Note: Descriptions are shown in the official language in which they were submitted.
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Specification
"Improved Apparatus For Mass Flow
Rate And Density Measurement"
Related Applications.
This application is related to the copending
U.S. application of Erik B. Dahlin entitled
"Apparatus For Mass Flow Rate And Density
Measurement", Serial No. 616,808, filed June 4, 1984
and assigned to the assignee of this application, now
U.S. Patent No. 4,711,132.
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 rake of a flowing mass using the effects of
Coriolis forces and centrifugal forces upon an
oscillatorally translated or deflected portion of one
or more loops of conduit through which the mass flow
is caused to pass.
Description of the Prior Art
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 conveyed through pipe lines and other var.ious
types of conduit. Prior art flow meters similar to
the present invention have in the past been embodied
as gyroscopic mass flow meters or Coriolis type mass
, ~
~2~
flow meters.
~ ne such device which utilizes Coriolis forces
to measure mass Elow is disclosed in U.S. P~tent ~Jo.
4,109,524 entitled "Method and ~pparatus for Mass ~low
Rate Measuremenl-", issued Aogllst 29, 1978 to ~James E.
Smith. In this patent an aPparat.US is lisclose~
wherein a mechanically reciprocating force is applied
to first and second sections of a linear conduit by
means of a beam that is dispossed parallel to the
first anfl second sections and has its ends mechani-
cally linked to the adjacent ends of the two conduit
sections. The adjacent ends o~ the first and second
conduit sections are connected together by means Oe a
short segment of conduit or flexible couplings and
the opposite ends of each conduit section is
separ~tely supported in cantilever fashion to a base
structure. The reciprocating forces applie-l to the
conduit are resisted by separate Coriolis forces 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
con~uits (and transferred to the beam) by the Coriolis
reactant forces, measurement of the mass flow through
the conduit may be made. ~owever, the measurement is
complicated because of the need to avoid spurious
measurements of the forces resulting from seismic or
other vibrational forces transmitted through the
support structure. Other similar devices are dis-
closed in the ~.S. patents to Wiley et al, No.
3,g80,750; Sipin, 3,218,851;Souriau, 3,3g6,579; and
Sipin, 3,329,019.
Rathee than use linear sections of conduit
that are pivoted at opposite ends and reciprocated at
~ ~577~
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the adjacent ends, a U-tube or similar con~iguration
is more commonly employed in mass flow measurement In
such cases the inlet and out1et ends Oe the leys o~
the U-shaped tube are fixedly mountecl to ~ base and
the bight end o~ the U-tube is reciprocated. 'rhe
differential displacement of corresponding portions
of the U-tube legs caused by Coriolis influence on
the flow is then measured as an indicator of mass
flow rate. Such a technique and apparatus is su~gested
in the above-mentioned Smith patent and is illustrat2d
in U.S. Patent No. 4,187,721 for "Method and Structure
for Flow Measurement" issued February 12, l9~ to
James E. Smith, now RE 31,450. As disclosed in the
referenced patent, a U-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 of the
U-shaped conduit and is used to provide up ancl 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
through a plane deined by the U-shaped conduit at
substantially the mid-point of its oscillation. The
time diEferential of passage 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-
ing electronics.are provided or cleveloping signal.s
corresponding to the passage of the side legs through
the midplane.
In U.S. Patent No. 4,127,028 entitled "Coriolis
~Z~
- ~ -
Mass Flow Rate Metering Means" issued Novernber ~,
1978 to Bruce M. Cox, et al, a pair of vibrating
generally U-shape~ tubes are fixedly mo~Jnted at the
inlet and outlet ends thereof, in parallely disposed,
spaced apart cantilevered ~ashion so that the bight
ends oE the respective tubes are free to move
relative to each other. An oscillatory drive
mechanism is connected between the bight ends of the
respoctive tubes and actuated to provide opposing
reciprocation thereof such that the U-shaped members
act as the tines of a tuning fork. The frequency of
the oscillation oE the tube is adjusted until the
tubes vibrate a fixed displacement when a known
material is flowing therethrough. The power needed to
vibrate the tubes the known dispiacement at a fixed
frequency determines the density of an unknown 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 ~or a single
tube embodiment. Cox also suggests that strain gages
or velocity sensors could be substituted for the
photodetectors, and acknowledges that it is known in
the prior art that there will be a phase shift between
the output-s or ~he two sensors which is proportional
to the Coriolis force couple.
The principle teaching of this re~erence 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 Eorces. This reference also illustrates a
looped tube configuration in Fig. 5 thereof, but fails
to teach or suggest how such configuration mi~ht be
used to provide enhanced flow measurement. It is
~2577~'~
therefore not believed to anticipat,e the present
invention.
