## Abstrict A signal processing apparatus and method for measuring a mass flow
rate of a fluid flowing in conjunction with a surface of a Coriolis
mass flow meter and a field-provable Coriolis mass flow meter. The
apparatus includes: (1) a driver for creating a prescribed vibration
in the surface, (2) a motion sensor for measuring a motion of the
surface, (3) response characteristic determination circuitry, coupled
to the motion sensor, for determining a response characteristic
of the surface and (4) flow rate calculation circuitry, coupled
to the response characteristic determination circuitry, for calculating
a measured mass flow rate of the fluid as a function of the motion
and the response characteristic. The field-provable meter employs
the response characteristic to monitor or compare meter performance
without requiring a separate proving device.
## Claims What is claimed is:
1. A signal processing apparatus for measuring a mass flow rate
of a fluid flowing in conjunction with a surface of a Coriolis mass
flow meter, comprising:
a driver for creating a prescribed vibration in said surface;
a motion sensor for measuring a motion of said surface;
response characteristic determination circuitry, coupled to said
motion sensor, for determining a response characteristic of said
surface; and
flow rate calculation circuitry, coupled to said response characteristic
determination circuitry, for calculating a measured mass flow rate
of said fluid as a function of said motion and said response characteristic.
2. The apparatus as recited in claim 1 wherein said response characteristic
determination circuitry determines a frequency response of said
surface.
3. The apparatus as recited in claim 2 wherein said response characteristic
determination circuitry determines said frequency response from
a reference excitation applied to said surface.
4. The apparatus as recited in claim 1 wherein said surface is
associated with a conduit, said fluid flowable within said conduit.
5. The apparatus as recited in claim 1 wherein said surface is
associated with a conduit, said fluid flowable without said conduit.
6. The apparatus as recited in claim 1 wherein said driver is selected
from the group consisting of:
a magnet/coil pair,
an electrostatic driver, and
a piezoelectric driver.
7. The apparatus as recited in claim 3 wherein said reference excitation
is selected from the group consisting of:
a force proportional to a reference mass flow rate,
a force proportional to a rotational velocity of said surface,
a force proportional to said prescribed vibration of said surface,
a Coriolis mode of vibration,
a force at an arbitrary frequency,
white or random noise, and
a swept frequency wave.
8. The apparatus as recited in claim 1 wherein said motion sensor
is selected from the group consisting of:
a magnet/coil pair,
an electrostatic sensor,
a piezoelectric sensor,
an optical sensor, and
a strain gage.
9. The apparatus as recited in claim 1 wherein said flow rate calculation
circuitry calculates said measured mass flow rate of said fluid
as a function of a one selected from the group consisting of:
time delay,
phase angle,
amplitude,
velocity,
acceleration, and
motion multiplied by frequency raised to a power N, where N is
any positive or negative real number or integer.
10. The apparatus as recited in claim 1 wherein said flow rate
calculation circuitry determines response at a driven vibration
frequency and determines a one selected from the group consisting
of:
damping ratio according to a response curve and a peak value,
damping ratio by determining the bandwidth of a response curve,
damping ratio by a logarithmic decrement method, and
damping ratio as a function of phase angle between excitation and
response.
11. The apparatus as recited in claim 1 wherein said flow rate
calculation circuitry calculates a one selected from the group consisting
of:
a Fourier transform of said prescribed vibration and said reference
excitation, and
a power necessary to maintain a Coriolis mode amplitude.
12. The apparatus as recited in claim 1 wherein said response characteristic
determination circuitry determines a sensitivity.
13. The apparatus as recited in claim 1 wherein said response characteristic
determination circuitry determines a zero.
14. The apparatus as recited in claim 3 wherein said response to
said reference excitation is selected from the group consisting
of:
an intermittent modulation of a mass flow-related signal,
a continuous modulation of a mass flow-related signal,
an average modulated value of a mass flow-related signal,
a magnitude of peak to peak modulation,
a magnitude of response motion,
a difference between modulated amplitude and average flow rate
value, and
a ratio of response in a Coriolis mode to response in a driven
mode.
15. The apparatus as recited in claim 1 further comprising a temperature
sensor and a temperature compensation circuit.
16. A method of measuring a mass flow rate of a fluid flowing in
conjunction with a surface of a Coriolis mass flow meter, comprising
the steps of:
creating a prescribed vibration in said surface;
measuring a motion of said surface;
determining a response characteristic of said surface; and
calculating a measured mass flow rate of said fluid as a function
of said motion and said response characteristic.
17. The method as recited in claim 16 wherein said step of determining
said response characteristic comprises the step of determining a
frequency response of said surface.
18. The method as recited in claim 17 wherein said step of determining
said frequency response comprises the step of determining said frequency
response from a reference excitation applied to said surface.
19. The method as recited in claim 16 wherein said surface is associated
with a conduit, said fluid flowable within said conduit.
20. The method as recited in claim 16 wherein said surface is associated
with a conduit, said fluid flowable without said conduit.
21. The method as recited in claim 16 wherein a driver performs
said step of creating, said driver selected from the group consisting
of:
an electrostatic driver,
a magnet/coil pair, and
a piezoelectric driver.
22. The method as recited in claim 18 wherein said prescribed vibration
is selected from the group consisting of:
a force proportional to said mass flow rate,
a force proportional to a rotational velocity of said surface,
a force proportional to said prescribed vibration of said surface,
a Coriolis mode of vibration,
a force at an arbitrary frequency,
white or random noise, and
a swept frequency wave.
23. The method as recited in claim 16 wherein a motion sensor performs
said step of measuring, said sensor selected from the group consisting
of:
an electrostatic sensor,
a magnet/coil pair,
a piezoelectric sensor,
an optical sensor, and
a strain gage.
24. The method as recited in claim 16 wherein said step of calculating
comprises the step of calculating said measured mass flow rate of
said fluid as a function of a one selected from the group consisting
of:
time delay,
phase angle,
amplitude,
velocity,
acceleration, and
motion multiplied by frequency raised to the power N, where N is
any positive or negative real number or integer.
25. The method as recited in claim 16 further comprising the steps
of:
determining response at a driven vibration frequency, and
determining a one selected from the group consisting of:
damping ratio according to a response curve and a peak value,
damping ratio by determining the bandwidth of a response curve,
damping ratio by a logarithmic decrement method, and
damping ratio as a function of phase angle between excitation and
response.
26. The method as recited in claim 16 wherein said step of calculating
comprises the step of calculating a one selected from the group
consisting of:
a Fourier transform of said prescribed vibration and said reference
excitation, and
a power necessary to maintain a Coriolis mode amplitude.
27. The method as recited in claim 16 wherein said step of determining
a response characteristic comprises the step of determining a sensitivity
of said surface.
28. The method as recited in claim 16 wherein said step of determining
a response characteristic comprises the step of determining a zero.
29. The method as recited in claim 18 wherein said response to
said reference excitation is selected from the group consisting
of:
an intermittent modulation of a mass flow-related signal,
a continuous modulation of a mass flow-related signal,
an average modulated value of a mass flow-related signal,
a magnitude of peak to peak modulation,
a magnitude of response motion,
a difference between modulated amplitude and average flow rate
value, and
a ratio of response in a Coriolis mode to response in a driven
mode.
30. The method as recited in claim 16 further comprising the step
of measuring and compensating for a temperature.
31. A field-provable Coriolis mass flow meter, comprising:
a motion sensor for measuring a motion of a surface of said Coriolis
mass flow meter; and
response characteristic determination circuitry for determining
a response characteristic of said surface of said Coriolis mass
flow meter as a function of said motion, said response characteristic
employable for monitoring a performance of said meter.
32. The meter as recited in claim 31 wherein said response characteristic
determination circuitry comprises circuitry for determining a frequency
response of said surface.
33. The meter as recited in claim 32 wherein said response characteristic
determination circuitry determines said frequency response from
a reference excitation applied to said surface.
34. The meter as recited in claim 31 wherein said surface is associated
with a conduit, said fluid flowable within said conduit.
35. The meter as recited in claim 31 wherein said surface is associated
with a conduit, said fluid flowable without said conduit.
36. The meter as recited in claim 33 wherein said reference excitation
is selected from the group consisting of:
a force proportional to a reference mass flow rate,
a force proportional to a rotational velocity of said surface,
a force proportional to said prescribed vibration of said surface,
a Coriolis mode of vibration,
a force at an arbitrary frequency,
white or random noise, and
a swept frequency wave.
37. The meter as recited in claim 31 wherein said response characteristic
determination circuitry determines response at a driven vibration
frequency and determines a one selected from the group consisting
of:
damping ratio according to a response curve and a peak value,
damping ratio by determining the bandwidth of a response curve,
damping ratio by a logarithmic decrement method, and
damping ratio as a function of phase angle between excitation and
response.
38. The meter as recited in claim 31 wherein said response characteristic
determination circuitry calculates a one selected from the group
consisting of:
a Fourier transform of said prescribed vibration, and
a power necessary to maintain a Coriolis mode amplitude.
39. The meter as recited in claim 33 wherein said response to said
reference excitation is selected from the group consisting of:
an intermittent modulation of a mass flow-related signal,
a continuous modulation of a mass flow-related signal,
an average modulated value of a mass flow-related signal,
a magnitude of peak to peak modulation,
a magnitude of response motion,
a difference between modulated amplitude and average flow rate
value, and
a ratio of response in a Coriolis mode to response in a driven
mode.
40. The meter as recited in claim 31 wherein said response characteristic
determination circuitry determines a sensitivity.
41. The meter as recited in claim 31 wherein said response characteristic
determination circuitry determines a zero.
42. The meter as recited in claim 31 further comprising a temperature
sensor and a temperature compensation circuit.
43. A method of field-proving a Coriolis mass flow meter, comprising
the steps of:
measuring a mass flow rate with said Coriolis mass flow meter;
calculating a response characteristic of a surface of said Coriolis
mass flow meter; and
monitoring said response characteristic of said Coriolis mass flow
meter with respect to said measured mass flow rate.
44. The method as recited in claim 43 wherein said step of calculating
said response characteristic comprises the step of determining a
frequency response of said surface.
45. The method as recited in claim 43 wherein said step of determining
a frequency response comprises the step of determining said frequency
response from a reference excitation applied to said surface.
46. The method as recited in claim 43 wherein said surface is associated
with a conduit, said fluid flowable within said conduit.
47. The method as recited in claim 43 wherein said surface is associated
with a conduit, said fluid flowable without said conduit.
48. The method as recited in claim 45 wherein said reference excitation
is selected from the group consisting of:
a force proportional to a reference mass flow rate,
a force proportional to a rotational velocity of said surface,
a force proportional to a prescribed vibration of said surface,
a Coriolis mode of vibration,
a force at an arbitrary frequency,
white or random noise, and
a swept frequency wave.
49. The method as recited in claim 43 wherein said step of calculating
a response characteristic comprises the steps of calculating response
at a driven vibration frequency and determining a one selected from
the group consisting of:
damping ratio according to a response curve and a peak value,
damping ratio by determining the bandwidth of a response curve,
damping ratio by a logarithmic decrement method, and
damping ratio as a function of phase angle between excitation and
response.
50. The method as recited in claim 43 wherein said step of calculating
a response characteristic comprises the step of calculating a one
selected from the group consisting of:
a Fourier transform of said prescribed vibration, and
a power necessary to maintain a Coriolis mode amplitude.
