Abstrict In the method for mass flow measurement by the Coriolis principle
a fluid-traversed elastically deformable measuring tube is periodically
deflected. As a measure of the mass flow phase displacements are
measured between deflections of portions of the measuring tube wall
which are arranged differently in the flow direction. For this purpose
a periodic deformation of the cross-section of the measuring tube
is effected in such a manner that portions of the measuring tube
wall lying diametrically opposite each other are deflected in each
case through about the same distance in opposite or the same direction
transversely of the flow direction of the fluid. This method can
be carried out with a simply constructed mass flow meter in the
operation of which a wandering of the center of gravity of the meter
is substantially avoided and which is also suitable for large nominal
widths.
Claims We claim:
1. A method for mass flow measurement according to the Coriolis
principle by means of an elastically deformable measuring tube through
which a fluid flows, said method comprising the steps of effecting
a periodic deformation of a cross-section of the measuring tube
with an exciter in such a manner that portions of the measuring
tube wall which lie diametrically opposite each other are radially
deflected through substantially equal distances in the same direction
or in opposite directions transversely of the flow direction of
the fluid, detecting the tube wall deflections at locations on the
measuring tube axially displaced from the exciter, and measuring
the phase difference between the detected tube wall deflections
which phase difference is indicative of the mass flow of the fluid.
2. A method as claimed in claim 1 wherein said periodic deformation
is effected with a frequency corresponding to one of the natural
resonance frequencies of radially directed peripheral oscillations
of the measuring tube wall.
3. A method as claimed in claim 2 comprising the further step
of superimposing on said radially directed peripheral oscillations
flexural oscillations of the measuring tube having a frequency corresponding
to one of the natural resonance frequencies of flexural oscillations
of the measuring tube.
4. A method as claimed in claim 3 wherein the frequency of said
radially directed peripheral oscillations corresponds to the natural
resonance frequency of the second order, and the frequency of said
flexural oscillations corresponds to a natural resonance frequency
of the third or fourth order.
5. A method as claimed in claim 1 wherein said periodic deformation
is produced by applying to the measuring tube wall at at least one
point thereof a radially directed force the direction of which is
periodically reversed with a frequency corresponding to one of the
natural resonance frequencies of radially directed peripheral oscillations.
6. A mass flow meter as claimed in claim 5 wherein the point or
each point at which a periodically reversed force is applied to
the measuring tube wall is situated substantially in the center
of the length of the measuring tube.
7. A method as claimed in claim 5 wherein at least one pair of
periodically reversed forces is applied to the measuring tube wall
at two points which are diametrically opposite each other.
8. A method as claimed in claim 7 wherein the directions of the
two forces of said pair or each pair are always opposite each other.
9. A method as claimed in claim 7 wherein the directions of the
two forces of said pair or each pair are always equal.
10. A Coriolis-type mass flow meter comprising a measuring tube
adapted to be inserted in a fluid conduit, at least one oscillation
exciter which acts on the measuring tube to produce a periodic deformation
of a cross-section of the measuring tube wall in such a manner that
portions of the measuring tube wall which lie diametrically opposite
each other are radially deflected through substantially equal distances
in the same direction or in opposite directions, and a phase detector
system comprising sensor means for detecting the tube wall deflections
at locations on the measuring tube which are axially displaced from
the exciter and means for measuring the phase difference between
said detected tube wall deflections.
11. A mass flow meter as claimed in claim 10 wherein said measuring
tube is rectilinear.
12. A mass flow meter as claimed in claim 10 wherein said measuring
tube has a circular cross-section.
13. A mass flow meter as claimed in claim 10 wherein said measuring
tube has a polygonal cross-section with an even number of corners.
14. A mass flow meter as claimed in claim 13 wherein each of said
sensor means is arranged to detect the tube wall deflections in
the center of the cross-section line extending between two corners.
15. A mass flow meter as claimed in claim 10 wherein each of said
sensor means comprises a light transmitter, a light receiver and
optical wave guide means for transmitting the light of said light
transmitter to the light receiver in such a manner that the intensity
of the transmitted light flux is influenced by the deflection of
the wall of the measuring tube.
16. A mass flow meter as claimed in claim 15 wherein said optical
wave guide means comprises two sapphire rods of which one is connected
at one end to the light transmitter and the other is connected at
one end to the light receiver, the other ends of the two sapphire
rods being constructed as totally reflecting prisms which are spaced
from each other with a gap therebetween, so that the light flux
going from the light transmitter through the one sapphire rod passes
through said gap and enters the other sapphire rod through which
it is conducted to the light receiver, at least one immersion lug
being disposed at the wall of the measuring tube in such a manner
that in dependence upon the deflection of the wall it projects to
a greater or lesser extent into the gap formed between the prism-like
ends of the sapphire rods.