Other prior art known to the present inventors
may be found in the U.S. Patents to Barnaby et al,
2,752,173, Roth 2,865,20l and 3,0~9,919; Sipin
3,355,9~4; ,Sipin 3,485,09~; Catheral,l 3,955,401 and
Shiota ~1,381,b~jt, and the EP~ application o~ Smith,
1 Publication No. EP 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 found in the
above-referenced Smith patent RE 3l,450.
A disadvantage of the Smith and Cox type of flow
measuring devices, as w9ll 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 imparted by Coriolis reaction forces, and
such forces interfere with the actual measurement of
mass flow.
Another disadvantage of the prior art U-tube
type devices is that they require right angle bends ',
outside the measuring sections of the conduit leading ,'
to an excessively large pressure drop.
Another disadvantage pertaining to the preferred
embodiments in the Smith Reissue RE 31,450 and Smith
4,42~,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 i,,
density is changing. ~,
Yet another disadvantage of the prior art ',
Coriolis type devices is that they are not capable Of b;
providing accurate flow data over a wide range of flow
due to limitations in sensitivity in the flow struc- .J,;
ture used.
.~,
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--6--
S~ill another disadvantage oE the prior art
devices is that they are not provided w;th dynclmic
damping means to reduce the sensitivity to externa]
vibrations.
Yet another disadvantafJe of the prior art
Coriolis type devices is that they utilize a directly
proportional relationship between mass flow rate and
differential phase angle or differential time measure-
ments.
Yet another disadvantage of the prior art
Coriolis type devices is that they have substantial
errors in mass flow rate if the temperature of the
sensing structure ch~nges.
SUMMA Y OF THE PRESENT I~VENTION
It is therefore a primary objective of the
present invention to provide a new and improved
apparatus oE the Coriolis type for measuring the mass
flow of a fluid or fluent solids, or mixtures oE
these passing through a conduit.
It is another object of the present invention
to provide a new an improved apparatus for measuring
the density of a mass flowing through a conduit.
A further object of the present invention is to
provide means for measuring mass flow rate and
density of a mass Elowing through a conduit without
introducing perturbing objects or mechanisms in the 5
fluid flow path.
~riefly, a preferred embodiment Oe the present
invention inc]udes at least one helically conEigured
loop of condult, means for causing oscillatory
translation of a portion of the loop in a direction
approximately normal to the direction of flow through
the conduit portion and approximately parallel to the
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central ~xis of the loop, and means for detecting the
effects of Coriolis forces e~erted on other portions
of the loop as a reslJlt o~ the mass flow therethrough
and the oscillatory translation thereof. ~ strain
gage and associated processing electronics are also
used in combination with the mass flo~ information to
determine the density of the flow.
An important advantage oE the present invention
is that it enables true mass flow measurement to be
made independent o-f variations of the physical proper-
ties 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
description of the perferred embodiments illustrated
in the several figures of the drawings.
IN THE DRAWINGS
Fig. 1 is a schematic diagram used to illustrate
theoretical operation of the present invention;
Fig~ 2 is a diagram schematically illustrating
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. 4 i~ a diagram schematically illustrating
a serial multi-loop embodiment in accordance with the 3
present invention;
Figs. 5-8 illustrate parallel flow multi-looped
embodiments of the present invention;
Fig. 9a is a diagram schematically illustratlng
one method of applying oscillatory energy to the loop i'
or loops in accordance with the present invention;
~;:
~'~5~77~'~
--8--
Fig. 9b is a diagram schematically illustrating
a damping technique used in accordanc0 with the
present invention;
Fig. 9c is a diagrarn schematically illust:ratincJ
a methoA of detecting the Coriolis ineluence on
multiple loops in accordance with the present
invention;
Fig. l~ is a set of waveforms illustrating
operatior. Qf he present invention;
Fig. 11 is a diagram illustrating an alternative
embodiment of a sensor for providing increased
sensitivity to measurement;
Fig. 12 is a partial cross section kaken along
the line 12-12 oE Fig. 11;
Fig. 13 illustrates an alternative method of
detecting the effects of 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
Fig. lS is a block diagram illustrating appara-
tus for computing density of a mass flow in accordance
with the present invention.
GENERAL T~IEORY OF OPERATION
~ he present invention is based upon the princi-
ple that ~ mass flowing through a looped tube or
other straight or curved conduit and experiencing a
velocity gradient transverse to the flow path will
interact with the wall of the conduit with a ~orce
directly related to the transverse velocity gradient
and the mass flow rate. When the velocity gradient
is caused by the transverse motion of the loop or
rotation of the loop about an axis other than the
., .
