CA1257783A - Apparatus for mass flow rate and density measurement - Google Patents

Abstract

ABSTRACT
A Coriolis mass flow rate measuring apparatus including at least one helically configured loop 30 of conduit, a drive mechanism 42 for causing oscillatory movement of a portion of the loop in a direction normal to the direction of flow through the conduit portion and generally parallel to the central axis of the loop, and one or more detectors 46, 48, 56 for detecting the Coriolis forces exerted on other portions of the loop as a result of the mass flow therethrough and the oscillatory translation thereof.
A strain gage 208 and associated processing electron-ics are also used in combination with the mass flow rate information to determine the density of the flow.

Description

~57'7~3~

1210-0~

Specification "Apparatus for Mass Flow Rate and ~ensity Measurement"

BACKGROUND OF THE INVENTION
Field of the Invention The present invention relates generally to mass flow rate and density measuring apparatus and more particularly to an improved means for measuring the mass flow rate of a flowing mass using the effects of Coriolis forces and centrifugal forces upon an oscillat~rially translated or deflected portion of one or more loops of conduit through which the mass flow is caused to pass.
Description of the Prior ~rt There has been a continuing need for more accurate and more efficient devices for determining the mass flow rate and density of fluids and flowing solids passed through pipe lines and other various types of conduit. Prior art flow meters of the type including the present invention have in the past been embodied as gyroscopic mass flow meters or Coriolis type mass flow mete~s and the like.
One such device which utilizes Coriolis forces to measure mass flow is disclosed in U.S. Patent No.
4,109,524 entitled "Method and ~pparatus for Mass Flow Rate Measurement", issued ~ugust 29, l978 to James E.
Smith. In this patent an apparatus is disclosed wherein a mechanically reciprocating force is applied to first and second sections of a straight conduit by means o~ a beam that is disposed parallel to the first and second sections and has its ends mechani-cally linked to the adjacent ends o the two conduit sections. The adjacent ends of the first and second conduit sections are connected together by means of a short segment of conduit and flexible couplings and the opposi~e ends of each conduit section is separately supported in cantilever fashion relative to a base structure. The reciprocating forces applied to the conduit are resisted by separate Coriolis forces developed in the first and second conduit sections which act in opposite directions and induce a force moment about the center of the beam which is measured by a torque sensor. By measuring the force moment induced in the conduits tqnd transferred to the beam) by the Coriolis reactant forces, measurement of the mass flow through the conduit may be made. However, the measurement is complicated because of the need to avoid spurious measure~ents of the forces resulting from seismic or other vibrational forces transmitted ~hrough the support structure. Other similar devices are disclosed in the U.S. patents to Wiley et al, No.
3,080,750; Sipin, 3,218,851; Souriau, 3~396,579; and Sipin 3,329,019.
Rather than use linear sections of conduit that are pivoted at opposite ends and reciprocated at the adjacent ends, a U-tube or similar configuation is more commonly employed in mass flow measurement. In such cases, the inlet and outlet ends of the legs of the U-shap~ tube are fixedly mounted to a base and the bight end of the U-tube is reciprocated. The di~ferential displacement of corresponding portions of the U-tube side legs ~a~l~ed by Coriolis influence S~7~

on the flow is then measured as an indicator of ~ass flow rate. Such a technique and apparatus i5 suggested in the above-mentioned Smith patent and is illus~rated in U.S. Patent No. 4,187,721 for "Method and Structure for Flow Measurement" issued February 12, 1980 to James E. Smith, now RE 31,450. ~s disclosed in the referenced patent, a V-shaped conduit is mounted in a cantilevered manner at the leg ends thereof, and an oscillating means is mounted on a spring arm having a natural frequency substantially equal to that oP the U-shaped conduit and is used to provide up and down motion to the center of the bight end thereof.
Measuring sensors (flags and photodetectors) are pro-vided which detect the leading and trailing portions of the legs of the U-shaped conduit as they pass ~hrough a plane defined by the U-shaped conduit at ~ubstantially the mid-point oP its oscillation. The time differential of pa~sa~ of the legs through the midplane is measured as an indication of mass flow rate. Essentially, the same structure is used in the subsequent Smith Patent No. 4,422,338 referenced below except that in the latter)a pair of velocity sensors are substituted for the photodetectors~and condition-lng electronics are provided for developing signals corresponding to the passaye of the side legs through the midplane.
In U.S. Patent No. 4,127,~28 entitled "Coriolis Mass Flow Rate Metering Means" issued November 28, 1978 to Bruce M. Cox, et al, a pair of vibrating generally V-shaped tubes are fixedly mounted at the inlet and outlet ends thereof, in parallelly disposed, spaced apart cantilevered fashion so that the bight ends of the respective tubes are Pree to move relative to each other. An ffsclllatory drive 7~33 mechanism is connected between the bight ends of the respective tubes and actuated to provide opposing reciprocation thereof such that the U-shape members act as the tines of a tuning fork. The frequency of the oscillations of the tubes are adjusted until the tubes vibrate a fixed displacement when a known material is flowing therethrough. The power nee~3ed to vibrate the tubes the known displacement at a fixed frequency determines the density of an ~Inknown fluent material flowing the U-shaped tubes. Mass flow rate is detected by photodetectors positioned to operate in the same manner as taught by Smith for a single tube embodiment. Cox also suggests that strain gages or velocity sensors could be substituted for the photode~ectors, and acknowledges that it is known in the prior art that there will be a phase shift between the outputs of the two sensors which is proportional to the Coriolis force couple.
The principle teaching of this reference is the narrowing of the separation of the legs of each U
shaped tube proximate the support ends thereof so as to improve the freedom of torsional twist that may be imposed upon the respective tubes by the Coriolis reactance forces. This reference also illustrates a looped tube configuration in Fig. 5 thereof, but fails to teach or suggest how such configuration might be u~ed to provide enhanced flow measurement. It is therefore not believed to anticipate the present invention.
Other prior art known to the pre~ent inventor may be found in the U.S. Patents to Barnaby et al,