17. A mass flow meter as claimed in claim 10 wherein said oscillation
exciter comprises one or more electromagnetic transducers.
18. A mass flow meter as claimed in claim 10 wherein said oscillation
exciter comprises one or more electrostatic transducers.
19. A mass flow meter as claimed in claim 10 wherein said oscillation
exciter comprises one or more electroacoustic transducers.
20. A mass flow meter as claimed in claim 17 wherein said oscillation
exciter comprises an electromagnet fixedly mounted outside of the
measuring tube and a permanent magnet mounted opposite said electromagnet
on the measuring tube wall, a compensating body being arranged on
the measuring tube wall diametrically opposite the permanent magnet,
the mass of said compensating body corresponding substantially to
that of the permanent magnet.
21. A mass flow meter as claimed in claim 10 comprising at least
two oscillation exciters which are arranged at diametrically opposite
portions of the wall of the measuring tube and generate oscillations
which are phase-displaced by 180 degrees with respect to each other.
Description The invention relates to a method for mass flow measurement by
the Coriolis principle with an elastically deformable measuring
tube through which fluid flows and which is periodically deflected,
and in which as a measure of the mass flow phase displacements between
deflections of portions of the measuring tube wall arranged differently
in the flow direction are measured, and to a mass flow meter operating
by the Coriolis principle.
It is known (JP-OS No. 57-137-818) to carry out mass flow measurements
with a single measuring tube The measuring tube is fixedly clamped
at both its ends In its centre it is stimulated to execute flexural
oscillations transversely of the flow direction, i.e. the inner
and outer profile of the measuring tube is deformed with predetermined
period duration in a plane along the flow direction of the fluid.
Due to the firm clamping at the two ends a single half-wave with
periodically varying antinode extends over the entire measuring
tube length. If fluid of a certain mass now flows through the measuring
tube due to the Coriolis forces occurring the form of the half-wave
is distorted (phase-displaced). However, these flexural oscillations
in the form of a single half-wave cause a periodic wandering of
the centre of gravity of the mass flow meter. The centre of gravity
wandering leads as a rule to vibrations of the housing of the measuring
device and the fluid conduit in which the mass flow meter is inserted.
These vibrations transmitted to the surroundings lead to a loss
of flexural oscillation energy of the measuring tube If the energy
dispersed is different on the entry side and the exit side, for
example due to different degrees of firmness of the clampings of
the measuring tube, this affects the phase displacements to be measured.
In particular, shifts of the zero point of the phase displacement
can occur and consequently measurement inaccuracies.
It is further known (German patent No. 3505166) to carry out
mass flow measurements with two measuring tubes The two measuring
tubes are connected hydrodynamically in parallel at the entry and
exit side by means of two tube connectors. The measuring tubes are
set in opposite flexural oscillations so that the walls of the first
measuring tube are deflected phase-displaced through 180 degrees
with respect to those of the second measuring tube. This avoids
a wandering of the centre of gravity of the mass flow meter. However,
an oscillating measuring tube system having at least two measuring
tubes is necessary.
In a mass flow meter of the type mentioned at the beginning (international
patent publication No. WO 87/06 691) a single measuring tube is
fixedly clamped at both its ends and stimulated to execute flexural
oscillations in a higher "antisymmetrical" oscillation
mode. This corresponds to a flexural oscillation form in which two
half-waves extend over the entire measuring tube length. Three socalled
oscillation nodes arise in the measuring tube centre and at the
two measuring tube ends and between the oscillation nodes oppositely
directed periodic bulges occur, i.e. between the oscillation nodes
socalled oscillation antinodes occur.
Although due to the oppositely identical bulging of the measuring
tube a periodic wandering of the centre of gravity of the meter
is avoided, an ovally formed cross-section is necessary for the
measuring tube at the points where the oscillation amplitudes are
greatest (oscillation antinodes) to reduce the flexural resistance
at these points. This construction of the cross-section leads to
more expenditure in production In addition, at the measuring tube
ends firm clamping points are necessary to form the oscillation
nodes, at which turning moments act due to the flexural oscillations.
Finally, with increasing measuring tube diameters (nominal widths)
the generation of the flexural oscillations becomes increasingly
more complicated and difficult, in particular in a higher oscillation
mode.