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~:~5~ 3~
central axis of the loop, the reaction i.s known as a
Coriolis force. The rnagnitude and direc~ion of the
reaction force depends upon the magnitude and direc-
tion of the mass flow. If two portions of the loop
have the same transverse velocity ~Jradient but have
opposite directions of flow, a force couple consisting
of equal and opposite reaction forces will result. In
accordance with the present invention the result of
this force couple is measured as a means of deterrnin-
ing the mass flow rate through the conduit.
Referring now to Fig. 1 of the drawings, for
purposes of illustation there is shown an example o~
a generali~ed helical loop of conduit 10, with its
crossed ends mounted to a base structure 12 and 1~.
The following general theory of the present invention
applies for any shape of helical structure and any
shape of tube cross-section.
The loop 10 may thus be considered to lie sub-
stantially in the X-Y plane only for purposes of sim-
plified mathematical ana]ysis; deviation o~ the tube
in the Z direction (normal to the X-Y plane) required
to permit crossover is ignored.
Accordingly, for a flow tube that is essentially
symmetric in the X-Y plane and around the X-axis, the
flow and total Coriolis force Pl/2 loop acting upon
each half section 16 and 18 respectively, is given by
the expression
Pl/2 loop Fmass VD (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 rate. f;
This equation can be used wlth anothe~ equation
, .
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to be presented be]ow to describe the dynamics of a
loop with the following approximations; narnely,
(1) the Cor;olis Eorces are assurned to be
lumped in a single point for each half loop "center oE
action point" instead of beiny distributed with
varying magnitude along the tube, (2) the ma.ss of
fluid and tube material are assumed to be lumped in a
single mass point for each half loop instead oE being
distributed 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, e~ch half-loop has a certain "participating
mass". The center of action is the point where the
resultant force of the distributed force for a half-
loop is applied and can be computed from th~ particu-
lar tube geometry and the general Coriolis force
formula for individual 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 natural frequency of the bending mode of
oscillation around the X-axis and by comparing it with
the theoretical natural frequency of the diEEerential
equation to be presented. The participating mass is ~;
determine~ so that the two natural Erequencies agree.
The differential equation describ;ng inertial
force, damping Eorce and spring action force is: ~
Mpd (Z2zn) ~ A d~t n) ~ s(Z-ZD) = P1/2 loop (2) ?
~,
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where
~ is the damping factor including both natural
damping in the rnaterial and damping introduced by a
damping coil as de3cribed hereinbelow;
~ is the spring Eactor 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 hal~ of
the loop;
t is time;
2D 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 tl) above
expressed in radians/unit time is
Wth = ~ (3)
The mode of natural oscillation defined by equa-
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 7'
a sinusoidal signal having the same frequency.
Equation (1) above determines approximately the ;
magnitude of the Coriolis Eorce where vD has a
,
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~257~
sinusoidal time variation.
The phase shift between Pl~ and (Z-zD) in
accordance with equation (2) ls well understood as
published in the literture. For example see Grabbe,
Ramo, Woodridge, "~landbook of Automation Computation
an~ Control" volumn 1, pages 20-59. Defining the
damping coefficient z as
z = (1/2Wth)(~/Mp) (~)
if, for example, the drive frequency W is chosen as
0.5 times the natural frequency, Wth , and the damping
coefficient z is chosen as 0.1, then using equations
(2) and (3) above, the phase shift can be found to be
about -0.8 degrees.
In this example, from equation (4) it can be
determined that the ratio of damping factor A to mass
Mp is
_ A _ = 0.02Wth
The amount of damping in this example results
from the application of a proper 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 oE 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 app~oximate phase shift
for a given fluid, and for implimenting an approximate
compensation for the phase shift by a particular
circuit to be described, the density change can be
.
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-13-
ignored.
A method to compensate approximately for the
phase shift between the Coriolis Eorce couple and the
structural position in a sinyle or multi-loop ernbodi-
ment will be described. [t is especia]ly useful for
digital signa] analysis of the waveforms such as
described herein. It is also applicablé for different
embodiments of the motion sensing devices as presented
herein, The structual deflection g, where g is
proportional to the magnitude of the Coriolis force
couple with a factor predetermined by calibration. A
linear combination of the time derivative g of g,
and the integral 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~gdt
= Klg + K2 g (6)
where g is a symbol defined by
g = dg/dt (7)
After L~nlace transformation G may be expressed
as
G(s) = KlS g(s) ~ K2g(s)
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
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~14-
will be no significant phase s~ift between the cornpu~
ted variable G and the drive point velocity vD in
equation (1) as loncJ as the drive velocity is apprGx-
imatel~ a si~ soidal ~unc~ion. Ilo~ever, ~ome
deviation from a sin~le sinewave ~harrnonic free) wave-
form is permissable; for example, as caused by
disturbing mechanical vibrations. Indeed, the
insensitivity to this type of disturbance is a strong
advantage of the present invention.
