Note: Descriptions are shown in the official language in which they were submitted.
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Vibratory Transducer
This invention relates to a vibratory transducer which is particularly suited
for
use in a Coriolis mass flowmeter.
To determine the mass flow rate of a fluid flowing in a pipe and particularly
of
a liquid, use is frequently made of measuring devices which induce Coriolis
forces in the fluid and derive therefrom a measurement signal representative
of mass flow rate by means of a vibratory transducer and of control and
evaluation electronics connected thereto.
Such Coriolis mass flowmeters have been known and in industrial use for a
long time. EP-A 317 340, U.S. Patents 5,398,554, 5,476,013, 5,531,126,
5,691,485, 5,705,754, 5,796,012, 5,945,609, and 5,979,246 as well as
WO-A 99/51946, WO-A 99/40349, and WO-A 00/14485, for example,
disclose Coriolis mass flowmeters with a vibratory transducer which responds
to the mass flow rate of a fluid flowing in a pipe and comprises:
a single straight flow tube for conducting the fluid which vibrates in
operation
and communicates with the pipe via an inlet-side tube section and an outlet-
side tube section;
an excitation system which in operation excites the flow tube into flexural
vibrations in one tube plane; and
a sensor system for sensing inlet-side and outlet-side
vibrations of the flow tube.
As is well known, straight flow tubes excited into flexural vibrations
according
to a first form of natural vibrations cause Coriolis forces in the fluid
passing
therethrough. These, in turn, result in higher-order and/or lower-order
coplanar flexural vibrations according to a second form of natural vibrations
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being superimposed on the excited flexural vibrations, so that the vibrations
sensed on the inlet and outlet sides by means of the sensor system exhibit a
measurable phase difference, which is also dependent on mass flow rate.
Usually, the flow tubes of such transducers, which are used in Coriolis mass
flowmeters, for example, are excited in operation at an instantaneous
resonance frequency of the first form of natural vibrations, particularly with
the
vibration amplitude maintained constant. Since this resonance frequency is
also dependent on the instantaneous density of the fluid in particular,
commercially available Coriolis mass flowmeters can also be used to measure
the density of moving fluids.
One advantage of straight flow tubes is that they can be drained residue-free
with a high degree of reliability in virtually any position of installation
and
particularly after a cleaning operation performed in-line. Furthermore, such
flow tubes are much easier and,
consequently, less expensive to manufacture than, for example, an omega-
shaped or helically bent flow tube. A further advantage of a straight flow
tube
vibrating in the above-described manner over bent flow tubes is that in
operation, virtually no torsional vibrations are caused in the connected pipe
via the flow tube.
A significant disadvantage of such transducers consists in the fact that as a
result of alternating lateral deflections of the vibrating single flow tube,
transverse forces oscillating at the same frequency can act on the pipe, and
that so far it has been possible to counterbalance these transverse forces
only in a very limited manner and with a very large amount of technical
complexity.
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To improve the dynamic balance of the transducer and particularly reduce
such transverse forces produced by the vibrating single flow tube and acting
on the pipe on the inlet and outlet sides, the transducers disclosed in
EP-A 317 340, U.S. Patents 5,398,554, 5,531,126, 5,691,485, 5,796,012, and
5,979,246 as well as WO-A 00/14485 each comprise at least one single-part
or multipart "antivibrator" which is fixed to the flow tube on the inlet and
outlet
sides. In operation, such antivibrators, which are implemented in the form of
beams and particularly of tubes or as a physical pendulum aligned with the
flow tube, vibrate out of phase with, particularly opposite in phase to, the
respective flow tube, whereby the effect of the lateral transverse forces
exerted by the flow tube and the antivibrator on the pipe can be minimized or
even neutralized.
Such transducers with antivibrators have proved particularly effective in
applications where the fluid to be measured has a substantially constant or
only very slightly varying density, i.e., in applications where a resultant of
transverse forces produced by the flow tube and counterforces produced by
the antivibrator, which resultant acts on the connected pipe, can be readily
preset to zero.