51. The method as recited in claim 45 wherein said response to
said reference excitation is selected from the group consisting
of:
an intermittent modulation of a mass flow-related signal,
a continuous modulation of a mass flow-related signal,
an average modulated value of a mass flow-related signal,
a magnitude of peak to peak modulation,
a magnitude of response motion,
a difference between modulated amplitude and average flow rate
value, and
a ratio of response in a Coriolis mode to response in a driven
mode.
52. The method as recited in claim 43 wherein said step of calculating
comprises the step of calculating a sensitivity.
53. The method as recited in claim 43 wherein said step of calculating
comprises the step of calculating a zero.
54. The method as recited in claim 43 further comprising the step
of measuring and compensating for a temperature.
## Description TECHNICAL FIELD OF THE INVENTION
The present invention is directed, in general, to vibrating instruments
and, more specifically, to signal processing and field proving methods
and circuits for Coriolis mass flow meters.
BACKGROUND OF THE INVENTION
In the field of flow meters, Coriolis flow meters are unique in
that they can directly measure the mass flow rate of a fluid with
little or no intrusion into the fluid stream. Because of this, they
have become increasingly popular and currently account for the fastest
growing segment of the overall flow meter market.
Over the last 15 years, there has been a rapid evolution of developments
in the field of Coriolis flow meters. These developments have concentrated
on improving performance by optimizing flow conduit shapes and introducing
improved signal processing techniques and different modes of vibration.
This evolutionary process began with the introduction of the first
commercially-viable Coriolis mass flow meter using a U-shaped flow
conduit vibrated in its first bending mode of vibration. The signal
processing scheme employed was a time delay measurement between
inlet and outlet motion signals. This method could give useful results,
however, it was understood at that time that the elastic modulus
of the vibrating portion of the flow conduit was itself a function
of temperature, and that any changes therein change the sensitivity
of the device. The temperature of the flow conduit had to be measured;
then, the effect of temperature upon the elastic modulus of the
flow conduit had to be characterized and a compensation value added
to the flow signal to minimize the effects of changes in the elastic
modulus of the flow conduit.
For example, 316L stainless steel is commonly used for the flow
conduit material in these devices, yielding a theoretical tensile
elastic modulus vs. temperature relationship of about -2.2% per
100.degree. F. increase (in the range between 0.degree. F. and 350.degree.
F.) and nearly linear for that material. Therefore, the compensation
value is commonly applied in a linear relationship to account for
the effects of temperature on tensile elastic modulus. It should
be noted here that some meter designs depend upon the shear modulus
rather than the tensile modulus, or a combination thereof, and a
corresponding compensation value exists thereto.
While the prior art compensation method was simple, it was also
known that 316L elastic modulus became increasingly non-linear as
the temperature became colder or hotter, and in general, for most
common conduit materials, the elastic modulus vs. temperature curves
are non-linear. This fact therefore necessitated adding more complex
temperature compensation methods to account for a wider range of
materials and non-linear temperature relationships.
As more Coriolis flow meters of different designs were put into
service, it was found that not only temperature, but fluid density
and pressure could also effect the sensitivity of the device. This
realization prompted the same type of response from manufacturers
as did the temperature problem earlier described in that the effects
were required to be characterized and compensated for.
In the case of density effects, many types of Coriolis flow meters
can calculate the density by virtue of the natural frequency of
the conduit thereby yielding a signal proportional to density that
can be used to compensate for density effects on sensitivity.
In the case of pressure effects, it was found that by restricting
the conduit geometry to certain design relationships, pressure effects
could be minimized. In either case however, the result was either
more compensation circuit complexity or geometric design restrictions.
Flow meters with straight flow conduits were later introduced into
the market. These meters are subject to temperature gradients between
the flow conduit and the surrounding support structure that cause
stresses in the flow conduit that can alter the sensitivity and
zero of the device. Several methods were therefore introduced to
accommodate this added problem, such as measuring the difference
in temperature between the flow conduit and its support and calculating
what the stress should be and deriving a compensation value based
on that difference. Methods employing strain gages have also been
employed for the purpose of determining the stress level and deriving
the requisite compensation value, again adding more complexity to
the circuit and necessitating greater understanding of the complex
relationships between stress and the change in the sensitivity of
a given device.
While the prior discussion has dealt primarily with effects on
the sensitivity of a flow meter, another important flow measurement
parameter is the zero. Since Coriolis flow meters are highly linear
devices (or are made to have linear outputs) relative to mass flow
rate, the two most important mathematical factors allowing their
use as flow measurement devices are therefore (a) the slope of the
output signal vs. the mass flow rate therein (here defined as the
"sensitivity" or "K-factor"), and (b) the value
of the output signal at the intercept of the line with a zero mass
flow point (herein defined as the "zero").
The zero has been a much more elusive parameter for manufacturers
to control because zero shifts are not usually caused by predictable
changes in material constants etc., but can be caused by a number
of subtle and interrelated problems in both the mechanics of the
flow conduit, and in the electronics, both by design or by imperfections
therein. These zero shifts are normally encountered along with changes
in fluid or ambient conditions on the device similar to those just
described for sensitivity effects, e.g., changes in temperature,
pressure, density, frequency, viscosity or conduit stress.
To summarize the history, as Coriolis flow meter manufacturers
have discovered effects on their devices that cause errors or changes
in the sensitivity of their devices, they have generally chosen
to characterize, measure and compensate for each effect individually,
thereby creating complex compensation methods that are more expensive
and less accurate than the method disclosed herein. A similar progression
has taken place toward zero effects as well.
Although these various means and methods just described (and others
not described) are employed to measure, and compensate for parameters
that effect Coriolis flow meter sensitivity and zero, the primary
and fundamental goal of all of these have been to simply determine
the sensitivity and/or zero of the device to fluid flow, and then
compensate for any changes therein. What is needed in the art is
a way of avoiding the need to measure and compensate. What is needed
is systems and methods for directly determining sensitivity or zero
characteristics, or both, of a Coriolis flow measurement device,
thereby allowing overall compensation for any changes in sensitivity
or zero characteristics, regardless of source.
SUMMARY OF THE INVENTION
To address the above-discussed deficiencies of the prior art, it
is a primary object of the present invention to provide methods
and apparatus to directly determine the sensitivity or zero, characteristics
(each an example of a "response characteristic") of a
Coriolis flow measurement device, and to compensate for any changes
therein, regardless of the cause of those changes.
In the attainment of the above-described primary object, the present
invention provides a signal processing apparatus and method for
measuring a mass flow rate of a fluid flowing in conjunction with
a surface of a Coriolis mass flow meter and a field-provable Coriolis
mass flow meter. The apparatus includes: (1) a driver for creating
a prescribed vibration in the surface, (2) a motion detector for
measuring the motion of the surface, (3) a circuit for determining
a response characteristic of the surface to mass flow rate or other
prescribed forces and (4) calculation circuitry for calculating
a measured mass flow rate of the fluid as a function of the motion
and the sensitivity. In a preferred embodiment, the circuit for
determining the response characteristics includes a circuit for
determining a frequency response of the surface to mass flow rate
or other prescribed forces. In a related embodiment, the circuit
for determining the frequency response determines the frequency
response from a reference excitation applied to the surface.
Both sensitivity and/or zero changes can thus be determined dynamically,
and compensated for using the present invention. This eliminates
the need to know the complex relationships between sensitivity and
zero, and temperature, pressure, density, viscosity, conduit stress,
etc., and likewise eliminates the need to include apparatus and
circuitry to individually measure and compensate for these effects.
The present invention introduces the concept of an excitation reference.
The excitation reference is employed to cause a prescribed excitation
(reference excitation) on the vibrating portion of the flow meter,
in addition to the normal driven vibration. The response to the
reference excitation is then measured and, from the measurement,
the response characteristic of the device can then be determined,
regardless of the combination of fluid or ambient effects that may
be acting upon it.
In a preferred embodiment of the present invention, the surface
is associated with a conduit. In alternative related embodiments,
the fluid is flowable within the conduit or without the conduit,
or relative to a surface of arbitrary shape.
In a preferred embodiment of the present invention, the driver
is selected from the group consisting of: (1) a magnet/coil pair,
(2) a piezoelectric driver and (3) an electrostatic driver.
In a preferred embodiment of the present invention, the surface
is associated with an arbitrary surface, the fluid flowable in conjunction
with the arbitrary surface.
In a preferred embodiment of the present invention, the additional
reference excitation is selected from the group consisting of: (1)
a force proportional to the reference mass flow rate, (2) a force
proportional to the vibration of the surface, (3) a Coriolis mode
of vibration, (4) a force at an arbitrary frequency, (5) white or
random noise and (6) a swept frequency wave.
In a preferred embodiment of the present invention, the motion
sensor is selected from the group consisting of: (1) a magnet/coil
pair, (2) a piezoelectric sensor, (3) an optical sensor, (4) a strain
gage and (5) an electrostatic sensor.
In a preferred embodiment of the present invention, the flow rate
calculation circuitry means calculates the measured mass flow rate
of the fluid as a function of a one selected from the group consisting
of: (1) time delay, (2) phase angle, (3) amplitude, (4) velocity,
(5) acceleration and (6) motion multiplied by frequency .OMEGA..sub.drv.sup.N,
where N is any positive or negative real number or integer.
In a preferred embodiment of the present invention, the flow rate
calculation circuitry determines response at a driven vibration
frequency and determines a one selected from the group consisting
of: (1) damping of a response curve and a peak value, (2) damping
by a logarithmic decrement method, (3) damping as a function of
phase angle between excitation and response and (4) damping as a
function of bandwidth.
In a preferred embodiment of the present invention, the flow rate
calculation circuitry calculates a one selected from the group consisting
of: (1) a Fourier transform of the vibration and the additional
reference excitation and (2) a power necessary to maintain a Coriolis
mode amplitude.
In a preferred embodiment of the present invention, the flow rate
calculation circuitry calculates a sensitivity and a zero.
In a preferred embodiment of the present invention, the response
to the additional reference excitation is selected from the group
consisting of: (1) an intermittent modulation of mass flow related
signal, (2) a continuous modulation of mass flow related signal,
(3) a magnitude of peak to peak modulation, (4) a difference between
modulated amplitude and average flow rate value, (5) a ratio of
response in Coriolis mode to response in driven mode, (6) an average
modulated value and (7) a magnitude of response motion.
Several embodiments and methods are hereinafter described wherein
the vibrating portion of the flow meter is excited via the excitation
reference and the response to that excitation is measured for the
determination of sensitivity and/or zero, and any changes therein.
Another preferred embodiment of the present invention is the ability
to precisely monitor any changes in the sensitivity and zero of
the device as just described, which is the fundamental goal of the
industry directed to "field proving" flow meters.
In many fluid flow measurement applications a periodic calibration
verification is required for the flow measurement device. This is
particularly true in custody transfer applications where the customer
is billed based on the amount registered by the flow meter. "Proving,"
is therefore a common term used to describe the periodic flow meter
calibration verification. Several techniques of proving flow meters
are commonly used in industry today, including: a conventional pipe
prover, a small volume prover, a master meter, a gravimetric tank
and a volumetric tank.
Each of the aforementioned proving techniques require substantial
ancillary equipment that must be transported to each flow meter
proving site. The equipment requires installation, preparation for
use, and then must be removed after the proving tests are completed.
