MXPA99001510A - Method and apparatus for measuring pressure in a coriolis mass flowmeter - Google Patents

Abstract

A method for determining pressure in an operating Coriolis effect mass flowmeter (10). The Coriolis flowmeter flow tubes (130, 130') are vibrated in both a bending mode (as is normal for measuring mass flow rate) and in a twisting mode. The ratio of the fundamental frequencies at which the flow tubes vibrate in each of the two vibration modes is proportional to the pressure within the flow tubes. In the preferred embodiment, a sum/difference method initially isolates the superposed sinusoids representing the fundamental frequencies of the two vibrational modes. Fast conjugate gradient (FCG) digital filters (512, 514) are then used to rapidly estimate the fundamental frequencies in each of the two vibration modes. The estimated frequencies are then used by filter chains including digital notch (518, 508) and band pass filters (506, 1520) as well as recursive maximum likelihood (RML) digital filter (510, 522) techniques to enhance the bending mode and twisting mode fundamental frequency estimates. The enhanced bending mode andtwisting mode frequency estimates are used to determine the pressure within the flow tubes as a function of the ratio of the two frequencies as well as to center the notch and band pass filter chains used to enhance the bending mode frequency of the two vibration sensor channels for mass flow rate computations. The pressureso determined may then be used to correct mass flow rate computations or for other pressure measurement purposes per se.

Description

METHOD AND APPARATUS FOR MEASURING THE PRESSURE IN A CORIOLIS MASS FLOW METER Field of the Invention The present invention concerns the measurement of pressure in association with the Coriolis effect main flow meters and in particular with a method and apparatus. to derive material pressure information in response to the operation of the Coriolis mass flow meter and to derive mass flow precision information in response to the operation of the flow meter.

Problem The use of Coriolis mass flow meters is known to measure mass flow and other information for materials flowing through a conduit. Such flow meters are described in U.S. Patent Nos. 4,109,524 of August 29, 1978, 4,491,025 of January 1, 1985 and Re. 31,450 of February 11, 1982, all issued to J. E. Smith et al.

These flow meters have one or more flow tubes of straight or curved configuration. Each configuration of the flow tube in a Coriolis mass flow meter has a set of natural vibration modes, which can be of a simple, torsional or type of bending type REF: 29441 coupled. Each flow tube is driven to oscillate in resonance in one of these natural modes. Flows of the material to the flow meter from a conduit connected to the inlet side of the flow meter are directed through the flow tube or tubes and exit the flow meter through the outlet side. The natural vibration modes of the system filled with vibrating material are defined in part by the combined mass of the flow tubes and the material that flows into the flow tubes. When there is no flow through the flow meter, all points along the flow tube oscillate with identical phase due to an applied impeller force. As the material begins to flow, Coriolis accelerations cause each point along the flow tube to have a different phase. The phase on the inlet side of the flow tube is delayed with respect to the impeller, while the phase on the outlet side is ahead of the impeller. Detectors are placed in the flow tube to produce sinusoidal signals representative of the movement of the flow tube. The phase difference between the two detector signals is proportional to the mass flow rate of the material through the flow tube. A complicating factor in this measurement is that the density of typical process materials varies. Changes in density cause the frequencies of the natural modes vary. Since the impeller control system of the flow meter keeps the flow tubes vibrating at resonance, the oscillation frequency varies in response to changes in density. The mass flow rate in this situation is proportional to the ratio or proportion of the phase difference and the oscillation frequency. The aforementioned US Patent No. Re 31,450, issued to Smith discloses a Coriolis flow meter which avoids the need to measure the phase difference and the oscillation frequency when the mass flow rate is measured. The phase difference is determined by measuring the time delay between the level crossings of the two sinusoidal signals of the flow meter. When this method is used, variations in the oscillation frequency are canceled and the mass flow rate is proportional to the measured time delay. This measurement method is hereinafter referred to as a measurement of the time delay or measurement of? T. The information concerning the characteristics of the material flowing in a Coriolis mass flow meter is usually derived by instrumentation that measures the phase or time delay between the two output signals of the flow meter detectors.