The invention is therefore based on the problem of providing a
method of the type mentioned at the beginning which whilst avoiding
the aforementioned disadvantages can be carried out with a meter
which can be made simply and economically and is of simple and compact
structure as well as being reliable in operation and substantially
without disturbing influence on its measuring environment; it is
to be operable without periodic wandering of the centre of gravity
and able to manage large nominal widths.
According to the invention for measuring tubes an oscillation mode
is chosen in which portions or sections of the measuring tube lying
opposite each other symmetrically with respect to the centre longitudinal
axis (centre axis) of the measuring tube are deflected in equal
or opposite senses, i.e. in phase with each other or phase-displaced
by 180 degrees. The deflections of the walls are achieved by elastically
reversible deformation of the measuring tube cross-section. If fluid
of a predetermined mass flows from a fluid conduit into the measuring
tube periodically deformed in this manner then it must absorb the
energy of the deformation oscillations at the entry side and give
up this absorbed energy again at the exit side. This means that
Coriolis forces occur which at the entry side retard the deformation
and thus the deflection of the measuring tube walls and at the exit
side accelerate said deformation. The thus resulting phase-displacement
of the deflections of the sections of the measuring tube wall, which
are differently distributed over the measuring tube length, can
be measured for determining the mass flow.
In the mass flow measuring according to the invention it is fundamentally
no longer necessary to stimulate measuring tubes to execute flexural
oscillations This achieves the advantage that in the regions of
the firm clamping and/or free suspension of the measuring tube ends
no turning moments act. A further advantage is that when using the
method according to the invention for large nominal widths, compared
with conventional measuring methods with tubes set in flexural oscillations,
shorter measuring tube lengths can be employed.
According to an expedient further development of the invention
the reciprocal of the period duration of the cross-sectional deformations
is substantially identical to one of the natural/resonance frequences
of oscillations of the periphery of the measuring tube in the radial
direction. This results in a deflection of the measuring tube walls
in such a manner that the position of the centroidal axis of the
measuring tube remains substantially constant. Consequently, with
the mass flow measurement according to the invention periodic wanderings
of the centre of gravity of the measuring device and thus vibrations
transmitted to the environment thereof are largely avoided without
any additional constructional expenditure being necessary.
According to a further development of the invention the resonance
frequency for the peripheral oscillations of the measuring tube
are selected so that an oscillation mode of higher order arises,
i.e. on the measuring tube wall in the peripheral direction of the
measuring tube waves of the number n where n is greater than zero
form. Oscillation nodes with antinodes therebetween form uniformly
distributed over the periphery of the measuring tube, in each case
twice n in number.
An additional problem is that of obtaining adequate measuring sensitivity
and/or oscillation stability. This is solved according to a further
development of the invention in which in the measuring tube flexural
oscillations are stimulated in addition to the peripheral oscillations
It appears particularly advantageous here to choose on the one hand
for the flexural oscillations a mode in which along the measuring
tube two half-waves with a node in the measuring tube centre arise
(mode of the second order). This oscillation node contributes to
increasing the stability of the peripheral oscillations on which
the mass flow measurement is based It appears particularly advantageous
to choose for the peripheral oscillations the mode of the order
n where n is three or four. In this further development of the invention
due to the flexural oscillations alternating turning moments inevitably
occur at the clamping points of the measuring tube. Their possibly
undesired effects can for example be attenuated or eliminated by
mechanical filter arrangements consisting for example of mass and/or
spring and/or damping elements.
The periodic deformation of the measuring tube can expediently
be achieved in that the measuring tube walls are correspondingly
deflected by externally generated alternating forces which are directed
onto the measuring tube wall and the frequency of which corresponds
to the natural/resonance frequency of the peripheral oscillations
of the measuring tube. This makes it possible to reduce the consumption
of oscillation energy to be applied in order to obtain sufficient
measuring effect.
According to a specific embodiment of the invention on diametrically
opposite portions or points of the measuring tube wall forces are
applied which are phase-displaced by 180 degrees with respect to
each other. As a result in this area the measuring tube is subjected
to tensile stress and compressive stress in mirror symmetry to its
centre axis. This makes it possible to obtain an easily detectable
deflection of the measuring tube wall over the measuring tube length.
Preferably, the engagement points of the forces are in the centre
region of the measuring tube because the fluid mass in said region
must not absorb or liberate deformation energy, i.e. practically
no Coriolis forces act. Moreover, this is the point of minimum influence
of any fixed clamping points of the measuring tube counteracting
the deflecting of the measuring tube wall.
