Electronic Circuit for Vibrating Tube Densimeter

The present invention relates to electronically monitoring the mechanical oscillation characteristics of one or more resonantly vibrating tubes through which flowable substances are passing to determine the density of the substances. Both the temperature and natural period of oscillation of one or more resonantly oscillating tubes are electronically monitored, and the resulting signals are processed to accurately determine the density of the flowing substances independent of temperature variations.

It is known that one end of an elastic container can be rigidly mounted and that the other end of the cantilever mounted container can be oscillated at a resonant angular velocity. For such a spring-mass mechanical system, the resonant angular velocity of oscillation can be calculated by taking the square root of the ratio of the oscillating container's mass to its spring constant about the oscillation axis. Since the mass of the container will vary as the density of the substances flowing through the container varies, monitoring the resonant angular velocity of oscillation of a cantilever mounted container potentially offers a convenient means for measuring the density of flowable substances.

Various container configurations have been applied to the construction of oscillating container densimeters. Among these has been U-shaped flow tubes, with the tube rigidly mounted to a fixed base at the open ends of the U-shaped flow tube. Thus, by flowing a substance through the U-shaped flow tube and vibrating the tube at its resonant angular velocity the density of substances flowing through the U-shaped flow tube can be measured. A known improvement for the vibrating U-shaped flow tube densimeter is the use of a second cantilever mounted U-shaped flow tube which is positioned along side the first U-shaped flow tube so as to have both U-shaped flow tubes act as the times of a tuning fork. Among the advantages achieved by such tuning fork operation is substantial attenuation, at the base, of vibration forces associated with the driving of the U-shaped flow tubes at their resonant angular velocities of oscillation.

An additional variable which affects measurements of the density of flowable substances passing through oscillating container densimeters is the temperature of the oscillating container. For, the spring constants of an elastic container are dependent on temperature. This dependency on temperature and its effect on the determination of density by measuring resonant angular velocity of oscillation has been known. Previous attempts to address the dependency of the resonant angular velocity of oscillation on temperature variations have included those disclosed in U.S. Pat. Nos. 4,170,128 and 3,910,101. Disclosed in U.S. Pat. No. 4,170,128 is a mechanical arrangement incorporating a length of cord or string attached to a vibrating U-shaped flow tube. According to the disclosure in U.S. Pat. No. 4,170,128, the length of the string is dependent on temperature, and, therefore, the tension of the mounted string is varied by temperature. As further disclosed this variation in tension modifies the vibration characteristics of the U-shaped flow tube to compensate for temperature variations. Disclosed in U.S. Pat. No. 3,910,101 is an electrical circuit for both monitoring and controlling the oscillation of a fluid filled container. Included as a part of the disclosed circuit is a bridge circuit having as the variable element a temperature dependent sensor. The output of the bridge circuit according to the teachings in U.S. Pat. No. 3,910,101 is used to alter, according to fluctuations in temperature, both the phase and amplitude of the signal driving the oscillation of the fluid filled container.

The disclosures in both U.S. Pat. Nos. 4,132,110 and 3,910,101 are directed to the monitoring of temperature variations for the purpose of altering the mechanical oscillations of oscillating containers.

Unlike the previous two patents U.S. Pat. No. 4,132,110 discloses a mechanical configuration and electrical circuit for determining the density of a fluid passing through an oscillating container without a feedback system for altering the mechanical oscillations of the container as a function of temperature variations. The electrical circuitry disclosed in U.S. Pat. No. 4,132,110 for determining fluid density incorporates an oscillator to generate a standard signal from which is subtracted the signal representative of the motion of the oscillating container. According to the disclosures in U.S. Pat. No. 4,132,110, this difference signal is then combined with the signal from a temperature probe to provide a signal proportional to the density of the fluid being measured based on a reference temperature.

In order to make precise density measurements using an oscillating container densimeter a relationship must be developed which incorporates not only the resonant angular velocity of oscillation of the container and the mass of the substance passing through the container, but also the variation in the spring constant about the oscillation axis of the oscillating container. For temperature changes cause variations in the spring constants of elastic materials, and for many practical applications either or both the ambient environment or the flowing substance being measured can produce substantial temperature fluctuations. Therefore, in addition to the resonant angular velocity of oscillation the temperature of the oscillating container must also be measured, and the temperature dependent spring constant about the oscillation axis calculated.

It will be shown below that the equation for the density of a substance passing through a resonantly oscillating container is, in general, a relationship where the first term is the oscillating container's spring constant about the oscillation axis, which is a function of temperature, multiplied by the square of the period of oscillation for the oscillating container, with this product being divided by a first constant. The second, and last term of this equation, is a constant which is subtracted from the first term to give a direct calculation of density.