In perEorming signal analysis, the variable G and
the velocity of the drive point vD are sampled period-
ically. The rate would typically be 20 times for each
full cycle of application of the drive force. However,
in the presence of high frequency disturbing vibration
of strong magnitude, a much higher frequency would be
more suitable. A lower sampling rate speeds up the
signal analysis and may be desirable if the flow meter
is used for fast acting flow control.
The samples for G and vD 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 coupling
acting as the Coriolis force couple and the static
structure measurement "g stat" is
g 3 1/2 loop-static ~ )
For dynamic Coriolis forces, using equation (6)
the function G describing dynamic gap changes may be
expressed as
G = K1'R3g -~ K2 K3g (10)
where Kl'K3 = Kl and K2'K3 = K2 in equation (6).
For simplicity, it may be assumed that K2 is
selected as equal to l/K3 and
~7~
~15-
g (Kl /K 2)g (Il)
This expression illustrates that G is essen-
tially the differential position, velocity or acceler-
ation measurement modified by a derivative term ko
correct for the phase lag defined by equation (2)
above.
Since the variables Pl/2l00pand G are approxi-
mately in phase due to the compensation defined by
equation (ll), one can for a dynamic system use the
equation
Pl/2 loop= (1/K3)G (l2)
Similar to equation (9), using thi.s expression in
equation (1) and solving for G one obtains
G = 2K F v (13)
3 mass D
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
~ = 2K3F (14) J
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 llnes .
related to equation (19a)
oC = (~ GiVi)/(;~vi2 ) (15)
i-l i=l ,.
One can also use the other regression line which
is defined by
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-16-
1/~ ( ) (~ Giv~ Gi ) ~l6)
The line which divide.s the angle between the
two regression lines in half is given by
~ ( g = tan [1/2(arcTan ~ -~ arcTar ~ )1 (17)
and the estimate of the mass Elow from this line is
obtained from equation (14) as
FmaSs = (1/2K3) ~ ~V9) (18)
One may, of course, use either one of the
regression lines instead of the middle line. ~n illu-
stration of FmaSs computed using equations (14) and
(15) is given below and in Fig. 15.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring now to Fig. 2 of the drawing, a
simplified embodiment of the present invention is
illustrated. Tn this embodiment a circular loop 30 of
conduit is mounted to a base 32 by means of two
standards 34 and 36. Note that loop 3~ is deformed
upwardly ~way from the pipe line axis 37 at 38 and
down~ardly at 90 to provide clearance at the cross-
over point 41. Alternatively, the pipe line matching
deformations could have taken place o~tside the
standards 39 and 36.
Opposite cross-over point 41 a loop actuating
mechanism 42 is mounted to base 32 and has its Eorce
applying armature, or the like, electromagnetically
coupled to loop 30 at 44. Actuating means 42 i5 of
any suitable type which is capahle 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
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17-
suitable sens~s 46 and 4~ which sirnultan~ously
detect the motion ~positions or any tirne derivative
or time integral thereof such as velocity OK accell-
eration) o~ the loop points 50 and 52 relatlve to base
32 and communicate such measurement to a suitable
indicator means 54 which will provide a tneasurement of
the effects of the Coriolis forces and thus the mass
flow though loop 30. A suitable circuit would be one
which first calculates the difference between the
properly weighted signals produced by 46 and 48. The
weighting factors can be determined so that the
difference is zero at zero flow. Alternatively,
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 of the loop separation, relative velocity
or relative acceleration; such signal also serving to
cause indicator 54 to indicate the mass flow through
t~ f~ 30.
~ lthough the present invention as illustrated
in the embodiment of ~ig. 2 is a substantial
improvement over other prior 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 ~2 so as to prevent any
vibration in the pipe line from being transmitted to
the apparatus 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 transmltted 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 me~surement.
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-]8-
However, it will also be appreciated that seismic
disturbances may cause the loop 30 to move relakive to
the base and thus effect the accuracy of rneasuretnent.
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 41, 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 drive means directly to the base, the
drive means 60 is mounted to a counter-balancing
structure 62 which is 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
the loop 68, and is further provided with an
adjustment slide weight 7~ for allowing it to be
adjusted to match different densities of the fluid
expected to flow in loop 68. Accordingly, 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 flow meter drive 60 are effectively prevented r'
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-
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--19--
tion by the drive means 42(60), i.e., drive modestresses, are torsional rather than bending. On the
other hand, stresses at such points caused by Coriol i5
forces, i.e., Coriolis mo~3e stre.qses, are primarily
bending in nature.