These measurements must be performed with great accuracy since it is frequently a requirement that the derived flow velocity information have an accuracy of at least 0.15% of the reading. These output signals of the flow meter are sinusoidal and are displaced in time or phase by an amount determined by the Coriolis forces generated by the meter through which the material flows. The signal processing circuits that receive these detector output signals accurately measure this phase difference and generate the desired characteristics of the flowing process material at the required accuracy of at least 0.15% of the reading. U.S. Patent No. 5,473,949 of December 12, 1995, issued to Cage et al., Describes a method for determining the pressure and density in a Coriolis mass flow meter. The Cage patent teaches the excitation of a vibratory duct in two different modes. The fluid is caused to flow in the conduit and measurements of the two vibration modes are taken at a "working point" of the flow meter. The pressure and density of the material flowing in the flow meter are then determined by the simultaneous resolution of two equations as stipulated by the Cage patent. Digital signal processing (DSP) techniques improve the accuracy of signal processing of the Coriolis flow meter detectors. The DSP techniques and the apparatus measure the phase difference between the detector signals without introducing phase shifts between the two signals through the measurement process. Any phase shift (delay) induced by the operation of the DSP is identical for the two detector signals. In addition, DSP techniques can more effectively filter the signals to extract the data from the ambient noise signals induced in the signals by the environment in which the flow meter is operated. It is known that changes in pressure within the flow tubes of the flow meter can affect the accuracy of mass flow measurements. Changes in the pressure of the material flowing within the flow tubes can change the stiffness or solidity of the flow tubes of the flow meter. This changes the resonance frequency of the flow tubes and causes errors in mass flow measurement. To minimize the effects of pressure changes on the resonance frequency and mass flow measurements, it is common to reinforce the walls of the flow tubes. However, increasing the rigidity of the flow tubes to decrease the effects of pressure changes can increase flow meter costs and also decrease the sensitivity of the flow meter. flowmeter. The decreased sensitivity due to the effects of pressure can limit the range of use for the application of the flow meter. It is known in the art to use a pressure meter in conjunction with the flow meter to measure the instantaneous pressure of the material and the use of the measured values of the pressure in the correction of mass flow rate measurements. However, the addition of an independent pressure meter adds to the complexity (and associated costs) of the flow measurement apparatus.

Solution The present invention solves the above and other problems, whereby an advance is made in the useful techniques, by providing methods and apparatus for measuring the pressure in a Coriolis mass flow meter without the addition of an independent pressure meter. A pressure measurement derived from the operation of a Coriolis mass flow meter is used to correct mass flow measurements of the flow meter. Pressure measurement can be used directly in the controlled process for other purposes that require pressure measurements in a conduit. The method and apparatus of the present invention put into operation the mass flow meter of Coriolis effect when making vibrate the flow tubes in a bending mode and in a torsion mode. Each vibration mode has a fundamental frequency associated with it. Well-known signal processing techniques are used in conjunction with detectors positioned in the flow tubes to derive the basic flow velocity as a function of the vibrations of the flow tubes. The methods of the present invention also make use of the fact that the ratio or ratio between a frequency of a first mode of vibration of the flow tubes (e.g., the frequency of the torsion mode) and a second mode of vibration of the Flow tubes (for example, the frequency of the bending mode) vary as a function of the pressure inside the flow tubes. The ratio of the two measured frequencies is used by the signal processing methods and apparatus of the present invention to determine the pressure of the material within the flow tubes. The same signal processing apparatus is used to derive the mass flow signal and to determine the pressure inside the flow tubes of the flow meter. This avoids the need for a separate pressure measuring apparatus in many material flow measurement applications. Numerous other correction factors, which include the temperature of the flow tube and the density of the material are measured by the signal processing apparatus and are used to correct the determination of the speed of the mass flow and the determination of the pressure. When determining the pressure in the flow tubes, mass flow velocity measurements can be corrected to take into account the effects of the pressure on mass flow rate measurements. The measurement of the pressure inside the flow tubes and the compensation of the measured mass flow rate to correct the effects of pressure changes on the vibration characteristics of the flow tubes allows the walls of the flow tube to be constructed of a thinner material. The flow tubes need only be thick enough to reasonably contain the static pressure of the material inside the flow tubes in operation. The walls of the flow tube need not be thickened for the sole purpose of reducing the effects of pressure changes on the mass flow rate measurements. This thinner construction allows the flow meter to maximize its sensitivity in flow measurement applications. The thinner walls of the flow tube provide better sensitivity for mass flow measurements. In particular, the construction of thinner walls allows the flow meter to measure lower mass flow rates, as is common in the mass flow measurement of low density materials. According to the present invention, the ratio or proportion of any two vibration mode frequencies can be used to determine the pressure if the two frequencies of vibrational mode coincide with certain characteristics. The two vibration modes must respond differently to changes in pressure within the flow tubes. Any two vibration mode frequencies that meet these criteria can be used to determine the pressure within the flow tubes from the ratio or proportion of the two vibration mode frequencies. Although the description that follows presents the methods of the present invention in view of two particular vibration modes (the first bending mode and the first twisting mode), other modes of vibration can satisfy this same criterion and can equally well serve to determine the pressure inside the flow meter. Also in accordance with the present invention, the pressure is derived by measuring the frequency of a single vibration mode. This can be done when one of the modes is either not subject to or unaffected by changes in mounting conditions, the temperature of the flow tubes and the density of the material.

