor technology. Derived from these reaction forces, a mass flow rate m, a 10 density p, andlor a viscosity r~ of the fluid, for example, can thus be measured in the manner familiar to those skilled in the art.
To conduct the fluid to be measured, the transducer comprises a curved flow tube 10, particularly a single tube, which is connected via an inlet-side tube section 11 and an outlet-side tube section 12 to a pipe (not shown) that supplies the fluid and carries it away. Flow tube 10, inlet-side tube section 11, and outlet-side tube section 12 are in alignment with each other and with a longitudinal axis A~ and are preferably of one-piece construction, so that they can be made from a single tubular semifinished product, for example; if necessary, flow tube 10, inlet-side tube section 11, and outlet-side tube section 12 may also be made from separate semifinished products that are subsequently joined together, for instance welded together. For flow tube 10, virtually any of the materials commonly used for such transducers, such as steel, Hastelloy, titanium, zirconium, tantalum, etc, may be employed.
For the preferred case where the transducer is to be detachable from the pipe, a first flange 13 is formed on inlet-side section 11 at an inlet end and a second flange 14 is formed on outlet-side tube section 12 at an outlet end; if necessary, inlet-side and outlet-side tube sections 11, 12 may also be connected with the pipe directly, for instance by welding or brazing.
Furthermore, as shown in Fig. 1 a, a transducer case 100, for instance a boxlike case or a case in the form of a hollow cylinder, is fixed, preferably May 08, 2002 rigidly, to the inlet end of inlet-side tube section 11 and to the outlet end of outlet-side tube section 12. Transducer case 100 may also serve to mount an electronics case 200 of the meter.
As shown in Fig. 1 a an 1 b, the transducer further comprises an antivibrator 20 for flow tube 10, which antivibrator is fixed to an inlet end of flow tube by means of an inlet-side first coupler 31 and to an outlet end of flow tube by means of an outlet-side second coupler 32 so as to be capable of vibratory motion, the second coupler 32 being preferably identical in shape to the first coupler 31. Coupler 31 may be implemented, for example, with one or, as shown in Fig. 1 a, two node plates which are fixed to flow tube 10 and antivibrator 20 at the inlet end; analogously, coupler 32 may be implemented with node plates fixed to flow tube 10 and antivibrator 20 at the outlet end.
The preferably likewise tubular antivibrator 20 is spaced from and extends essentially parallel to flow tube 10. Flow tube 10 and antivibrator 20 are preferably designed to have equal or at least similar mass distributions, particularly mass distributions proportional to each other, while having identical surface shapes if possible. It may also be advantageous, however, to form antivibrator 20 nonidentically to flow tube 10; for instance, antivibrator 20 may be coaxial with flow tube 10 if necessary.
Preferably, antivibrator 20 is made heavier than flow tube 10.
To permit easy adaptation of antivibrator 20 to a mass distribution effective at the flow tube, in a further preferred embodiment of the invention, counterbalance bodies 21 serving as discrete additional masses are mounted, preferably detachably, on antivibrator 20. Counterbalance bodies 21 may be, for example, disks screwed on to staybolts provided on flow tube 10, or short tube sections slipped over the flow tube. Furthermore, a corresponding mass distribution over antivibrator 20 may be implemented by forming longitudinal or annular grooves, for example. A mass distribution suitable for the respective application can be easily determined by the May 08, 2002 person skilled in the art using the finite element method andlor suitable calibration measurements, for example.
In operation, flow tube 10, as is usual with such vibratory transducers, is excited into cantilever vibrations at an excitation frequency feX~ such that the flow tube, oscillating in this so-called useful mode about the transducer's longitudinal axis A~, deflects essentially according to a first natural vibration mode shape. At the same time, antivibrator 20 is so excited into cantilever vibrations as to oscillate in essentially the same mode but in phase opposition to flow tube 10, which is oscillating in the useful mode. In other words, flow tube 10 and antivibrator 20 then move in the manner of vibrating tuning fork tines.
In another preferred embodiment of the invention, the excitation or useful-mode frequency feX~ is selected to correspond as exactly as possible to a preferably lowest natural frequency of flow tube 10. If use is made of a flow tube of special steel with a nominal diameter of 29 mm, a wall thickness of about 1.5 mm, a straight length of about 420 mm, and a cord length of 305 mm measured from inlet end to outlet end, the lowest resonance frequency of the tube at zero density is about 490 Hz.