To obtain over the measuring tube length a high resolution in the
measurement of the phase displacement of the deflections of the
measuring tube walls two measuring points are arranged as far apart
as possible. Preferably, they are provided in the vicinity of the
entry and exit end of the measuring tube.
In a measuring device or meter for application of the invention
the essential point is that the oscillation exciter generating the
periodic deformations of the measuring tube is so constructed and
arranged that the measuring tube wall is deflected substantially
uniformly with respect to the central axis or centroidal axis of
the measuring tube and perpendicularly to the flow direction of
the fluid. The wall movements compensate each other in such a manner
that the original centre of gravity balance of the measuring device
is substantially retained.
This is done according to a particular embodiment of the invention
in that two for example electromagnetic, electroacoustic and/or
electrostatic oscillation exciters are in each case in operative
contact with wall portions of the measuring tube which lie opposite
each other. Preferably, the oscillations generated by the oscillation
exciters are phase-displaced with respect to each other by 180 degrees.
This results in a deformation of the measuring tube which is particularly
uniform about the centroidal axis of the measuring tube and easily
detectable
According to an alternative embodiment of the invention the peripheral
oscillations of the measuring tube are generated by a single oscillation
exciter which is in operative connection with at least one portion
of the measuring tube wall. This permits a particularly economical
production of a mass flow meter. Depending on the construction of
the oscillation exciter unbalances are produced on the measuring
tube. To balance these out, according to the invention at the region
of the measuring tube wall diametrically opposite the oscillation
exciter a compensating body is disposed.
To permit the use of simply constructed and applicable vibration
exciters measuring tubes may be employed which have a form symmetrical
about their longitudinal axis, for example a cylindrical form. Advantageously,
measuring tubes are used which are polygonal in section transversely
of the flow direction. If the measuring tube has for example a square
cross-sectional form the four corners each form zones in which the
measuring tube walls undergo practically no deflection (oscillation
nodes). This means on the other hand that zones of maximum deflection
of the measuring tube wall occur mainly in the centre regions of
the side portions formed by the corners (antinodes). This results
in regions on the measuring tube wall which have particularly favourable
requirements for detection of the phase displacement.
Advantageously, for measuring the deflection of the measuring tube
walls optically operating sensors are employed. These have a very
rapid response behaviour compared with electromechanical systems
and thus a low inherent phase-displacement.
Fundamentally, it lies within the scope of the invention to arrange
the oscillation exciters both outside the measuring tube and within
the measuring tube to generate the cross-sectional deformations.
With regard to further advantageous embodiments of the invention
attention is drawn to the subsidiary claims and to the following
description of the drawings, wherein:
FIGS. 1A, 1B, 1C and, 1D, and 1E show in schematic illustration
instantaneous states of measuring tube cross-sections which are
set in peripheral oscillations of different modes,
FIG. 2 shows a measuring arrangement according to the invention
in partially sectioned view,
FIG. 3 shows an alternative embodiment of the oscillation excitation
for generating the oscillations according to FIG. 2
FIG. 4A shows a longitudinal portion of a measuring tube without
mass flow,
FIG. 4B shows cross-sections of the measuring tube used according
to the invention along the lines I--I, II--II and III--III of FIG.
4A at a given instant,
FIG. 4C shows cross-sections of the measuring tube used according
to the invention along the lines I--I, II--II and III--III of FIG.
4A at another instant,
FIG. 5A shows a longitudinal section of a measuring tube with schematically
indicated mass flow and
FIG. 5B shows cross-sections of the measuring tube used according
to the invention along the lines I--I, II--II and III--III of FIG.
5A at a given instant.
Corresponding parts in the drawings are provided with identical
reference numerals.
According to FIGS. 1A-1E for the flow measurement according to
the invention peripheral oscillations are imparted to a measuring
tube 1 and have frequences corresponding to the natural resonance
frequences of the measuring tube in the peripheral oscillation mode.
This leads to the aforementioned periodic deformations of the cross-section
of the measuring tube 1. These are shown in dashed line in FIGS.
