Dec. 23, 1958
`
`Filed Auk. 26. 1954
`
`w. ROTH
`GYROSCOPIC MASS FLOWMETER
`
`' 2,865,201
`
`4 Sheets-Sheet 1
`
`m.
`F
`
`em
`
`FREQUENCY
`
`.
`INVENTOR.
`WILFR ED ROTH
`
`Quiz/‘,4
`
`AT T0 R NEXS ‘
`
`Micro Motion 1004
`
`1
`
`

`

`Dec. 23, 1958‘
`
`w. ROTH
`GYROSCOPIC MASS FLOWMETER
`
`2,865,201
`
`Filed Aug. 26. 1954
`
`4 Sheets-Sheet 2
`
`.3
`
`Lil»
`
`INVENTOR.
`WILFRED ROTH
`
`BY
`
`.
`
`£2 5
`
`%~¢,,,@-f%¢~
`
`5
`
`ATTORNEYS
`
`2
`
`

`

`Dec. 23, 1958
`
`Filed Aug. 26. 1954
`
`W. ROTH
`GYROSCOPIC MASS FLOWMETER
`
`2,865,201
`
`4 Sheets-Sheet 3
`
`FIG. 7b
`
`IN VEN TOR.
`WILFR E D ROTH
`
`ATTOR NEYS
`
`3
`
`

`

`Dec. 23, 1958
`
`w, RQTH _ f
`
`‘2,865,201
`
`I
`
`v
`
`GYROSCOPIC MASS FLQWMETER
`
`7
`
`Filed Aug. 26. 1954
`
`4 Sheets-Sheet 4
`
`FIG. 9
`
`78
`
`' 92)
`CURRENT
`AMPLIFIER
`
`IN V EN TOR.
`WILFRED ROTH
`
`BY
`QM,’ M2,“,
`ATTORNEYS
`
`4
`
`