When fluid flows in the pipe, so that the mass flow rate m is nonzero, Coriolis forces are induced by the vibrating flow tube 10 in the fluid passing therethrough. The Coriolis forces react on flow tube 10, thus causing an additional deformation of the flow tube essentially according to a second natural vibration mode shape, this deformation being detectable using sensor technology. An instantaneous form of this so-called Coriolis mode, which is superimposed on and has the same frequency as the excited useful mode, is also dependent on the instantaneous mass flow rate m, particularly with respect to its amplitudes. As is usual with such transducers, the second natural vibration mode may be the antisymmetric twist mode, for example, i.e., the natural mode in which flow tube 10, as mentioned above, also performs torsional vibrations about a vertical axis A2 which is perpendicular May 08, 2002 to longitudinal axis A~ and lies in a single plane of symmetry of the transducer shown.
To generate mechanical vibrations of flow tube 10, the transducer further comprises an excitation system 40, particularly an electrodynamic system.
This excitation system serves to convert electric excitation energy EeXo supplied from control electronics (not shown) housed in electronics case 200, for instance with a regulated current andlor a regulated voltage, into an excitation force FeXC that acts on flow tube 10, for example in a pulsed manner or harmonically, and deflects the tube in the manner described above. Control electronics suitable for adjusting the excitation energy Eex~
are disclosed, for example, in U.S. Patent 4,777,833, 4,801,897, 4,879,911, or 5,009,109.
As is usual with such transducers, the excitation force Fexc may be bidirectional or unidirectional and be adjusted in amplitude, for instance by means of a current- andlor voltage-regulator circuit, and in frequency, for instance by means of a phase-locked loop, in the manner familiar to those skilled in the art. The excitation system may be, for example, a simple solenoid assembly with a cylindrical excitation coil that is mounted on antivibrator 40 and traversed in operation by a suitable excitation current, and with a permanent magnetic armature that is fixed to the outside of flow tube 10, particularly at the midpoint thereof, and rides at least in part in the excitation coil. Excitation system 40 may also be implemented with an electromagnet, for example.
To detect vibrations of flow tube 10, the transducer comprises a sensor system 50. For sensor system 50, virtually any of the sensor systems commonly used for such transducers, which senses motions of flow tube 10, particularly on the inlet and outlet sides, and converts them into corresponding sensor signals, may be employed. Sensor system 50 may be formed, for example, by a first sensor, mounted on flow tube 10 on the inlet side, and a second sensor, mounted on flow tube 10 on the outlet side, in 14 Fl_4139-US
May 08, 2002 the manner familiar to those skilled in art. The sensors may be electrodynamic velocity sensors, which perform relative vibration measurements, or electrodynamic displacement sensors or acceleration sensors, for example. In place of electrodynamic sensor systems, sensor systems using resistive or piezoelectric strain gages or optoelectronic sensor systems may be used.
If necessary, sensors adapted for the measurement andlor the operation of the transducer may be provided in the manner familar to those skilled in the art, such as additional vibration sensors mounted on antivibrator 20 andlor transducer case 100, see also U.S. Patent 5,736,653, or temperatur sensors mounted on flow tube 10, on antivibrator 20 andlor transducer case 100, see also U.S. Patent 4,68,384 or WO-A OOI102816.
As is readily apparent from the foregoing explanations, antivibrator 20 serves as a support system for excitation system 40 and sensor system 50.
However, antivibrator 20 also serves to dynamically balance the transducer for a predetermined fluid density value, for example a value most frequently expected during operation of the transducer or a particularly critical value, to the point that transverse forces produced in the vibrating flow tube 10 and acting essentially perpendicular to longitudinal and vertical axes A~, AZ are completely offset by counterforces produced by antivibrator 20, cf. U.S.