2,752,173; Roth 2,865,201 and 3,g49,919; Sipin,

3,355,944; sipin 3,485,098; Catherall 3,9S5,401; and Shiota 4,381,680, and the EPO application of Smith, i 5~7~3 Publication No. BP O 083 144 Al which corresponds to U.S. Patent No. 4,422,338. A listing of prior art utilizing the Coriolis principle may be Eound in the above-referenced Sipin patent RE 31,450.
A disadvantage of the Smith and Cox type of flow measuring devices, as well as those of others in the prior art, is that they are highly sensitive to to external vibrations which cause the measuring tube or tubes to be subjected to twisting forces other than those impartecl by Coriolis reaction forces, and such forces interfere with the accurate measurement of mass flow.
Another disadvantage pertaining to the preferred embodiments in the Smith Reissue RE 31,450 and Smith

4,422,338 patents is that the proposed methods of time differential measurement at the midplane of the U-tube will produce flow measurement errors when the fluid density is changing.
Yet another disadvantage of the prior art Coriolis type devices is that they are not capable of providing accurate flow data over a wide range of flow due to limitations in sensitivity in the flow struc-ture used.
Still another disadvantage of the prior art devices is that they are not provided with dynamic damping means to reduce the sensitivity to external vibrations.
SUMMARY OF THE PRESENT INVENTION
It is therefore a primar.y objective of the present invention to provide a new and improved apparatus of the Coriolis type for measuring the mass flow rate of a fluid or fluent solids, or mi~tures of these passing through a conduit.
It is another object of the present invention ~57'7~3 to provide a new an improved apparatus for measuring the density of a ma~s flowing through a conduit.
A further object o the present lnvention is to provide means for measuring mass flow rate and density of a mass flowing through a conduit without introducing perturbing objects or mechanisms into the fluid flow path.
sriefly~ a preferred embodiment of the present invention includes at least one helically configured loop of conduit, means for causing oscillatory movement of a portion of the loop in a direction normal to the direction of flow through the conduit portion and generally parallel to the central axis of the loop, and means for detecting the Cor;olis forces exerted on other portions of the loop as a result of the mass flow therethrough and the oscillatory translation thereof. A strain gage and associat~d ~rocessing electronics are also used in combination with the mass flow rate information to determine the density of the flow.
An important advantage of the present invention is that it enables true mass flow measurement to be made independent of variations of the properties of the material flowing through the measuring apparatus.
These and other advantages of the present inven-tion will no doubt become apparent to those skilled in the art after having read the following detailed descript;on of the perferred embodiments illustrated in the several figures of the drawings.

IN THE DRAWINGS
.
Fig. 1 is a schematic diayram used to illustrate theoretical operation of the present inventlon;
Fig. 2 is a diagram schematically illustrating 5778~

a simplified embodiment of one form of the present invention;
Fig. 3 is a diagram schematically illustrating a first alternative embodiment of the present invention;
Fig. ~ is a diagram schematically illustrating a multi loop embodiment in accordance with the present invention;
Figs. 5 and 6 illusteate parallel flow multi-looped embodiments of the present invention;
Fig`. 7 is a diagram schematically illustrating one method of applying oscillatory energy to the loop or loop~ in accordance with the present invention;
Fig. 8 is a diagram schematically illustrating a damping technique used in accordance with the present invention;
Fig. 9 is a diagram schematically illustrating a method of detecting the coriolis influence on multiple loops in accordance with the present invention;
Fig. 10 is a set of wave forms illustrating operation of the present invention;
Fig. 11 is a diagram schematically illustrating an alternative embodiment of the present invention modified to allow increased sensitivity to measure-ment;
Fig. 12 illustrates a further alternative embod-iment of the present invention modified to have increased sensitivity to measurement and reduced sensitivity to outside vibrations;
Fig. 13 illustrates an alternative method of detecting Coriolis forces in accordance with the present invention;
Fig. 14 illustrates an embodiment including a strain gage and electronic processing apparatus in accordance with the present invention; and '7 Fig. 15 is a block diagram illustrating cornpu-tational algorithms used in accordance with the present invention.

GENERAL THE:ORY OF OPERP.TION
The present invention is based upon the princi-ple that a mass flowing through a looped tube or other conduit and experiencing a veloeity gradient transverse to the flow path will intsract with the wall of the conduit with a force directly related to the transverse veloeity gradient and the mass flow rate. When the velocity gradient is caused by the transverse motion of ~he loop or rotation of the loop about an axis other than the central axis o the loop, the reaction is known as a Coriolis force. The magnitude and direction of the reaction force depends upon the magnitude and direetion of the transverse velocity change and the magnitude and direction of the mass flow. If two portion~ of the loop have the same transverse velocity gradient but have opposite directions of flow, a force couple consisting of equal and opposite reaction forces will result. In aeeordance with the present invention this force eouple is measured as a mean~ of determining the mass flow rate through the conduit.
Referring now to Fig. l of the drawings, for purposes of illustra'tion there is shown an example of a generalized helical loop o conduit 10, with its crossed ends mounted to a base structure 12 and 14.
The following general theory of the present invention applies for any shape of helical structure and any shape of tube cross-stection.

~5~78~

The loop 10 may thus be considered to lie sub-stantially in the X-~ plane for purposes of simplified mathematical analysis; deviation of the tube in the Z
direction (normal to the X-Y plane) required to permit crossover is ignored.
Accordingly, for a flow tube that i5 essentially symmetric in the X-Y plane and around the X-axis, the flow and total Coriolis force actlng upon each half section 16 and 18 respectively, is given by the expression 1/2100p mass D (1) where VD is the velocity in the Z direction ~normal to the X-Y plane) at the drive-point of the loop~ such as point 20 in Fig. l, and FmaSS is the fluid mass flow.
This equation can be used with another equation to be presented below to describe the dynamics of a loop with the following approximations; namely, (l) the Coriolis forces are assumed to be lumped at a single point for each half loop "center of action point" instead of being distributed with varying magnitude along the tube, (2) the mass of fluid and tube material are assumed to be lumped in a single mass point for each left loop instead of being di~tributed along the half loop, and (3) the motion which is different for the different points on the loop is represented by the motion of the two respec-tive mass points.
At the "center of action point" of the Coriolis force, each half loop has a certain "participating mass". The center of action is the point where the result3nt force of the di~tributed force for a half loop is applied and can be computed from the particu-~2577~3 lar tube geometry and the general Coriolis forceformula for ind;vidual mass elements. "Participating mass" is approximately the weight of the tubing and the fluid in each half loop but ignores the section between the X-axis and the suspension point. This concept takes into account that the motion is not uniform for different points on the half loop. The participating mass can be experimentally determined by measuring the nat~ral frequency of the bending mode of oscillation around the X-axis and by comparing it with the theoretical nat~ral frequency of the differ-ential equation to be presented. The participating mass is determined so that the two natural frequencies agree.
The differential equation describing inertial force, damping force and spring action force is:

Mpd2~Z-Z~_ + ~ t D) ~ B(Z-ZD)= Pl/21OOP (2) where A is the damping factor including both natural damping in the material and damping introduced by a damping coil as described hereinbelow;
B is the spring factor describing the restoring force from the spring action due to fixed attachment of the ends of the tube 10;
Mp is the participating mass for one half of the loop;
t is time;
ZD is the motion of the center of action point due to drive motion alone; and Z is the motion due to drive motion and Cori-olis force at the center of action point.
The natural frequency of equation (l~ above expressed in radians/unit time is Wth = ~ (3) The mode of natural oscillation related to eyua-tions 2 and 3 will be referred to as the "Coriolis mode".
The spring factor B can be determined by static application of a force couple at the center of action points (working in opposite directions approximately at the points 24 and 26 of the two sides of the loop 10) in the Z direction, and measuring the deflection of the center of action points.
If the loop 10 is excited at point 20 by an oscillatory force in the Z direction which varies sinusoidally with an angular frequency of w, the Coriolis force Pl/2 (at constant flow rate) will be a sinusoidal signal having the same frequency.
Equation (1) above determines approximately the magnitude of the Coriolis force where vD has a sinusoidal time variation.
The phase shift between P1/2 and (Z-zD~ in accordance with equation (2) is well understood as published in the literature. For example see Grabbe, Ramo, Woodridge, "Handbook of Au~omation Computation and Control" volume 1, pages 20-59. Defining the damping coefficient ~ as z = (1/2Wth)~/Mp), (4) if, for example, thé drive frequency W is chosen as 0.5 times the natural frequency, Wth, and the damping coefficient z i~ cho~en as 0.01, then using equations (2) and (3) above, the phase ~hift can be found to be about -0.8 degrees.
In this example, from equation (4) it can be , ~57~3 determined that the ratio of damping factor A to ma~ss Mp is _ = 0.02Wth (5~
The amount of damping in this example results from the application of a certain amount of damping force to the loop as will be explained further below.
With a different amount of damping, or a different selection of drive frequency w, but the same natural frequency in the Coriolis mode, a different amount of phase shift would occur.
If the fluid density changes, the natural fre-quency of the coriolis mode will change and the phase shift at the drive frequency will also change some-what. For normal density changes of a fluid and for the purpose of calculating an approximate phase shift for a given fluid, and for implementing an approximate compensation for the phase shift by a particular circuit to be described, the density change can be ignored.
In order to determine an approximate compensa-tion for phase shift between the Coriolis force couple and the structural position, velocity, or acceleration of the loops, either gap separation or the point differential measurements may be used. In such case, the structual deflection g, where g is proportional to the magnitude of the Coriolis force couple with a factor predetermined by weighing. A linear combina-tion of the time derivative g of g, and the lntegral of the same variable g (for example, performed by an analog integration as will be shown below ) may be designated G where G = Klg + K2 f gdt = Klg + X2g ~6) ~ ~i7~

where g is a symbol defined by g = dg/dt (7~
After Laplace transformation G may be expressed as G(s) = Kls g(s) ~ K2g(s) (8) By selection of the ratio Kl/K2 , an arbitrary positive phase shift between 0 degrees and 90 degrees can be introduced relating the new function G to the measurement of g. This ratio is selected so that it creates a positive phase shift equal to the negative phase shift resulting from the inertia of movement as approximately described by the differential equation (2). By the proper selection of Kl/K2 there will be no significant phase shift between the compu-ted variable G and the drive point velocity vD in equation (1) as long as the drive velocity is approx-imately a sinusoidal function. However, some deviation from a single sinewave (harmonic free) wave-form is permissible; for example, as caused by disturbing mechanical vibrations. Indeed, the insensitivity to this type of disturbance is ~ strong advantage of the present invention.
In performing signal analysis, the varia~leG and the velocity of the drive point ~ are sampled period-ically. The rate would typically be 20 times for each full cycle of application of the drive force. However, in the prese~ e of high frequency disturbing vibration of strong magnitude, a much higher frequency would be more s~itable. A lower sampliny rate speeds up the signal analysis and may be desirable if the flow meter 3l 257 ~'~3 is used for fast acting flow control.
The samples for G and v D are called Gi and Vi respectively where i = 1,2,3...N, and N is the number of sample pairs used for each measurement. The static relationship between a static force couple actlng as the CorioliY force couple and the static structure measurement "g stat" is g stat = K3Pl/2 loop-static For dynamic Coriolis forces, using equation (6) the function G describing dynamic gap changes may be expressed as G = Kl'K3g ~ K2 K3g (10 where Kl'K 3= Kl and K2'K3 = K2 in equation (6~
For simplicity, it may be assumed that K2 is selected as equal to l/K3 and G = g ~ (Kl'/K 2~g (11~
This expression illustrates that G is essen-tially the differential position, velocity or acceleration .measurement modified by a derivative term to correct for the phase lag defined by equation (2) above.
Sin~e the variables P1/2 loop and G are approxi-mately in phase due to the compensation defined by equation (11), one can for a dynamic system use the equation Pl/2 loop ~(l/K3~G (1~
Similar to equation (9~using this expression in equation (1~ and solving for G one obtains ~5778~