If used for fluids with widely varying densities, such as different fluids to
be
measured in succession, such a transducer, particularly one as disclosed in
U.S. Patent 5,531,126 or 5,969,265, has practically the same disadvantage,
even though to a lesser degree, as a transducer without antivibrator, since
the
aforementioned resultants are also dependent on the density of the fluid and
thus may differ considerably from zero. In other words, in operation, even an
overall system composed of flow tube and antivibrator will be nonlocally
deflected from an assigned static rest position as a result of density-
dependent unbalances and associated transverse forces.
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One possibility of reducing the density-dependent transverse forces is
proposed, for example, in U.S. Patent 5,979,246, in WO-A 99/40394, or in
WO-A 00/14485. WO-A 00/14485, in particular, discloses a vibratory
transducer for a fluid flowing in a pipe, said transducer comprising:
a flow tube vibrating in operation, for conducting the fluid, the flow tube
communicating with the pipe via an inlet-side tube section and an outlet-side
tube section, and the vibrating flow tube being, at least temporarily,
laterally
displaced from an assigned static rest position as a result of transverse
forces
produced therein, so that transverse impulses occur in the transducer;
an excitation system for driving the flow tube;
a sensor system for sensing vibrations of the flow
tube; and
a first antivibrator, fixed to the inlet-side tube section, and a second
antivibrator, fixed to the outlet-side tube section, for producing
compensating
vibrations, the compensating vibrations being such that the transverse
impulses are compensated, so that a centroid of a vibration system formed by
the flow tube, the excitation system, the sensor system, and the two
cantilevers is kept in the same position.
WO-A 99/40394 discloses a vibratory transducer for a fluid flowing in a pipe,
said transducer comprising:
a flow tube vibrating in operation, for conducting the the fluid, the flow
tube
communicating with the pipe via an inlet-side tube section and an outlet-side
tube section; and
an antivibrator fixed to the flow tube on the inlet side and outlet side, with
transverse forces being produced in the vibrating flow tube and in the
antivibrator;
a transducer case fixed to the inlet-side tube section and the outlet-side
tube section;
an excitation system for driving the flow tube;
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a sensing system for sensing vibrations of the flow tube;
a first cantilever, fixed to the inlet-side tube section and to the transducer
case, for producing counterforces counteracting the transverse forces on the
inlet side; and
5 a second cantilever, fixed to the outlet-side tube section and to the
transducer case, for producing counterforces counteracting the transverse
forces on the outlet side, the counterforces being such that the flow tube is
held in an assigned static rest position despite the transverse forces
produced.
In the aforementioned transducers, including those described in U.S. Patent
5,979,246, the problem of density-dependent unbalances is solved in principle
by adapting an amplitude variation of the antivibrator to the flow-tube
vibrations in advance and/or in operation, particularly by making the spring
constants of the antivibrator amplitude-dependent, such that the forces
produced by the flow tube and the antivibrator neutralize each other.
Another possibility of reducing density-dependent transverse forces is
described, for example, in U.S. Patent 5,287,754, 5,705,754, or 5,796,010. In
the transducers disclosed therein, the transverse forces produced by the
vibrating single flow tube, which oscillate at medium or high frequencies, are
kept away from the pipe by means of an antivibrator that is very heavy in
comparison with the flow tube, and by coupling the flow tube to the pipe
relatively loosely, i.e., practically by means of a mechanical low-pass
filter. A
big disadvantage of such a transducer is, however, that the antivibrator mass
required to achieve sufficient damping increases disproportionately with the
nominal diameter of the flow tube. Use of such massive components, on the
one hand, entails both increased assembly costs during manufacture and
increased costs during installation of the measuring device in the pipe. On
the
other hand, it must always be ensured that a minimum natural frequency of
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the transducer, which decreases with increasing mass, is still far from the
likewise very low natural frequencies of the connected pipe. Thus, use of such
a transducer in industrial Coriolis mass flowmeters or Coriolis mass
flowmeter-densimeters and particularly in meters for measuring liquids is
limited to relatively small nominal diameters less than or equal to 10 mm.