Patent 5,549,009. For a flow tube 10 of special steel and at a vibration amplitude of about 0.03 mm, for example, such transverse forces in flow tube 10, which are produced as a result of mass accelerations when the tube is excited into cantilever vibrations in its first natural vibration mode, would lie in the range of 45 N.
If, however, the aforementioned transverse forces of flow tube 10 are not counterbalanced, as is quite possible in a transducer as disclosed in U.S.
Patent 5,549,009, for example, an internal system formed by flow tube 10, May 08, 2002 antivibrator 20 with any counterbalance bodies 21 attached thereto, excitation system 40, and sensor system 50 and suspended from inlet-side tube section 11 and outlet-side tube section 12, and the couplers 31, 32 fixed to the internal system, will be deflected laterally from an assigned static mounting position. In this manner, the transverse forces may act at least in part via inlet-side and outlet-side tube sections 11, 12 on the connected pipe, thus causing the latter to vibrate as well. Furthermore, such transverse forces, as a result of an unbalanced suspension of the internal system or entire transducer, for instance because of virtually unavoidable manufacturing tolerances, may result in flow tube 10 being additionally excited into cantilever vibrations in a second natural mode, which are then no longer distinguishable from the Coriolis mode proper by means of sensors.
As repeatedly mentioned, flow tube 10 can be dynamically balanced solely by means of antivibrator 20, but only for a single fluid density value, and only for a very narrow fluid density range at best.
If the mass of antivibrator 20, which is preferably identical in shape to flow tube 10, is less than the mass of the fluid-carrying flow tube 10, the vibrating flow tube 10 and antivibrator 20 may additionally perform common oscillating motions about longitudinal axis A~ which, as shown in Fig. 1 b, at least with the fluid at rest, are essentially in phase with each other and with the cantilever vibrations of antivibrator 20; if the mass of the fluid-carrying flow tube 10 is less than the mass of antivibrator 20, these common or nonlocal oscillating motions may be in phase with the cantilever vibrations of flow tube 10. In other words, as a result of unbalances, particularly of density-dependent unbalances, between flow tube and antivibrator 20, the entire internal system may perform torsional vibrations about longitudinal axis A~
which are in phase with the cantilever vibrations of flow tube 10 or with those of antivibrator 20.
As a result of these torsional vibrations of the internal system, the two couplers 31, 32, which are virtually rigidly connected with the internal system, May 08, 2002 are subjected to a corresponding torsion about longitudinal axis A~, i.e., they, too, vibrate, namely in phase with the internal system and with each other.
To the same degree, an essentially torsional, elastic deformation of inlet-side and outlet-side sections 11, 12, which are fixed to transducer case 100 and flow tube 10 so as to be capable of vibratory motion, is forced at least in parts thereof.
To the inventors' surprise it turned out that merely by suitably tuning the aforementioned torsion vibrators, namely inlet-side tube section 11 together with coupler 31 and outlet-side tube section 12 together with coupler 32, the transducer can be dynamically balanced virtually independently of the density p of the fluid, so that its sensitivity to internally produced transverse forces can be substantially reduced.
To accomplish this, according to the invention, a inlet-side moment of inertia about longitudinal axis Ai, here adjusted by means of at least coupler 31, and the torsional rigidity of inlet-side tube section 11 are so adapted to each other that an inlet-side inherent torsion eigenmode, i.e., an eigenmode merely to be computed, of coupler 31 and inlet-side tube section 11 about longitudinal axis A1 has a natural frequency f~ essentially equal to or less than the excitation frequency fex~. Furthermore, a outlet-side moment of inertia about longitudinal axis A~, here adjusted by means of at least coupler 32, and the torsional rigidity of outlet-side tube section 12 are so adapted to each other that an outlet-side inherent torsional eigenmode of coupler 32 and outlet-side tube section 12 about longitudinal axis A, has a natural frequency f2 essentially equal to the natural frequency f~. In the transducer shown in Fig. 1 a, the tube segments between the two node plates of coupler 31, which practically do not vibrate, must also be taken into account in the selection of the moment of inertia for adjusting the inlet-side torsion eigenmode; analagously, the tube segments between the two node plates of coupler 32 must be added on to the moment of inertia of the coupler 32 in adjusting the outlet-side torsion eigenmode.

