HK1243173B - Determining a vibration response parameter of a vibratory element - Google Patents

Description

Determine the vibration response parameters of the vibrating element

Technical Field

The embodiments described below relate to vibration sensors, and more particularly to determining vibration response parameters of a vibrating element in a vibration sensor.

Background Art

Vibration sensors, such as vibrating densitometers and vibrating viscometers, operate by detecting the motion of a vibrating element that vibrates in the presence of a fluid to be characterized. The vibrating element has a vibration response, which may have vibration response parameters such as resonant frequency or quality factor (Q). The vibration response of the vibrating element is typically influenced by the combined mass, stiffness, and damping characteristics of the vibrating element in combination with the fluid. Properties associated with the fluid (such as density, viscosity, temperature, etc.) can be determined by processing one or more vibration signals received from one or more motion transducers associated with the vibrating element. Processing of the vibration signals may include determining vibration response parameters.

Figure 1 illustrates a prior art vibration sensor, which includes a vibrating element and meter electronics coupled to the vibrating element. The prior art vibration sensor includes a driver for vibrating the vibrating element and a pickup element (pickoff) that generates a vibration signal in response to the vibration. The vibration signal is typically a continuous-time or analog signal. The meter electronics receives the vibration signal and processes it to generate one or more fluid properties or measurements. The meter electronics determines both the frequency and amplitude of the vibration signal. The frequency and amplitude of the vibration signal can be further processed to determine the density of the fluid.

Conventional vibration sensors use closed-loop circuits to provide a drive signal to an actuator. The drive signal is typically based on a received vibration signal. Conventional closed-loop circuits modify or incorporate the vibration signal or parameters of the vibration signal into the drive signal. For example, the drive signal may be an amplified, modulated, or otherwise modified version of the received vibration signal. The received vibration signal can therefore include feedback that enables the closed-loop circuit to achieve a target frequency. Using this feedback, the closed-loop circuit incrementally changes the drive frequency and monitors the vibration signal until the target frequency is reached.

Fluid properties such as viscosity and density can be determined based on the frequencies at which the phase difference between the drive signal and the vibration signal is 135° and 45°. These ideal phase differences, represented as a first off-resonant phase difference φ1 and a second off-resonant phase difference φ2, can correspond to the half-power or 3dB frequency. The first off-resonant frequency ω1 is defined as the frequency at which the first off-resonant phase difference φ1 is 135°. The second off-resonant frequency ω2 is defined as the frequency at which the second off-resonant phase difference φ2 is 45°. Density measurements made at the second off-resonant frequency ω2 can be independent of fluid viscosity. Therefore, density measurements made at a second off-resonant phase difference φ2 of 45° can be more accurate than density measurements made at other phase differences.

The first and second off-resonant phase differences φ1, φ2 are typically not known before measurement. Therefore, using feedback as described above, a closed-loop circuit must incrementally approximate the first and second off-resonant phase differences φ1, φ2. This incremental approximation associated with the closed-loop circuit can cause delays in determining the vibration response parameter, and therefore, in determining the viscosity, density, or other properties of the fluid. Delays in determining such measurements can be prohibitively expensive in many applications of vibration sensors.

Therefore, there is a need to determine vibration response parameters of a vibrating element.There is also a need to determine vibration response parameters in a desirably fast and accurate manner.

Summary of the Invention

A method for determining a vibration response parameter of a vibration element is provided. According to an embodiment, the method includes vibrating the vibration element at a first frequency with a first drive signal, receiving a first vibration signal from the vibration element vibrating at the first frequency, and measuring a first phase difference, the first phase difference being the phase difference between the first drive signal and the first vibration signal. The method also includes vibrating the vibration element at a second frequency with a second drive signal, receiving a second vibration signal from the vibration element vibrating at the second frequency, measuring a second phase difference, the second phase difference being the phase difference between the second drive signal and the second vibration signal, and using the first phase difference and the second phase difference to determine at least one of a frequency and a phase difference of the vibration element.

A vibration sensor for determining a vibration response parameter of a vibrating element is provided. According to an embodiment, a vibrating meter includes a vibrating element configured to vibrate at a first frequency using a first drive signal and at a second frequency using a second drive signal. According to an embodiment, the vibration sensor also includes meter electronics communicatively coupled to the vibrating element and configured to receive the first drive signal, receive a first vibration signal from the vibrating element vibrating at the first frequency, and receive a second vibration signal from the vibrating element vibrating at the second frequency. According to an embodiment, the meter electronics is further configured to measure a first phase difference, which is a phase difference between the first drive signal and the first vibration signal, measure a second phase difference, which is a phase difference between the second drive signal and the second vibration signal, and use the first phase difference and the second phase difference to determine at least one of a phase difference and a frequency of the vibrating element.