It is therefore an object of the invention to provide a transducer which is
particularly suited for a Coriolis mass flowmeter or a Coriolis mass flowmeter-
densimeter and which in operation, even if it uses only a single, particularly
straight, flow tube, is dynamically well balanced over a wide fluid density
range and nevertheless has comparatively little mass.
To attain this object, the invention provides a vibratory transducer for a
fluid
flowing in a pipe, said transducer comprising:
a flow tube vibrating in operation, for conducting the fluid, the flow tube
communicating with the pipe via an inlet-side tube section and an outlet-side
tube section, and the vibrating flow tube being, at least temporarily,
laterally
displaced from an assigned static rest position as a result of transverse
impulses occurring in the transducer;
an excitation system for driving the flow tube;
a sensor system for sensing vibrations of the flow tube;
a first cantilever, fixed to the inlet-side tube section, for causing bending
moments that elastically deform the inlet-side tube section; and
a second cantilever, fixed to the outlet-side tube section, for causing
bending moments that elastically deform the outlet-side tube section,
the bending moments being such that in the deforming inlet-side tube
section and in the deforming outlet-side tube section, impulses are produced
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which are directed opposite to the transverse impulses produced in the
vibrating flow tube.
Furthermore, the invention provides a vibratory transducer for a fluid flowing
in
a pipe, said transducer comprising:
a flow tube vibrating operation, for conducting the fluid, the flow tube
communicating with the pipe via an inlet-side tube section and an outlet-side
tube section, and the vibrating flow tube being, at least temporarily,
laterally
displaced from an assigned rest position as a result of transverse forces
produced in the flow tube;
an excitation system for driving the flow tube;
a sensor system for sensing vibrations of the flow tube;
a first cantilever for causing bending moments that elastically deform the
inlet-side tube section, said first cantilever having a cantilever arm rigidly
fixed
to the inlet-side tube section and a cantilever mass formed thereon;
a second cantilever for causing bending moments that elastically deform the
outlet-side tube section, said second cantilever having a cantilever arm
rigidly
fixed to the outlet-side tube section and a cantilever mass formed thereon,
both the cantilever mass of the first cantilever and the cantilever mass
of the second cantilever being spaced from the flow tube, from the inlet-side
tube section, and from the outlet-side tube section, and
the cantilever arm and cantilever mass of the first cantilever and the
cantilever arm and cantilever mass of the second cantilever being so adapted
to one another that a centroid of the first cantilever, located in the area of
the
inlet-side tube section, and a centroid of the second cantilever, located in
the
area of the outlet-side tube section, remain essentially in a static rest
position
although the flow tube is laterally displaced from its assigned static rest
position.
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In a first preferred embodiment of the invention, the deforming inlet-side
tube
section and the deforming outlet-side tube section bend essentially in a
direction opposite to that of the lateral displacement of the flow tube.
In a second preferred embodiment of the invention, the flow tube is
substantially straight.
In a third preferred embodiment of the invention, the vibrating flow tube
performs flexural vibrations.
In a fourth preferred embodiment of the invention, each of the two cantilevers
is at least as heavy as the flow tube.
In a fifth preferred embodiment of the invention, the transducer comprises an
antivibrator fixed to the flow tube on the inlet and outlet sides.
In a sixth preferred embodiment of the invention, the antivibrator is tubular
in
form.
In a seventh preferred embodiment of the invention, the flow tube at least
partly is enclosed by the antivibrator.
In an eighth preferred embodiment of the invention, the flow tube and the
antivibrator are coaxial.
In a ninth preferred embodiment of the invention, discrete mass pieces are
fixed to the antivibrator.
In a tenth preferred embodiment of the invention, grooves are formed in the
antivibrator.
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In an eleventh preferred embodiment of the invention, the mass pieces fixed
to the antivibrator are annular in shape and coaxial with the antivibrator.
A fundamental idea of the invention is to convert lateral displacement motions
of the vibrating flow tube, which tend to interfere with the measurements
and/or have a disturbing effect on the connected pipe and which are
superimposed on the tube's primary deformations, i.e., on the deformations to
be measured, into oppositely directed deformations of the inlet-side and
outlet-side tube sections that dynamically balance the transducer.