G = 2K3FmassVD (13~
where G and vD are nearly in phase. In a digital system the variables G and vD are sampled and the sampled pair, i, is called Gi and vi.
Defining ~ = 2K3Fmass (14) we then have from equation (13) G =~ vD (14a) may then be determined by linear regression analysis of sample population of Gi and Vi . The solution to this expression is for one of the two regression lines related to equation (14a).
= ,(~ Givi)/ ~Vi ) (15) One can also use the other regression line which is defined by (2) N N
Giv~ Gi2 ) (16) The line which divides the angle between the two regression lines in half is given by ~ g = tan [1/2(arcTan~ + arcTan ~ )] (17) and the estimate of the mass flow from this line is obtained from equation (14) as Fmass = (1/2R3) ~ vg (l8) One may, of course, use either one oE the regression lines instead of the middle llne. An illu-~ ~57 ~ ~3 stration of F ~ s computed using equations (14) and (15) is given below and in Flg. 15.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
. . . _ . _ _ . . . _ Referring now to Fig. 2 of the drawing, a simplified embodiment of the present invention is illustrated. In this embodiment a circular loop 30 of conduit is mounted to a base 32 by rneans of two standards 34 and 36~ Note that loop 30 i5 deformed upwardly away from the pipe line axis 37 at 38 and downwardly at 40 to provide clearance at the cross-over point 41. Alternatively, the pipe line matching deformations could have taken place outside the standards 34 and 36.
Opposite cross-over point 41 a loop actuating mechanism 42 is mounted to base 32 and has its force applying armature, or the like, electromagnetically coupled to loop 30 at 44. Actuating means 42 is of any suitable type which is capable of causing reciprocating motion of the engaged loop portion along the Z-axis as defined in equation (2) above.
Disposed on each side of the loop 30 are suitable sensors 46 and 48 which simultaneously detect the mo tion of the loop points 50 and 52 relative to base 32 and communicate such measurement to a suitable computing circuit and indicator means 54 which will provide a measurement of the Coriolis moment and thus the mass flow though loop 30.
~lternatively, indicator 54 could be coupled to a suitable means 56 coupled to the crossing portions of loop 30 at the cross-over point 41 and operative to output a signal indicative o~ the loop separationt relative velocity or relative acceleration; such signal also serving to cause indicator 54 to indicate ., .

~ 2.57 78~

the mass flow through tube 30.
Although the present invention as illustrated in the embodiment of Fig. 2 is a substantial improvement over other prlvr art devices, it does have the disadvantage that it requires a rigid base 32 for suPporting the standards 34 and 36 as well as the actuating mechanism 42 so as to prevent any vibration in the pipe lin~ from being transmitted to the apparat~ in a manner which would influence the measurement obtained thereby. It will be appreciated that in this embodiment, because of the rigid base, any vibrational motion transmitted from the pipe line to the base 32 will likewise be transmitted to the drive mechanism 42 and the loop position detectors 46 and 48. Accordingly, vibrational disturbances will not normally affect the accuracy of the measurement.
However, it will also be appreciated that seismic disturbances may cause the suspended loop to move relative to the base and thus affect the accuracy of measurement. But, if the loop detection source is the detector 56, a large degree of isolation against seismic disturbance is afforded due to the fact that seismic motion in the Z direction will be equally applied to the upper and lower loop portions at the cross-over point, and the two will be deflected in the same direction with equal intensity.
In Fig. 3 of the drawing, a modification of the Fig. 2 embodiment is illustrated wherein instead of mounting the deive means directly to the base, the drive means 60 is mounted to a counter balancing structure 62 which i.s rigidly attached to the standards 64 and 66. In this embodiment the counter balancing arm 62 is configured to have the same natural frequency about its support axis as that of ~ ~577~

the loop 68, and is fur~her provided with an adjustment slide weight 70 for allowing it to be adjusted to match different densities of the mass expected to flow in loop 68. Accordingl~, in this embodiment, even though rigid end mounts are required, the base does not need to be vibration resistant since the drive mechanism 60 is not attached directly to the base. Using this alternative, another possible source of error is also avoided in that vibrations generated by the ~low meter drive 60 are effectively prevented from influencing the attached pipe line which might reflect energy back into the subject apparatus.
A feature of the present invention that should be noted from the embodiments of Figs. 2 and 3 is that stresses induced in the tube at its attachment points to standards 34(64) and 36(66) due to actua-tion by the drive means 42(60), i.e., drive mode stresses, are torsional rather than bending. On the other handt stresses at such points caused by Coriolis $Drces, i.e., Coriolis mode stresses, are primarily bending in nature.
In order to increase the sensitivity of the present invention to Coriolis forces, serial combina-tions of cross-over loops, such as are illustrated in Fig. 4~6 of the drawing, may be utilized. In the case the serial double-cross-over loop of Fig. 4, a drive force might be applied between the two loops 70 and 72 at 74 causing deflection of the two loops in opposite directions. Means provided at 76 and 78 could detect changes in separation, l.e., relative position, velo-city or acceleration between the loops, with the dynamic difference in separation being used as an indication of mass flow rate. Alternatively, detec-tion of the loop separations at 80 and 82, or the , .