`

`United States Patent
`10- rice
`
`2,865,203
`Patented Dec. 23, 1958
`
`2,865,201
`GYROSCOPIC MASS FLOWMETER ‘
`Wilfred Roth, West Hartford, Conn.
`Application August 26, 1954, Serial No. 452,437
`30 ‘Claims. (c1. 73-194) '
`
`10
`
`2
`strument, as described above. While the oscillation re
`moves the need for rotating joints, the rotating ?ywheel
`is considered highly undesirable for the reasons given
`above.
`It is a primary object of the present invention to'pro
`vide a mass ?owmeter of the gyrosco-pic type, wherein the
`loop is oscillated so as to avoid the need for rotating
`joints, and in which the need for a‘ rotating ?ywheel is
`avoided. An oscillating instrument is here termed the
`A.-C. type. Certain features of the invention, however,
`are applicable to a‘continuously rotating instrument, here
`ermed the D.-C. type. Although the apparatus of the
`invention is particularly useful in measuring the mass
`flow of fluids, generally speaking it is capable, with suit
`able design parameters, of measuring the mass ?ow of
`any ?uid-likev material.‘ ‘Such materials include emul
`sions, slurries of solid'particles'in a liquid or gaseous
`carrier, multi-phase mixtures of‘ liquids or gases, etc;
`The invention ‘will [be explained in conjunction with
`the accompanying drawings, and certain features will in
`part be pointed out and in part be evident from the draw
`ings and description thereof.
`In the drawings:
`Fig. 1 is a side view'of an AC.‘ mass ?owmeter; Figs.
`1a and lb are details illustrating suitable damping means;
`Fig. 2 is a view at right angles to that of Fig. 1;
`Fig. 3 is a detail showing the arrangement of the inlet
`and outlet conduit’ sections;
`Fig. 4 shows curves to explain‘ the non-resonant opera
`tion of the‘apparatus' of Figs. 1-3;.
`Fig. 5 is a circuit diagramv of an indicating device which
`may be used with the apparatusv of Figs. 1-3;
`Fig. 6 is another embodiment of an A.-C. mass flow
`meter with'simpli?ed indication;
`Fig. 7 is a further embodiment of .an A.-C. mass flow
`
`20
`
`This invention relates to ‘mass ?owmeters utilizing
`the gyro-scopic principle. The invention is especially di—
`rected to the provision of satisfactory A.-C. or oscillat
`ing ?owmeters, as distinguished from those of the D.-C.
`or continuously rotating type, although certain features
`are applicable to the latter.
`There is a considerable needin industry for an instru
`ment which will measure mass ?ow, as distinguished from
`volume ?ow. In many industrial processes it is the mass
`of a reagent that is important, rather than merely volume.
`Also, it is often advantageous to market ?uid-like mate
`rials according to their mass rather than volume. While
`mass ?ow is the product of volume ?ow and density, the
`density may vary depending upon‘ the exact constituents
`of the material, and usually varies considerably with tem
`perature.
`Thus the conversion of volume ?ow to mass "
`?ow is often di?icult. Even when such conversion is
`possible, it is advantageous to have an instrument which
`indicates mass ?ow directly.
`It has been suggested to employ the gyroscopic prin
`ciple in order to measure mass ?ow directly. In such an
`instrument the ?uid-like material is caused to ?ow in‘ a
`curved conduit, speci?cally a conduit in the form of a
`loop. For a given ?uid and conduit, the angular mo
`mentum varies with the rate of ?ow of the ?uid through
`the conduit. By virtue of the ?owing ?uid, the conduit
`is equivalent to the rotor of an ordinary gyroscope. If
`the loop is caused to rotate about an axis perpendicular
`to that of the angular momentum, a torque will be pro
`duced about the mutually‘ orthogonal axis. If, for ex
`ample, the loop is circular and is caused to rotate about
`a diameter thereof by a drive source, a torque or couple
`will be produced about an axis mutually perpendicular
`.to the axis of rotation and the axis of the loop. The in
`stantaneous value of this torque will be proportional to
`the instantaneous value of the angular momentum as de
`termined by the rate of mass ?ow of the ?uid, and the
`instantaneous value of the angular velocity of the loop
`about the drive axis.
`In one instrument of this general type which has been
`proposed, continuous rotation of the loop about one axis
`has been employed, and a rotating mass mounted con
`centrically with theaxis of the loop has been driven at
`an angular velocity controlled by gyroscopic couples pro
`duced by the ?owing liquid, but in a counter direction, so
`that the angular. momentum of the ?owing liquid is coun
`teracted by the angular momentum of the rotating mass.
`This produces a null type instrument. The use of a rotat
`ing mass in this manner is considered undesirable be
`cause of vthe added weight and complexity involved, to
`gether with the need for careful maintenance. Further
`more, a continuously rotating loop requires sealed rotat
`in‘g bearings which are relatively expensive, require care
`ful maintenance and may be troublesome with chemically
`active ?uids. or?uids at:h‘igh-‘pres‘sure.
`.
`"
`._
`It has alsobeen proposedto oscillate the loop, and
`employ a rotating ?ywheeltto produce a null type in- '
`
`meter;
`‘
`Fig. 7a is a detail showing the inlet and outlet con
`duit sections;
`.
`,
`Figs. 7b and 7c are details of a torque drive which
`may be employed with the apparatus of Fig. 7;
`Figs. 8 and 9 show curves illustrating the resonant op
`eration' of the apparatus of Fig. 7;
`,
`v
`Figs. 10 and 11 are details of an alternative form of
`torque drive which may be employed in the apparatus of
`Fig. 7; and
`V
`'
`,
`Fig. 12 is a diagram showing a torque feedback sys
`tem in accordance with the invention.
`Referring .now to Fig. 1, .a ?uid conduit-10 is arranged
`in the form‘ of a loop and attached to support members
`31, 31'. As speci?cally shown the loop is circular, but
`other conrigurations‘could'be employed if desired. Inlet
`and outlet ?uid conduit‘ sections 11 and Y12 extend from
`adjacent points 13, 13’ of the loop to approximately the
`center of the loop. ‘As here shown, conduit sections 11
`and 12 are of ?exible hose and secured to the horizontal
`support member 14 by 'a band 15. Or, the sections 11, 12
`can be extensions ofthe tubing of 'loop IlLeXtending in
`wardly to the loop axis in the manner shown" but without
`the restraining band 15, and v?exiblecouplings attached
`to the tube sections near the center of the loop.
`The loop 10 is‘mounted for angular movement with
`respect to member14 by suitable means which are here
`shown as short lengths of ‘music wire 16, 16'. Thus, the
`loop 10 is mounted for‘ angular movement about an axis
`approximately in the plane' of the loop, and the lengths
`of music wire form torsional springs which produce a re~
`storing moment when the loop 10 is angularly de?ected on
`either side of the. central position illustrated.
`The loop‘ vand its associated support member 14' is
`mounted for rotation about an axis approximately per
`pendicular to‘ that ofmcmber 14 by a member 17, here
`
`40
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`45
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`55
`
`60
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`65
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`70
`
`5
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`