All aspects

According to one aspect, a method (900, 1000) for determining a vibration response parameter of a vibration element (104) includes vibrating the vibration element (104) at a first frequency with a first drive signal, receiving a first vibration signal from the vibration element (104) vibrating at the first frequency, and measuring a first phase difference, the first phase difference being the phase difference between the first drive signal and the first vibration signal. The method (900, 1000) also includes vibrating the vibration element (104) at a second frequency with a second drive signal, receiving a second vibration signal from the vibration element (104) vibrating at the second frequency, and measuring a second phase difference, the second phase difference being the phase difference between the second drive signal and the second vibration signal. The method (900, 1000) also includes using the first phase difference and the second phase difference to determine at least one of a phase difference and a frequency of the vibration element (104).

Preferably, at least one of the determined phase difference and the frequency of the vibrating element (104) is a substantially linear approximation calculated from the first phase difference and the second phase difference.

Preferably, the determined at least one frequency of the vibration element (104) is one of a resonant frequency ω0, a first non-resonant frequency ω1, and a second non-resonant frequency ω2 of the vibration element (104).

Preferably, the determined at least one phase difference is one of a resonant phase difference φ0, a first non-resonant phase difference φ1 and a second non-resonant phase difference φ2.

Preferably, the method (900, 1000) further comprises calculating a linear approximation of a Q value of the vibrating element (104) using the first phase difference and the second phase difference.

Preferably, the determination of at least one of the phase difference and the frequency of the vibration element (104) is determined by one of linear interpolation and linear extrapolation.

Preferably, at least one of the determined phase difference and frequency of the vibrating element (104) is used to calculate at least one of the viscosity and density of the fluid measured by the vibrating element (104).

Preferably, the method (900, 1000) further comprises determining whether the first measured phase difference and the second measured phase difference are within a linear region of the phase response of the vibrating element (104).

According to one aspect, a vibration sensor (5) for determining a vibration response parameter of a vibration element (104) includes a vibration element (104) configured to be vibrated at a first frequency using a first drive signal and at a second frequency using a second drive signal. The vibration sensor (5) also includes meter electronics (20) communicatively coupled to the vibration element (104) and configured to: receive the first drive signal, receive a first vibration signal from the vibration element (104) vibrating at the first frequency, and receive a second vibration signal from the vibration element (104) vibrating at the second frequency. The meter electronics (20) is further configured to measure a first phase difference, the first phase difference being the phase difference between the first drive signal and the first vibration signal, measure a second phase difference, the second phase difference being the phase difference between the second drive signal and the second vibration signal, and use the first phase difference and the second phase difference to determine at least one of a phase difference and a frequency of the vibration element (104).

Preferably, at least one of the determined phase difference and the frequency of the vibrating element (104) is a substantially linear approximation calculated from the first phase difference and the second phase difference.

Preferably, the determined at least one frequency of the vibration element (104) is one of a resonant frequency ω0, a first non-resonant frequency ω1, and a second non-resonant frequency ω2 of the vibration element (104).

Preferably, the determined at least one phase difference is one of a resonant phase difference φ0, a first non-resonant phase difference φ1 and a second non-resonant phase difference φ2.

Preferably, the meter electronics (20) is further configured to calculate a linear approximation of the Q value of the vibrating element (104) using the first phase difference and the second phase difference.

Preferably, the meter electronics (20) is configured to determine at least one of the phase difference and the frequency of the vibrating element (104) using one of linear interpolation and linear extrapolation.

Preferably, the meter electronics (20) is further configured to use at least one of a phase difference and a frequency of the vibrating element (104) to calculate at least one of a viscosity and a density of a fluid measured by the vibrating element.

Preferably, the meter electronics (20) is further configured to determine whether the first measured phase difference and the second measured phase difference are within a linear region of the phase response of the vibrating element (104).

BRIEF DESCRIPTION OF THE DRAWINGS

Like reference numerals represent like elements throughout the drawings. It should be understood that the drawings are not necessarily to scale.

FIG. 1 shows a prior art vibration sensor comprising a vibrating element and meter electronics coupled to the vibrating element.

FIG2 shows a vibration sensor 5 according to an embodiment.

FIG3 shows a vibration sensor 5 according to an embodiment.

FIG4 shows a block diagram of the vibration sensor 5 with a more detailed representation of the driver circuit 138 .

FIG. 5 shows a frequency response graph 500 illustrating the vibration response of a vibratory element.

FIG6 shows a phase response graph 600 illustrating a vibration response of a vibratory element.

FIG. 7 shows a low viscosity phase response graph 700 , which is an enlarged view of the phase response graph 600 shown in FIG. 6 .

FIG8 shows a high viscosity phase response graph 800 , which is an enlarged view of the phase response graph 600 shown in FIG6 .

FIG9 illustrates a method 900 for determining vibration response parameters according to an embodiment.

FIG. 10 illustrates a method 1000 for determining vibration response parameters according to an embodiment.

DETAILED DESCRIPTION

Figures 2-10 and the following description depict specific examples to teach those skilled in the art how to implement and use the best mode of the embodiments for determining the vibration response parameters of a vibration element. For the purpose of teaching the principles of the invention, some conventional aspects have been simplified or omitted. Those skilled in the art will recognize variations from these examples that fall within the scope of this description. Those skilled in the art will recognize that the features described below can be combined in various ways to form multiple variations for determining the vibration response parameters of a vibration element. Therefore, the embodiments described below are not limited to the specific examples described below, but are only defined by the claims and their equivalents.