May 08, 2002 By adjusting the useful mode and the torsion eigenmode in the manner described, the internal system, which in operation oscillates at the same frequency as flow tube 10, which vibrates at the excitation frequency feX~, is caused to excite practically exactly the inlet-side and outlet-side torsion eigenmodes. In that case, the torsional vibrations of the internal system are opposed by no or only very small reaction torques of the two torsion vibrators vibrating at their natural frequencies f~ and f2, respectively, and in phase with the internal system. Thus, in operation, the internal system is mounted so "torsionally soft" that it can be regarded as being practically perfectly isolated from inlet-side and outlet-side tube sections 11, 12.
Because of the fact that despite a practically perfect isolation, the internal system oscillates about longitudinal axis A~ and does not rotate, no total annular momentum of the internal system can exist. As a result, however, a total lateral momentum nearly directly dependent on the total annular momentum, particularly with similar mass distributions in flow tube 10 and antivibrator 20, and, consequently, lateral transverse forces derived from this total lateral momentum, which may be transmitted from the internal system to the outside, are also zero. In other words, in the transducer according to the invention, density-dependent unbalances will result nearly exclusively in a change in the instantaneous amplitude of the torsional vibrations of the internal system, but will cause no or only negligibly small displacements of the internal system from its assigned mounting position.
Investigations on transducers incorporating the above-described flow tube of special steel have shown that despite a variation of the excitation frequency fexc over a range of about 100 Hz, which is usual with such transducers and corresponds approximately to a fluid density range between 0 and 2000 kg m-3, a maximum transverse force Q* acting on the internal system, normalized to a maximum interior force produced in couplers 31, 32 by the antiphase motions of flow tube 10 and antivibrator 20, can be kept well below 5%, i.e., at about 2 N, see Figs. 2 and 3.