~2577~33 difference therebetween, could be used as mass flow rate indicators. Similarly, detection of ~eparation between the loops at 84 could likewise be utilized.
It will o~ course also be appreciated that the relative positions of corresponding portions of the individual loop above a base or other reference could also be detected as depicted in Fig. 2 of the draw-ings, and the differences therebetween used to deter-mine mass flow rate. The serial double-cross-over loop has excellent flow sensitivity and is especially suited for measuring low flow rates. However, the structure is somewhat sensitive to outside vibrations and requires the use of damping schemes, as will be described below.
In the parallel loop embodiment illustrated in Fig. 5, both loops are wound spirally in the same direction, while in the Fig. 6 embodiment, the upper loop is wound spirally advancing downwardly while the lower loop i~ wound spirally advancing upwardly. With actuating forces applied between the loops at 86 in Fig. 5, and 88 in Fig. 6, in addition to the loop separation differential measurements (position, ~elocity, accelleration or other time derivatives or integrals) discussed relative to the Fig. 2 embodiment, measurements could be taken of the top gap 100 (114 in Fig. 6) or the bottom gap 102 (116), or the difference between the top gap 100 (114) and bottom gap 102 (116) could be measured. Similarly, the differential loop characteristics of separation at 108 (118), 110 (120), 112 (122), could be taken as indicators, as could the differences between 110 and 112, (120 and 122). Measuring the position difference, or velocity of relative motion or acceleration between the upper and Lower loops on opposite .~ides of the loo~s, and then calcu~ating the differences between these distances (or velocities or acceleration~) is the mea~urement mode which i5 believed to be the most ~ensitive to mass ~low.
As an alternative embodiment of difference mea-surement, the difference in phase angle ~ measured at a ~iven signal level for the position, velocity or aeceleration signals produced by sensors 46 and 48 in Fig. 2 can be used. If velocity sensors are used, FmaSs would be calculated by computational electronics from the equation tan ~4 mass 2XRwD(sinp - cos ~ tan ~ (19) where ~ 4 is the phase angle difference between the outputs of the two velocity sensors, arctan(Wcz WD2 )' (20) R ~ Wc2 _ _ ~/(WC2-W!j) 2+4ZC2WD2 K = a loop "flexibility constant" defining the change in loop position at one of the velocity sensor loca-tions per unit Coriolis force on the corresponding half-loop.
w ~s the actual natural frequency of the mode excited by the Coriolis forces (the Coriolis mode) and c:orresponds to the theoretical value Wth in equation ~); and Zc is the actual damping coefficient for the Coriolis mode (correspoinds to the theoretical value z in ~quation (4)).
Note that the 'phase angle diFference ~ is equal to the drive frequency w D times the time difference ~ :3 ;7783~

between the waveforms developed by the detectors operating at left and right positions such as 46 and 48 respectively in Fig. 2, 76 and 78 in Fig. 4, or lla and 112 in Fig. 5. See ~lectronic and ~adio Engineering by Frederick E. Terman, McGraw-Hill (1955).
It should also be noted that the constant K depends on the temperature as well as material and geometrical dLmensions of the loop because in most materials the elasticity (or Young's) modulus is varying with temper-ature. As a special embodiment, one can, during flow~ter:
usage in a process, measure the temperature of the tubular wall and input the value of this variable into a computing circuit or digital computer and calculate the current value of K. The change in Young's modulus with temperature is tabulated in literature or can be determined experimentally.
The value of K at a given reference temperature is determined by calibration for each flowmeter design or each individual unit.
Equation (19) is different from and more accur-~te than the equations presented and implemented in the prior ~rt.
~ sing differential phase angle and drive frequency measurement, it is desirable to drive the device at its resonant frequency because the waveform developed by detectors responding to Coriolis forces will be free of harmonics. Using po~ition or acceller-ation sensors one can easily derive similar formulas Well known prior art apparatus capable of detec-ting the phase angle differences is di~closed in A~ cations Handbook of Preci~ion Phase Measurement (1975) by Dranetz Engineering Laboratorie~, Inc. of South Plainfield, New Jersey, and Hewlett-Packard Application Note 200-3 ~1974) entitled "Precision Time Interval Measurement Using an Electronic Counter'' Turning now to Fig. 7 of the drawing, one possi-ble implementation of a drive system of the type ~57~

- 21a -depicted at 42 in Fig. 2 is illustrated ln detail.
Mounted to one tube 130 by means of a standoff 131 is a permanent magnet 132. Attached to the loop directly above, as illustrated by the tube segment 134, is a double coil mechanism 133 including an upper winding 136 and a lower winding 138 which are mechanically attached to each other by a member 140, but are electrically isolated from each other. The assembly 133 is mounted relative to magnet 132 such that as current is input to winding 136 a motive force will be applied the magnet which will tend to drive the loop segment 130 relative to the loop segment 132. As the magnet 132 moves within the lower ~oil 138, a -~gnal will be induced therein which is proportional ;77~3~

~22-to the velocity of the magnet with respect to the velocity of the coil as it moves along the axis of the assembly 133. This signal, illustrated as the current ~ is proportional to the velocity diference between the tubes 130 and 134. The voltage created by il in the resistor Rl is input to a differential amplifier ~1 , which in turn will generate a voltage signal Vl that is also proportional to the velocity difference.
The voltage Vl is then fed through an amplifier whose output V is subtracted by an analog comput-ing device 142 from an input voltage VO generated by an oscillator 144 that generates a suitable periodic voltage signal VO in a form such as a sign wave. The difference VO-V =V2 is then fed into an amplifier A2 that generates a drive current i2 which, on passing through the drive coil 136, produces a magnetic field that creates a magnetic force which acts on permanent magnet 132 causing it to oscillate up and down within the winding 136, thereby causing loop 13~ and loop 134 t~ be driven alternately together and apart.
The purpose of the velocity feedback loop, including winding 138 and amplifier Al, is to control the amplitude of the tube oscillation at a desirable magnitude, even if the oscillator is operated at or near the natural frequency of the tube. Without this velocity feedback, or some other means for applying damping force to the tubes, should the oscillatory frequency be set at the natural frequency of the tubes it would cause the tubes to be driven to their elastic limit and perhaps failure.
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~257'~