FIG2 illustrates a vibration sensor 5 according to an embodiment. The vibration sensor 5 may include a vibrating element 104 and meter electronics 20, wherein the vibrating element 104 is coupled to the meter electronics 20 via one or more wires 100. In some embodiments, the vibration sensor 5 may include a vibratory tine sensor or a fork density sensor (see FIG3 and the accompanying discussion). However, other vibration sensors are contemplated and are within the scope of the specification and claims.

The vibration sensor 5 can be at least partially immersed in the fluid to be characterized. The fluid can include a liquid or a gas. Alternatively, the fluid can include a multiphase fluid, such as a liquid including entrained gas, entrained solids, multiple liquids, or a combination thereof. Some exemplary fluids include cement slurries, petroleum products, etc. The vibration sensor 5 can be mounted in a pipe or conduit, a tank, a container, or other fluid container. The vibration sensor 5 can also be mounted in a manifold or similar structure for directing fluid flow. However, other mounting arrangements are contemplated and are within the scope of the specification and claims.

The vibration sensor 5 operates to provide fluid measurements. The vibration sensor 5 can provide fluid measurements including one or more of fluid density and fluid viscosity for a fluid, including flowing or non-flowing fluids. The vibration sensor 5 can provide fluid measurements including fluid mass flow rate, fluid volume flow rate, and/or fluid temperature. This list is not exhaustive, and the vibration sensor 5 can measure or determine other fluid properties.

The meter electronics 20 can provide electrical power to the vibrating element 104 via one or more wires 100. The meter electronics 20 can control the operation of the vibrating element 104 via the one or more wires 100. For example, the meter electronics 20 can generate a drive signal and provide the generated drive signal to the vibrating element 104, where the vibrating element 104 uses the generated drive signal to generate vibrations in one or more vibrating components. The generated drive signal can control the vibration amplitude and frequency of the vibrating element 104. The generated drive signal can also control the vibration duration and/or vibration timing.

Meter electronics 20 may also receive one or more vibration signals from vibrating element 104 via one or more conductors 100. For example, meter electronics 20 may process the one or more vibration signals to generate a density measurement. Meter electronics 20 processes the one or more vibration signals received from vibrating element 104 to determine the frequency of the one or more signals. Alternatively or additionally, meter electronics 20 processes the one or more vibration signals to determine other fluid properties, such as viscosity or a phase difference between the signals, which can be processed to determine, for example, fluid flow rate. As will be appreciated, phase difference is typically measured or expressed in spatial units (e.g., degrees or radians), but any suitable units, such as time-based units, may be used. If time-based units are used, the phase difference may be referred to by those skilled in the art as the time delay between the vibration signal and the drive signal. Other vibration response characteristics and/or fluid measurements are contemplated and are within the scope of the specification and claims.

The meter electronics 20 may also be coupled to a communication link 26. The meter electronics 20 may communicate the vibration signal via the communication link 26. The meter electronics 20 may also process the received vibration signal to generate one or more measurements, and may communicate the one or more measurements via the communication link 26. Additionally, the meter electronics 20 may receive information via the communication link 26. For example, the meter electronics 20 may receive commands, updates, operating values or changes in operating values, and/or programming updates or changes via the communication link 26.

FIG3 illustrates a vibration sensor 5 according to an embodiment. In the illustrated embodiment, meter electronics 20 is coupled to a vibrating element 104 via a shaft 115. Shaft 115 can have any desired length. Shaft 115 can be at least partially hollow. Wires or other conductors can extend through shaft 115 between meter electronics 20 and vibrating element 104. Meter electronics 20 includes circuit components such as a receiver circuit 134, an interface circuit 136, and a driver circuit 138. In the illustrated embodiment, receiver circuit 134 and driver circuit 138 are directly coupled to the wires of vibrating element 104. Alternatively, meter electronics 20 may include components or devices separate from vibrating element 104, with receiver circuit 134 and driver circuit 138 coupled to vibrating element 104 via one or more wires 100.

In the illustrated embodiment, the vibrating element 104 of the vibration sensor 5 comprises a tuning fork structure, wherein the vibrating element 104 is at least partially immersed in the fluid being measured. The vibrating element 104 includes a housing 105, which can be attached to another structure, such as a pipe, conduit, tank, container, manifold, or any other fluid handling structure. The housing 105 holds the vibrating element 104, while the vibrating element 104 remains at least partially exposed. The vibrating element 104 is thus configured to be immersed in the fluid.

The vibrating element 104 in the illustrated embodiment includes first and second teeth 112 and 114 that are configured to extend at least partially into the fluid. The first and second teeth 112 and 114 include elongated elements that can have any desired cross-sectional shape. The first and second teeth 112 and 114 can be at least partially flexible or elastic in nature. The vibration sensor 5 also includes corresponding first and second piezoelectric elements 122 and 124 that include piezoelectric crystal elements. The first and second piezoelectric elements 122 and 124 are positioned adjacent to the first and second teeth 112 and 114, respectively. The first and second piezoelectric elements 122 and 124 are configured to contact the first and second teeth 112 and 114 and mechanically interact therewith.