One advantage of the invention is that, on the one hand, the transducer is
very well balanced despite possible operation-dependent variations of the
internal mass distribution, and thus also independently of the density of the
fluid, namely exclusively as a result of its internal geometry forced by means
of cantilevers, whereby internal transverse impulses and transverse forces
can be largely kept away from the connected pipe. On the other hand, the
internal deformation forces necessary therefor essentially do not act beyond
the transducer, particularly not on the pipe.
The transducer according to the invention is further characterized by the fact
that because of the dynamic vibration isolation, it can be made very compact
and very light. It turned out that such a transducer can have more than 25%
less mass than, for example, a transducer whose internal transverse forces
are counterbalanced to a comparable extent by means of the above-
mentioned mechanical low-pass filter system. Therefore, the transducer is
particularly suited for measurements in pipes of great nominal diameter, e.g.,
greater than 80 mm.
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The invention and further advantages will become more apparent by
reference to the following description of an embodiment taken in conjunction
with the accompanying drawings. Like reference characters have been used
to designate like parts throughout the various figures; reference characters
5 that were already assigned are not repeated in subsequent figures if this
contributes to clarity. In the drawings:
Fig. 1 is a partially sectioned side view of a Coriolis-type transducer
with one flow tube;
Fig. 2 is a partially sectioned side view of a development of the
transducer of Fig. 1;
Figs. 3a show schematically deflection lines of the flow tube during
to 3d operation of the transducer of Fig. 1 or 2; and
Fig. 4 shows schematically a portion of the flow tube during operation
of the transducer of Fig. 1 or 2.
Figs. 1 and 2 show a vibratory transducer in schematic side views. The
transducer serves to produce in a fluid passing therethrough mechanical
reaction forces, such as mass-flow-rate-dependent Coriolis forces, density-
dependent inertial forces, and/or viscosity-dependent friction forces, which
react on the transducer and are measurable, particularly with sensor
technology. From these reaction forces, a mass flow rate m, a density p,
and/or a viscosity q of the fluid, for example, can thus be derived in the
manner familiar to those skilled in the art.
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To conduct the fluid, the transducer comprises a substantially straight flow
tube 10, particularly a single tube, which in operation, oscillating about a
static
rest position, is repeatedly elastically deformed.
To this end, flow tube 10 is mounted in a first support system 20 so as to be
capable of vibratory motion, the support system 20 being fixed to flow tube 10
at the inlet and outlet ends. For the support system 20, a supporting frame or
a supporting tube can be used, for example. Further preferred embodiments
of support system 20 are explained below.
To permit flow of fluid through flow tube 10, the latter is connected to a
fluid-
conducting pipe via an inlet-side tube section 11 and an outlet-side tube
section 12. Flow tube 10, inlet-side tube section 11, and outlet-side tube
section 12 are aligned with each other and with an imaginary longitudinal axis
L and are advantageously of one-piece construction, so that they can be
fabricated from a single tubular semifinished product, for example; if
necessary, however, flow tube 10 and tube sections 11, 12 can also be made
from separate semifinished products that are subsequently joined together,
for instance welded together. For flow tube 10, virtually any of the materials
commonly used for such transducers, such as steel, titanium, zirconium, etc,
can be used.
If the transducer is to be detachable from the pipe, a first flange 13 and a
second flange 14 are preferably formed on inlet-tube section 11 and outlet-
side tube section 12, respectively; if necessary, inlet- and outlet-side tube
sections 11, 12 may also be connected with the pipe directly, for instance by
welding or brazing.
Furthermore, as shown schematically in Fig. 1, a second support system 30
may be fixed to inlet- and outlet-side tube sections 11, 12; preferably, this
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second support system may be implemented as a transducer case 30' that
houses the flow tube 10, see Fig. 1.
In operation, flow tube 10 is excited into flexural vibrations, particularly
in the
range of a natural resonance frequency, such that in this so-called useful
mode, it deflects essentially according to a first form of natural vibrations.