In order to increase the sensitivity of the
present invention to Coriolis forces, serial and
parallel combinations of cross-over loops such as
are illustrated in Figs. 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 loop$ 70 and 72 at 74 causing deflection oE
the two loops in opposite directions. Means provided
at 76 and 78 could detect changes in separation, i.e.,
relative position, ve]ocity or acceleration between
the loops, with the d~namic difference in separation
being used for computation of the mass flow rate.
~lternatively, detecting of the loop separations at 80
and 82, or the diEference therebetween, could be
used as mass flow rate indicators. Similarly, detec-
tion of separation between the loops at 84 could like-
wise be utilized.
It will oE course also be appreciated that the
relati-ve posit.ons 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 of Fig. 4 has excellent flow sensitivity and is
especially suited for measuring low flow rates.
However, the structure is somewhat sensitive to
outside vibrations and may require the use of damping
schemes as described below.
In the parallel loop embodiment illustrated in
7~
-20-
Fig. 5, both loops are wound spirally in the same
direction, while in the Fig. 6 embodiment, the ~pper
loop is wound spirally advancin-~ downwardly whil~ the
lower loop is wound spirally advancing upwardly. With
actuating Eorces applied between the loops at 86 in
Fig. 5, and 88 in Fig. 6, in addition to the loop
separation differential measurements (position,
velocity, acceleration or other time derivatives or
integrals~ discussed relative to the Fig. 2
embodiment, measurements could be taken of the top gap
1~0 (114 in Fig. 6) or the bottom gap 102 (ll6), or
the difference between the top gap l00 (11~) and
bottom gap 102 (116) could be measured. Simllarly, 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 an(l lower loops on opposite sides of the
loops, and then calct~lating the differences between
these distances (or velocities or accelerations) is
the measurement mode which is believed to be the most
sensitive to mass -Elow rate. The mass flow rate
measurement sensitivity of the devices depicted in
Fig. 5 and Fig. 6 can be further improved by
configurin~ the loops in such a fashion that the ratio
of ~he length L to the height 1l is greater than unity, i~
i.e., L/l-l>l as shown in Fig. 8.
One such embodiment is illustrate~3 in Fig. 7
and 8 and includes a pair of axially elongated loops !~
125 and 127. The shape of the loops need not be ~.
precisely oval or rectangular but can be of arbitary
shape so long as L/H>l, where L is the loop length in
axis flow direction and 1l is the loop height in the ~I
1,
,,
transverse flow direction. Loops of this confiyura-
tion exhibit higher sensitivity to measuriny mass flo~
in comparison with loops that have L/fJ - l or L/fl < 1.
In general, this higher sensitivity results from the
fact that loops having L/~l > I exhibit a drive mode
natural fr?quel,cy Wth closer to the natural frequency
in the Coriolis mode, and therefore execute a larger
vibrational amplitude, i.e., a higher dynamic ampli-
fication factor, in the Coriolis mode for a given mass
flow rate and Coriolis force. Loops of this general
configuration exhibit significantly larger measurement
sensitivity and signal-to-noise ratios compared to
prior art devices. In fact, the sensitivity of the
loop, i.e., the desired degree of dynamic ampliEica-
tion, can be specified and selected by a suitable
choice of the L/H ratio. The ability to enhance the
measurement sensitivity of the loops in this fashion
is of particular interest when optimizing their
ability to measure small mass flow rates associated
with the flow of highly viscou~ fluids or dense gases.
In order to increase the sensitivity of some of
the devices heretofore described, one possible modi-
fication is to incorporate structural linkages at the
cross-over points in the loop configurations depicted
in Figs. 5, 7 and 8. These linkages are depicted in
dashed lines at 128 and 129 in Figs. 7 and 8 wherein
one link 129 connects the outermost legs of the loops
and another link 128 interconnects the innermost legs
at the loop cross-over points. These "cross-links"
are rigidly affixed to the flow tubes and would
typically be we~lded thereto. The width or thickness
oE the links is not cruicial to their performance.
The cross-links 128 and 129 enhance measurement
sensitivity to mass flow rate as revealed by the fol-
I
.,
~Z~7',, ~
-22-
lowing analysis. Careful examination of the structure
with cross-links, as shown in Fig. 7, indicates that
the structural sti~fness of the loop pair has been
substantially increased for vibrations in the drive
mode, i.e., response to forces applied approximately
a]ong the line of arrow D. However, the structures
stiffness for vibrational motion in the Coriolis mode
indicated by the arrow C remains substantially
unchanged from that when the linkages are absent.
Thus, the incorporation of these cross-links has the
effect of increasing the natural frequency of the
drive mode relative to the natural frequency of the
Coriolis mode, thereby increasing the dynamic
amplification factor of the structure and, hence, its
sensitivity to mass flow.