First piezoelectric element 122 contacts at least a portion of first tooth 112. First piezoelectric element 122 is also electrically coupled to driver circuit 138. Driver circuit 138 provides a generated drive signal to first piezoelectric element 122. First piezoelectric element 122 expands and contracts in response to the generated drive signal. Thus, first piezoelectric element 122 can alternately deform and, in a vibrating motion (see dashed lines), displace first tooth 112 from side to side, thereby disturbing the fluid in a cyclical, reciprocating manner.

The second piezoelectric element 124 is shown coupled to a receiver circuit 134, which generates a vibration signal corresponding to the deformation of the second tooth 114 in the fluid. The movement of the second tooth 114 causes the second piezoelectric element 124 to generate a corresponding electrical vibration signal. The second piezoelectric element 124 transmits the vibration signal to the meter electronics 20. The meter electronics 20 includes an interface circuit 136. The interface circuit 136 can be configured to communicate with an external device. The interface circuit 136 transmits one or more vibration measurement signals and can communicate determined fluid characteristics to one or more external devices. The meter electronics 20 can transmit vibration signal characteristics, such as the vibration signal frequency and vibration signal amplitude, via the interface circuit 136. The meter electronics 20 can transmit fluid measurements, such as the density and/or viscosity of the fluid, among other things, via the interface circuit 136. Other fluid measurements are contemplated and are within the scope of the specification and claims. In addition, the interface circuit 136 can receive communications from the external device, for example, including commands and data used to generate the measurement values. In some embodiments, receiver circuit 134 is coupled to driver circuit 138 , where receiver circuit 134 provides a vibration signal to driver circuit 138 .

Driver circuit 138 generates a drive signal for vibration element 104. Driver circuit 138 can modify the characteristics of the generated drive signal. Driver circuit 138 includes an open-loop drive. Driver circuit 138 can use the open-loop drive to generate the drive signal and supply the generated drive signal to vibration element 104 (e.g., to first piezoelectric element 122). In some embodiments, the open-loop drive generates the drive signal to achieve a target phase difference φ _t , starting at an initial frequency ω _i . The open-loop drive may operate without feedback from the vibration signal, as will be described in more detail below with reference to FIG.

FIG4 shows a block diagram of the vibration sensor 5 with a more detailed representation of the driver circuit 138. The vibration sensor 5 is shown with the driver circuit 138. For clarity, the receiver circuit 134 and the interface circuit 136 are not shown. The driver circuit 138 includes an analog input filter 138a and an analog output filter 138b, which are coupled to the open-loop drive 147. The analog input filter 138a filters the vibration signal, and the analog output filter 138b filters the generated drive signal.

Open-loop drive 147 includes an analog-to-digital converter 147a coupled to a phase detector 147b. Phase detector 147b is coupled to a signal generator 147c. Also shown is vibrating element 104, which includes a first piezoelectric element 122 and a second piezoelectric element 124. Open-loop drive 147 can be implemented using a digital signal processor configured to execute one or more codes or programs for sampling, processing, and generating signals. Additionally or alternatively, open-loop drive 147 can be implemented using electronic circuitry coupled to a digital signal processor or the like.

The vibration signal provided by the first piezoelectric element 122 is sent to the analog input filter 138a. The analog input filter 138a filters the vibration signal before it is sampled by the analog-to-digital converter 147a. In the illustrated embodiment, the analog input filter 138a may comprise a low-pass filter having a cutoff frequency approximately half the sampling rate of the open-loop drive 147, however, any suitable low-pass filter may be used. The low-pass filter may be provided by passive components, such as inductors, capacitors, and resistors, however, any suitable components (distributed or discrete), such as an operational amplifier filter, may be used.

The analog-to-digital converter 147a can sample the filtered vibration signal to form a sampled vibration signal. The analog-to-digital converter 147a can also sample the generated drive signal via a second channel (not shown). The sampling can be performed using any suitable sampling method. As can be appreciated, the generated drive signal sampled by the analog-to-digital converter 147a is free of the noise associated with the vibration signal. The generated drive signal is provided to the phase detector 147b.

Phase detector 147b can compare the phases of the sampled vibration and the generated drive signal. Phase detector 147b can be a processor configured to execute one or more codes or programs that sample, process, and generate signals to detect a phase difference between the two signals, as will be described in more detail below with reference to FIG5 . Still referring to the embodiment of FIG4 , the comparison provides a measured phase difference φ _m between the sampled vibration signal and the sampled generated drive signal.

The measured phase difference _φm is compared to a target phase difference _φt . The target phase difference _φt is the desired phase difference between the vibration signal and the generated drive signal. For example, in an embodiment where the target phase difference _φt is approximately 45°, if the measured phase difference _φm is also approximately 45°, the difference between the measured phase difference _φm and the target phase difference _φt can be zero. However, in alternative embodiments, any suitable target phase difference _φt can be used. By comparing the measured phase difference _φm with the target phase difference _φt , the phase detector 147b can generate the command frequency _ωc .