`

`,.
`
`2,865,201 -
`
`Y
`
`Cl
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`10
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`20
`
`4.0
`
`3
`shown ‘as mounted for rotation about a vertical axis by
`bearings 18, 18' in a suitable housing 19. The loop 10
`may be oscillated about the vertical axis by motor 21 and
`eccentric cam 22 hearing against a rod 23 a?ixed to ver
`tical member 17 by a collar 24. Spring means 25 is at
`tached at one end to rod 23 and at the other end to a
`stationary support 26 so as to hold rod 23 in engagement
`.with eccentric cam 22. For convenience of illustration,
`the point at Which the spring 25 is attached to support 26
`is shown lying above the rod, but in practice it will be
`understood that the point of attachment will ordinarily
`be substantially on a line with rod 23. While an eccentric
`cam is speci?cally illustrated, any other suitable means
`for oscillating the loop about the vertical axis may be
`employed.
`Since a constant frequency of oscillation at the selected
`frequency of operation is desirable for accuracy, motor 21
`is advantageously of the synchronous type. Other types
`may of course be employed if due care is taken to assure
`constant speed under existing operating conditions.
`In operation, ?uid is supplied to the loop through one
`of conduit sections 11, 12 and led away from the loop
`through the other section. In ?owing through loop 10,
`the mass of the ?uid creates an angular momentum which
`is proportional to the rate of mass ?ow of the ?uid. When
`the loop is rotated about the vertical axis, a torque is
`developed about the horizontal axis of member 14 which
`is proportional to the vector product of the instantaneous
`value of the angular momentum and the instantaneous
`value of the angular velocity about the vertical axis.
`Both of these quantities have direction as well as magni
`tude. Hence if the direction of ?uid ?ow or angular
`velocity is reversed, the resulting torque will be reversed.
`With a sinusoidal oscillation, as provided by the drive
`motor 21 and cam 22 in Fig. 1, the resulting torque will
`also be sinusoidal.
`The movement produced by this torque is restrained by
`music wires 16, 16' and hence the loop 10 oscillates
`about the horizontal axis at the frequency of the vertical
`oscillation and with an amplitude proportional to the rate
`of mass ?ow.
`A transducer is associated with the loop which is sensi
`tive to gyro-scopic couples produced by the loop about the
`horizontal axis of 14. As here illustrated, the transducer
`is of the velocity type so as to yield an output proportional
`to the angular velocity of thewloop about the axis of 14.
`In the form illustrated, a coil 27 is attached to the loop 10
`and a portion thereof moves in an air gap of magnet 28.
`The magnet may be of the permanent type or magnet
`ized by a suitable ?eld coil.
`Connections 29 to the coil
`are provided so that the electric potential induced in the
`coil as the position of the coil in the magnetic ?eld varies
`may be supplied to an indicating instrument.
`Although many types of transducers to measure dis
`placement or vits time derivatives, or stresses, strains and
`the like, can be employed, such as resistance wire strain
`gauges, magnetostrictive strain gauges, piezoelectric strain
`gauges, differential transformers, etc., those of the veloc
`ity type are preferred at the present time.
`In a structure of the type described, the maximum or
`peak angular displacement of the loop from its central
`position varies with the rate of mass ?ow. Also, the
`angular acceleration of the loop is a maximum at maxi
`mum displacement. If a transducer is employed which
`is responsive to either displacement or acceleration, the
`peak instantaneous values of the output will occur when
`the loop is at its maximum excursion from the zero or
`neutral position. This varies with each value of rate
`of mass ?ow. Consequently, if an output linear with rate
`of mass ?ow is desired,the peak displacement of the loop
`must be linear over the desired range of mass ?ow
`measurements. This may be di?icult to achieve in prac
`tice since any non-linearity in the restoring moment of