~ s an alternative embodiment of difference mea-
surement, the difference in phase angle O measured at
a given signal level for the position, velocity or
acceleration signals produced by sensors g6 and ~8 in
Fig. 2 can be used. If velocity sensors are used,
F would be calculated from the equation
tan 2 (19)
mass 2KRwD(sin~ - cos 0 tan ~ ~ )
where
ae is the phase angle difference between the
outputs of the two velocity sensors,
= ~r arctan( ~ z-) (20)
2 Wc -wD
wc
R = 2
~ (WC2-WD2~2+4Zc2 WD
K = loop "flexibility constant" definin~ the
change in loop position at one of the velocity sensor
:' '
~X7~,a,
-23-
locations per unit Coriolis force on the corresponding
half-loop. This constant K related to (~ouny's
Modu]~s) depencls on the temperature as well as
material and geometrical, dirnensions Oe t~le loop. As
a special embodiment, one can, durinq flowtneter usage
in a process, measure the ternperature of the tuhular
wall and input the value o-E the variable into a
computing circuit or digital computer and calculate
the current value of K. The change in K
with temperature is tabulated in literature or can be
determined experimentally. The value of K at a given
reference temper~ture is determined by calibration for
each flowmeter design or each individual unit.
Wc is the actual frequency of the mode excited
by the Coriolis forces (the Coriolis mode) and corre-
sponds to the theoretical value Wthin equation (3);
and
Zc is the actual damping coefficient for the
Coriolis mode (corresponds to the theoretical value z
in equation (4)).
Note that the phase angle differencea ~ is equal
to the drive frequency wD times the time difference
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
ll0 and 112 in Fig. 5. See Electronics and Radio
Engineering by Frederick E. Terman, McGraw-Hill
(1955).
Equation (193 is different from and more accur-
ate than the equations presented and implemented in
the prior art.
Using differential phase angle and drive
frequency measurement, it is desirable to drive the
device at its resonant frequency because the waveform
.:i
~,~
L~
--2~--
developed by detectors responding to Coriolis forces
will be free of harmonics. Using position or acceler-
ation sensors one can easily derive similar formulas.
Well known prior art apparatus capable of
detecting the phase angle diff~erence.s is disc]osed in
~pplications ~andbook of Precision Phase Measurement
(1975) by Dranet~ Engineering Laboratories, Inc. of
South Plainfield, New Jersey, and 11 lett-Packard
A~lication Note 2~0-3 (1974) entitled "Precision
~ .
Time Interval Measurement Using an Electronic
Counter".
'rurning now to Fig. 9a of the drawing, one
possible implementation of a drive system of the type
depicted at 42 in Fig. 2 is illustrated in detail.
Mounted to one tube 130 by means of a standoff 131 i 5
a permanent magnet 132. Attached to the loop directly
above, as illustrated by the tube segment l34, 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 coil 138, a
signal will be induced thereln which is proportional
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 a~ the current
il is proportional to the velocity diE~erence. The
voltage creatéd by il in the resistor Rl is input to
a diEferential applifier ~1, which in turn will gen-
erate a voltage signal Vl that is also proportional to
: ~,
. ,. . ,, .~;
;7~
-25-
the velocity diEEerence.
The voltage Vl is then subtracted by an analog
computing device 142 from an input voltage V0 gener-
ated by an oscillator 1~ that generates a suitable
periodic voltage signal Vo in a form such as a sine
wave. The difference V0-Vl =V2 is then fed into an
amplifier ~2 that generates a drive current i2 which,
on passing through the drive coil 136, produces a
magnetic fie1d that creates a magnetic force which
acts on permanent magnet 132 causing it to osc;llate
up and d~wn wi.hin the winding 136, thereby causing
loop 130 to be move~ up and down relative to loop 134.
The purpcse of the velocity feedback loop,
including winding 138 and amplifier A, 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.
The behavior of the closed feedback loop illu-
strated in Fig. 9a can be approximately described by
the transfer function
X = K2K3 (21)
V0 ms2+ s [a + KKl ~ K3 K4]
where K = velocity feedback loop gain (V/Vl)
X = the separation between the tubes at points
161 and 165 in Fig. 9c.
Kl is the gain factor (Vl/il),
K2 is the gain factor (i2/V2), r!
K3 is the force between drive coil l36, Fig. 7, 5:
and magnet 132 per unit current i2,
;i
j7 ~
-26-
K4 is the maynitude of current il per unit
velocity difference between drive coil 136 and
permanent magnet 13~,
s is the r~aplace oper~tor symbol,
m is the mass of both tubes 130 and 13~ and the
fluid contained therein including only the cir-
cular portion of the loops,
a is the damping factor of the structure for
\ the drive motion, and
b is the spring constant of the structure for
the drive motion.