Obviously, considerable time and expense are required for conventional
field proving of flow meters. In addition, many applications cannot
be successfully "proved" in the field because of fluid,
pressure, flow rate, or other restrictions that a prover device
may not be rated to handle.
Therefore, a method for field proving Coriolis flow meters that
eliminates the need for ancillary equipment, and reduces the time
and expense required to prove a flow meter, would greatly benefit
many industries.
The present invention therefore describes methods and apparatus
for proving Coriolis mass flow meters by means of independently
determining the response characteristics of the device. This is
preferably accomplished by applying prescribed excitations to the
flow sensing element. The response of the flow sensing element to
these excitations can be used to determine the sensitivity and/or
zero of the device that can be compared to those determined at the
time of original calibration, thereby determining whether or not
a change has occurred in the sensitivity or zero of the flow meter.
These sensitivity and zero values, or any changes therein, are normally
then recorded and used for custody transfer rate determination purposes,
and often compared to a limit beyond that the flow meter may be
required to be recalibrated.
It is further a primary object of the present invention to provide
a circuit and method for field proving flow measurement devices
to determine any shifts in the sensitivity of the meter. The circuit
comprises response characteristic determination means for determining
a response characteristic of the meter (preferably done by creating
an additional reference excitation in the surface simulating an
effect of a reference mass flow rate of a fluid flowing relative
to the surface on the vibration of the surface).
The foregoing has outlined rather broadly the features and technical
advantages of the present invention so that those skilled in the
art may better understand the detailed description of the invention
that follows. Additional features and advantages of the invention
will be described hereinafter that form the subject of the claims
of the invention. Those skilled in the art should appreciate that
they can readily use the disclosed conception and specific embodiment
as a basis for designing or modifying other structures for carrying
out the same purposes of the present invention. Those skilled in
the art should also realize that such equivalent constructions do
not depart from the spirit and scope of the invention in its broadest
form.
BRIEF DESCRIPTION OF THE DRAWINGS
For a more complete understanding of the present invention, and
the advantages thereof, reference is now made to the following descriptions
taken in conjunction with the accompanying drawings, in which:
FIG. 1 illustrates a section of a vibrating surface of a Coriolis
mass flow meter shown deflected in its driven mode of vibration,
along with the moving fluid with which it interacts;
FIG. 2 illustrates the vibrating surface of FIG. 1 shown deflected
due to the Coriolis force distribution that results from movement
of the fluid;
FIG. 3 illustrates a signal processing and field proving circuit
of one embodiment of the present invention;
FIG. 4 illustrates electrical signals that occur in conjunction
with various embodiments of the present invention;
FIG. 5 illustrates an electrical circuit that could be used as
an alternate to that shown in FIG. 3;
FIG. 6 illustrates characteristic curves illustrating the sensitivity
dependency of a Coriolis flow meter to a variety of parameters such
as fluid pressure and density, conduit temperature and stress;
FIG. 7 illustrates electrical signals that occur in conjunction
with various embodiments of the present invention;
FIG. 8 illustrates characteristic frequency response curves of
the driven mode of vibration and the Coriolis mode of vibration;
FIG. 9 illustrates a section of a vibrating surface of a Coriolis
mass flow meter along with the moving fluid with which it interacts;
FIG. 10 is an alternate circuit diagram that could be used for
the present invention using variable impedances;
FIG. 11 is an alternate circuit diagram that could be used for
the present invention using combined vibration drivers and reference
exciters;
FIG. 12 illustrates electrical signals that occur in conjunction
with various embodiments of the present invention;
FIG. 13 illustrates electrical signals that occur in conjunction
with various embodiments of the present invention; and
FIG. 14 illustrates an alternate circuit diagram that could be
used for the present invention using alternate reference excitation
methods.
FIG. 15 illustrates relationships between surface geometry, mass
flow and Coriolis forces.
DETAILED DESCRIPTION
Basic Theory of Operation
A Coriolis mass flow meter is a device that measures the mass flow
rate of a fluid flowing past a vibrating surface. The vibrating
surface is often provided in the form of a flow conduit or tube
through which the fluid is caused to flow. More recently, Coriolis
flow meters using tubular or surfaces of arbitrary shape, outside
or over which fluid is caused to flow, have also been employed.
This distinction is immaterial in the discussion of the present
invention, since it applies to any of these devices. Therefore,
the term "vibrating surface" will be henceforth used primarily
and can be taken to mean a traditional flow conduit or tube through
which fluid is passed, outside of which fluid is passed, or an arbitrary
surface interacting with the fluid to be measured.
Referring initially to FIGS. 1 2 and 6 illustrated are (in FIG.
1) a section of a vibrating surface of a Coriolis mass flow meter
shown deflected in its driven mode of vibration, along with the
moving fluid with which it interacts, (in FIG. 2) the vibrating
surface of FIG. 1 shown deflected due to the Coriolis force distribution
that results from movement of the fluid and (in FIG. 6) characteristic
curves illustrating the sensitivity dependency of a Coriolis flow
meter to a variety of parameters such as fluid pressure and density,
surface elasticity and stress.
A vibrating surface 1 interacts with a fluid 2 to be measured in
such a way as to cause a Coriolis acceleration of the fluid and
thereby resulting Coriolis forces to bear against the vibrating
surface 1. This in turn causes physical distortions in the vibrating
surface 1 as shown in FIG. 2 that can be measured and related to
the mass flow rate of the fluid passing over or through the vibrating
surface 1. These Coriolis forces occur in accordance with the following
general equation (1).
where:
F.sub.cor =resulting Coriolis force,
m=mass of the moving fluid,
.OMEGA..sub.cor =rotational velocity vector of the moving fluid
mass,
V=linear velocity vector of the moving fluid mass and
x=a cross product operator.
For the purpose of clarification, it is useful to derive some basic
relationships concerning Coriolis forces and their effects on a
vibrating surface with regard to the type of sensor or measurement
method used to determine these Coriolis forces and the mass flow
rate.
Turning now to FIG. 15 depicted is the fluid 2 having a mass flow
rate and associated with the vibrating surface 1 where mass flow
m' 2 is initially moving horizontally to the right, as shown, in
conjunction with the vibrating surface 1. A moment later in time,
due to the vibration of the vibrating surface 1 the mass flow 2
has rotated through some angle .PHI. 66 and is then moving in a
new direction 2'. The motion sensor 4 mounted on the vibrating surface
1 moves from its initial position to its new position 4', thereby
displacing a distance A 65. Equation (1) gives the fundamental relationship
for determining the Coriolis force of a moving mass. Since the fluid
mass per unit length along the vibrating surface 1 multiplied by
its velocity is the mass flow rate m', this substitution may be
made into equation (1) (and changing the cross product to a multiplication
due to the 90.degree. relationship), yielding equation (2) describing
the Coriolis force per unit length F'.sub.cor 68 along the vibrating
surface 1:
where:
F'.sub.cor =resulting Coriolis force per unit length,
m'=Mass flow rate interacting with vibrating surface 1 and
.OMEGA..sub.cor =rotational velocity of the mass flow.
Since the vibration of the vibrating surface 1 is sinusoidal in
time, the displacement A 65 of the sensor 4 is also a sinusoidal
function of time as in equation (3):
where:
A=Displacement of motion sensor 4 as a function of time,
a=Maximum displacement of motion sensor 4
.OMEGA..sub.drv =Driven vibration frequency and
t=time.
Since, for small angles, the sine of an angle approximates the
angle itself, the angle .PHI. 66 can be taken to be equal to A/L:
therefore, substituting equation (3) into equation (4) yields equation
(5):
Since the Coriolis rotational velocity .OMEGA..sub.cor is the rate
of change of angle .PHI. as a function of time, then:
Substituting equation (6) back into equation (2) yields the following
equation (7):
Simplifying equation (7) and removing constants yields the following
relation involving the resulting Coriolis force over the length
considered.
where:
F.sub.cor =resulting Coriolis force over the length considered
Assuming, for the moment, that the Coriolis force F.sub.cor is
caused to act on a surface that has the characteristics of a linear
spring without any dynamic or other complicating effects, equation
(9) would describe the displacement of that surface as follows:
where:
F.sub.cor =resulting Coriolis force,
x.sub.cor =Coriolis force-related displacement of the vibrating
surface 1 and
k=linear static spring constant of the vibrating surface 1.
Substituting equation (9) into equation (8) yields the following:
Rearranging equation (10) to solve for mass flow rate m' yields
the following relation (11):
Historically, it was found that the time delay .DELTA.t for the
motion sensor 4 to move the distance of the Coriolis deflection
x.sub.cor was roughly proportional to the mass flow rate in certain
situations. Since this time delay is equal to the Coriolis displacement
x.sub.cor divided by the velocity of the motion sensor 4 (the rate
of change of displacement A 65 with respect to time), then:
Substituting equation (12) into equation (11) yields the simple
relation (13):
Therefore, in this simplified analysis, the mass flow rate m' is
proportional to the time delay .DELTA.t multiplied by the spring
constant k of the vibrating surface 1. As the stiffness k of the
vibrating surface 1 changes due to temperature, compensation can
be added. The early developers of Coriolis mass flow meters took
this approach and initially gave reasonable results for certain
flow tube (surface) geometries and designs. However, in a more general
case, this method is inadequate. Many surface designs were found
to change sensitivity to flow rate as a function of other fluid
and ambient related parameters such as: temperature, elasticity,
material damping in the vibrating surface, pressure, density, viscosity,
stress or driven amplitude.
Therefore, the present invention addresses the more general case,
allowing the true mass flow rate to be determined regardless of
the combination of affects that may be acting on the vibrating surface
1.
Not only are the magnitude of the resultant physical distortions
greatly affected by ambient and fluid parameters, these ambient
and fluid parameters have varying effects on the sensitivity of
a device depending upon the "domain" in which the flow-related
signal is acquired and used. For example, most signal processing
methods employed today, as in the previous analysis, measure time
delay and therefore operate in the time delay domain, reducing pressure
and density effects on certain restricted conduit or surface geometries.
However, this domain tends to exacerbate sensitivity changes due
to temperature, stress, viscosity, and other effects.
To highlight the point, FIG. 6 graphically depicts the response
characteristics of a given Coriolis flow meter design. On the graph,
the vertical axis represents the percentage change in the sensitivity
of a given Coriolis flow meter design for a given change in a fluid
or conduit-related parameter such as pressure, density, viscosity,
temperature or stress. The horizontal axis represents the domain
in which the Coriolis-related signal is processed. The identified
positions along the domain axis are time delay 25 displacement
(or phase multiplied by driven amplitude) 26 velocity 27 and acceleration
28. Each identified domain is related to the next by virtue of a
mathematical relationship through the frequency of driven vibration.
For example, if a signal represents the velocity of motion, the
displacement of that motion is related to the integral of that velocity
over time. The units of velocity for example could be represented
by inches per second, and therefore dividing by the driven frequency
(.OMEGA..sub.drv) with units of 1/seconds yields a displacement-related
signal with units of inches. Therefore, simply by dividing the velocity
signal by a signal proportional to the driven frequency (.OMEGA..sub.drv)
a signal proportional to the displacement is obtained. By dividing
this displacement signal with units of inches by the driven frequency
with units of 1/seconds, a signal proportional to the time delay
times the driven amplitude, with units of inch-seconds, is thereby
obtained. Alternately the time difference between the upstream and
downstream motion could be measured directly yielding a similar
result without the amplitude dependence (units of seconds rather
than inch-seconds). This measurement of time delay is the most commonly
used method on currently available Coriolis mass flow meters today
as was previously explained with regard to the analysis of equations
(1) through (13) above.