In a preferred embodiment of the invention, flow tube 10 is excited at a
vibration frequency that corresponds as exactly as possible to a natural
resonance frequency of the so-called f1 eigenmode of flow tube 10, i.e., to a
symmetrical eigenmode, in which, as shown schematically in Fig. 3, the
vibrating, but empty flow tube 10 has a single antinode. For example, in the
case of a flow tube 10 of special steel with a nominal diameter of 20 mm, a
wall thickness of about 1.2 mm, and a length of about 350 mm, the resonance
frequency of the f1 eigenmode is approximately 850 to 900 Hz.
When fluid flows through the pipe, so that the mass flow rate m is nonzero,
Coriolis forces are induced in the fluid by the flow tube 10 vibrating in the
manner described above. The Coriolis forces react on flow tube 10, thus
causing an additional deformation (not shown) of flow tube 10 according to a
second form of natural vibrations, which is superimposed on the excited
useful mode as a coplanar mode. This deformation can be detected using
sensor technology. The instantaneous shape of the deformation of flow tube
10, particularly in terms of its amplitudes, is also dependent on the
instantaneous mass flow rate m. The second form of natural vibrations, the
so-called Coriolis mode, can be, for instance, the antisymmetric f2
eigenmode, i.e., the mode with two antinodes, and/or the antisymmetric f4
eigenmode with four antinodes, as is usually the case in such transducers.
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When the useful mode is excited, transverse forces Q, are produced in the
vibrating single flow tube 10 by mass accelerations associated with the
flexural vibrations, as is well known; thus, corresponding laterally directed
transverse impulses occur in the transducer. At a vibration amplitude of
approx. 0.03 mm, for example, a transverse force of about 100 N would result
for the above-mentioned flow tube of special steel.
If these transverse forces Q, are not counterbalanced, a transverse impulse
remains in the transducer. As a result, the flow tube 10, mounted via inlet-
side
tube section 11 and outlet-side tube section 12, together with the first
support
system 20 fixed thereto, will be laterally deflected from the assigned static
rest
position. Accordingly, the transverse forces Q, would at least partly act via
inlet-side and outlet-side tube sections 11, 12 on the connected pipe and thus
cause the latter to vibrate as well.
To minimize such oscillating transverse forces Q, acting on the pipe, in a
preferred embodiment of the invention, the first support system 20 is
implemented as an antivibrator 20' which vibrates out of phase with,
particularly opposite in phase to, flow tube 10, and which therefore is
preferably flexible.
Antivibrator 20' serves to dynamically balance the transducer for a
predetermined fluid density value, for instance a value most frequently
expected during operation of the transducer or a critical value, to the point
that
the transverse forces Q1 produced in the vibrating flow tube 10 are
compensated as completely as possible and that flow tube 10 then practically
does not leave its static rest position, cf. Figs. 3a, 3b. Accordingly, in
operation, antivibrator 20', as shown schematically in Fig. 3b, is also
excited
into flexural vibrations that are essentially coplanar with the flexural
vibrations
of flow tube 10.
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To this end, antivibrator 20', as shown in Fig. 1, is preferably implemented
in
the form of a tube, particularly a tube that is coaxial with flow tube 10. If
necessary, antivibrator 20', as also shown in U.S. Patent 5,969,265,
EP-A 317,340, or WO-A 00/14485, for example, can also be implemented as
a multipart, composite unit or by means of two separate antivibrators fixed to
flow tube 10 at the inlet end and outlet end, respectively, cf. Fig. 2.
Particularly
in the latter case, where the inner support system 20 is formed by means of
an inlet-side antivibrator and an outlet-side antivibrator, the outer support
system 30 can also be implemented as a two-part system consisting of an
inlet-side subsystem and an outlet-side subsystem, cf. Fig. 2.