May 08, 2002 For this aforementioned case and at a length L~~ of inlet-side tube section 11 of about 170 mm, for example, that said inlet-side moment of inertia would have to be approximately 1.5 ~ 10-3 kg ~ m2 to set the associated torsion eigenmode at the excitation frequency feXC in the aforementioned manner, cf.
Fig. 2. The parameters then to be set on the concrete transducer to optimally adjust the inlet-side and outlet-side torsion eigenmodes to the useful mode, i.e., suitable mass distributions, moments of inertia, torsional rigidities, and geometrical dimensions of flow tube 10, antivibrator 20, inlet-side and outlet-side tube sections 11, 12, and couplers 31, 32, which are derived therefrom, can be determined in the manner familiar to those skilled in the art using the finite element method or other computer-aided simulation computations in conjunction with suitable calibration measurements.
To permit the inlet-side torsion eigenmode to be adjusted as accurately as possible, particularly if the transducer's mounting length is specified, in a further preferred embodiment of the invention, at least a first rotating-mass counterbalance body 33 is rigidly fixed to inlet-side tube section 11, preferably in proximity to coupler 31, and to correspondingly adjust the outlet-side torsion eigenmode, at least a second rotating-mass counterbalance body 43 is rigidly fixed to outlet-side tube section 12, preferably in proximity to coupler 32. Rotating-mass counterbalance bodies 33 and 34 are preferably disks of identical shape and may be mounted on inlet-side tube section 11 and outlet-side tube section 12, respectively, either concentrically as shown in Fig. 1 a, 1 b, i.e., with their respective centroids located on longitudinal axis A~, or eccentrically. For the transducer shown, the above-mentioned moment of inertia of 1.5 ~ 10-3 kg ~ m2 can thus be implemented in a very simple manner using two rotating-mass counterbalance bodies 33, 34 in the form of annular disks of special steel with a diameter of about 100 mm and a thickness of about 15 mm.
It also turned out that in order to reliably avoid antiphase torsional vibrations of the inlet-side and outlet-side torsion vibrators, an additional, torsionally May 08, 2002 stiff connection from the two couplers 31, 32 or the two rotating-mass counterbalance bodies 33, 34 to an inner support frame may be advantageous. Furthermore, the excitation frequency fex~ should preferably be set at a value not higher than 85% of a lowest natural frequency of transducer case 100, which acts as an external support frame in the above sense.
In a further preferred embodiment of the invention, the transducer comprises an inlet-side first torsion absorber 60 and an outlet-side second torsion absorber 70, which is essentially identical in shape to the first torsion absorber 60. The latter serves in particular to suppress torsional moments caused by the oscillating internal system and transmitted via inlet-side tube section 11 to the connected pipe andlor the transducer case 100 fixed at the inlet end.
Torsion absorber 60 is fixed at the inlet end of inlet-side tube section 11 or at least in the vicinity of that end, for instance directly to transducer case 100;
analogously, the second torsion absorber, which also serves to avoid torsional moments on the connected pipe andlor the transducer case 100, is attached at the outlet end of outlet-side tube section 12.
As shown in Fig. 4, torsion absorber 60 comprises a torsion spring 61 which is preferably tubular and essentially coaxial with inlet-side tube section 11, and which is fixed to the inlet end so as to be capable of torsional vibration, i.e., of being twisted at least in sections with respect to inlet-side tube section 11. Furthermore, torsion absorber 60 comprises a preferably disk-shaped rotating-mass body 62 attached to the torsion spring on the side remote from the inlet end of inlet-side tube section 11. Torsion spring 61 and rotating-mass body 62 are so adapted to each other that torsion absorber 60, excited in operation by the twisting inlet-side tube section 11 andlor by the likewise slightly deforming transducer case 100 into torsional vibrations about longitudinal axis A~, vibrates out of phase with respect to, and particularly in phase opposition to, the above-mentioned inlet-side torsion vibrator, May 08, 2002 consisting of coupler 31 and inlet-side tube section 11. To support the excitation of torsion absorber 60, torsion spring 61 may advantageously be extended up to rotating-mass counterbalance body 33, if present, or up to coupler 31, and fixed to one of the two. This also serves to reduce lateral flexural vibrations of torsion absorber 60.
Because of its good dynamic balance even at varying densities p of the fluid passing through it, the transducer according to the invention is particularly suited for use in a Coriolis flowmeter, a Coriolis mass flowmeter-densimeter, or a Coriolis mass flowmeter-densimeter-viscometer.
While the invention has been illustrated and described in detail in the drawings and forgoing description, such illustration and description is to be considered as exemplary not restrictive in character, it being understood that only exemplary embodiments have been shown and described and that all changes and modifications that come within the spirit and scope of the invention as described herein are desired to protected.