The expression a ~ KKlK2K3K4 shows that the nor-
mally small damping constant "a" without the velocity
~eedback loop has been enhanced. By selection of
appropriate gain factors, damping can be chosen to
make the drive amplitude and response c~ignal 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
illustrated in Fig. 9a. ~owever, to accomplish damping
without velocity and amplitude control, a similar
system, such as is illustrated in Fig. 9b, 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 15~ such as was previously clescribed at 133 ''
in Fig. 9a. Th~ magnet 150 is disposed to move verti-
cally within a damping coil 156 which is rigidly
attached to a device base 15a. Connected acr~s~ the
l;
,, ~,
.
--27--
winding of coil 156 is a variable load resistor R.
The current induced in coil 156 by motion of the
magnet 150 therewithin creates a current whih passes
through resistor R and which i5 proportional to the
velocity of the motion of the maynet relative to coil
156. Energy generated by motion of the magnet within
coil 156 will be absorbed by energy dissipated in the
resistor R. Accordingly, 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
application.
~ s another alternative which is shown in ~ig. 9c
damping coi]s 160 and 162 can be physically tied to
velocity sense coils 164 and 166 in a double loop
serial (~ig. 4) or parallel (Figs. 5-8) device
configuration. In this particular 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 0. The output currents developed by
coils 16~ 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 S that is proportional to
the velocity difference between the relative motions
of tube portions 161 and 165, and 163 and 167 respec-
tively. lhe amplifiers 170 and 172, and the potentio-
meters Pl and P2 perform a phase-shieting function
to compensate for the phaseshift between the Coriolis
and the related motion oE the flow tubes as described
mathematically by the equations (2)-(8). This compen-
sation is an alternative design eeature which is
especially useful with digital signal analysis schemes
~;
i`
7~
-2~-
such as described by equations (9)-(18). The signal
Sl is fed through the variab~e potentiometer Pl to
generate a proportional voltage that is fed into one
side of the difference amplieier 170. Sim~ltaneously,
Sl is also fed through the integrator 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 Eed into the
nther side of amplifier l70. The resultant output
signal S2 generated is described by equation (~) where
the coefficients Kl and K2 correspond to the settings
of the pol-?ntiometèrs Pl and P2 respectively.
Position information is obtained in this
embodiment by integration oE velocity (or double
integration of acceleration if such sensors are used),
and difference in position can be computed by
integration of the velocity difference (or double
integration of the acceleration difference), as shown
in Fig. 9c, velocity data is equivalent to position
information for the purpose of measurement. The
effect of initial conditions associated with
inte~ration disappear quickly since the analysis of
amplitude is made during many cycles of periodic
excitation of the loop for each point of measurement
of mass flow rate.
In the illustrated embodiment, the sense coils
l6~ and 166 are connected serially so that, as
suggested above, in-phase motion of the tube portions
165-167 will produce opposing currents in the resistor j~
R, thus resulting in a net voltage drop ac~oss R of 0 Z
Under influence of ~low through the tubes, induced
Coriolis forces in the portions 165 and 167 will cause
relative movement of these tube sections in opposite p
directions, and a net current resulting from the sum
3~
3l~
.
--29--
of the induced voltages in the sense coils 15~ and l66
will be delivered through the resistor R As indica-
ted above, the voltage developed across resistor T~ is
then fed into the differential amplifier L68 and the
output thereof is integrated by 172 to convert the
signal Sl, which represents the velocity difference
between the relative motion between thé tubes 161 and
165 and the tubes 163 and 167, to a separation
difference 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 réla-
tive drive position of the tubes 130-13~ is shown by
the solid line 174, while the relative 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-
of-phase therewith. If there were no flow in the
illustrated tubes, it will be appreciated that the
position of the tube segments 165 and 167 would be
in phase with the position of tube segment 130. These
positions are illustrated by the drive component
curves 176 in part (c) and 177 in part (b) of ~ig. 10.
Similarly, it will be appreciated that any Coriolis
induced deflection will be nearly in-phase with the
velocity component of the drive motion, and will be
positive with respect to tube 5egment 167 and negative F
with respect to tube segment 165. ~ccordingly, by
summing the Coriolis components and the drive compon-
ents, 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
.
!,
::;
~57~7~
-30-
of curves 165 and 167 is depicted as 18~ with no
visible phase lag between drive velocity and Coriolis
force. In actuality, it will be noted that khere is
a small phase ]ag of approximately minus one deyree
depending upon drive, "Coriolis rnode", n~tural fre-
quency ratio and damping. Curve 181 illustrates this
with exaggerated magnitude. Note also that the magni-
I 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 ease of illustration.
For effective signal analysis using 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. 9c
appropriate compensation can be made such that the
signal S2 is caused to be exactly in phase with the
drive velocity signal.