Similarly, since a phase angle can be defined as the time delay
times the driven frequency (.OMEGA..sub.drv *.DELTA.t), measuring
the phase angle between the upstream and downstream motion yields
the same position 26 along the domain line as displacement except
that a phase measurement is independent of driven amplitude and
would therefore have no units. Therefore, the positions 25 26
27 28 along the domain line are related to each other by virtue
of integer divisions (or multiplications) of the driven frequency
.OMEGA..sub.drv.
Any position along the domain line can therefore be achieved by
either obtaining one or more Coriolis-related flow signals by virtue
of a sensor type (e.g., velocity, displacement or acceleration sensor)
or by a measurement method (e.g., phase or time delay measurement).
The primary difference between these two approaches is that if an
amplitude-related sensor or method is used to measure the Coriolis-related
signals (e.g., velocity, displacement or acceleration sensor) the
result is amplitude dependent, whereas the result is independent
of the driven amplitude if a phase or time delay method is used.
While these integer-related positions 25 26 27 28 are understandable
because of their applicability to actual types of motion sensors
or processing methods (e.g., velocity sensors, displacement sensors,
accelerometers or strain gages, time delay or phase measurements)
characteristic curves 29 30 31 32 are continuous along the domain
line, including all points between the positions 25 26 27 28.
Therefore, to alter the domain of the acquired signal from, for
example, the velocity domain, to an arbitrary point 33 along a domain
line, a velocity signal could be divided (or multiplied) by a signal
proportional to the frequency raised to a power of N (.OMEGA..sub.drv).sup.N,
where N is the number of multiples (whole or fractional) of frequency
necessary to move to that domain, and can be any real number or
integer, positive or negative. In this example, dividing the velocity
domain signal by the frequency raised to an N value of 1 therefore
represents a shift to the displacement domain 26. Similarly, dividing
the velocity domain signal by the frequency raised to an N value
of 2 therefore represents a shift to the time delay domain 25. To
achieve the arbitrary position 33 located 1/4th of the way between
time delay and displacement domains, the velocity domain signal
should be divided by the frequency raised to an N value of 1.75.
Characteristic curves 29 30 31 32 therefore represent the percent
sensitivity change of a given meter design for a given parameter
change, as a function of the domain in which the signals are processed.
The curve 29 represents the change in the sensitivity of a given
meter to a given increase in the fluid pressure as a function of
the domain in which the signals are processed. The curve 30 represents
the change in the sensitivity of a given meter to a given increase
in the fluid density as a function of the domain in which the signals
are processed. The curve 31 represents the change in the sensitivity
of a given meter to a given decrease in the vibrating surface 1
elastic modulus as a function of the domain in which the signals
are processed. Finally, the curve 32 represents the change in the
sensitivity of a given meter to a given increase in the tensile
stress of the vibrating surface 1 as a function of the domain in
which the signals are processed.
Any parameter that can effect the sensitivity of a given meter
design therefore has a corresponding characteristic curve lying
on the graph of FIG. 6. With reference to the specific curves 29
30 31 32 of FIG. 6 it is apparent that (for this example) the
pressure and density characteristic curves 29 30 intersect a zero
sensitivity change line 33 near (but not exactly in) the time delay
domain 25. Since this is characteristic of many currently commercially-available
Coriolis flow meter designs, virtually all signal processing schemes
to date operate in the time delay domain to take advantage of this
coincidence to minimize pressure and density effects. To eliminate
pressure and density effects, the proper domain in which to work
is that of domain 33 achieved by dividing the velocity domain signal
by the frequency raised to a value of N equal to 1.75 since this
is the position at which the meter experiences no substantial density
or pressure effect.
Although this example clearly illustrates that pressure and density
effects may be eliminated, the elastic modulus characteristic curve
31 and stress characteristic curve 32 both have finite, nonzero
sensitivity change values in the domain 33. Therefore, these parameters
must still be known and factored out in processing resulting mass
flow signals.
The shapes and zero intercepts of these characteristic curves can
vary widely depending on a number of factors, including the design
of the vibrating surface 1 and the manner in which the driven vibration
is controlled. With regard to controlling the driven vibration,
if the displacement amplitude of the driven vibration is held constant,
the characteristic curves can appear similar to those depicted in
FIG. 6. However, if the driven velocity is instead held constant,
the characteristic curves in FIG. 6 are shifted by N=1 domain. (This
pertains to amplitude related signals only since measuring time
delay or phase automatically compensates for driven amplitude.)
While a Coriolis mass flow meter designer has some theoretical freedom
to adjust the design and the working domain to try to minimize or
eliminate sensitivity changes on the meter, this freedom may be
quite difficult to realize in practice.
FIG. 6 depicts why it is so difficult to individually measure and
compensate for every parameter that can effect the sensitivity of
a given flow meter design. Since it is very difficult and restrictive
from a designer's standpoint to create a flow meter design that
minimizes all these effects in a given domain, it is understood
that the ability to measure and compensate for the total combined
effects of all these parameters in any working domain would be of
tremendous value to the industry. This is the object of the present
invention.
Typically, the flow-related distortions shown in FIG. 2 of the
vibrating surface 1 are measured in a prescribed domain, for example
the velocity domain, since the most commonly-employed motion detectors
on these devices are magnets and coils that produce signals proportional
to relative velocity between the magnetic field and its associated
coil. The motion detectors in combination with circuit 10 therefore
produce a signal that is proportional to these flow-related distortions
in the velocity or some other domain.
The flow-related signal is proportional to mass flow rate multiplied
by the sensitivity, that, in turn, is dependent upon the selected
signal domain and the combined effect of vibrating surface, ambient,
and fluid-related parameters, such as temperature, elasticity, material
damping in the vibrating surface, pressure, density, viscosity or
stress in the vibrating surface 1. In addition, the flow-related
signal is often offset by some value relating to an innate zero
offset of the device. As stated previously, a primary object of
the present invention is to determine and compensate for any changes
in the response characteristic.
To determine the sensitivity, the present invention makes use of
equations (1) through (8) above. The angular rotation vector .OMEGA..sub.cor
can be determined from the geometry of the design, and the driven
vibration amplitude and frequency of the vibrating surface 1 (that
is typically controlled or measured by a drive circuit 8 of FIG.
3). This relationship is defined in equation (6) above. Therefore,
for a given geometry and vibration amplitude and frequency, the
resulting Coriolis force that results from a given flow rate is
mathematically determined through equation (8). However, this force
can only be measured indirectly by measuring the distortional effects
of the force on the vibrating surface 1.
By determining the frequency response of vibrating surface 1 the
sensitivity and zero can be determined and compensated for any changes
therein. The preferred method of determining this frequency response
is by the use of a prescribed reference excitation.
By exciting the vibrating surface 1 with a prescribed reference
excitation force and then measuring the response to that force,
the net sensitivity and zero can be determined and any changes compensated
for regardless of the causes of those changes. The prescribed excitation
force is in addition to the forces necessary to maintain the normal
driven vibration of vibrating surface 1 as shown in FIG. 1.
A prescribed reference excitation force is therefore applied to
the vibrating surface 1. Several embodiments are hereinafter described
for achieving the application of the additional excitation force,
including the use of current brakes mounted in conjunction with
the vibrating surface that can be switched on or off as required,
auxiliary magnets and coils mounted in association with the vibrating
surface that can be activated in a prescribed manner to modulate
the mass flow-related signal, variable impedance components associated
with the motion sensors, the addition of excitation signals to the
drive signals that maintain the driven vibration of vibrating surface
1 piezoelectric exciters and others.
Another method described involves exciting a Coriolis reaction
mode of vibration on vibrating surface 1 (similar to FIG. 2) to
determine its frequency response characteristics and then calculating
the response at the driven vibration frequency.
Any of these excitations can be applied continuously or intermittently
as required for a given design. In addition, the excitation can
be applied plurally both upstream and downstream, or singularly
either upstream or downstream. These methods have different effects
and can be used to separately determine both the effects on sensitivity
and on zero.
Once the prescribed excitation has been applied, the response is
then measured by one of several methods described including measuring
the magnitude of the distortion of surface 1 due to the reference
excitation, observing the modulating effect of the prescribed excitation
on the mass flow-related signal, calculating a frequency response
by methods including a Fourier transform (fast or discrete), and
others.
With the excitation and the response thereby determined, the mathematical
relationships between them yield the desired measurement parameters
for the device that include the response characteristic (including
sensitivity and zero). Sensitivity and zero compensation values
are thereby determined and applied to the mass flow-related signal
to correct that signal for any changes therein.
As previously mentioned, an important area in the flow measurement
industry is that of field proving flow measurement devices to determine
any shifts in the sensitivity of the meter. Since the present invention
further addresses the issue on Coriolis flow meters, it directly
follows that the apparatus and methods herein described can be applied
to that end.
The act of field proving a flow meter normally involves creating
a reference flow rate through the meter and measuring the meter's
response to that reference flow rate. The sensitivity and/or zero
of the meter is then determined (by dividing meter output by a reference
flow rate) and compared to previously-determined values of those
numbers to determine if there has been any change therein.
The key to the prior art procedure is providing the reference flow
rate, normally involving an additional piece of equipment designed
to provide a highly accurate measure of flow rate such as those
previously mentioned. The additional equipment often requires costly
and time-consuming setup and operational efforts.
A unique aspect of a Coriolis flow meter is, as previously mentioned,
the fact that the Coriolis force that results from a given flow
rate is easily determined through equation (8), above. This force,
or one proportionally related thereto, can therefore be applied
onto the vibrating surface 1 simulating that same force (or one
proportionally related thereto) that results from an actual reference
fluid flow rate. Therefore, applying the force is analogous to creating
a reference flow rate through the meter and thus can be made to
serve the same purpose as that of a field prover.
Therefore, by applying a prescribed excitation force proportionally
related to the force that results from a given mass flow rate, and
by monitoring the mass flow-related output signal change therefrom,
the response characteristics of the device can thereby be determined
and compared to those taken at previous times and conditions for
comparison for any changes therein. From this, an output signal
can be created proportionally related to the sensitivity and/or
zero of the flow meter. The method can be used in lieu of any additional
equipment, and can be actuated periodically or continuously, as
required in a particular application.
The Signal Processing Aspect of the Present Invention
The detailed description of a first embodiment of the signal processing
aspects of the present invention is better understood when taken
in conjunction with FIGS. 1 through 6.
Referring again to FIGS. 1 and 6 illustrated is a section of a
vibrating surface of a Coriolis mass flow meter shown deflected
in its driven mode of vibration, along with the moving fluid with
which it interacts. As previously mentioned, the present invention
applies to all Coriolis type flow meters, whether they use internal
flow through a flow conduit, external flow over a conduit or flow
adjacent to an arbitrary surface. For the purposes of this discussion,
a vibrating surface (such as the vibrating surface 1 of FIG. 1)
will therefore be used and be taken to represent a vibrating tube
or conduit or surface in any type of Coriolis mass flow meter.