`torsional springs 16, 16’ or non-linearities elsewhere in
`
`the system will impair the linearity of the transducer
`output.
`On the other hand, the angular velocity of the loop is
`a maximum as the loop passes through the zero or neu
`tral position. Consequently, if a transducer responsive
`to the velocity of the loop is employed, the peak in
`stantaneous values of the output will always be produced
`at the same point in the oscillating arc of the loop, namely,
`at the zero position thereof, regardless of the rate of mass
`?ow therethrough. Thus, the effect of non-linearities in
`the oscillatory motion of the loop is greatly reduced or
`entirely eliminated.
`‘
`A velocity-type transducer or pick-up is particularly
`advantageous‘ when combined with a peak detector cir
`cuit. An example of such a circuit will be described here
`inafter in connection with Fig. 5.
`An important aspect of the present invention lies in
`the arrangement of the conduit sections for leading ?uid
`to and from the loop. Among the advantages of the ar
`rangement provided is that of preventing so-called Coriolis
`forces from affecting the accuracy of measurement.
`When a pipe or conduit containing a ?owing ?uid is
`subjected to angular movement transverse to its axis, the
`walls of the pipe must exert a force on the ?owing ?uid
`to impart angular acceleration thereto. This is known
`as Coriolis force. The force varies with rate of mass ?ow
`of the ?uid in the pipe, and in an apparatus of the type
`herein considered would introduce an error unless the
`force is eliminated or the apparatus designed so that the
`force does not affect the output.
`In the apparatus of Fig. 1, conduit section 11 rotates
`about the drive axis 17 and hence, when ?uid is ?owing
`outwardly from the center, a Coriolis force is present
`which is substantially in a plane perpendicular to the
`drive axis (horizontal plane as speci?cally illustrated)
`and creates a torque about the drive axis. Similarly, a
`Coriolis force is present due to fluid ?ow in conduit sec
`tion 12, but since the ?uid ?ow is inwardly toward the
`center, the force and resulting torque about the drive
`axis opposes that of conduit 11. Hence, the effects of
`the two Coriolis forces substantially cancel and do not
`affect the output indication.
`In the arrangement of Fig. 1 a constant velocity drive
`source is employed, that is, a drive source whose angular
`velocity is relatively unaffected by the load thereon. In
`this case it is not essential that the Coriolis forces cancel,
`so long as they are effective only about the drive axis,
`since only an additional load would be imposed on the
`drive source and the output would be unaffected. This is
`accomplished in Fig. 1 by leading ?uid to and from the
`loop 10 by conduits substantially parallel to and closely
`adjacent the horizontal axis 14 about which the loop
`moves to produce an output signal, that is, the output
`axis of rotation. This relationship is helpful in the event
`that perfect cancellation of Coriolis forces is not obtained
`by the parallel counterilow feed. Rotation of the feed
`lines by 90° is of course possible with a close parallel
`counter?ow arrangement, or where the unbalance in
`Coriolis force is sufficiently small for the intended appli
`cation.
`An added feature is that by connecting the inlet and
`outlet conduit sections 11, 12 to external pipe lines, etc.,
`from points near the intersection of the axes of vertical
`member 17 and horizontal member 14, and by providing
`?exibility in the conduit sections near the intersection of
`the axes, any restraint in the freedom of the loop to oscil
`‘late due to the connections to the external pipe line, etc. -
`is reduced to a very small or negligible amount, since the
`moment arm about the center of rotation is small. In
`‘Fig. 1 this is accomplished by employing ?exible tubes or
`conduit sections 11, 12 and providing substantially right
`angle bends in the sections, as shown in Figs. 2 and 3.
`Fig. 7, to be described hereinafter, shows an alternative
`arrangement to the same end. In both figures, the loop
`structure can be dynamically balanced by adding or re
`
`60
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`75
`
`6
`
`