To permit easy tuning of antivibrator 20' to the aforementioned density value
and the actually excited vibration mode of flow tube 10, in another preferred
embodiment of the invention, discrete first and second mass pieces 201, 202
are mounted, preferably detachably, on antivibrator 20'. Mass pieces 201, 202
may be, for example, disks screwed onto staybolts provided on flow tube 10,
or short tube sections slipped over the flow tube. Furthermore, a
corresponding mass distribution over antivibrator 20' can be realized by
forming longitudinal or annular grooves, for example. A mass distribution
suitable for the respective application can be easily determined by the person
skilled in the art using the finite element method and/or suitable calibration
measurements, for example. If necessary, more than two mass pieces 201,
202 can be used, of course. At this point it should be noted that both support
systems 20, 30, but at least the antivibrator 20' and the transducer case 30',
can be retrofitted on an existing pipe, as proposed in WO-A 99/51946 or
EP-A 1 150 104, for example.
To generate mechanical vibrations of flow tube 10, the transducer further
comprises an excitation system 40, particularly an electrodynamic system.
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The excitation system serves to convert electric excitation energy Eexc
supplied from control electronics (not shown), for instance with a regulated
current and/or a regulated voltage, into an excitation force Fe1 that acts on
flow tube 10, for example in a pulsed manner or harmonically, and elastically
deforms the tube in the manner described above. The excitation force Fexc
may be bidirectional as shown schematically in Fig. 1, or unidirectional, and
can be adjusted in amplitude, for instance by means of a current- and/or
voltage-regulator circuit, and in frequency, for instance by means of a phase-
locked loop, in the manner familiar to those skilled in the art. The
excitation
system can be, for example, a simple solenoid with a cylindrical excitation
coil
that is mounted on antivibrator 20' and traversed in operation by a suitable
excitation current, and with a permanent magnetic armature that is fixed to
the
outside of flow tube 10, particularly at the midpoint thereof, and rides in
the
excitation coil at least in part. Excitation system 40 can also be implemented
as an electromagnet or, as shown in WO-A 99/51946, as a seismic exciter, for
example.
To detect vibrations of flow tube 10, a sensor system as is commonly used for
such transducers can be employed, in which the motions of flow tube 10 are
sensed with an inlet-side first sensor 50A and an outlet-side second sensor
50B and converted into corresponding first and second sensor signals S, and
S2, respectively, in the manner familiar to those skilled in the art. Sensors
50A, 50B can be electrodynamic velocity sensors as shown schematically in
Fig. 1, which perform relative vibration measurements, or electrodynamic
displacement sensors or acceleration sensors, for example. In place of
electrodynamic sensor systems, sensor systems using resistive or
piezoelectric strain gages or optoelectronic sensor systems can be employed.
As repeatedly mentioned, flow tube 10 can also be dynamically balanced by
means of antivibrator 200 for only a single fluid density value, but for a
very
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narrow fluid density range at best, cf. Fig. 3b. During variations in density
p,
however, flow tube 10 will be laterally displaced from its rest position,
symbolized in Fig. 3a to 3d by the longitudinal axis L, namely at high
densities
p above the aforementioned fluid-density value in the direction of its own
vibratory motion, as shown schematically in Fig. 3c, and at low densities p
below that fluid-density value in the direction of the vibratory motion of the
inner support system 20, which may be implemented as antivibrator 20', as
shown in Fig. 3d.
To improve the dynamic balance of the transducer, particularly for fluids with
significantly varying density p, the transducer further comprises a first
cantilever 15, fixed as rigidly as possible to inlet-side tube section 11, and
a
second cantilever 16, fixed as rigidly as possible to outlet-side tube section
12
and preferably identical in shape to cantilever 15.
According to the invention, the two cantilevers 15 and 16, which are
preferably disposed symmetrically with respect to the midline of flow tube 10,
serve to dynamically produce bending moments in inlet-side tube section 11
and outlet-side tube section 12, respectively, particularly near the adjoining
flow tube 10, when the vibrating flow tube 10, together with antivibrator 20'
if
present, is laterally displaced from its static rest position. To this end,
cantilever 15 and cantilever 16 are positively and/or nonpositively connected,
for instance welded or clamped on, to an outlet end 11# of inlet-tube section
11 and an inlet end 12# of outlet-tube section 12, respectively.