The vibrating surface 1 therefore represents a vibrating surface
of a Coriolis flow meter that interacts with the moving fluid 2
the flow rate of which is to be measured. The sensitivity dependency
of vibrating surface 1 to various fluid effects are, for this example,
represented by the characteristic curves of FIG. 6. The vibrating
surface 1 is caused to vibrate by forces applied by a vibration
driver 3 that is typically a magnet and coil arrangement electrically
excited at a prescribed amplitude, frequency and phase by a circuit
8 to cause the requisite vibration that is typically a natural
mode of vibration of the vibrating surface 1 (driven mode). FIG.
1 therefore depicts the vibrating surface 1 deflected during its
driven natural mode of vibration. The resulting vibration of the
vibrating surface 1 is designed to interact with a moving fluid
2 so as to cause a Coriolis force distribution to bear upon the
vibrating surface 1 thus, in turn, causing physical distortions
in the vibrating surface 1 proportionally related to the mass flow
rate of the moving fluid 2.
Turning now to FIGS. 2 though 4 illustrated are (in FIG. 2) the
vibrating surface of FIG. 1 shown deflected due to the Coriolis
force distribution that results from movement of the moving fluid
2 (in FIG. 3) a signal processing and field proving circuit of
one embodiment of the present invention and (in FIG. 4) an illustration
of electrical signals that occur in conjunction with various embodiments
of the present invention. It is the magnitude of the deflection
illustrated in FIG. 2 that is proportionally related to the mass
flow rate, however this magnitude is modified by fluid parameters,
thereby affecting the sensitivity of the device. It should be noted
that the forced vibration mode shape of FIG. 1 and the resulting
Coriolis distortion shape of FIG. 2 are examples of those commonly
used in Coriolis flow meters today. Many other modes of vibration
involving higher order modes are possible. Therefore, the exact
mode of vibration chosen is immaterial to this discussion, since
the general principle applies to all types of forced vibration modes
and their corresponding Coriolis distortion shapes.
Two motion sensors 4 5 are preferably coupled to the vibrating
surface 1 to sense the physical motions in the vibrating surface
1 at two different places along the length of the vibrating surface
1 and thereby create motion signals 11 and 12 (FIG. 4) respectively
related to the motions sensed by the two sensors 4 5. The two sensors
4 5 are preferably magnet and coil pairs, whereby they measure
velocity. However they could be any other type of sensor responsive
to motion such as displacement transducers, accelerometers, electrostatic
sensors, optical sensors, optic fibers or strain gages. The sensor
4 is shown deployed toward the upstream direction of the vibrating
surface 1 and the sensor 5 is shown deployed toward the downstream
direction of the vibrating surface 1. The two sensors 4 5 are deployed
at different places along the vibrating surface 1 so that there
is a difference sensed between the two sensors 4 5 proportionally
related to mass flow rate. In this embodiment the difference is
used for the determination of an uncompensated (or "raw")
mass flow-related signal 9 (M'.sub.raw signal 9) by one of several
methods employed in a circuit 10.
It should be noted that certain designs of Coriolis mass flow meters
can employ a single motion sensor to determine the M'.sub.raw signal
9. This is the case for a vibrating surface that is designed to
create a Coriolis force distribution and a resulting distorted shape
that is best sensed at a single position. Therefore, it is anticipated
that the present invention can be used with a single motion sensor,
however two are used in the preferred embodiment. As an example
of this idea, if the distorted shape in FIG. 2 were used for the
driven mode shape, the Coriolis reaction mode shape would be the
next higher mode shape that could easily be sensed with a single
motion detector located in the center of surface 1 near that depicted
by driver 3 of FIG. 2.
The preferred method employed in the circuit 10 to determine the
M'.sub.raw signal 9 is to measure the AC component of the difference
between signals 11 12 synchronously demodulated in phase with the
Coriolis forces. The signal therefore represents the M'.sub.raw
signal 9 in the velocity domain 27 modified by any changes in the
sensitivity or zero as previously described.
Alternatively, another method commonly employed in the circuit
10 to determine the M'.sub.raw signal 9 is to measure the time delay
between the signals 11 12 from the motions sensed at the sensors
4 5. The time delay represents a raw mass flow-related signal in
the time delay domain 25 modified by any changes in the sensitivity
or zero as previously described.
Other methods of determining the raw mass flow-related signal include
using Fourier transform methods to determine the phase angle between
the signals 11 12 of the sensors 4 5 either by fast or discrete
methods. The phase angle represents a raw mass flow-related signal
in the phase (or displacement) domain 26 modified by any changes
in the sensitivity or zero as previously described.
The M'.sub.raw signal 9 used in the velocity domain 27 as shown
in FIG. 6 has a small sensitivity dependency upon vibrating surface
1 elastic modulus changes (illustrated by the characteristic curve
31). However, the M'.sub.raw signal 9 has relatively large sensitivity
dependencies upon pressure (illustrated by the characteristic curve
29) and density (illustrated by the characteristic curve 30) and
vibrating surface 1 stress changes (illustrated by the characteristic
curve 32). This is the point where traditional signal processing
methods apply individual compensations for each parameter according
to their characteristic individual effects (e.g., temperature compensation
using temperature sensor or strain compensation using strain gages)
or by changing the domain of the acquired signal (e.g. from the
velocity to the displacement or time delay domain).
In the present invention, however, the response characteristics
of overall sensitivity and zero are determined by applying a prescribed
reference excitation or excitations to the vibrating surface and
by measuring the response thereof. This allows the signals to be
acquired and processed in any signal domain in which the designer
may choose to work, regardless of the sensitivity dependencies that
correspond to that domain.
Reference exciters 6 7 are preferably deployed in association
with vibrating surface 1 at two different positions thereon. The
reference exciters 6 7 are preferably magnet and coil pairs designed
to apply a prescribed force upon the vibrating surface 1 at a prescribed
amplitude, frequency and phase supplied by exciter drivers 13 14
of FIG. 3 respectively. In this embodiment, the reference exciters
6 7 are located along the vibrating surface 1 where their forces
best simulate the net distributed Coriolis force that occurs along
the vibrating surface 1 due to the motion of the moving fluid 2
interacting with the forced vibration of the vibrating surface 1.
The reference excitation to be applied can be of any prescribed
magnitude, but are preferably proportionally related to the driven
motion of the vibrating surface 1 (and therefore proportional to
the magnitude of the signals 11 12) by the exciter drivers 13
14 respectively. By using excitation proportionally related to the
driven motion of the vibrating surface 1 driven amplitude dependency
of the resultant flow signals is automatically compensated for.
Excitation signals 15 16 are thereby determined and applied to
reference exciters 6 7 respectively, in an alternating fashion
as shown in FIG. 4. The reference excitation signals 15 16 are
preferably applied in the same phase relationship as is the Coriolis-related
flow signals, that themselves are typically in phase with the velocity-related
signals 11 12. It should be noted here that any arbitrary phase
relationship could here be used to apply the reference excitation,
however, the signal processing circuitry is normally designed to
detect signals in phase with the Coriolis forces, therefore it is
a practical convenience to apply these reference excitations in
this phase and thereby detect their effects as modulations on the
flow-related signals.
First, the excitation signal 15 is applied to the reference exciter
6 for a period of time (termed a "modulation period")
as necessary to determine its effect on the M'.sub.raw signal 9.
Next, the excitation signal 15 is terminated and the excitation
signal 16 applied to reference exciter 7 for a modulation period
as necessary to determine its effect on the M'.sub.raw signal 9.
The polarity of the excitation signals 15 16 is preferably applied
to produce the opposite effect on the M'.sub.raw signal 9 (i.e.,
the signal 15 causes a positive effect and the signal 16 causes
a negative effect, or vice versa) as shown in the M'.sub.raw signal
9 of FIG. 4. The logic and timing of the reference excitations are
controlled by reference exciter logic circuitry 19.
A circuit 20 then receives the modulated M'.sub.raw signal 9 and
excitation information from the reference exciter circuitry 19 and
thereby determines a "nominal" value 34 (a value without
any reference excitation), a modulation amplitude 17 and a modulation
offset 18 (a difference between the average modulation value and
the nominal value of signal 9 with no reference excitation applied).
It should be noted that the modulation of the M'.sub.raw signal
9 in this case, causes deviation from the nominal value 34 that
can be attributable to a zero flow condition or some finite amount
of flow. The accurate determination of the sensitivity and zero
is preferably accomplished during a period of time when the nominal
value 34 of signal 9 does not change significantly over the modulation
period.
The response characteristics then are determined as follows. The
modulation amplitude 17 is proportionally related to the sensitivity
of the vibrating surface 1 regardless of the cause of any changes
therein, and is therefore proportionally related to the sensitivity
of the device at that moment. In contrast, the modulation offset
18 is proportionally related to the attenuation of one end of the
vibrating surface 1 with respect to the other end of the vibrating
surface 1 and is therefore indicative of a zero offset. Thus, the
modulation offset 18 is proportionally related to the zero of the
device at that moment.
The modulation amplitude 17 and offset 18 along with excitation
information, are then supplied to a circuit 21. The circuit 21 also
receives the modulated M'.sub.raw signal 9 and transforms the M'.sub.raw
signal 9 into a true mass flow signal (M'.sub.true signal 22) corrected
for any changes in the sensitivity or zero offset. The M'.sub.true
signal 22 additionally can be demodulated to remove unwanted modulations
prior to delivery to the user. One such correction method is as
shown in relation (14) below.
The preferred method of measuring the modulation amplitude 17 in
the circuit 20 is to demodulate the M'.sub.raw signal 9 synchronously
using the modulation period determined from the reference exciter
circuitry 19 as the synchronous reference. This can be done using
a lock-in amplifier or its equivalent in a digital processor. Alternate
methods include a precision root mean square ("RMS") circuit
or peak detection methods.
In addition, the modulation can be done intermittently or continuously
as preferred by the designer. However, if done continuously, the
modulation offset 18 is lost, since the excitation is not turned
off to allow the M'.sub.raw signal 9 to return to a nominal value.
Continuous modulation however can be used effectively.
Turning now to FIG. 7 illustrated are electrical signals that
occur in conjunction with various embodiments of the present invention.
The reference exciter circuitry 19 of FIG. 3 controls continuous
reference excitation alternating between the exciters 6 7 via the
signals 15 16 respectively, as shown in FIG. 7. The result is
a continuously-modulated signal 9 as shown in FIG. 7. Here, the
average modulated value 33 is proportionally related to the M'.sub.raw
signal 9 with the zero offset value removed, and the modulation
amplitude 17 is proportional to the sensitivity. Therefore, the
true mass flow rate signal is achieved in this example by dividing
the average modulated value 33 by the modulation amplitude 17 as
in relation (15) below.
In this way, if, at a constant flow rate, the sensitivity of the
vibrating surface 1 increases (perhaps due to a change in the pressure,
density, viscosity, temperature or driven amplitude), the average
modulated value 33 also increases. The modulated amplitude 17 also
increases, thereby holding the final M'.sub.true signal to be constant
(as was the mass flow rate for this example).
Since it may be preferable not to have modulation on the M'.sub.true
signal 22 several methods are anticipated to remove the modulation
prior to delivery of the M'.sub.true signal 22 to the user. Some
of these methods include holding the last value of the M'.sub.true
signal 22 determined prior to modulation through the modulation
sequence, and then resuming the M'.sub.true signal 22 with updated
sensitivity and zero offset compensation values. Another method
is synchronously to add 1/2 of the modulated amplitude 17 value
back onto the M'.sub.raw signal 9 alternately in the correct phase
and polarity to effectively demodulate the signal and rid the M'.sub.raw
signal 9 of unwanted modulations.