`

`5
`moving weight frommember >l4ionthej=opposite side- of
`the verticalaxis frornthe conduit sections.
`In an arrangement such as shown in-Eig; -1; the<loop10
`has a natural resonant'frequency of oscillation about the
`axis of member 14 due to the moment of inertia of the
`loop and the restoring moment provided by torsional
`springs 16, 16'. In accordance with well-known‘prin
`ciples of mechanics, the moment of inertia ofv the loop
`10 will include not only the mass and con?guration of
`the conduit itself, but also the mass and location of any
`members associated therewith such as the pickup coil 27
`and the inwardly projecting supports 31, 31'. Also, any
`stiffness of the conduit sections 11, 12 must be taken iinto
`account along with the stiffness of the torsional springs
`16, 16'. Furthermore, the natural resonant frequency
`of the loop 10 will be affected by the mass of the ?uid
`contained therein. While the volume of the ?uid is essen
`tially ?xed for a given instrument, the effective mass of
`the loop when ?lled with ?uid will vary with the density
`of the ?uid.
`,
`It has been found very important to select properly
`the frequency of oscillation of the loop about the vertical
`axis with respect to the natural resonant frequency of the
`loop about the horizontal axis in order to obtain an accu
`rate indication of mass flow when metering ?uids of
`varying density, or to meter ?uids of different densityv
`Without changing calibration. In accordance with one
`aspect of the invention, it is contemplated to oscillate the
`loop at a frequency which is low compared to'the natural
`resonant frequency of the loop.
`The curves of Fig. 4 will be helpful in understanding
`this condition of operation. Fig. 4 shows three sets of
`curves 32, 32’, 33, 33' and 34, 34’ for ?uids of different
`density. Frequency of oscillation is plotted along the
`horizontal axis and peak angular displacement (9m about
`axis of 14 is plotted for the vertical axis. The conditions
`plotted are for equal rates of mass flow.
`Analysis of a system such as that shown in Fig. 1 indi
`cates that the displacement 0 can be represented approxi
`mately by the following equation:
`9=_1_d_dW __2.’T.R_.._12¢‘: eim!
`g
`i kr(_l__w_2)
`was
`
`(1)
`
`.
`
`where 0=angular displacement in radians of loop 10
`about axis of 14.
`g=acceleration of gravity
`W=pounds of material ?owing across any cross-section
`t=time in seconds
`1
`R=radius of the loop in feet
`<p=maximum angular displacement of loop 10' about axis
`of 17 due to the constant velocity driving source in
`radians
`w=angular velocity of the constant velocity driving‘ source
`in radians/sec.
`kx=spring constant of the constraint about the torque
`axis 14 in lb.-ft./radian.
`v
`p
`,
`wx=natural resonant angular velocity of the loop 10
`about the torque axis 14.
`'
`The maximum or peak angular displacement, 4%,, is
`given by Equation 1 when 2”“:1.
`‘
`>
`This analysis indicates, as will be noted from Equation
`1, that the maximum angular displacement of the loop
`10, when driven by a constantvelocity source such as
`motor 21, varies vlinearly with the driving angular ve
`locity w regardless of the value of density at low driving
`frequencies where the quantity
`
`55
`
`60
`
`65
`
`70
`
`is small’ compared to unity.; This is the region 35 shown
`‘in Fig. 4. Frequency, rather than angular velocity, is
`
`75
`
`.
`‘6
`plotted‘in 'Fig. 4 since‘ it is the ‘quantity commonly
`measured; it being understood that frequency is
`1
`E
`
`10
`
`a times angular velocity.
`When the driving frequency approaches the natural
`resonant frequency f’ of the loop for a liquid of given
`density, a very large increase in displacement is ob
`tained, as shown by curves 32, 32’. In Fig. 4 damping
`has been neglected so that curves 32, 32' would intersect
`at in?nity. In any practical system, damping is of course
`present and will affect the shape of the curves. If the
`driving frequency is increased appreciably beyond the
`natural resonant frequency, the displacement 0m drops
`off inversely with frequency.
`-
`With a ?uid of lower density, similar curves will be
`obtained but the natural resonant frequency will lie at a
`higher frequency such as shown at f” in Fig. 4. For a
`?uid of still lower density the natural resonant frequency
`will be still higher, as indicated at f'”.
`As above mentioned, in accordance with one feature
`of the present invention it is contemplated applying a
`driving frequency which will be su?iciently low com
`pared with the natural resonant frequency of the loop
`when ?lled with ?uid of density within a predetermined
`range so that the apparatus will operate within the region
`35 indicated in Fig. 4.
`1
`For a given selected frequency in this range, i. e., for
`
`30
`
`(032
`small compared to unity, Equation 1 indicates that the
`maximum angular displacement will be proportional to
`the mass ?ow.
`The selection of a particular operating frequency will,
`of course, depend upon the design parameters of the ap- 4
`paratus and the range of‘ ?uid densities over which it is
`desired to employ the instrument. It will be understood
`that a portion of the moment of inertia of the loop struc
`ture will be that due to the material of which the loop
`is constructed, and the remainder will be contributed by
`the mass of the ?uid therein. Thus, only a fraction of
`the total moment of inertia will be subject to change by
`variations in ?uid density. The torque per se about the
`axis of member 14 Will be unaffected by the moment of
`inertia of the loop structure, since it is a function of rate
`of mass iiow through the loop. However, the displace
`merit of the loop about the axis of member 14, and the
`resulting angular velocity and acceleration, will be af
`fected by the moment of inertia of the loop structure.
`Thus with a pickup transducer sensitive to one of these
`quantities, the greater the ?xed component of inertia, the
`less the output of the transducer will be affected by
`changes in the ?uid density. Of course, it is not desirable
`to make the loop structure too massive, since the sensi
`tivity of the instrument will be reduced or more ampli?
`cation required, more driving power will be required, and
`greater acceleration forces will be encountered.
`For a given field of use, the variation in density of
`liquids likely to be encountered is not so great as to pre
`clude the selection of a proper driving frequency which
`will give accurate indications and adequately high output
`
`signal.
`
`'
`
`I
`
`It has been mentioned that damping inherent in any
`practical system will affect the shape of the curves of Fig.
`4. Where desired, damping can be introduced inten
`tionally so as to increase the frequency range of region
`35. Such damping can be introduced at 16, 16’ by in
`serting viscous material, by employing dash pots between
`loop 10 and the vertical member 17, by employing elec
`trical damping such as eddy current damping, etc. These
`and many other forms ofdamping are well known in the
`art.
`
`7
`
`