A command frequency _ωc may be used to generate the drive signal. Additionally or alternatively, an initial frequency that is not determined based on a comparison between the measured phase difference _φm and the target phase difference _φt may be used. The initial frequency _ωi may be a preselected frequency used to form the initial generated drive signal. The initial generated drive signal may be sampled as described above and compared to the sampled vibration signal. The comparison between the sampled initial generated drive signal and the sampled vibration signal may be used to generate the command frequency _ωc . The command frequency _ωc and the initial frequency _ωi may have units of radians per second, however, any suitable units may be used, such as, for example, Hertz (Hz). The command frequency _ωc or the initial frequency _ωi may be provided to the signal generator 147c.

The signal generator 147c can receive the command frequency _ωc from the phase detector 147b and provide the generated drive signal with the same frequency as the command frequency _ωc . As discussed above, the generated drive signal can be sent to the analog-to-digital converter 147a. The generated drive signal is also sent to the first piezoelectric element 122 via the analog output filter 138b. Additionally or alternatively, in other embodiments, the generated drive signal can be sent to other components.

As discussed above, the vibrating element 104 has a vibration response due to the drive signal. This vibration response includes vibration response parameters, such as the resonant frequency ω0 and the quality factor Q, which can be used to calculate various properties of the measured fluid. The vibration response and exemplary vibration response parameters, and how the vibration response parameters can be used to calculate fluid properties, are discussed in more detail below.

FIG5 shows a frequency response graph 500 illustrating the vibration response of a vibration element. The vibration element may be the exemplary vibration element 104 described above with reference to FIG2-4. Frequency response graph 500 includes a frequency axis 510 and an amplitude axis 520. Frequency axis 510 is shown in units of Hz, but any suitable frequency unit may be used, such as, for example, radians per second. Amplitude axis 520 is shown with a decibel (dB) scale. Amplitude axis 520 may be determined in any suitable units, such as, for example, volts or amperes.

Frequency response graph 500 also includes frequency response plot 530. Frequency response plot 530 can represent the vibration response of vibrating element 104 described above, but any suitable vibrating element can be used in alternative embodiments. As shown in FIG. 5 , frequency response plot 530 includes individual frequency response plots for fluids having different vibration damping properties. For example, because vibrating element 104 is immersed in a viscous and dense fluid, the plot having the lowest amplitude at the resonant frequency may be the flattest. Because vibrating element 104 is immersed in a fluid having a low viscosity relative to the fluid associated with the other plots in frequency response plot 530, the plot having the largest amplitude at the resonant frequency may be the least flat. As can be appreciated, each of frequency response plots 530 has a different associated vibration response parameter.

For example, in the embodiment shown in FIG5 , each of the frequency response curves 530 has three markers indicating a first non-resonant frequency ω1, a second non-resonant frequency ω2, and a resonant frequency ω0 as vibration response parameters of the vibration response. The first non-resonant frequency ω1 is indicated by a circle marker 532. The second non-resonant frequency ω1 is indicated by a vertical dot (tic) marker 536. The resonant frequency ω0 is indicated by a diamond marker 534. As can be appreciated by referring to the diamond marker 534, the resonant frequency ω0 is substantially the same for each of the frequency response curves 530.

In some embodiments, the resonant frequency ω0 may be determined based on the first non-resonant frequency ω1 and the second non-resonant frequency ω2. For example, the resonant frequency ω0 may be determined based on the average of the first non-resonant frequency ω1 and the second non-resonant frequency ω2:

.

However, in alternative embodiments, the resonant frequency ω0 may be determined in other ways, such as by measuring the frequency at peak amplitude while sweeping a frequency range.

The quality factor Q may be determined based on the first non-resonant frequency ω1, the second non-resonant frequency ω2, and the resonant frequency ω0. For example, the quality factor Q may be determined based on:

.

As can be appreciated, the quality factor Q for each curve is different.The quality factor Q may be different for each of the frequency response curves 530 due to various reasons such as, for example, the fluid associated with each of the frequency response curves 530 having a different viscosity or density.

The foregoing describes how the vibration response parameter can be determined by measuring the first non-resonant frequency ω1 and the second non-resonant frequency ω2. However, as will be described below, the vibration response parameter can also be determined by measuring the phase difference between the drive signal and the vibration signal. Furthermore, the vibration response parameter can also be determined by using frequencies other than the first or second non-resonant frequencies ω1, ω2.

FIG6 shows a phase response graph 600 illustrating the vibration response of a vibration element. The vibration element may be the vibration element described above with reference to FIG2-4. The phase response graph 600 includes a frequency axis 610 as the abscissa of the phase response graph 600. The phase response graph 600 also includes a phase difference axis 620 as the ordinate of the phase response graph 600. The phase response graph 600 also includes a low-viscosity phase response curve 630 and a high-viscosity phase response curve 640.