Claims (13)

1. A vibratory transducer for a fluid flowing in a pipe, said transducer comprising:

a curved flow tube for conducting the fluid which vibrates in operation and communicates with the pipe via an inlet-side tube section and an outlet-side tube section;

an antivibrator which in operation oscillates in a phase opposition to the flow tube and is mechanically connected with the flow tube by means of a first coupler on the inlet side and by means of a second coupler on the outlet side;

an excitation system for vibrating the flow tube and the antivibrator at an excitation frequency; and a sensor system for sensing inlet-side and outlet-side vibrations of the flow tube, wherein an internal system formed by at least said flow tube, said antivibrator, said excitation system, and said sensor system, oscillating about a longitudinal axis of the transducer which is essentially in alignment with the inlet-side tube sections, forces a torsion of the first and second couplers about the longitudinal axis and an essentially torsional elastic deformation of at least parts of the inlet-side and outlet-side tube sections, and wherein in order to achieve a torsionally soft oscillation of the internal system, at least the first coupler, tuned to a torsional rigidity of the inlet-side tube section, and at least the second coupler, tuned to a torsional rigidity of the outlet-side tube section, are so dimensioned that an inlet-side inherent torsion eigenmode of the first coupler and of the inlet-side tube section has a natural frequency approximately equal to the excitation frequency, and an outlet-side inherent torsion eigenmode of the second coupler and of the outlet-side tube section has a natural frequency essentially equal to the natural frequency of the inlet-side inherent torsion eigenmode.
2. The transducer as claimed in claim 1 wherein the natural frequency of the inlet-side inherent torsion eigenmode is lower than the excitation frequency.
3. The transducer as claimed in claim 1 wherein the antivibrator extends essentially parallel to the flow tube.
4. The transducer as claimed in claim 1 wherein the antivibrator has a mass distribution at least similar to that of the flow tube.
5. The transducer as claimed in claim 1 wherein the antivibrator is tubular in form.
6. The transducer as claimed in claim 1 wherein the antivibrator is essentially coaxial with the flow tube.
7. The transducer as claimed in claim 1 wherein the antivibrator is essentially identical in shape to the flow tube.
8. The transducer as claimed in claim 1 wherein counterbalance bodies are attached to the antivibrator for adjusting the mass distribution of the antivibrator.
9. The transducer as claimed in claim 1 wherein the antivibrator is heavier than the flow tube.
10. The transducer as claimed in claim 1 wherein a first rotating-mass counterbalance body is rigidly fixed to the inlet-side tube section to adjust the inlet-side torsion eigenmode, and a second rotating-mass counterbalance body is rigidly fixed to the outlet-side tube section to adjust the outlet-side torsion eigenmode.
11. The transducer as claimed in claim 1 wherein the transducer comprises a first torsion absorber, which is essentially coaxial with the inlet-side tube section, and a second torsion absorber, which is essentially coaxial with the outlet-side tube section.
12. The transducer as claimed in claim 1 wherein the transducer comprises a transducer case fixed to the inlet-side tube section and to the outlet-side tube section and having a lowest natural frequency which is at least 20% above the excitation frequency.
13. A Coriolis mass flowmeter incorporating a transducer as claimed in claim 1.
CA 2448377 2001-05-23 2002-05-14 Vibratory transducer Active CA2448377C (en)

Priority Applications (3)

Application Number Priority Date Filing Date Title
EP01112546.5 2001-05-23
EP20010112546 EP1260798A1 (en) 2001-05-23 2001-05-23 Vibration type measuring transducer
PCT/EP2002/005276 WO2002099363A1 (en) 2001-05-23 2002-05-14 Transducer of the vibration type

Publications (2)

Publication Number Publication Date
CA2448377A1 CA2448377A1 (en) 2002-12-12
CA2448377C true CA2448377C (en) 2008-08-26

Family

ID=8177517

Family Applications (1)

Application Number Title Priority Date Filing Date
CA 2448377 Active CA2448377C (en) 2001-05-23 2002-05-14 Vibratory transducer

Country Status (7)

Country Link
EP (2) EP1260798A1 (en)
JP (1) JP2004538449A (en)
CN (1) CN100335866C (en)
CA (1) CA2448377C (en)
DK (1) DK1389300T3 (en)
RU (1) RU2292014C2 (en)
WO (1) WO2002099363A1 (en)