The present invention utilizes this analytical description of the mechanics of an oscillating container densimeter to provide an accurate method and electronic circuitry for directly determining the density of substances passing through the densimeter.

The measurement technique of the present invention is dependent on the outputs of two sensors which are mounted either on or in conjunction with the oscillating container. One of these sensors can be a velocity sensor, such as an electrical coil and magnet, which monitors the movement of the container and provides a sinusoidal signal corresponding to such movement. The other sensor can be a temperature variable resistor mounted on the container or in any other isothermal location relative to the container. Obviously, other sensor types could be used as long as (1) a signal is provided which corresponds to the movement of the container so that the resonant period of oscillation can be determined; and (2) a signal is provided which corresponds to the temperature of the container so that the temperature coefficient for the spring constant of the container about the oscillation axis can be determined.

The circuit of the present invention includes two integrators which are connected in series. An input to the first of these integrators is a reference voltage. The outputs of these two integrators are controlled by electronic switches so that the output from the second integrator is a function of the square of the time that the inputted reference voltage is integrated. The duration of time during which the integrators function is determined by the output of the sense coil monitoring the movement of the oscillating container so that the combined output from the integrators is a function of the square of the resonant period of oscillation of the container. Controlling the reference voltage inputted to the first integrator is a circuit incorporating a bridge, one arm of the bridge being the temperature variable resistor which is mounted on the container so that as the temperature of the container varies the reference voltage is accordingly varied, and, therefore, the output of the integrators represents a product of a temperature dependent function and the square of the period of oscillation of the resonantly oscillating container. By controlling the output of the bridge circuit, an accurate representation of the variation in the spring constant of the container about the oscillation axis as a function of temperature can be provided to the series integrator circuitry. Thus, the output of the integrators after passing through a buffer circuitry gives a direct readout of the density of substances passing through the densimeter.

The various objects, advantages and novel features of the present invention will be more readily apprehended from the following detailed description when read in conjunction with the appended drawings, in which:

FIG. 1 is a block diagram of the electrical circuit of the present invention;

FIG. 2 is a perspective view of a twin vibrating tube densimeter with both motion and temperature sensors being mounted on the densimeter vibrating tubes; and,

FIG. 3 is a graphical presentation of waveforms characteristic of the operation of the invention.

Referring now to the drawings, wherein corresponding components are designated by the same reference numerals throughout the various figures, a block diagram of the circuit of the present invention is shown in FIG. 1.

A densimeter, as generally designated by numeral 10, with two vibrating tubes 12, for which the electronic circuit of the present invention can be used, is shown in FIG. 2. The configuration of densimeter 10 includes the supports 14, the plenums formed by manifolds 16 and end plates 18, and the electromagnetic drive and sensor mechanism 20. Such a configuration provides for parallel fluid flow through the two tubes 12, which act as the tines of a tuning fork when vibrated. A detailed description of the construction and fluid dynamics associated with this configuration is set forth in detail in pending U.S. patent application Ser. No. 439,035, filed Nov. 3, 1982 for Parallel Path Coriolis Mass Flow Rate Meter by inventors James E. Smith and Donald Cage.

As is known in the art, electromagnetic drive and sensor mechanism 20 can consist of such known means as a magnet fixed to one of the vibrating tubes 12, and a drive coil along with a sense coil 22 fixed to the other of the vibrating tubes 12. As is also known in the art, by passing an oscillating electrical current through the drive coil the two tubes 12 can be sinusoidally driven about their respective bending axes, W--W, at their common resonant angular velocity of oscillation. Such oscillation will result in the tubes operating as the two tines of a tuning fork. As the tubes 12 resonantly oscillate an electrical signal correlating to the relative movement of tubes 12 is generated by the magnet and sense coil 22.

Irrespective of whether a single or multiple oscillating container structure is used, the solution for the equation of motion for a resonantly oscillating spring mounted mass is the same, and is accordingly applicable to the quantitative description of the mechanics of an oscillating container densimeter. This solution is

where

.omega. is the angular velocity of oscillation for the resonantly oscillating spring mounted mass,

K(t) is the spring constant about the oscillation axis and is a function of temperature t, and

M is the mass affixed to the spring.

For a densimeter as shown in FIG. 2 the mass M is the sum of the masses of vibrating tubes 12, which can be identified as M.sub.T, plus the mass of the substance flowing through the vibrating tubes 12, which can be identified as M.sub.F. Therefore,

The mass of the substance flowing through the vibrating tubes 12 is equal to the product of the density, .rho., of the substance times the internal volume, V.sub.o, of the vibrating tubes 12.