As can be appreciated, a substantial portion of the low-viscosity and high-viscosity phase response curves 630, 640 are linear. For example, the low-viscosity phase response curve 630 is nearly vertical, having a substantially constant slope from approximately 1610 Hz to approximately 1613 Hz. In the high-viscosity phase response curve 640, the magnitude of the phase difference increases at a relatively constant slope between the vibration response frequencies of approximately 1455 Hz and 1610 Hz. As can also be appreciated, the linear portion of the low-viscosity and high-viscosity phase response curves 630, 640 extends between a first non-resonant frequency ω1 (shown as approximately 1612.55 Hz at a 135° phase difference) and a second non-resonant frequency ω2 (shown as approximately 1610.65 at a 45° phase difference). The linearity in the low-viscosity and high-viscosity phase response curves 630, 640 can be used to determine the frequency or phase difference between the first non-resonant frequency ω1 and the second non-resonant frequency ω2, as will be explained in more detail below with reference to Figures 7 and 8.

FIG7 shows a low-viscosity phase response graph 700, which is an enlarged view of the phase response graph 600 shown in FIG6 . Due to the enlargement, the low-viscosity phase response graph 700 includes a frequency axis 710 that ranges from 1610.50 to 1613.00 degrees. Also due to the enlargement, the low-viscosity phase response graph 700 includes a phase difference axis 720 that ranges from 45.00 degrees to 135.00 degrees. The low-viscosity phase response graph 700 also includes the substantially linear portion of the low-viscosity phase response curve 630 described above. Also shown in FIG7 is an exemplary low-viscosity linearization 632 of the low-viscosity phase response curve 630.

Low viscosity linearization 632 is relatively close to low viscosity phase response curve 630. For example, at least two points on low viscosity linearization 632 are shared with low viscosity phase response curve 630. Low viscosity linearization 632 is also relatively close to low viscosity phase response curve 630 along the entire length of low viscosity phase response curve 630. To illustrate that phase response curves of fluids having different viscosities can be linearized, we now turn to a magnified view of high viscosity phase response curve 640.

FIG8 shows a high viscosity phase response graph 800, which is an enlarged view of the phase response graph 600 shown in FIG6 . Due to the enlargement, the high viscosity phase response graph 800 includes a frequency axis 810 that varies from 1440.00 to 1620.00. Also due to the enlargement, the high viscosity phase response graph 800 includes a phase difference axis 820 that varies from 45.00 degrees to 135.00 degrees. The high viscosity phase response graph 800 also includes the substantially linear portion of the high viscosity phase response curve 640 described above. Also shown in FIG8 is an exemplary high viscosity linearization 642 of the high viscosity phase response curve 640.

High viscosity linearization 642 is relatively close to high viscosity phase response curve 640. For example, at least two points on high viscosity linearization 642 are shared with high viscosity phase response curve 640. High viscosity linearization 642 is also relatively close to high viscosity phase response curve 640 along the entire length of high viscosity phase response curve 640.

In embodiments where linearization is employed to determine the vibration response parameters of a vibrating element, two or more points on each of the phase response curves 630 and 640 may be employed to determine the frequency or phase difference. For example, the linearizations 632 and 642 described above may be employed to calculate the first non-resonant frequency ω1 and the second non-resonant frequency ω2. Similarly, the linearizations 632 and 642 may be employed to calculate the first non-resonant phase difference φ1 and the second non-resonant phase difference φ2. Exemplary methods for determining the vibration response using the non-resonant frequencies and phase differences ω1, ω2, φ1, and φ2 are described in greater detail below with reference to FIG9 and FIG10.

FIG9 illustrates a method 900 for determining a vibration response parameter according to an embodiment. Method 900 begins by vibrating a vibration element at a first frequency using a first drive signal in step 910. The vibration element may be vibration element 104 as described above with reference to FIGs. 2-4. In step 920, method 900 vibrates the vibration element at a second frequency using a second drive signal. The second drive signal may be different from the first drive signal. Additionally or alternatively, the vibration element may be vibrated by the first drive signal and the second drive signal at the same or different times. For example, a composite drive signal comprising the first and second drive signals may be applied to the vibration element to generate the first and second frequencies.

In step 930, method 900 uses the first frequency and the second frequency to determine a first non-resonant frequency ω1 and a second non-resonant frequency ω2. For example, meter electronics 20, as described above, may measure the first frequency along with the first phase difference. Meter electronics 20 may also measure the second frequency along with the second phase difference. Meter electronics 20 may determine whether the first frequency and the corresponding first phase difference, as well as the second frequency and the corresponding second phase difference, are within the linear region of the phase response of vibrating element 104. Referring to the exemplary phase response curves 630 and 640 described above, meter electronics 20 may determine whether the first and second phase differences are greater than 45 degrees and less than 135 degrees. Method 900 may then calculate a linear approximation of the first non-resonant frequency ω1 and the second non-resonant frequency ω2. Additionally or alternatively, first and second non-resonant phase differences φ1 and φ2 may also be calculated, as will be explained in more detail below.