`

`‘2,865,201
`
`Illustrative of the foregoing, Figs. 1a and 1b show eddy
`current and viscous damping, respectively. In Fig. 1a an
`electrically conductive metal plate 96 is secured to loop
`10 and arranged to oscillate in the ?eld of a magnet 97
`which may be of the permanent magnet type or energized
`by a suitable coil. Magnet 97 is stationary with respect
`to member 14 and is attached thereto by support mem
`ber 98. As the conductive plate 96 moves in the ?eld
`of magnet 97, eddy currents are created in plate 96 and
`damp the movement of the loop 10. Advantageously the
`plate 96 is mounted on loop 10 diametrically opposite the‘
`transducer coil 27 (Fig. 1) so as to lie in a plane per
`pendicular to the plane of the loop and passing through
`the axis of vertical member 17, as shown.
`In. Fig. 1b a plate 99 is attached to the loop 10 in a
`manner similar to plate 96 of Fig. 1a. In this ?gure, the
`plate 99 is arranged to oscillate in a container ltii?lled
`with a viscous liquid, such as a viscous oil, and the con
`tainer is attached to member 14 similar to magnet 97 in
`Fig. la. As plate 99 moves back and forth, it will shear
`the viscous liquid and hence dissipate energy.
`While variations in the displacement 0m with mass ?ow
`may be measured by a suitable transducer and used to
`indicate mass flow, as above pointed out it is advantageous
`to employ a velocity-type transducer. The output of such
`a transducer will be proportional to the time rate of
`change of 9 rather than 9 directly.
`Thus:
`
`10
`
`30
`
`where
`V=voltage output of the transducer
`k=a constant dependent on design of the transducer
`R'=-_—distance of the pickup from the axis 14 of rotation
`Curves similar to Fig. 4 may be drawn which indicate
`~ the variation in output with velocity-type pickups by dif-'
`ferentiating Equation 1 and plotting the results, exclusive
`of the factor aim‘. Although the shape of the curves will
`differ from those shown in Fig. 4, the conclusion as to the
`operating region described above will be evident there
`from.
`.
`The amplitude of oscillation in an apparatus like that
`of Fig. 1 can be made quite small. For example in one
`speci?c construction of an instrument designed to measure
`relatively low rates of mass ?ow, up to 10 pounds per
`minute. the amplitude of oscillation about the vertical axis
`was 10.5 degrees. For a full-scale mass flow of 10
`lbs/min. the maximum displacement of the loop about
`the horizontal axis was approximately 10.005 degree.
`The loop radius was 3.5", the operating frequency was 10
`cycles/second and the natural resonant frequency of the
`loop was 100 cycles/second. A relatively simple velocity
`pickup gave suf?cient output for convenient ampli?cation
`and indicationby a circuit similar to that shown in Fig. 5.
`Referring now to Fig. 5, a circuit is shown for receiving
`the output of apparatus such as shown in Fig. l, and giv
`ing a direct indication of rate of mass flow on a suitably
`calibrated meter. In Fig. 5 coil 27 is that shown in Figs.
`1 and 2 and supplies a voltage proportional to rate of
`mass flow to the circuit. A rejection ?lter 41 is advan- _
`tageously employed to reject any 60-cycle power line fre
`quencies. As here shown, it is of the so-called “twin T”
`type, but of course any suitable form of ?lter can be em
`ployed. The voltage variations from input coil 27 are
`ampli?ed in stages including tubes 42. Any suitable low
`frequency ampli?er design can be employed, that shown
`being found satisfactory. Such ampli?ers are well-known
`in the art so that detailed description is unnecesssary.
`The output of the last ampli?er stage is supplied to a
`recti?er 43, here shown as the crystal type. The recti?er
`is connected as a peak detector and the output ?ltered by
`suitable R-Q ?lter 44. The output of the ?lter circuit at
`point 45 thus consists of a D.-C. or slowly varying A.-C.
`
`00
`
`75
`
`8
`wave corresponding to the peak values of the signal in coil
`27. Ifthe rate of mass ?ow is constant, a constant D.-C.