As shown schematically in Figs. 1 and 2, the two cantilevers 15, 16 are so
positioned in the transducer, preferably as close as possible to flow tube 10,
that a centroid M15 of cantilever 15 and a centroid M1s of cantilever 16 are
spaced from, and particularly located in line with, flow tube 10. In this
manner,
moments of inertia are developed by means of cantilevers 15, 16 which are
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applied at the respective fixing points, namely outlet at end 11# and inlet
end
12#, eccentrically, i.e., not at the associated centroids M15, M16. These
moments of inertia, in turn, cause cantilevers 15, 16 to oscillate about their
respective, nearly stationary centroids M15, M16, thus forcing additional
twisting
of outlet end 11# about an imaginary first axis of rotation D15, which is
perpendicular to the lateral displacement motion V of flow tube 10 and to the
longitudinal axis L, and of inlet end 12# about an imaginary second axis of
rotation D1s, which is essentially parallel to the first, see Figs. 3c and 3d.
This twisting of outlet end 11#, which is shown enlarged in Fig. 4, causes
additional bending of at least parts of inlet-side tube section 11 which is
directed opposite to the displacement motion V of flow tube 10 and which
corresponds to a uniaxial, transverse-force-free and, thus, shear-stress-free
bending; analogously, outlet-tube section 12 is bent in opposite direction to
the displacement motion V.
According to findings of the inventors, this bending of inlet-side and outlet-
side
tube sections 11, 12 can be optimized, for instance by means of computer-
assisted simulation calculations or by means of experimental measurements,
such that the above-mentioned transverse forces Q, in the vibrating flow tube
10 are completely or at least partially balanced by counterforces Q2 produced
by the bending, such that practically no transverse forces caused by the
vibrating flow tube 10 and the possibly likewise vibrating internal support
system 20 will act on the connected pipe. Any deformations of the connected
pipe caused by the resulting bending moments can be easily suppressed by
support system 30, for instance by a suitably high flexural rigidity of the
above-mentioned transducer case 30'.
The invention is also predicated in the surprising recognition that through a
suitable deformation of inlet-side tube section 11 and outlet-side tube
section
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12 independently of instantaneous vibration amplitudes and/or frequencies of
flow tube 10 in the above-mentioned useful mode, i.e., through a suitable
shape of a corresponding deflection line, a force value and a momentum
value per unit length along the longitudinal axis L can be set within the
transducer in such a way that transverse impulses directed opposite to the
transverse impulses produced in the vibrating flow tube 10 can be produced
such that the transverse impulses neutralize each other, so that the
transverse forces Q, produced by the vibrating flow tube 10 can be essentially
balanced by means of transverse forces Q2 produced by the deforming inlet-
side tube section 11 and the deforming outlet-side tube section 12.
In a further preferred embodiment of the invention, cantilever 15 is so shaped
and attached to flow tube 10 that its centroid M15 is located essentially in a
range of one half the length of inlet-side tube section 11, and cantilever 16
is
so shaped and attached to flow tube 10 that its centroid M1s is located
essentially in a range of one half the length of outlet-side tube section 12.
To develop the moments of inertia, cantilever 15, as shown in Fig. 1, has a
cantilever arm 15A on which a cantilever mass 15B is formed remote from
outlet end 11#; similarly, cantilever 16 has a cantilever arm 16A with a
cantilever mass 16B formed thereon remote from inlet end 12#. Cantilever
masses 15B and 16B are chosen so as to be capable of twisting in response
to a lateral deflection of flow tube 10, and thus of inlet and outlet ends 11#
and
12#, respectively, but, in translatory terms, to remain essentially in the
respective static rest positions assigned to them on the basis of the concrete
mechanogeometrical parameters of cantilevers 15, 16. In a corresponding
manner, the respective centroids M15, M1s of the two cantilevers 15, 16 remain
essentially in their static rest positions although flow tube 10 is laterally
displaced from its assigned static rest position; they thus serve as a center
for
CA 02443375 2003-10-02
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September 08, 2003
the rotary motions of cantilevers 15, 16, which cause the above-mentioned
bending moments.