FIG10 illustrates a method 1000 for determining a vibration response parameter according to an embodiment. Method 1000 begins by vibrating a vibration element at a first frequency using a first drive signal in step 1010. The vibration element may be vibration element 104 described above with reference to FIG2-4. In step 1020, method 1000 vibrates the vibration element at a second frequency using a second drive signal. The second drive signal may be different from the first drive signal. Additionally or alternatively, the vibration element may vibrate at the first drive frequency and the second drive frequency at the same or different times. For example, the drive signal may include first and second drive signals, which are applied to the vibration element to generate the first and second vibration signals.

In step 1030, method 1000 measures a first phase difference and a second phase difference. For example, the first phase difference may be the phase difference between the first vibration signal and the first drive signal. Similarly, the second phase difference may be the phase difference between the second vibration signal and the second drive signal.

In step 1040, method 1000 may use the first phase difference and the second phase difference to determine a first non-resonant phase difference φ1 and a second non-resonant phase difference φ2. For example, meter electronics 20, as described above, may measure the first phase difference along with the first frequency. Meter electronics 20 may also measure the second phase difference along with the second frequency. Meter electronics 20 may determine whether the first frequency and the corresponding first phase difference, as well as the second frequency and the corresponding second phase difference, are within the linear region of the phase response of vibrating element 104. Referring to the exemplary phase response curves 630 and 640 described above with reference to Figures 6-8, meter electronics 20 may determine whether the first and second phase differences are greater than 45 degrees and less than 135 degrees. Method 900 may then calculate a linear approximation of the first non-resonant frequency ω1 and the second non-resonant frequency ω2.

The foregoing describes calculating linear approximations of frequencies or phase differences, which may be first and second non-resonant frequencies and phase differences ω1, ω2, φ1, φ2. Various methods can be used to calculate linear approximations of the first and second non-resonant frequencies and phase differences ω1, ω2, φ1, φ2. For example, the meter electronics 20 described above can measure the first and second frequencies and phase differences. The meter electronics 20 can determine whether the first frequency and corresponding first phase difference, as well as the second frequency and corresponding second phase difference, are within the linear region of the phase response of the vibrating element 104. For example, referring to the exemplary phase response curves 630, 640 described above, the meter electronics 20 can determine whether the first and second phase differences are greater than 45 degrees and less than 135 degrees. Methods 900, 1000 can then calculate linear approximations of the first non-resonant frequency and phase difference ω1, φ1, and the second non-resonant frequency and phase difference ω2, φ2.

The linear approximation can be calculated by using extrapolation or interpolation. For example, with reference to the linearizations 632, 642, the first and second frequencies, and the phase differences described above, the methods 900, 1000 can assume that the first and second frequencies and the phase differences are two points along the linearizations 632, 642. Thus, the methods 900, 1000 can extrapolate or interpolate the first and second frequencies and the phase differences to the first and second non-resonant phase differences φ1, φ2 and the corresponding first and second non-resonant frequencies ω1, ω2. Although the foregoing describes an embodiment in which the phase difference is greater than 45 degrees and less than 135 degrees, the measured phase difference can be less than 45 degrees and greater than 135 degrees.

Additionally or alternatively, other methods of calculating approximations of the first and second non-resonant frequencies and phase differences ω1, ω2, φ1, φ2 may be employed, such as, for example, fitting a high-order polynomial, exponential curve, etc. to two or more measured frequencies and phase differences. However, when compared to alternative approximations, a linear approximation may be desirably more efficient, faster, etc.

The steps of measuring the first and second frequencies and the corresponding phase differences and calculating the frequency and/or phase difference, which may be a linear approximation of the first and second non-resonant frequencies and phase differences ω1, ω2, φ1, φ2, can be performed within a desired time frame. For example, because the frequency and phase difference can be determined without iteration of phase and frequency measurements, the vibration response parameters can be determined within a desirably short time period. Thus, fluid properties such as, for example, density and viscosity can be calculated and provided within a desired time frame.

Furthermore, it may be advantageous to determine whether the measured first and second phase differences are within a range, such as less than 135 degrees and greater than 45 degrees. For example, determining that the measured first and second phase differences are within the first and second non-resonant phase differences φ1, φ2 can prevent the inclusion of nonlinear regions, such as in the phase response curves 630, 640. Consequently, the determined first and second non-resonant frequencies and phase differences ω1, ω2, φ1, φ2 can be more accurate.

Although the foregoing describes the non-iterative determination of the first and second non-resonant frequencies and phase differences ω1, ω2, φ1, φ2, this determination can be performed as part of an iterative process. For example, the determined first and second non-resonant frequencies and phase differences ω1, ω2, φ1, φ2 can be used as an estimate of the command frequency _ωc provided to the signal generator 147c in the open-loop drive 147 described above with reference to FIG4. Thus, the frequency of the drive signal can be relative to the actual first or second non-resonant frequency and phase difference ω1, ω2, φ1, φ2 prior to the iteration, thereby reducing the time required to measure the actual first and second non-resonant frequencies ω1, ω2.

The detailed descriptions of the above embodiments are not exhaustive descriptions of all embodiments contemplated by the inventors as being within the scope of this specification. Indeed, those skilled in the art will recognize that certain elements of the above embodiments may be variously combined or eliminated to create further embodiments, and such further embodiments fall within the scope and teachings of this specification. It will also be apparent to those skilled in the art that the above embodiments may be combined in whole or in part to create additional embodiments within the scope and teachings of this specification.