The behavior of the closed feedback loop illu-strated in Fig. 7 can be approximately described by the transfer function 2 (21) VO ms ~ s [a ~ RKl K ~K3 K4]~ b where R = velocity feedback loop gain (V/Vi) X = the separation between the tubes at points 161 and 165 in Fig. 9, Kl is the gain factor (Vl/Il), K2 is the gain factor (I2/~ ), K3 is the force between drive coil 136 Fig. 7 and magnet 132 per unit current I2, K~ is the magnitude of current Il per unit velocity difference between drive coil 136 and permanent magnet 132, s is the Laplace operator symbol, m is the mass of both tubes 130 and 134 and the fluid contained therein including only the cir-cular portion of the loops, a is the damping constant of the structure for the drive motion, and b is the spring constant of the structure for the drive motion.
The expression a + RKlK2K3K4 shows that the nor-mally small damping constant "a" without the velocity i feedback loop has been enhanced. By selection of appropriate gain factor~, damping can be chosen to make the drive amplitude and velocity signal Vl follow the oscillation signal VO in a desirable fashion.
Any flow tube will exhibit a natural mode of vibration with low damping. Artificial damping and control of the drive may of course be achieved as 7~3 illustrated in Fig. 7. However, to accomplish damping without velocity and amplitude control, a similar system, such as is illustrated in Fig. 8, can also be used. Such a device would be a valuable addition to any type of Coriolis flow sensor, but would be an important improvement over the apparatus shown in the above-referenced Smith patents.
In this embodiment, a permanent magnet 150 is attached to the center loop portion 152 of a double serial loop device that is driven by an actuating assembly 154 such as was previously described at 133 in Fig. 7. The magnet 150 is disposed to move verti-cally within a damping coil 156 which is rigidly attached to -I device base 158. Connected across the winding of coil 156 is a variable load resistor R.
The current induced in coil 156 by motion of the magnet 1~0 therewithin creates a current which passes through resistor R and which is proportional to the velocity of the motion of the magnet relative to coil 156. Energy generated by motion of the magnet within coil 156 will be absorbed by energy dissipated in the resistor R. ~ccordingly, by selection of coil size, number of turns, permanent magnet strength, and the value of resistor R, the extent of damping achieved by such device can be selected to accomodate a particular appIication.
~ s another alternative which is shown in Fig. 9, damping coils 160 and 162 can be physically tied to velocity sense coils 164 and 166 in a double loop serial or parallel device configuation. In this par-ticular embodiment, the velocity sense coils 164 and 166 are wound in opposite directions and connected together serially so that when both gaps close at the same rate, the total induced EMF is ~. The output 57~

currents developed by coils 164 and 166 in this embodiment are passed through a resistor R to develope a voltage that is fed into a differential amplifier 168 which in turn generates an output signal Sl that is proportional to the velocity difference between the relative motions of tube portions 161 and 165, and 163 and 157 resp ~tively. The amplifiers 170 and 172, and the potentiometers Pl and P2 perform a phase-shifting function to compensate for the phaseshift between the Coriolis and the reiated motion of the flow tubes as described mathematically by the equations (2)-(8).
This compensation is an alternative design feature which is especially useful with digital signal analysis schemes such as described by equations ~9)-(18). The signal ~ is fed through the variable potentiometer Pl to generate a proportional voltage that is fed into one side of the difference amplifier 170. Simultaneously, Sl is also fed through the lntegrator 172 to develop a corresponding position signal SO, and this signal is passed through the second potentiometer P2 to generate a proportional voltage that is fed into the other side of amplifier 170. The resultant output signal ~ generated is described by squation (8) where the coefficients K 1 and K~ correspond to the settings of the potentio-meters Pl and P2 respectively.
Position information may be obtained in this embodiment by integration of velocity (or double integration of accelération if such sensors are used), and difference in position can be computed by integra-tion of the velocity difference (or double integration of the acceleration difference) as shown ln Fig. 9, velocity data is equivalent to position information for the purpose of measurement. The effsct of initial 1 ~2577~

-2~-conditions associated with integration disappear quickly since the analysis of amplitude is made duriny many c~cles of periodic excitation of t~e loop for each point of measurement o~ mass flow rate.
In the illustrated embodiment, the s~nse coils 164 and 166 are connected serially so that, as suggested above, parallel motion of the tube portions 165-167 will produce opposing currents in the resistor R, thus resulting in a net voltage drop across R of 0.
Under influence of flow through the tubes, induced Coriolis forces in the portions 165 and 167 will cause relative movement of these tube sections in opposite directions, and a net current resulting from the sum of the induced voltages in the sense coils 164 and 166 will be delivered through the resistor R. As indica-ted above, the voltage developed across resistor R iS
then fed into the differential amplifier 168 and the output thereof is integrated by 172 to convert the signal Sl, which represents the velocity difference between the relative motion between the tubes 161 and 165 and the tubes 163 and 167, to a separation dif-~erence signal So.
In Fig. 10 the relationship between steady state signals with sinusoidal drive velocity is illustrated.
More particularly, in part (a) of Fig. 10, the drive position of tube 130 is shown by the solid line 174, while the velocity curve corresponding thereto is shown by the dashed line 175. It will be noted that the velocity is the derivative of the driving motion and is therefore 90 degree out-o~-phase the~ewith. If there were no flow in the illustrated tube, it will be appreciated that the position o~ the tube segments 165 and 167 would be in phase with the position of tube segment 130. These positions are illustrated by the 57~78;~

drive component curves 176 in part (c) and 177 in part (b) of Fig. 10. Similarly, it will be appreciated that any Corioli~ induced deflection will be nearly in-phase with the velocity component o~ the drive motion, and will be positive with respect to tube ~egment 167 and negative with respect to tube segment 165.
Accordingly, by summing the Coriolis components and the drive components, the Coriolis induced positional displacements of tube segments 167 and 165 can be derived, and such displacements are respectively illustrated in parts (b) and (c) by the indicated waveforms 178 and 179.
In part (d), the difference between the position of curves 165 and 167 is depicted as 180 with no visible phase lag between drive velocity and Coriolis force. In actuality, it will be noted that there is a small phase lag of approximately minus ~ne degree depending upon drive~"Coriolis mode", natural fre-quency ratio and damping. Curve 181 illustrates this with exaggerated magnitude. Note also that the magni-tude of the Coriolis component 178 or 179 is very small compared with the drive components 171 and 176, and that Fig. 10 shows exaggerated size of the Coriolis component for ea~e of illustration.
For effective signal analysis ~sing digital sam-pling of the drive velocity and the response to the Coriolis force, it is desirable that these signals be synchronized. By suitable selection of the settings of potentimeters Pl and P2 of the circuit of Fig. 9 appropriate compensation can be made such that the signal S2 is caused to be closely in pha~e with the drive velocity signal.
In order to increase the sensitivity of the devices heretofore described, one possible modifica-~ ~5'77~