Each of the two cantilevers 15, 16 is preferably clamped at one end, i.e.,
they
are fixed only to outlet and inlet ends 11# and 12#, respectively, as also
shown
in Figs. 1 to 4. To suppress any unwanted vibration modes, however,
additional spring and/or damping elements as shown schematically in Fig. 4
may be provided which, fixed to the respective cantilever mass 15B, 16B and
to transducer case 30', stabilize the centroids M15, M1s of cantilevers 15, 16
in
their respective rest positions.
Experiments on transducers with the above-mentioned flow tube of special
steel have shown, for example, that each of the cantilever masses 15B, 16B,
which should be as inert as possible to any lateral displacements,
particularly
in comparison with flow tube 10, should advantageously be chosen to be
about five times as large as the mass of flow tube 10. Surprisingly, however,
the two cantilever masses 15B, 16B and their cantilever arms 15A, 16A can
be proportioned virtually independently of the vibration frequencies of the
vibrating flow tube 10 which are expected in operation; it must only be
ensured that cantilever masses 15B are made as heavy as possible,
particularly heavier than flow tube 10, and that cantilever arms 15A, 16A, as
indicated above, are made as rigid as possible.
To permit the cantilever masses to be twisted with as little resistance as
possible, cantilevers 15 and 16 are preferably shaped and fixed to flow tube
10 in such a manner that a quotient of the aforementioned moment of inertia
and the respective associated cantilever mass 15B, 16B is as low as possible.
Investigations have shown that, if flow tube 10 is made of special steel as
described above, for example, cantilevers 15 and 16 should be so shaped
and fixed to inlet-side tube section 11 and outlet-side tube section,
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September 08, 2003
respectively, that the aforementioned quotient is less than 10-4kg = m2 / kg.
The quotient can advantageously be set very accurately by implementing
cantilever masses 15B and 16B in the form of elongate prisms or cylinders,
symbolized in Figs. 3a to 3d and 4 by their respective cross sections, and
respectively attaching them via cantilever arms 15A and 16A to inlet-side and
outlet-side tube sections 11 and 12 in such a way that respective principal
axes of inertia for associated minimum principal moments of inertia of
cantilever masses 15B and 16B are parallel to the aforementioned axes of
rotation D15, D16.
The aforementioned quotient can also be minimized dynamically as a function
of the lateral displacement motions V of flow tube 10. To accomplish this, in
a
further preferred embodiment of the invention, cantilever masses 15B, 16B
are at least partially made pliable, for instance by forming grooves
substantially parallel to the axes of rotation D15, D16, as shown
schematically
in Fig. 1.
Furthermore, cantilevers 15 and 16 are preferably designed so that their arms
15A and 16A have a higher flexural rigidity than, and preferably at least
three
times the flexural rigidity of, inlet-side and outlet-side tube sections 11
and 12,
respectively. To this end, cantilever arms 15A, 16A may, for instance, be
tubular in form, as already described for antivibrator 20'; then, they can be
fixed to inlet-side and outlet-side tube sections 11 and 12, respectively,
coaxially with flow tube 10 and in line with antivibrator 20', if the latter
is
present. In that case, cantilever arms 15A, 16A and antivibrator 20' can be
made in one part from a single tubular semifinished product or in two parts
from two tube halves, for example. The above-described ratio of flexural
rigidities can also be set, for example, by selecting inlet-side and outlet-
side
tube sections 11, 12 of suitable length.
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September 08, 2003
To the inventors' surprise, however, it turned out that the bending moments
for inlet-side tube section 11 and outlet side tube section 12 can also be
developed with sufficient accuracy by means of cantilever arms 15A, 16A that
elastically deform significantly within certain limits. Cantilever masses 15B,
16B can then be designed to be subject to virtually no twisting, remaining in
their assigned rest positions, preferably relatively far from flow tube 10. In
the
above-mentioned case where cantilever arms 15A, 16A are tubular, the arms
may, for instance, be longitudinally slotted for setting both their flexural
rigidity
and the above-mentioned quotient.
As is readily apparent from the above explanations, the transducer according
to the invention is characterized by a multitude of possible settings which
enable the person skilled in the art, particularly after specification of
external
or internal mounting dimensions, to achieve high-quality balancing of
transverse forces developed in flow tube 10 and in antivibrator 20', if
present.