Therefore, although specific embodiments are described herein for illustrative purposes, various equivalent modifications are possible within the scope of this specification, as those skilled in the relevant art will recognize. The teachings provided herein can be applied to other methods and apparatus for determining vibration response parameters of a vibrating element, and not only to the embodiments described above and shown in the accompanying drawings. Therefore, the scope of the embodiments described above should be determined in accordance with the following claims.

Claims (16)

1. A method (900, 1000) for determining vibration response parameters of a vibrating element (104), the method (900, 1000) comprising: The vibrating element (104) is vibrated at a first frequency using a first driving signal; Receive a first vibration signal from the vibrating element (104) vibrating at the first frequency; Measure the first phase difference, which is the phase difference between the first drive signal and the first vibration signal; The vibrating element (104) is vibrated at a second frequency using a second driving signal. Receive a second vibration signal from the vibrating element (104) vibrating at the second frequency; The second phase difference is measured, which is the phase difference between the second drive signal and the second vibration signal; and The relationship between the first phase difference and the second phase difference is used to determine at least one of the following: Phase difference; and The frequency of the vibrating element (104). 2. The method (900, 1000) according to claim 1, wherein at least one of the determined frequency and phase difference of the vibrating element (104) is a fundamental linear approximation calculated based on the first phase difference and the second phase difference. 3. The method (900, 1000) according to claim 1 or claim 2, wherein at least one frequency of the determined vibrating element (104) is one of the resonant frequency ω0, the first non-resonant frequency ω1, and the second non-resonant frequency ω2 of the vibrating element (104). 4. The method (900, 1000) according to claim 1 or claim 2, wherein the determined at least one phase difference is one of a resonant phase difference φ0, a first non-resonant phase difference φ1, and a second non-resonant phase difference φ2. 5. The method (900, 1000) according to claim 1 or claim 2, further comprising: using the first phase difference and the second phase difference to calculate a linear approximation of the Q value of the vibrating element (104). 6. The method (900, 1000) according to claim 1 or claim 2, wherein the determination of at least one of the phase difference and frequency of the vibrating element (104) is determined by one of linear interpolation and linear extrapolation. 7. The method (900, 1000) according to claim 1 or claim 2, wherein at least one of the determined phase difference and frequency of the vibrating element (104) is used to calculate at least one of the viscosity and density of the fluid measured by the vibrating element (104). 8. The method (900, 1000) according to claim 1 or claim 2, further comprising: determining whether the first measured phase difference and the second measured phase difference are within the linear region of the phase response of the vibrating element (104). 9. A vibration sensor (5) for determining vibration response parameters of a vibrating element (104), the vibration sensor (5) comprising: Vibrating element (104), which is configured to: Vibrated at a first frequency by a first driving signal; It is vibrated at a second frequency using a second driving signal; A metering electronic device (20), which is communicatively coupled to the vibrating element (104) and configured to: Receive the first drive signal; Receives a first vibration signal from the vibrating element (104) vibrating at the first frequency; and Receive a second vibration signal from the vibrating element (104) vibrating at the second frequency; The first phase difference is measured, which is the phase difference between the first drive signal and the first vibration signal; Measure the second phase difference, which is the phase difference between the second drive signal and the second vibration signal; and The relationship between the first phase difference and the second phase difference is used to determine at least one of the following: Phase difference; and The frequency of the vibrating element (104). 10. The vibration sensor (5) according to claim 9, wherein at least one of the determined phase difference and frequency of the vibration element (104) is a fundamental linear approximation calculated based on the first phase difference and the second phase difference. 11. The vibration sensor (5) according to claim 9 or claim 10, wherein at least one frequency of the determined vibration element (104) is one of the resonant frequency ω0, the first non-resonant frequency ω1, and the second non-resonant frequency ω2 of the vibration element (104). 12. The vibration sensor (5) according to claim 9 or claim 10, wherein the determined at least one phase difference is one of a resonant phase difference φ0, a first non-resonant phase difference φ1, and a second non-resonant phase difference φ2. 13. The vibration sensor (5) according to claim 9 or claim 10, wherein the metering electronics (20) is further configured to use the first phase difference and the second phase difference to calculate a linear approximation of the Q value of the vibration element (104). 14. The vibration sensor (5) according to claim 9 or claim 10, wherein the metering electronics (20) is configured to determine at least one of the frequency and phase difference of the vibration element (104) using one of linear interpolation and linear extrapolation. 15. The vibration sensor (5) according to claim 9 or claim 10, wherein the metering electronics (20) is further configured to use at least one of the frequency and phase difference of the vibration element (104) to calculate at least one of the viscosity and density of the fluid measured by the vibration element. 16. The vibration sensor (5) according to claim 9 or claim 10, wherein the metering electronics (20) is further configured to determine whether the first measurement phase difference and the second measurement phase difference are within the linear region of the phase response of the vibration element (104).