tion is to extend the portions of the loop which are ~ubject to Coriolis forces. In Figs. 1] and 12 such extensions are illustrated wherein the loop sides 182 and 183 are lengthened. However, in so doing two potential problems may be encountered, i.e., "wobble"
and l'roll". In Fig. 11 the problem of wobble due to bending of the lengthened tube sections in the vertical direction, as illustrated by the dashed lines 184, as the loop is driven. In order to stiEfen the sides 182 to avoid the wobble problem, one solution is to attach stiffening plates 185 to each side 182 so that the sides are no longer free to bow.
The second problem that is encountered with such modification, the problem o rolling, is illustrated in Fig. 12 by the dashed lines 186. In this situation there is a tendency for the loop 182 to deflect in the plane of the loop, or in effect to "roll", either leftwardly or rightwardly (parall~l to the X-Y
plane). In order to eliminate this tendency, roll restraint arms such as those illustrated at 187 and 188 may be utilized. The restraint arms may be in the form of rigid or semi-rigid rods or bars welded directly to the tube at either end. However, these members could also be in the form of flexible cables since the restraint imposed is tensil in nature. It will also be appreciated that a combination of the two solutions shown in Figs. Ll and 12 might also be utilized to avoid both roll and wobble deformation.
In Fig. 13 an alternative sensing arrangement is illustrated wherein instead of utilizing an electro-magnetic sensing means to ~ense relative motion between adjacent tube segments, or a tube segment and a base, a fiber optic sensor may be utilized. In this case a ~iber ~ptic bundle 190 is attached to the upper s~

tube 192 and a reflective plate 195 is attached to the low~r tube l94 ~or to a base). The fiber optic sensor apparatus 196 then causes a beam of 1ight to pass through a portion of the optical bundle l90, be reflected by the surface 195 and be returned through a different portion of the bundle l90 to the sensor 196 to effect positional detection. It will of course be understood that any other suitable means of detecting relative position or relative velocity or accellera-tion information may also be used in accordance with the present invention.
The inclusion of density measurement as part of this invention is illustrated in Fig. 14 wherein for simplicity the Coriolis measuring apparatus is not shown. This feature utilizes the fact that the cen-trifugal forces acting upon each element of the fluid flowing in the looped portion 202 of tube 200 is directed from the center of curvature for the element perpendicular to the tube section the element is in.
Since the loop is relatively flat, the centrifugal forces for the elements are not far removed from the plane of the drawing. Thus, the centrifugal force is inversely proportional to the radius of curvature for the element, proportional to the mass within the element and proportional to the square of the fluid velocity. Moreover, the centrifugal forces on the output half 204 of the loop will cause a pull to the left at point 205 and the forces on the input half 206 of the loop will cause a pull to the right at point 205. The opposing orces at 205 will thus cause a qtrain in the material that is related to the aggregate of the centrifugal forces on the whole test ~ection. Since the Coriolis forces cause no strain at the point 205, measurement of the strain at that point ~ ~7~7~1~

204 may be accomplished usiny a simple strain gauye 208. Moreover, a straln gauge measurement taken anywhere along the loop will urnish information permitting the accomplishment of a densit~ measure-ment in conjunction with the Coriolis mass flow rate measurement although the! calibration relationship will be more complex.
For the illustrated configuration, the ratio of the total centrifugal force for the half circle 2~4 acting in the horizontal direction at the point 2~5, and the total Coriolis force acting upon the same half circle is directly proportional to the velocity of the material in the fluifl and is independent of all other characteristics of the fluid.
The density of the material in the conduit is directly proportional to the square of the measured mass flow rate divided by the centrifugual force act-ing upon the half loop. One circuit by which such information may be developed i8 illustrated in Fig. 15 and includes a means 210 for sampling the drive signal Vl (from Fig. 7) and signal S2 (from Fig. 9), and strain gauge signal C (from Fig. 14), a means 212 for computing the mass flow rate Fmassfrom the sampled signals Vl and S~, a means 214 for calculating the centrifugal force Pcentr. from the strain gauge signal C, and a means 216 for calculating the density from mass flow rate and centrifugal force.
Although the present invention has been described above by referring to several examples illustrated in ~he drawing, it is to be understood that such embodi-ments are presented for illustration only and are not intended to in any way be limiting. It is intended that the appended claims be interpreted as covering all embodiments, alterations and modifications as fall 7~3 within the true spirit and scope of the invention.
What is claimed is:

Claims (20)

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. A flow meter for measuring the mass flow rate in a stream of flowing material, comprising:
tubular conduit means arranged to form at least one loop having an entrance portion, an exit portion crossing said entrance portion in spaced apart relationship, an actuated portion, a first detection portion coupling said entrance portion and said actuated portion, and a second detection portion coupling said actuated portion and said exit portion, said conduit means being adapted to receive, conduct and then emit said stream of flowing material and having a natural frequency of oscillation in the Coriolis mode of WC and a natural frequency of oscillation in the drive mode of WD, where wDis substantially different from wC;
actuating means for causing said actuated portion to oscillate between positions on opposite sides of a rest position;
damping means coupled to said tubular conduit means for allowing selective adjustment of the damping coefficient thereof;
detection means for detecting motive differences occurring between said entrance portion and said exit portion caused by Coriolis forces induced in said first detection portion of said second detection portion as said actuating means causes said actuated portion to oscillate;
and computing and indicator means responsive to said detection means and operative to indicate the mass flow rate of material flowing through said tubular conduit means.

2. A flow meter as recited in claim 1 wherein said detection means includes a first sensor means for detecting the dynamic position of said first detection portion relative to a reference and for generating a first position signal, and second sensor means for detecting the dynamic position of said second detection portion relative to said reference and for generating a second position signal, said computing and indicator means utilizing the difference between said first and second position signals to provide an indication of the mass flow rate of material flowing through said tubular conduit means.