As an alternate to the first embodiment wherein the excitation
signals 15 16 are created and actively applied to the reference
exciters 6 7 respectively, dampers can be used to create the reference
excitation forces proportionally related to the rotational velocity
of the vibrating surface 1 and thereby simulate Coriolis forces
being applied. Dampers are devices that create forces proportionally
related to velocity, that is analogous to the Coriolis forces themselves
as previously explained in conjunction with equations (1) through
(6) above. Therefore, the reference exciters 6 7 can be used as
dampers that can be turned on or off as necessary to accomplish
reference excitation.
Turning now to FIG. 5 illustrated is an electrical circuit that
could be used as an alternate to that shown in FIG. 3. Damping is
accomplished by using the circuit of FIG. 5 wherein the reference
exciter circuits 13 14 of FIG. 3 are replaced by switches 23 24.
When these switches 23 24 are activated, the coil portion of the
reference exciters 6 7 then become "shorted," allowing
current to flow through the loop thus created in conjunction with
the motion of the vibrating surface 1. The current then repels the
magnetic fields in the exciters 6 7 thereby creating forces proportionally
related to the velocity of the vibrating surface 1 and analogous
to Coriolis forces. This is similar to a current brake (another
type of damper that could be used). Many other types of dampers
are known to those of ordinary skill in the pertinent art and also
fall within the broad scope of the present invention.
The motion of the vibrating surface 1 from the driven vibration
creates a voltage on the coils of the reference exciters 6 7 if
the switches 23 24 are held in their open positions by the reference
exciter circuitry 19 of FIG. 5. To modulate the M'.sub.raw signal
9 as before, the reference exciter circuitry 19 first closes the
switch 23 for a period of time (again, the "modulation period").
Closure of the switch 23 then creates a current brake, whereby the
aforementioned voltage is converted into a current that then repels
the magnetic field portion of the exciter 6. This creates a force
proportionally related to the velocity of the vibrating surface
1. Since the velocity is related to the rotational velocity of the
vibrating surface 1 through its geometry and driven amplitude and
frequency (as previously mentioned), the force is therefore proportionally
related to the rotational velocity of the moving fluid 2 interacting
with the vibrating surface 1 and thereby proportionally related
to the Coriolis force that is created from a prescribed flow of
the fluid 2.
The braking force then has the same effect as in the previous embodiment
and causes a change in the magnitude of the distortion of surface
1 and can thus be measured as a change in the level of the M'.sub.raw
signal 9. Next, the reference excitation circuitry 19 opens the
switch 23 and closes the switch 24 for a period of time that, again,
has the same effect as previously mentioned and causes a force proportionally
related to the rotational velocity of the vibrating surface 1 to
be applied to the vibrating surface 1 through the reference exciter
7 thereby simulating a prescribed amount of flow of the fluid 2.
The second force from the reference exciter 7 causes a similar
change in the level of the M'.sub.raw signal 9 but in the opposite
direction as did the force from the exciter 6 similar to the previous
embodiment. Therefore, similar to the previous example, the M'.sub.raw
signal 9 of FIG. 4 depicts the modulation that occurs due to these
applied braking forces. These modulations again have a modulation
amplitude 17 and a modulation offset 18 that are proportionally
related to the sensitivity and the zero. The circuit 20 then determines
these values and thereby the values of the sensitivity and the value
of the zero and passes the information on to the circuit 21 where
the appropriate compensation values are applied to the M'.sub.raw
signal 9 to correct for any changes in the sensitivity or the zero.
Also, the M'.sub.raw signal 9 may be demodulated to remove the excitation
modulation prior to creating and delivering the final M'.sub.true
signal 22 to the user.
With regard to the design of the current braking system, the amount
of force that the system creates, and therefore the amount of mass
flow this force represents, is dependent upon the force per unit
velocity that the system is designed to deliver. Therefore, the
force is dependent upon the velocity of the vibrating surface 1
as mentioned, the magnetic field of the exciter 6 and the length
and conductivity of the conductor that is placed in the magnetic
field (whose values are preferably held to be constant). Since current
brake designs are well understood, it is not necessary to elaborate
the point, except that the design should accommodate changes in
temperature while still producing forces representing the motion
of the vibrating surface 1. Some trade names of conductors that
do not appreciably change conductivity as a function of temperature
include CUPRON.RTM., EVANOHM.RTM. and MANGANIN.RTM., with MANGANIN.RTM.
being the preferred type. For providing the magnetic field, the
use of a permanent magnet made of ALNICO-9 is most preferable, because
of its superior performance over changes in temperature, but ALNICO-8
is a viable alternative, as are samarium cobalt and other similar
conventional materials.
Because temperature is principally the only parameter that affects
the magnetic fields or the conductivity of the wires used in the
motion sensors 4 5 or the reference exciters 6 7 and since temperature
measurement is relatively easy to implement, a temperature sensor
49 and a temperature compensation circuit 50 can be added as an
alternative or addition to using magnets and wire that do not appreciably
change as a function of temperature (FIGS. 3 and 5).
As an alternate to using separate reference exciters 6 7 the
functionality of reference exciters can be effectively included
in the motion sensors 4 5 by one of several methods. One method
of incorporating the functionality of reference exciters within
the motion sensors 4 5 is simply to wind separate turns of wire
on the coils of the motion sensors 4 5 and connect those turns
to the circuits 13 14 respectively, of FIG. 3 or to the circuits
23 24 respectively, of FIG. 5 as before. This simply eliminates
the need to place extra magnets on the vibrating surface 1 thereby
simplifying geometry.
Turning now to FIG. 10 illustrated is circuit diagram of an alternate
embodiment of the present invention that uses variable impedances.
Another method to incorporate the functionality of reference exciters
into the motion sensors 4 5 is to couple variable impedances 35
36 to the coils of the motion sensors 4 5. These variable impedances
are then controlled in the same way as were the circuits 13 14
of FIG. 3 or the switches 23 24 of FIG. 5 via the reference excitation
circuitry 19. By changing the impedance across the coil of the motion
sensor 4 via the variable impedance 35 the amount of current passing
through the coil changes, thereby changing its braking effect and
representing a prescribed amount of force and thus of fluid flow.
Similarly, the variable impedance 36 can therefore be used to have
a similar effect on the coil of the motion sensor 5. Therefore,
by alternately changing the impedance of the circuits 35 36 over
some modulation period, forces are created that modulate the M'.sub.raw
signal 9 as described in previous embodiments. By measuring these
modulations on the M'.sub.raw signal 9 the changes in the sensitivity
or zero offsets can be determined and compensated for.
As an alternative to having a separate vibration driver and reference
exciters, the functionality of reference exciters can be incorporated
into the vibration driver that causes the requisite driven vibration
of the vibrating surface 1.
Turning now to FIGS. 8 through 14 illustrated are (in FIG. 8)
characteristic frequency response curves of the driven mode of vibration
and the Coriolis mode of vibration, (in FIG. 9) a section of a vibrating
surface of a Coriolis mass flow meter along with the moving fluid
with which it interacts, (in FIG. 10) an alternate circuit diagram
that could be used for the present invention using variable impedances,
(in FIG. 11) a circuit diagram that could be used for the present
invention using combined vibration drivers and reference exciters,
(in FIG. 12) electrical signals that occur in conjunction with various
embodiments of the present invention, (in FIG. 13) electrical signals
that occur in conjunction with various embodiments of the present
invention and (in FIG. 14) an alternate circuit diagram that could
be used for the present invention using alternate reference excitation
methods.
The motion sensors 4 5 of FIG. 9 have the same functionality as
in previous embodiments, that is, to sense the vibration of the
vibrating surface 1. Vibration drivers 51 52 are combined vibration
drivers and reference exciters that are mounted on the vibrating
surface 1 and located to supply both of these functions from their
respective locations. The vibration drivers 51 52 therefore need
to be coupled to the vibrating surface 1 where they can impart energy
into both the desired driven vibration motion and also into the
Coriolis deflected motion. Preferably, the vibration drivers 51
52 are magnet/coil pairs as previously described, but could also
be any other type of force transducer. The circuit of FIG. 11 is
then used in conjunction with the embodiment of FIG. 9. A drive
circuit 8 (of FIG. 11) serves the same functionality as in previous
embodiments by receiving motion signals from the motion sensors
4 5 and creating drive signals as necessary to maintain the driven
vibration of the vibrating surface 1 in accordance with design parameters.
Drive signals thus created are transmitted to the circuits 53 54
that receive those drive signals and pass a selected amount of those
signals on to the vibration drivers 51 52 in the appropriate phase
and amplitude to maintain the driven vibration. In addition to receiving
the drive signal from the circuit 8 the circuits 53 54 also receive
signals individually from the motion sensors 4 5 and can (when
directed to do so by the reference excitation circuitry 19) also
add a reference excitation signal that is of appropriate amplitude
(and typically in phase with the driven motion) to simulate the
Coriolis force of a prescribed amount of fluid flow rate.
The reference excitation circuitry 19 first activates the circuit
53 to sum the drive signal with the reference excitation signal
and apply the combination to the vibration driver 51 for a period
of time (modulation period). At the same time, the reference excitation
circuitry 19 prevents the circuit 54 from summing the drive signal
with the reference excitation signal and only allow the drive signal
to pass through to the vibration driver 52. A simulated Coriolis
force is then applied only to the upstream end of the vibrating
surface 1 through the vibration driver 51 and thereby causes the
M'.sub.raw signal 9 to change in response to the applied simulated
Coriolis force as shown in FIG. 4.
Next, the reference excitation circuitry 19 activates the circuit
54 to sum the drive signal with the reference excitation signal
and apply the combination to the vibration driver 52 for a period
of time (modulation period). At the same time, the reference excitation
circuitry 19 prevents the circuit 53 from summing the drive signal
with the reference excitation signal and only allow the drive signal
to pass through to the vibration driver 51. A simulated Coriolis
force is then applied only to the downstream end of the vibrating
surface 1 through the vibration driver 52 and thereby causes the
M'.sub.raw signal 9 to change in response to the applied simulated
Coriolis force, but in the opposite polarity, as shown in FIG. 4.
Analogous to the previous embodiments, the M'.sub.raw signal 9 is
thereby modulated first in a positive sense and secondly in a negative
sense as shown in FIG. 4 the magnitude of modulation 17 and the
deviation 18 from the average value 34 are respectively related
to the sensitivity and the zero offset of the device at that moment.
The circuit 20 of FIG. 11 then performs the same function as previously
by determining these values 17 18 34 and passes the information
on to the circuit 21 that applies the appropriate compensation for
any changes in the sensitivity and zero offsets, and demodulates
the M'.sub.raw signal 9 into an unmodulated M'.sub.true signal 22.
Analogous to the modulation methods described for earlier embodiments,
this embodiment can also be modulated on a continuous basis instead
of intermittently. By modulating continuously, the unmodulated value
34 is lost; however, compensation for the zero offset is accommodated
automatically by using the average modulated value 33 and the modulation
amplitude value 17 analogous to that described for FIG. 7.