A shortcoming of prior art velocity sensors of
the type disclosed in the above-identified EPO appli-
cation of J.E. Smith, is that they are prone to mass
flow measurement errors resulting from static deflec-
tions caused by thermal changes and variations in
static pressure within the flow tube structure. This
results from ~',e fact that the velocity sense coil of
the said prior art device is moving in a fringing and
s~atially non-uniform magnetic field. This results
in several undesirable effects all Oe which contrib~te
to mass flow measurement error.
The spatially non-uniform field within which
the sense coil moves results in unequal induced
current contributions (due to non~uniform flux
concentrations) in the upper and lower legs of the
~.
r:!
~.
~5~7~3.~
--3l--
coil. This can result in variations oE the induced
EMF and unwanted harmonic distortions in the induced
EMF that are spatially dependent and that also change
with static defections of the magnet and coil eyuili-
brium positions resulting in flow errors and ~ero
flow offset errors. Additionally, velocity sensors
o~ the type depicted in the above referred to
reference are more sensitive to relative motion of
the magnet and coil in directions other than that of
preEerential interest in maasuring mass flo~/. This
resul ts in more (unacceptable) sens i ti vi ty to
unwanted vibrations that degrade measurement accuracy
and signal-to-noise ratio.
The above-mentioned shortcomings can be alle-
vitated by configuring the sensor as shown in Figs.
11 and 12. In this embodiment, a permanent magnet
182 carried by ei ther another loop or a base
structure (not shown) Eorms a gap 184 into which i5
placed, for vertical movement as indicated by the
arrow 183, of slectrical conductor 186 wrapped about
a spool 187. Spool 187 is rigidly connected by a
bracket 188 to the loop conduit shown in broken part
at 189. ~s is well known by those skilled in the
art, the fl~x field created is the gap between the
pole faces of a magnet such as that illustrated, is
quite uniform, and a straight conductor (or bundle of
conductors) cutting through the flux field will have
induced therein an EMF that is directly proportional i
to its movement across the field so long as such
movement remains ~ ithin the conEines oE the gap.
~ccordingly, the EMF induced in the winding 186 will
be directly proportional to the vertical movement
(velocity) to loop 189 relative to the magnet 182 and i~
will not be subject to the disadvantages oE the prior
577~'~
-32
art mentioned above.
In Fig. l3 an alternative sensing arrangernent is
illustrated wherein instead oE utilizing an electro-
magnetic sensing means to sense relative motion
between adjacent tube segments, or a tube segment and
a base, a fiberoptic sensor may be utilized. In this
case a fiberoptic bundle 190 is attached to the upper
tube l92 and a reflective plate 195 is attached to the
lowe~ tube 194 (or to a base). The fiberoptic sensor
apparatus 196 then causes a beam of light to pass
through a portion of the optical bundle 190, be
reflected by the surface 195 and be returned through a
different portion of the bundle 190 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.
For the purpose oE technical analysis, it is assumed
that 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 curvacure 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 20~ of the loop
;1
3_2~j~7~1~
will cause a pul] to the left at point 2~5 and the
forces on the input half 206 of the loop will cause a
pull to the right at point 205, The oppo~ing forces
at 205 will thus cause a strain in the material that
is related to the aggregate of the centrifugal forces
on the whole test section. Since the Coriolis forces
cause no strain at the point 205, measurement of the
strain at that point 20~ may be accomplishecl using a
simple strain gauge 2U8. Moreover, a strain gauge
measurement taken anywhere along the loop will furnish
inEormation permitting the accomplishment of a density
measurement in conjunction with the Coriolis mass
flow rate measurement although the calibration rela-
tionship will be more complex.
- For the illustrated confiyuration, the ratio of
the total centrifugal force ~or the half-]oop 20
acting in the horizontal direction at the point 205,
and the total Coriolis force acting upon the same
half-loop is directly proportional to the velocity
of the material in the fluid 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 divided by the centrifugual force acting
upon the half-loop. One circuit by which such
information may be developed is illustrated in Fig. 15 t
and includes a means 210 for sampling the drive signal
Vl (from Fig. 9a) and signal S2 (from Fig. 9c), and
strain gauge signal C (Erom Fig. I4), a means 212 for
computing F~ssfrom the sampled signals Vl and S2 , a
means 214 Eor calculating the centri~ugal ~orce Pcentr ~l
from the strain gauge signal C, and a means 216 for ~l
calculating the density from Fma~S and Pcent. I~,
Although the present invention has been described il
!.~;,~
~'
7~ h
-3~-
above by referring to several examples illustrated in
the drawing, it is to be understood that such embo-li-
ments are presentqcl for ilLustration onl.y and are r,ot
intended to in any way be limiting. It is intended
that the appenZed claims be interpreted as covering
all embodiments, alterations and modifications as fall
within the true spirit and scope of the invention.