3. A flow meter as recited in claim 2 wherein said first sensor means includes an electromagnetic signal generator having a first magnetic element affixed to said reference and a second magnetic element affixed to said first detection portion, said second element being magnetically coupled to said first element and disposed to move relative thereto.

4. A flow meter as recited in claim 1 wherein said tubular conduit means includes two identical serially connected loops of the type recited in claim 1 wherein the exit portion of one loop is connected to the entrance position of the other loop and wherein said damping means is coupled between the juncture of said first and second loops and said reference.

5. A flow meter as recited in claim 4 wherein said damping means includes an electromagnetic signal generator having a first magnetic component affixed to said reference and a second magnetic component affixed to said juncture, said second component being magnetically coupled to said first component and disposed to move relative thereto, and resistive load means coupled to said first magnetic component and operative to dissipate energy induced therein by relative movement of said second component.

6. A flow meter as recited in claim 1 wherein said tubular conduit means includes two loops of the type recited in claim 1 connected to form parallel flow paths and having corresponding parts disposed in spaced apart parallel relationship, and wherein said actuating means is coupled between the actuated portions of each loop and serves to apply simultaneous equal and oppositely directed actuating forces to each loop.

7. A flow meter as recited in claim 6 wherein said detection means includes a first sensor means coupled between the first detection portion of said first loop and the first detection portion of said second loop, and a second sensor means coupled between the second detection portion of said first loop and the second detection portion of said second loop, said first and second sensors being operative to develop output signals indicative of the motive relationships of the corresponding portions of said first and second loops.

8. A flow meter as recited in claim 7 wherein said first and second sensor means each include a pair of coaxially disposed electromagnetic windings and a permanent magnetic element magnetically coupled to both said windings, said windings being rigidly secured to one of said loops, and said magnetic element being rigidly secured to the other of said loop, and resistive impedance means connected to one winding of each said pair of windings for dissipating energy induced therein by movement of said magnet relative to said windings, and means connecting the other winding of each said pair of windings to said computing and indicator means.

9. A flow meter as recited in claim 1 wherein said tubular conduit means includes at least first and second loops of the type recited in claim 1 wherein the exit portion of one loop is connected to the entrance portion of the other loop to form a serial flow path for said flowing material.

10. A flow meter as recited in claim 7 wherein said first and second sensor means are velocity sensors and said computer and indicator means calculates mass flow rate according to the formula where .DELTA..theta. is the phase angle difference between the output signals developed by said first and second velocity sensor means;

K is a constant, or alternatively, a variable computed from measurement of the flow tube temperature related to Young's modulas;

WD is the natural frequency of the tubes in the drive mode;
WC is the actual natural frequency of tubes in the Coriolis mode; and ZC is the actual damping coefficient for the Coriolis mode.

11. A flow meter as recited in claim 7 wherein the outputs generated by said first and second sensor means are input to a difference amplifier in said computing and indicating means which generates a velocity difference signal that is input to a first input of a second difference amplifier and to an integrator which develops a separation difference signal which is input to a second input of said second differenceamplifier, and wherein in response thereto said second difference amplifier develops an output signal corresponding to the net Coriolis force sensed by said detection means.

12. A flow meter as recited in claim 6 or 9 wherein said actuating means includes a pair of coaxially disposed electromagnetic windings connected to one of said loops, and a permanent magnet element magnetically coupled to both said windings and physically connected to the other of said loops, one of said windings having a drive current applied thereto and acting to electromagnetically drive said magnet element and said other loop relative to said one loop, the motion of said magnet element relative to the other of said windings causing a velocity feedback current to be induced in said other winding proportional to the velocity of said other loop relative to said one loop.

13. A flow meter as recited in claims 6 or 9 wherein said actuating means includes a pair of coaxially disposed electromagnetic windings connected to one of said loops, and a permanent magnet element magnetically coupled to both said windings and physically connected to the other of said loops, one of said windings having a drive current applied thereto and acting to electromagnetically drive said magnet element and said other loop relative to said one loop, the motion of said magnet element relative to the other of said windings causing a velocity feedback current to be induced in said other winding proportional to the velocity of said other loop relative to said one loop, and wherein said actuating means further includes a source of periodic voltage, means responsive to said feedback current and operative to develop a feedback voltage, means responsive to said periodic voltage and said feedback voltage and operative to develop a drive voltage, and means responsive to said drive voltage and operative to develop said drive current.

14. A flow meter as recited in claim 1 wherein said tubular conduit means has a pair of elongated leg portions disposed to extend generally parallel with each other and respectively forming said first detection portion and said second detection portion, and further includes stiffener means attached to each said elongated leg portion to prevent it from bowing in the direction normal to a plane generally including said elongated leg portions.

15. A flow meter as recited in claim 1 wherein said tubular conduit means includes a pair of elongated leg portions respectively forming said first detection portion and said second detection portion, and further including a first roll restraint member coupling said entrance portion to one of said elongated leg portions, and a second roll restraint member coupling said exit portion to the other of said elongated leg portions whereby said loop is prevented from deflecting in the plane generally defined by said elongated leg portions.

16. A flow meter as recited in claim 1 and further comprising strain gauge means affixed to said tubular conduit means for developing a strain signal proportional to the centrifugal forces developed in said loop by said flowing material, and wherein said indicator means is further responsive to said strain signal and operative to use said strain signal in combination with the indicated mass flow rate to further indicate the density of the mass flowing through said tubular conduit means.

17. The flow meter as recited in claim 1 wherein said detection means detects a characteristic of the change in the spacing between said entrance portion and said exit portion at the crossover point.

18. A flow meter as recited in claim 17 wherein the said motive differences are the differences in arrival times of velocity signals corresponding to the motion of said entrance portion and said exit portion at one or more predetermined reference values.

19. A flow meter as recited in claim 1 wherein the said motive differences are the differences in arrival times of said entrance portion and said exit portion at one or more predetermined reference points of position, velocity or acceleration.

20. A flow meter as recited in claim 1 wherein said detection means detects a characteristic of the change in the spacing between said entrance portions and said exit portions at the crossover point.