`value will be obtained at 45, and as the rate of mass ?ow
`varies the voltage at point 45 will likewise vary.
`.
`' The detector output at point 45 is supplied to a thermi
`onic vacuum tube 46 connected as a cathode follower,
`and the voltage across cathode resistor 47 is supplied to
`one terminal of a micro-ammeter 48. Ammeter 48 may
`be shunted by a variable resistance 49 for calibration
`purposes. In order to make the indicator insensitive to
`line voltage variations and also to provide for setting the
`zero of meter 48, another tube 51 is provided which
`has its anode energized from the same B+ source as tube
`46, and its grid supplied with a constant positive bias
`from the same B-t- source through the voltage divider
`resistors 52, 53. The cathode circuit of tube 51 includes
`resistors 54, 54' and potentiometer 55 whose total re
`sistance is advantageously approximately equal to that
`of resistor 47. The other side of meter 48 is then con
`nected to the cathode of tube 51. The lower terminal of
`recti?er 43 is returned to a variable tap on potentiom
`eter 55, as shown, so that an adjustable D.-C. bias can be
`applied to the recti?er.
`Before making a measurement of mass flow, the zero
`of meter 48 can be set by adjusting the arm of potenti
`ometer 55. This impresses a positive bias on the grid
`on tube 46 through recti?er 43 and the resistance of
`?lter 44. The bias is so adjusted that the difference in
`potential between the cathodes of tubes 46 and 51 re
`sults in sufficient current through meter 48 to bring the
`pointer to the zero setting. Thereafter the pcsition of
`the pointer will vary with the rate of mass ?ow. Meter
`38 may be calibrated in arbitrary units or directly in
`terms of rate of mass ?ow for a given instrument.
`As before pointed out, it is advantageous in a mass
`?owmeter such as shown in Fig. 1 to employ a trans
`ducer of the velocity type which gives voltage peaks at
`the neutral axis which are proportional to rate of mass
`?ow. Thus, the effect of possible non-linearities in the
`oscillation of- the fluid conduit loop are relatively unim
`portant. Since the indicator of Fig. 5 employs peak
`detection, the meter 48 is sensitive only to variations
`in the peak amplitude of the applied wave and varia
`tions in the instantaneous voltage between peaks are un
`important. Thus, with relatively simple instrumentation
`an accurate indication of rate of mass flow is obtainable.
`The circuit arrangement of Fig. 5 is given merely as
`an example of a suitable arrangement employing peak
`detection which has been found satisfactory in practice.
`However, many other circuits are known in the art em
`ploying peak detection and any suitable form can be em
`ployed if desired. Also, with adequate linearity in the
`oscillation of the ?uid conduit loop, or wIth transducers
`other than those of the velocity type, other forms of de
`tectors can. of course, be employed.
`If the integrated mass ?ow is desired, rather than the
`instantaneous rate of mass flow, a suitable form of inte
`grating indicator can be employed in place of meter 48.
`For example, a watt-hour meter with one coil connected
`in place of meter 48 and the other coil energized from
`a constant voltage source could be employed.
`For less stringent applications the displacement of the
`loop may be indicated directly, as by means of a pointer,
`rather than employing a pickup transducer and associated
`circuitry such as described above.
`Fig. 6 illustrates such an arrangement, together with a
`loop and mounting arrangement which,-although not pos
`sessing all the advantages of that shown in Fig. 1, may
`nevertheless be employed in some applications. Here the
`loop 10 is mounted for rotation about a diameter thereof
`by bearings 56, 56"carried by a U-shaped frame 57.
`Frame 57 is mounted for rotation about an axis perpen
`dicular to that of bearings 56, 56’ by shaft 58 rotating
`in bearing housing 58’. p The loop may be oscillated about
`the'axis of 58 in the same manner as in Fig. 1.
`
`8
`
`