Substituting the last relation into equation 1 and solving for density results in the following: ##EQU1## Where t is the period of oscillation of the resonantly vibrating tubes 12. Noting that on the right side of equation 2 all of the quantities except for the period of oscillation, T, and the spring constant, K(t), which is a function of temperature, are constants permits rewriting of equation 2 in the following useful format. ##EQU2## where K.sub.1 and K.sub.2 are constants.

Thus processing the signals from sense coil 22 and temperature variable resistor 24 in a circuit according to the present invention which performs calculations according to equation 3 provides for a direct readout of accurate density measurements of the substances flowing through tubes 12.

The circuit of the present invention operates as follows, initially switches S1 and S3 are both closed thereby holding integrator capacitors C1 and C2 in a fully discharged condition while switches S2 and S4 are both initially open. As shown in FIGS. 1 and 3, the output of sense coil 22 is fed into comparator 26 which provides a square wave output having a period equal to that of the oscillating tubes 12. By feeding the output of comparator 26 into data flip-flop 28 and NOR gate 30, switches S1 and S3 are opened and switch S2 is closed when tubes 12 reach their maximum displacements from their mid-planes of oscillation. Integrator capacitor C1 is then charged due to the current supplied from reference voltage source V.sub.1 through resistor R1. Accordingly, the output of amplifier 32 is a linear ramp, as shown in FIG. 3, having a magnitude proportional to time. Now integrator capacitor C2 charges due to the increasing current through resistor R2. The output of amplifier 34, as shown in FIG. 3, is a parabolically decreasing voltage proportional to time squared. At the end of a complete cycle of oscillation of vibrating tubes 12, the combination of sense coil 22, comparator 26, data flip-flop 28, inverter 36, NOR gates 30 and 38 provides control signals, as shown in FIG. 3, which open switch S2, thus holding the charge on integrator capacitor C2, and close switch S4 to transfer the output voltage of amplifier 34 to hold capacitor C3. During the next cycle of oscillation of tubes 12 a time measurement is not made, but as shown in FIG. 3 switch S4 opens, and switches S1 and S3 close to reinitiate the circuitry for the next measurement cycle.

As explained above the voltage retained on hold capacitor C3 is proportional to the square of the period of oscillation of the resonantly vibrating tubes 12. This voltage, V.sub.H, can be calculated using the following relationship: ##EQU3##

The circuitry which modifies V.sub.H so as to reflect changes due to temperature fluctuations includes bridge 42 and amplifier 44. A 100 ohm platinum resistance thermometer has been used for temperature variable resistor 24. This temperature variable resistor 24 is attached to one of tubes 12 by methods known in the art to sense temperature changes. The resistance changes caused by temperature fluctuations are measured by bridge 42 and amplified by amplifier 44 to produce a substantially linear increasing voltage as the temperature of temperature variable resistor 24 is increased. The voltage, V.sub.2, therefore supplies a temperature controlled current to the summing node 46 to modify V.sub.H as follows: ##EQU4## where K(temp) is effectively a temperature dependent factor.

Finally, the combination of amplifiers 48 and 50, variable resistors R7 and R5, and resistor R6 is used to obtain a voltage whose transfer function takes the form of equation 3. Amplifier 48 provides a buffer for hold capacitor C3, and a current proportional to V.sub.H is summed with a current set by variable resistor R5 and constant voltage V.sub.3. This current is amplified by amplifier 50 to provide voltage V.sub..rho. which can be calculated using the following relationship. ##EQU5## Thus, the output voltage, V.sub..rho., can be scaled by means of resistors R5 and R7 to produce a voltage equivalent to the density or specific gravity of the substance flowing through the resonantly oscillating tubes 12. The output voltage, V.sub..rho. can be measured using known digital voltmeter circuitry.

Typical components employed in one embodiment of the invention are listed in the following table, though of course numerous other components and values would be operable in equivalent and variant designs.

The electronic circuit shown in FIG. 1 has been built and tested using a densimeter having twin 1/4 inch 316L stainless steel tubes. To test the accuracy of the electronic circuitry the densimeter tubes were filled with distilled water, and the densimeter was then placed in an oven. At the various temperatures at which data were taken the temperature was allowed to stabilize for thirty minutes before the following data was recorded.

This same densimeter equipment was also tested by calibrating the circuitry at zero with air in the tubes, and at 1.00 with distilled water in the tubes. Three different fluids of known specific gravity were then used to determine the accuracy of the readings provided by the circuitry of the present invention.

The above discussion and related illustrations of the present invention are directed primarily to preferred embodiments and practices of the invention. However, it is believed that numerous changes and modifications in the actual implementation of the concepts described herein will be apparent to those skilled in the art, and it is contemplated that such changes and modifications may be made without departing from the scope of the invention as defined by the following claims.