1A-1D whilst the circular full line therein shows the measuring
tube cross-section in the unoscillating state of rest. The number
n according to FIGS. 1A-1D denotes the order of the oscillations
and modes and represents the number of the wavelengths which extend
over the periphery of the measuring tube. In accordance with the
arrows in FIGS. 1A-1D, according to the invention the deflection
of the wall of the measuring tube is always in radial direction
either towards the centre point of the measuring tube cross-section
or away from said point. Any oscillation nodes occurring along the
cross-section are denoted in FIGS. 1A-1D by the letter K. As indicated
in each of FIGS. 1A-1E by an encircled point in the cross-sectional
centre of the measuring tube 1 the flow direction of the fluid runs
perpendicularly to the measuring tube cross-section into the plane
of the drawings.
According to FIG. 1A the periphery of the measuring tube 1 is in
the oscillation mode with n equal to zero. This means that over
the measuring tube periphery no wave and no anti-nodes and nodes
form The diameter of the measuring tube 1 increases and decreases
with a period duration corresponding to the predetermined resonance
frequency uniformly over the measuring tube wall forming the measuring
tube periphery.
In accordance with FIG. 1B the periphery of the measuring tube
1 is in the oscillation mode with n equal to two. This means that
over the periphery of the measuring tube 1 two waves have propagated
themselves each in full length and four nodes K have formed which
lie uniformly distributed over the measuring tube periphery and
substantially at equal distances apart In the region of the antinodes
disposed between the nodes diametrically opposite wall portions
of the measuring tube 1 are deflected in opposite senses, i.e. in
opposite direction.
In accordance with FIG. 1D the periphery of the measuring tube
1 is in the oscillation mode with n equal to four which means that
there are four waves with eight oscillation nodes uniformly distributed
over the periphery of the measuring tube 1. Otherwise, the remarks
made on FIG. 1B apply here accordingly.
According to FIG. 1C the periphery of the measuring tube 1 is in
the oscillation mode with n equal to three which means that three
wavelengths with six nodes are distributed uniformly over the measuring
tube periphery. As apparent from the arrows in this embodiment of
the invention diametrically opposite wall portions, unless they
coincide with the regions of the nodes K, are deflected in the same
sense, i.e. in each case in the same direction.
The oscillation modes with n greater or equal to two are generally
known as "HOOPE oscillation modes".
FIG. 1E illustrates a measuring tube having a polygonal cross-section
taken transverse to the flow direction through the measuring tube.
The four corners of the measuring tube shown in FIG. 1E form four
oscillation nodes K.
In accordance with FIG. 2 the mass flow meter of the invention
comprises essentially a measuring tube 1 a first and second oscillation
exciter 56 and two optical sensor means T,R. The wall of the measuring
tube 1 forming the cavity traversed by fluid is shown in longitudinal
section in FIG. 1. As indicated schematically, the entry-side end
3 and the exit-side end 4 of the measuring tube 1 are each fixedly
clamped. Fundamentally, a free suspension of the measuring tube
ends 34 is also possible. Substantially in the centre of the measuring
tube 1 the first and second oscillation generator 56 are arranged
in such a manner that they lie opposite each other symmetrically
with respect to the centre axis of the measuring tube 1. The electromechanical
oscillation exciters 56 each comprise substantially an exciter
coil 9 fed via the terminals 8 with alternating current and a permanent
magnet 10 which is in operative connection therewith and has a southpole
S and northpole N. The permanent magnets 10 are mounted directly
on the measuring tube wall 2 whilst the exciter coils 9 are externally
mounted. The optical sensors T,R are arranged in the entry and exit
region respectively and consist essentially of a light transmitter
T, an optical waveguide means 11 a light receiver R and immersion
lugs 12 attached directly to the measuring tube wall 2.
The mode of operation is as follows: When an alternating current
of predetermined frequency flows through the exciter coils 9 the
permanent magnets 10 are alternately attracted and repelled with
predetermined period. Correspondingly, forces act on the measuring
tube wall 2 so that the latter is alternately subjected to tension
and pressure with predetermined period. This leads to elastically
reversible deformations of the cross-section of the measuring tube
1. On mass flow these deformations and the resulting deflections
of the measuring tube wall 2 are phase-displaced over the length
of the measuring tube 1. Immersion lugs 12 mounted on the measuring
tube wall 2 take place which are time-displaced with respect to
each other and correspond to the phase-displacement. The immersion
lugs 12 each project into a gap which is formed by the optical waveguide
means 11. In the example of embodiment illustrated the optical waveguide
means consists of two rods of light-guide material, for example
sapphire rods. The transmitter T generates a light flux which passes
via the optical waveguide means 11 including the (air) gap formed
thereby to the light receiver R. The intensity of the transmitted
light flux depends on the depth to which the immersion lugs project
into the (air) gap. The deeper they project the smaller the light
flux. The depth to which the immersion lugs 11 project into the
gap depends on the deflection of the measuring tube wall 2. Consequently,
the difference between the two light intensities furnished by the
optical sensors T,R is a measure of the time displacement or phase
displacement of the deformation of the cross-section of the measuring
tube over the length thereof.