Families Citing this family (31)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP4105685B2 (en) * 2002-05-08 2008-06-25 エンドレス ウント ハウザー フローテック アクチエンゲゼルシャフトEndress + Hauser Flowtec AG Vibration type transducer
DE10344742A1 (en) * 2003-09-25 2005-04-14 Endress + Hauser Flowtec Ag, Reinach Setting or adjusting resonance frequency of a ductile hollow body, e.g. a measurement pipe or sensor housing, by generation of differential pressure over body and causing resultant plastic deformation
BRPI0418687A (en) * 2004-04-16 2007-06-12 Micro Motion Inc method and apparatus for balancing forces
DE102004035971A1 (en) 2004-07-23 2006-02-16 Endress + Hauser Flowtec Ag Vibration-type transducers for measuring media flowing in two media lines, and in-line meter having such a transducer
US7127952B2 (en) 2004-07-23 2006-10-31 Endress + Hauser Flowtec Ag Vibration-type measurement pickup for measuring media flowing in two medium-lines, and inline measuring device having such a pickup
EP1851516B1 (en) 2005-02-25 2017-11-08 Endress+Hauser Flowtec AG Vibration-type sensor
WO2006118557A1 (en) * 2005-04-06 2006-11-09 Micro Motion, Inc. Compact vibratory flowmeter for measuring flow characteristics of a cement flow material
KR20130022427A (en) * 2005-04-06 2013-03-06 마이크로 모우션, 인코포레이티드 Compact vibratory flowmeter for measuring flow characteristics of a multi-phase flow material
US7490521B2 (en) 2005-11-15 2009-02-17 Endress + Hauser Flowtec Ag Measurement transducer of vibration type
US7475603B2 (en) 2005-11-15 2009-01-13 Endress + Hauser Flowtec Ag Measurement transducer of vibration-type
DE102005054855A1 (en) * 2005-11-15 2007-05-16 Flowtec Ag Vibration type fluid measurement transducer has counter oscillator coupled to inlet and outlet sides and balanced extension arms generating flexural torques
US7472607B2 (en) 2005-11-15 2009-01-06 Endress + Hauser Flowtec Ag Measurement transducer of vibration type
DE102005059070A1 (en) * 2005-12-08 2007-06-14 Endress + Hauser Flowtec Ag Transducer of vibration type
US7325461B2 (en) 2005-12-08 2008-02-05 Endress + Hauser Flowtec Ag Measurement transducer of vibration-type
DE102005062007A1 (en) 2005-12-22 2007-06-28 Endress + Hauser Flowtec Ag Vibration-type measuring transformer used e.g. as a mass flow measuring device comprises a housing, an inner part arranged in the housing, a curved partially vibrating measuring tube and a counter oscillator
US7325462B2 (en) 2005-12-22 2008-02-05 Endress + Hauser Flowtec Ag Measuring transducer of vibration-type
WO2007074015A1 (en) * 2005-12-22 2007-07-05 Endress+Hauser Flowtec Ag Vibratory measuring transducer
DE102005062004A1 (en) * 2005-12-22 2007-06-28 Endress + Hauser Flowtec Ag Mass converter housing for use in coriolis mass through-flow measurement has an inner section and a vibrating mass pipe which has greater dead-point stability
US7360451B2 (en) 2005-12-22 2008-04-22 Endress + Hauser Flowtec Ag Measuring transducer of vibration-type
US7631561B2 (en) 2006-03-22 2009-12-15 Endress + Hauser Flowtec Ag Measuring transducer of vibration-type
DE102006013601A1 (en) 2006-03-22 2007-09-27 Endress + Hauser Flowtec Ag Transducer of the vibration type
US7555962B2 (en) 2006-03-22 2009-07-07 Endress + Hauser Flowtec Ag Measuring transducer of vibration-type
US7546777B2 (en) 2006-03-22 2009-06-16 Endress + Hauser Flowtec Ag Measuring transducer of vibration-type
DE102010001973A1 (en) 2010-02-16 2011-08-18 Endress + Hauser Flowtec Ag Vibration-type transducers with two counteroscillator arms
DE102011006919A1 (en) * 2011-04-07 2012-10-11 Endress + Hauser Flowtec Ag Method for trimming a pipe
DE102011006997A1 (en) * 2011-04-07 2012-10-11 Endress + Hauser Flowtec Ag Frequency adjustment method for a pipe arrangement
WO2014102037A1 (en) * 2012-12-30 2014-07-03 Endress+Hauser Flowtec Ag Vibration-type measuring transducer and measuring system formed therefrom
US9546890B2 (en) 2012-12-30 2017-01-17 Endress + Hauser Flowtec Ag Measuring transducer of vibration-type as well as measuring system formed therewith
DE102013102711A1 (en) * 2013-03-18 2014-09-18 Endress + Hauser Flowtec Ag Vibration-type transducers and measuring system formed thereby
DE102013102708A1 (en) * 2013-03-18 2014-09-18 Endress + Hauser Flowtec Ag Vibration-type transducers and measuring system formed thereby
EP3326743A1 (en) * 2014-08-07 2018-05-30 Micro Motion, Inc. Apparatus for controlling a weld penetration profile with application of shielding gas in an inner region of a workpiece