As an alternate to applying the reference excitation forces serially
first to the upstream vibration driver then to the downstream vibration
driver, these forces can be applied in parallel to both vibration
drivers at the same time. This is preferably accomplished in the
following way with reference to the embodiment of FIG. 9 and the
circuit of FIG. 11 although those of ordinary skill in the pertinent
art should note that this alternate modulation method applies to
most of the other embodiments as well.
First, the reference excitation circuitry 19 preferably has the
same functionality as in previous embodiments and controls the application
of reference excitation signals to the vibration drivers. The reference
exciter circuitry 19 therefore directs the circuits 53 54 to simultaneously
apply both drive forces and reference excitation forces to the vibrating
surface 1 to simulate a prescribed amount of fluid flow. Accordingly,
the circuit 53 of FIG. 11 receives two inputs: the drive signal
applied to both vibration drivers from the circuit 8 and input from
the motion sensor 4. The circuit 53 uses the input from motion sensor
4 to determine the appropriate reference excitation signal (55 of
FIG. 12) that should be applied to the vibration driver 51. The
excitation is typically a signal proportionally related to the amplitude
of the motion sensed by the motion sensor 4 and in phase with the
Coriolis forces (in phase with the driven velocity). The reference
excitation signal 55 once determined, is then summed with the drive
signal from the circuit 8 within the circuit 53 and delivered to
the vibration driver 51. The summed signal then serves both the
purpose of maintaining the requisite vibration of the vibrating
surface 1 and applying the reference excitation as well.
At the same time the circuit 54 of FIG. 11 receives two inputs:
the drive signal applied to both vibration drivers from the circuit
8 and input from the motion sensor 5. The input from the motion
sensor 5 is used by the circuit 54 to determine the appropriate
reference excitation signal 56 that should be applied to the vibration
driver 52. This is typically a signal proportionally related to
the amplitude of the motion sensed by the motion sensor 5 and in
phase with the Coriolis forces (in phase with the driven velocity).
The reference excitation signal 56 once determined, is then summed
with the drive signal from the circuit 8 within the circuit 54 and
delivered to the vibration driver 52. The summed signal then serves
both the purpose of maintaining the requisite vibration of the vibrating
surface 1 and applying the reference excitation as well. With the
reference excitation signals applied at both vibration drivers 51
52 the M'.sub.raw signal 9 of FIG. 12 is modulated as shown by
the modulation amplitude 58 indicative of a prescribed amount of
simulated mass flow rate. This situation is held for a modulation
period.
Next, the reference exciter circuitry 19 directs one of the circuit
53 or the circuit 54 (the circuit 54 is directed for this example)
to invert the phase of the reference excitation signal 56. This
action has the effect of applying reference excitation signals that
are in the same phase as each other and therefore represent a zero
flow condition to both ends of the vibrating surface 1. While, under
perfect conditions, this results in a zero flow signal, or a return
to a nominal flow value 57 on M'.sub.raw signal 9 in an actual
situation where the response at one end of the vibrating surface
1 may have changed with respect to the other end, this may result
in a finite amount of offset 59 of the M'.sub.raw signal 9 with
respect to the nominal value 57. The offset value 59 therefore represents
the zero offset of the device at that moment, and can be used to
correct the final output signal for any changes in the zero of the
device.
Finally, the circuit 20 determines the value of the modulation
amplitude 58 and the zero offset 59 and nominal value 57 preferably
by using synchronous demodulation methods with input from the reference
exciter circuitry 19 for the synchronous reference typically in
synchronism with the modulation period. These values are then passed
to the circuit 21 where they are used to compensate the M'.sub.raw
signal 9 and thereby create a corrected M'.sub.raw signal 22 according
to the following relation (16) representing true mass flow rate:
As in the previous embodiment, the intermittent modulation can
be replaced with a method to modulate the M'.sub.raw signal 9 as
just described but continuously as shown in FIG. 13. This alternate
method then applies the reference excitation signals 55 56 in phase
with the Coriolis forces for a modulation period, then the phase
of signal 56 is reversed for another modulation period, and this
sequence then repeated continuously, preferably never allowing the
reference excitation signals to stop. Using this continuous modulation
method, the zero offset value 59 of the previous method in FIG.
12 is lost, however compensation for a change in the zero offset
is accommodated automatically. M'.sub.raw signal 9 is continuously
modulated as shown in FIG. 13. During the modulation period where
the reference excitation forces are applied out of phase with each
other as are the Coriolis forces, M'.sub.raw signal 9 increases
in value by the modulation amplitude 60. During the next modulation
period when the reference excitation forces are applied in phase
with each other simulating no (or counteracting) Coriolis forces,
M'.sub.raw signal 9 decreases in value to the zero modulation value
61. As before, the circuit 20 determines these values 60 61 by
synchronous demodulation and relays the information to the circuit
21 where the M'.sub.true signal 22 is created using the following
relation (17) representing true mass flow rate:
Another method for determining the sensitivity and zero, and compensating
for any changes therein, involves determining the frequency response
values of the Coriolis-deflected shape at one or both motion sensor
positions of the vibrating surface 1 determined at the driven mode
frequency. It should be noted that, for certain designs, the response
may be measured with a single motion sensor, however the preferred
method is to use two motion sensors. From these values both sensitivity
and zeros can be determined and any changes therein can be compensated
for.
As previously mentioned, FIG. 1 represents a vibrating surface
1 of a Coriolis mass flow meter deflected in a driven natural mode
of vibration. FIG. 2 represents the deflection of the vibrating
surface 1 due to the Coriolis force distribution that thereby occurs
as a reaction to mass flow rate. The distorted shape of the vibrating
surface 1 in FIG. 2 is due to the Coriolis force distribution; however,
it is closely related to the shape of a natural mode of vibration
of the vibrating surface 1 (Coriolis mode) that is different than
the driven mode of vibration.
FIG. 8 represents the frequency response curves of both the driven
and Coriolis modes at both motion sensor positions of the vibrating
surface 1. A curve 39 represents the dynamic response at the motion
sensor 4 due to vibrational energy directed into the Coriolis mode
shape as a function of excitation frequency. A curve 40 represents
the dynamic response at the motion sensor 5 due to vibrational energy
directed into the Coriolis mode shape as a function of excitation
frequency. The vibrational energy could be directed into the Coriolis
mode shape as a result of Coriolis forces from mass flow rate or
as a result of reference excitation from the exciters 6 7 (or 51
52 on alternate embodiments). It should be noted that the driven
mode of vibration has similar frequency response curves 37 38 corresponding
to the dynamic response at the motion sensors 4 5 respectively,
due to vibrational energy directed into the driven mode shape as
a function of excitation frequency.
Peak values 41 42 of the curves 37 38 correspond to the driven
mode frequency .OMEGA.1 47. Peak values 43 44 of the curves 39
40 correspond to the Coriolis mode frequency .OMEGA.2 48. One important
aspect of curves 39 40 is the frequency response values 45 46
respectively, determined at the driven mode frequency .OMEGA.1 47.
These values 45 46 represent the magnitude of the dynamic response,
as seen by the motion sensors 4 5 from either Coriolis forces
from flow rate or reference excitation forces from the exciters
6 7. They are therefore proportionally related to the sensitivity
and the zero offset of the device. The specific mathematical formula
relating the values 45 46 with the sensitivity and zero depends
upon the specific method of signal processing that is chosen. However,
for this example, the circuit of FIG. 14 is used and therein, the
circuit 62 is a signal generator that creates the reference excitation
signals at a prescribed frequency, amplitude and phase; and the
circuit 63 demodulates the response to that reference excitation.
The circuit 64 can calculate the sensitivity and zero of the device
using a variety of mathematical relations as hereinafter described.
In the first embodiment previously described, reference excitation
forces are applied to the device at the driven mode frequency, and
the response to those forces is determined and related to the sensitivity
and zero. This is analogous to measuring the response values 45
46 directly by virtue of the modulation effects on the M'.sub.raw
signal 9. Similarly, by determining alternate points on the response
curves 39 40 and knowing the shape of those curves, the values
45 46 thereon can be mathematically determined. Several methods
are hereinafter described to determine the values 45 46 by determining
the response values at alternate frequencies and then solving for
the response at the driven mode frequency .OMEGA.1 47 by knowing
or approximating the shape of the curves 39 40. These values can
then be related to the sensitivity and zero offset of the device
and any changes therein compensated for.
The equation for the response curves 39 40 can be approximated
by the second order equation (18) below:
where:
Response=dynamic response amplitude due to the excitation force,
Force=reference excitation force,
k=dynamic spring constant (or "stiffness") of the system,
c=damping value of the system,
.OMEGA..sub.x =excitation frequency and
M=dynamic mass of the system.
Inspection of equation (18) reveals the reasons why the sensitivity
of a Coriolis mass flow meter can change as a function of fluid
and ambient properties. For example, the stiffness (k) can be a
function of a combination of effects including the elasticity of
the vibrating surface 1 (itself a function of temperature and frequency),
and stress level (a function of fluid pressure, differential expansion,
axial stress and other factors) of the vibrating surface 1. Similarly,
the damping value (c) can change with temperature, fluid viscosity
and frequency. The Mass (M) can change with fluid density etc.
Of these variables, the response, force, and excitation frequency
are known or can easily be measured leaving the stiffness (k), the
damping (c) and the mass (M) to be determined. However, the natural
frequency of the Coriolis mode can also be excited and measured
for its frequency value and the damping ratio (.zeta.) can be measured
by alternate means hereinafter explained. Therefore, by making appropriate
substitutions into equation (18), it can be rewritten into the form
of equation (19) involving the stiffness (k), damping ratio (.zeta.)
and frequency ratio (r) leaving only stiffness (k) as the unknown
variable.
where:
r=ratio of excitation to natural frequency and .zeta.=damping value
as a fraction of the critical damping value.
Therefore, by determining the values of the variables of equation
(19) the form of the response curves 39 40 can be mathematically
determined and therefore solved for the values 45 46 at the driven
mode frequency .OMEGA.1 47. These values can then be used to determine
and compensate for the sensitivity and zero offset of the device.
The relationship between the response values 45 46 and the sensitivity
and zero offset are typically as follows in relations (20) and (21)
understanding that different signal processing techniques may cause
the values 45 46 to have different mathematical relationships yet
achieving the same goal of determining the sensitivity and zero,
and compensating for any changes therein. For this example, the
sensitivity of the device is proportionally related to the sum (or
average value) of the response values 45 46 at both of the motion
sensors 4 5. The zero offset for the device is related to the difference
between the response values 45 46 at the motion sensors 4 5.
Several methods for the determination of the variables in equation
(19) and thus the response values 45 46 will hereinafter be explained.
The basic method employed for these embodiments are as follows (with
specific reference to FIGS. 1 2 8 and 14). The normal driven mode
of vibration is established via the vibration driver 3 and the circuit
8. The circuit 62 then creates reference excitation signals at a
frequency (or multiple frequencies) other than the driven frequency
.OMEGA.1 47 and passes these signals on through to the reference
exciters 6 7. The vibrating surface 1 then responds to those reference
excitations in a shape similar to that shown in FIG. 2 and at an
amplitude according to the reference excitation frequency and the
response curves 39 40. The circuit 63 then receives motion signals
from the motion sensors 4 5 and synchronously demodulates (peak
detection, fast Fourier transform ("FFT") and other methods
can be used) the response values at the reference excitation frequency
(or frequencies) and in the appropriate phase. These values then
represent some point(s) along both the curves 39 40 depending
on the selected reference excitation frequency. Once these values
are known, then several mathematical methods can be employed to
solve for the values 45 46 on those curves at the driven frequency
.OMEGA.1 47.