According to FIG. 3 it is also within the scope of the invention
to perform the oscillation excitation with a single oscillation
exciter 6. If this is implemented as according to FIG. 2 with exciter
coil and permanent magnet 10 attached to the measuring tube wall
2 a weight compensation of the mass of the permanent magnet 10 is
advisable. For this purpose in accordance with FIG. 3 a compensation
body 20 is provided. The latter can be secured from the outside
to the wall 2 of the measuring tube 1 in the region diametrically
opposite the wall region to which the permanent magnet 10 is secured.
The mass/weight of the compensation body 20 is so dimensioned in
accordance with the invention that imbalances caused by the permanent
magnet are compensated. Otherwise, the part of the measuring arrangement
not illustrated in FIG. 3 can be constructed as shown in FIG. 2.
The mode of operation of the flow measurement according to the
invention is further illustrated in FIGS. 4A-4C and 5A and 5B.
In FIG. 4A the essential length portion of the measuring tube of
a mass flow meter is schematically illustrated. It is assumed that
the section line II--II (shown in dot-dash line) lies substantially
in the centre region of the measuring tube. This is the preferred
location of the oscillation excitation system which can be constructed
for example in accordance with FIG. 2 or 3. The intersection lines
I--I and III--III denote the points at which the sensors for detecting
the phase displacement are located along the measuring tube length.
Furthermore, in the illustration according to FIG. 4A it is assumed
that there is no mass flow through the measuring tube. When the
oscillation excitation system is set in operation the cross-section
of the measuring tube is approximately overly deformed over its
entire length as illustrated in FIGS. 4B and 4C. In the latter the
deformations of the cross-sections along the lines I--I, II--II
and III--III of FIG. 4A are shown in each case in full line. The
dashed line indicates the cross-sections as they would appear if
the oscillation excitation system were not in operation FIGS. 4B
and 4C represent separate time-displaced instantaneous states, the
time displacement corresponding to a phase displacement of the stimulated
measuring tube oscillations of about 180 degrees This means that
the peripheral portions of the measuring tube wall, which according
to FIG. 4B are outwardly deflected with respect to the initial cross-section
as shown by the dashed line, are pressed in towards the measuring
tube interior in FIG. 4C. The deformations of the cross-sections
of the measuring tube are substantially in phase, as illustrated,
in the regions of the lines I--I, II--II and III--III because in
the absence of mass flow no Coriolis forces act here.
In the schematically illustrated longitudinal portion of a tube
according to FIG. 5A there is mass flow as indicated by the arrows
therein directed to the right. It is further assumed that the cross-section
of the measuring tube is deformed by peripheral oscillations according
to FIGS. 4B and 4C substantially over the entire measuring tube
length. Now, the fluid flowing through the measuring tube must take
up energy on the entry side due to the peripheral oscillations and
give up this absorbed energy again on the exit side. This leads
to the formation of Coriolis forces which in the region of the entry-side
half of the measuring tube retard the deflections of the measuring
tube wall and in the region of the exit-side half of the measuring
tube accelerate the deflections of the measuring tube wall. This
results in phased displacements between the deflections of the wall
portions along the fluid-traversed length of the measuring tube.
Accordingly, the cross-section of the measuring tube according to
line I-I of FIG. 5A is deformed differently to that according to
the line III--III of FIG. 5A, as indicated in FIG. 5B by means of
the four lines (greatly exaggerated). The dashed line in FIG. 5B
shows the measuring tube cross-section as it would appear without
the impression of deformation oscillations. According to FIG. 5B
in the sectional illustration along the line II--II of FIG. 5A the
cross-section coincides without deformation oscillations with that
arising on impression of deformation oscillations. This is due to
the fact that the section line II--II denotes the centre of the
measuring tube and at this point the flowing fluid mass neither
absorbs oscillation energy nor liberates such energy. Consequently,
in the centre of the measuring tube no Coriolis forces arise so
that the reference point and/or zero point of the phase displacement
is assumed to be at said centre. To obtain a high measuring resolution
the phase-displacement is preferably measured at the wall portions
denoted by the section lines I--I and III--III. |