`

`10
`
`15
`
`25
`
`a decrease in resonant frequency due to increased ?uid
`density will result in an increased angular displacement
`of the loop (0). On the other hand, if the operating
`frequency is above the natural resonant frequency of the
`loop, a decrease in resonant frequency due to increased
`?uid density will result in a smaller angular displacement
`of the loop. With a constant torque drive source and a
`restoring moment about the vertical axis, such as shown
`in Fig. 7, similar statements can be made with respect
`to the amplitude of oscillations (<p in Equation 1) about
`the vertical axis. If the operating frequency is below
`the vertical resonant frequency, an increase in ?uid
`’ density will result in an increase in (p and hence an
`increase in angular displacement of the loop, 6, and vice
`versa.
`Since the moments of inertia and spring constants of
`the system about the vertical axis can be made different
`from those about the horizontal axis, the natural resonant
`frequencies about the two axes can be made different.
`Then, by selecting an operating frequency intermediate
`the two resonant frequencies, an increase in ?uid density
`will tend to increase the amplitude of oscillation about
`one axis and decrease it about the other. These two
`effects will tend to counteract each other, yielding an
`output relatively independent of. change of density over
`a limited range.
`' The functioning can be developed ,mathematically
`from Equation 1 by introducing the following equation
`for the maximum angular displacement about the vert