Two basic methods are here employed for this purpose. One method
is to find an arbitrary point along the curves of 39 40 and, by
assuming the curves fit an equation similar to (18) or (19), solve
for points 45 46. A second method is to determine the response
at two points close to the driven frequency .OMEGA.1 47 along the
curves of 39 40 and then employ interpolation or extrapolation
(either linear or non-linear) techniques to solve for values 45
46.
Once these values are determined within the circuit 63 the circuit
64 determines the sensitivity and zero based on relations (20) and
(21) above (or some other relationship) and passes the information
on to the circuit 21 that has the same functionality as in other
embodiments and compensates the M'.sub.raw signal 9 for any changes
in the sensitivity and the zero. A M'.sub.true signal 22 is then
created that is fully compensated for any changes in the sensitivity
and zero, regardless of the cause of those changes. Some specific
examples to implement these methods follow.
The Response in equation (19) is the displacement magnitude(s)
at each motion sensor 4 5 from a given reference excitation force.
Therefore, the circuit 62 activates the reference exciters 6 7
intentionally to drive the Coriolis mode frequency with a prescribed
excitation force. The resulting amplitudes in the Coriolis mode
are the Response values of equation (19) and the prescribed excitation
force is the Force value. With the Coriolis mode running at its
natural frequency, the ratio (r) of the driven mode to the Coriolis
mode is then determined for equation (19). Then .zeta. is determined
by one of a number of methods, preferably by the logarithmic decrement
method that involves periodically turning the Coriolis mode excitation
off. The fractional reduction in amplitude (.DELTA.) over a number
of cycles (N) of the Coriolis mode is measured and .zeta. thereby
determined from the relation in equation (22):
Once .zeta. is thus determined, its value can then be substituted
back into equation (19) to determine the last variable, the stiffness
(k). Once (k) is known, the response curves 39 40 are thereby determined
and can then be solved for their values 45 46 at the driven frequency
.OMEGA.1 47.
For very small values of .zeta., the natural frequency 48 (at the
peak values) of the curves 39 40 can be approximated to be .OMEGA.2.
Since most Coriolis mass flow meters are designed to have very low
damping values, this is a good approximation. Therefore, if the
Coriolis mode of vibration is excited using exciters 6 7 at its
natural frequency .OMEGA.2 48 the maximum response values 43 44
due to the prescribed excitation can be measured. This can be accomplished
using Fourier transform methods, peak detection methods or synchronous
demodulation methods. Assuming that, at this frequency, the value
of (r) equals 1 then equation (19) reduces to equation (23) to
describe the maximum response value as follows:
From relation (23), and knowing the maximum response values 43
44 determined in the circuit 63 the damping factor .zeta. can be
determined in the circuit 64. This is accomplished by substituting
the maximum response values 43 44 into relation (23) and solving
for the corresponding values of .zeta.. Once these values are known,
they can be substituted back into equation (19) to determine the
responses for any excitation frequency. For purposes of this discussion,
then, the value of the excitation frequency of the driven vibration
.OMEGA.1 47 is therefore substituted into equation (19) (into the
value of r where r=.OMEGA.1/.OMEGA.2) along with the damping factors
.zeta., and the response values 45 46 is thus determined.
Once determined, relations (20) and (21) can then be used by the
circuit 64 to determine the sensitivity and zero offset values.
Similarly, .zeta. can be determined by exciting the .OMEGA.2 frequency
48 with a prescribed excitation and measuring the power necessary
to maintain a prescribed amplitude. The power necessary to maintain
a given amplitude of vibration (x) can be related to the damping
by the following relation (24):
Once .zeta. is thus determined, its value can then be substituted
back into relation (19) to determine the response curves 39 40.
The components and the circuitry to measure power for relation (24)
are not shown since they are well understood in the industry. As
a simple example however, by measuring the voltage (v) and the current
(I) being supplied to the reference exciters necessary to maintain
vibration amplitude, the product of (V*I*cos(phase angle between
V & I)) yields the driven power, of which a proportional amount
is dissipated in the vibration of the Coriolis mode of vibration.
The curves 39 40 can be determined by the circuit 62 exciting
the vibrating surface 1 with white or random noise or a swept frequency
wave type excitation (sine, triangle, sawtooth, etc.) and measuring
the response to that excitation in the circuit 63 by using direct
motion detection methods or by calculating the response spectrum
using Fourier transform techniques. Also by sweeping a frequency
wave (sine, triangle, sawtooth, etc.) to either side of the Coriolis
resonance frequency .OMEGA.2 48 until the frequency ratios (r2 above
resonance, r1 below resonance where the ratio is the excitation
frequency divided by the resonance frequency) are found with response
values of maximum response/.sqroot.2. Here r2-r1 equals the bandwidth
of the response, therefore by measuring this bandwidth, the damping
can be determined. .zeta. therefore corresponds to a value proportional
to the bandwidth divided by 2:
Once .zeta. is thus determined, its value can then be substituted
back into equation (19) to determine the response curves 39 40.
Also by exciting the vibrating surface 1 with the reference exciters
6 7 at some arbitrary frequency with regard to the Coriolis frequency,
and by measuring the phase angle (.theta.) between the reference
excitation and the response to that excitation, and by measuring
the Coriolis frequency .OMEGA.2 48 the damping value .zeta. can
be thus determined by the following equation (26):
After .zeta. is determined, .zeta. and .OMEGA.2 are then substituted
back into equation (19) to determine the response values 45 46
at the driven frequency.
The Field Proving Aspect of the Present Invention
As previously mentioned, an important part of the flow measurement
industry is dedicated to the activity of "field proving"
of flow meters in order to verify their calibration, usually for
custody transfer applications. The methods of field proving usually
employed normally include applying a reference flow rate through
the meter to be proved by using an ancillary piece of equipment
that regulates or independently measures that reference flow rate.
Once the reference flow rate has been established, the output of
the flow meter to be proven is measured and compared to the reference
flow rate to determine the sensitivity of the device. In addition,
at a no flow rate condition, the output of the device is measured
to determine the zero. These values are then usually documented
and compared to previously-measured values or against prescribed,
preprogrammed values to determine if the sensitivity or zero has
changed. If the sensitivity or zero has changed beyond some preset
maximum tolerance, the flow meter is often sent for recalibration.
Coriolis flow meters are unique in that the forces that results
from a given amount of mass flow rate can be mathematically determined
through equation (8) above, as previously mentioned. Since these
forces can be determined, proportionate forces can also be applied
and the resulting responses measured to determine the response characteristics
of the device.
This method of determining the response characteristics of a flow
meter holds for other types of flow measurement devices. However,
other flow measurement technologies do not lend themselves as readily
to this method as do Coriolis meters, because of the deterministic
nature of the Coriolis forces on the vibrating surface 1 and the
ease with which proportional forces can be applied to this vibrating
surface, thereby simulating a prescribed mass flow rate.
The act of proving a meter implies that the measurement method
used to "prove" the meter is more accurate or more believable
than the measurement method used in the meter itself, and also that
there are two independent measurement systems at work that are being
compared.
Therefore, to use the present invention to prove a Coriolis flow
meter, the meter is preferably designed and equipped with the necessary
instrumentation to measure mass flow rate and compensate the measured
flow rate for any anticipated changes in sensitivity due to changes
in the aforementioned fluid and ambient parameters. Exemplary of
this is any Coriolis flow meter currently commercially available.
Therefore a Coriolis flow meter of any type could be used in conjunction
with the present invention to create a field provable flow meter.
In addition, the meter is equipped with the necessary instrumentation
to determine the sensitivity and zero of the device. This is preferably
done by the application of reference excitations to simulate a prescribed
amount of mass flow. The meter then responds to the reference excitations,
causing a change in the output of the device that should be substantially
equal to the prescribed simulated flow rate value if the device
is working properly. If the device is not working properly, then
the output signal deviates from the value represented by the reference
excitation. This deviation can then be monitored or compared to
prescribed values to determine if the sensitivity or zero of the
device has changed.
Alternately, sensitivity and zero determination means can be applied
that do not modulate the output signal as just described, but determines
the sensitivity and zero of the device and makes these values available
for comparison or monitoring purposes.
The elements necessary for a field-provable Coriolis mass flow
meter are therefore a Coriolis flow meter of any type or construction,
complete with circuitry for measuring the mass flow rate of a fluid.
In addition, the vibrating surface of the Coriolis mass flow meter
is also equipped with response characteristic determination means.
The preferred means of sensitivity and zero determination employs
reference exciters as necessary to cause forces on the vibrating
surface to evoke a response and preferably to simulate a prescribed
amount of mass flow rate and circuitry to determine the sensitivity
and zero from the response of the reference excitation. Any of the
aforementioned methods to determine the sensitivity or zero of a
vibrating surface could be used for this purpose of proving a Coriolis
mass flow meter.
The preferred method of proving a Coriolis mass flow meter according
to this aspect of the present invention is therefore as follows.
First, the mass flow rate is preferably brought to zero or some
steady state value so that the additional "flow" as caused
by the reference exciters is easily measured as an addition or subtraction
to the magnitude of the flow rate that is currently being measured.
Once a steady state or zero flow rate is established, the reference
exciter is activated, thus causing a prescribed amount of simulated
mass flow rate. The simulated mass flow rate is then measured by
the Coriolis meter using its normal methods and compensations and
the final output signal is read to determine the magnitude of the
mass flow rate that the meter measured. Any difference between what
the meter measured and the prescribed amount of mass flow rate as
represented by the reference exciters thereby represents a change
in the sensitivity of the meter that was not effectively compensated
for. The difference is usually documented and compared with previous
values to watch for any changes over time and often is compared
to some critical deviation value beyond which the meter is sent
for recalibration.
Alternate methods of determining the response characteristics of
the device include any of the aforementioned methods described herein.
The difference between the field-provable meter embodiment and those
earlier described is that the earlier-described embodiments used
various methods to determine the sensitivity and zero of a surface
for the purpose of compensating for any changes therein and thereby
accurately calculating the mass flow rate, whereas in the field
provable meter embodiment, those same methods of sensitivity and
zero determination are used, not to calculate the mass flow rate
but to compare and/or monitor that determined sensitivity or zero
value that characterizes the accuracy of the output signals from
that Coriolis flow meter.
From the above description, it is apparent that the present invention
provides, in part, a signal processing apparatus and method for
measuring a mass flow rate of a fluid flowing in conjunction with
a surface of a Coriolis mass flow meter and a field-provable Coriolis
mass flow meter. The apparatus includes: (1) a driver for creating
a prescribed vibration in the surface, (2) a motion sensor for measuring
a motion of the surface, (3) response characteristic determination
circuitry, coupled to the motion sensor, for determining a response
characteristic of the surface and (4) flow rate calculation circuitry,
coupled to the response characteristic determination circuitry,
for calculating a measured mass flow rate of the fluid as a function
of the motion and the response characteristic. The field-provable
meter employs the response characteristic to monitor or compare
meter performance without requiring a separate proving device.
Although the present invention and its advantages have been described
in detail, those skilled in the art should understand that they
can make various changes, substitutions and alterations herein without
departing from the spirit and scope of the invention in its broadest
form. |