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE4027936A1 (en) * 1990-09-04 1992-03-05 Rota Yokogawa Gmbh & Co Kg Massedosierautomat
EP0518124B1 (en) * 1991-06-09 1995-09-06 Krohne AG Coriolis-mass flow meter
JP2758798B2 (en) * 1992-11-19 1998-05-28 株式会社オーバル Coriolis flow meter
US5979246A (en) * 1998-02-09 1999-11-09 Micro Motion, Inc. Spring rate balancing of the flow tube and a balance bar in a straight tube Coriolis flowmeter
DE19840782C2 (en) * 1998-09-08 2001-09-06 Krohne Messtechnik Kg The mass flow meter

Also Published As

Publication number Publication date
RU2292014C2 (en) 2007-01-20
JP2004538449A (en) 2004-12-24
EP1260798A1 (en) 2002-11-27
CN1613002A (en) 2005-05-04
RU2003136827A (en) 2005-04-10
EP1389300A1 (en) 2004-02-18
EP1389300B1 (en) 2015-08-12
DK1389300T3 (en) 2015-11-30
CN100335866C (en) 2007-09-05
CA2448377A1 (en) 2002-12-12
WO2002099363A1 (en) 2002-12-12

Similar Documents

Publication Publication Date Title
US6401548B1 (en) Coriolis mass flow/density sensor
EP0597021B1 (en) Coriolis effect mass flow meter
US4823614A (en) Coriolis-type mass flowmeter
AU691773B2 (en) Coriolis flowmeter
JP4545365B2 (en) Coriolis flowmeter for large flow with reduced dimensions
EP1055101B1 (en) Spring rate balancing of the flow tube and a balance bar in a straight tube coriolis flowmeter
JP2778836B2 (en) Coriolis effect flowmeter sensitivity is increased using a sensor in proximity to the section
EP2417425B1 (en) Measuring system for media which flow in a tube conduit
US6651513B2 (en) Vibration meter and method of measuring a viscosity of a fluid
RU2312310C2 (en) Flow meter
US7062977B2 (en) Vibratory transducer
CN100387943C (en) Vibratory transducer
US7171859B2 (en) Process meter for measuring at least one physical process variable of a medium stored in a container or flowing in a line
US4895031A (en) Sensor mounting for coriolis mass flow rate meter
US5323658A (en) Coriolis mass flowmeter
US6516674B1 (en) Mass flow measuring instrument
US7966863B2 (en) Viscometer
KR20010086232A (en) Spring rate balancing of the flow tube and a balance bar in a straight tube coriolis flowmeter
JP3188483B2 (en) Sensor method and for its measuring the mass flow rate
DE69633208T2 (en) Mass flow meter
US5670709A (en) Transducer for the measurement of attributes of flowable media
WO2001075399A2 (en) Mass flow rate measuring device
WO1995003528A1 (en) Coriolis mass flow rate sensor
DE102005012505B4 (en) Method for operating a mass flowmeter
US7040181B2 (en) Coriolis mass measuring device

Legal Events

Date Code Title Description
EEER Examination request