The present invention drives the flow tubes to vibrate in the first of the phase bending mode (in the present, the bending mode) and in the first of the phase twist mode (in the present twisting mode). Depending on the needs of a particular flow meter application, the flow tubes can be driven to vibrate in both modes simultaneously or in an alternative, the tubes can be driven sequentially and repeatedly in the torsion mode followed by the bending mode . In addition, the tubes can be vibrated continuously in the bending mode for the normal mass flow measurements and be vibrated simultaneously periodically in the torsion mode in order to periodically determine the pressure and "mass flow corrections to The signal processing apparatus samples the output signals of the detectors attached to the vibratory flow tubes to isolate and measure the frequency of each vibration mode. Mass flow from the sample of the vibration signal of the bending mode as is well known in the art The ratio or proportion of the frequency of the bending mode and the frequency of the torsion mode varies, in part, as a function of the pressure of the material in the flow tubes of the mass flow meter. The signal processing apparatus calculates and uses this ratio to determine the pressure in the flow meter. Then, a correction factor of the mass flow rate is determined by using the pressure measurement. This correction factor is used by the signal processing apparatus to correct the mass flow rate. Then, this corrected mass flow rate measurement is used to control or otherwise report information concerning the flow of the process. In addition to the correction of the mass flow rate measurements, the pressure measurement of the present invention can be used per se to eliminate the need for independent pressure measuring devices. The present invention satisfies the need for a pressure measuring device in Coriolis flow meter applications where pressure measurements are also required.

BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 illustrates a typical mass flow meter coupled to mass flow instrumentation in which the methods of the present invention can be advantageously applied; Figure 2 is a block diagram illustrating additional details of the mass flow instrumentation of Figure 1; Figure 3 is a perspective view of a typical flow tube in the bending vibration mode; Figure 4 is a top view of the typical flow tube in the torsional vibration mode; Figure 5 is a block diagram illustrating the various digital filters applied to isolate and improve the signals processed by the programs in the DSP in the mass flow instrumentation of Figure 1, by using the sum / difference method of the modality preferred of the present invention; Figure 6 is a block diagram illustrating the various digital filters applied to isolate and improve the signals processed by the programs in the DSP in the mass flow instrumentation of Figure 1, which uses the fourth order filter method of the alternative embodiment of the present invention; Figures 7-9 are flow charts describing the methods of one embodiment of the present invention, which may be put into operation in the DSP of the mass flow instrumentation of Figure 1; Figure 10 is a block diagram of the driving circuit of Figure 2 isolating the frequencies desired fundamentals of vibratory flow tubes when using a sum / difference method; Figure 11 is a circuit diagram of the balanced op-amp circuit of Figure 10; Figure 12 is a block diagram illustrating the integrated circuit devices in the mass flow instrumentation of Figure 1; Figure 13 is a graph illustrating a typical relationship between the calibration factor of a flow meter and the pressure in the flow tubes of the flow meter; and Figure 14 is a graph illustrating a typical relationship between the ratio of the vibration frequency of the torsion mode with respect to the vibration frequency of the bending mode and the pressure in the flow tubes of the flow meter.

DETAILED DESCRIPTION OF THE INVENTION Overview - Coriolis Flow Meter Applications: A typical Coriolis mass flow meter 10 is illustrated in Figure 1 and has two flow tubes 12, 14 fixed to a manifold body 30 to have constants of spring and substantially identical moments of inertia around their respective bending axes out of phase W-W and W'-W. Those of ordinary skill in the art will readily recognize that the cantilevered flow meter design of Figure 1 is proposed only as an example of a Coriolis effect mass flow meter in which the methods of the present invention can be advantageously applied. invention. The methods of the present invention are advantageously applicable to flow meters having many different flow tube geometries, also as flow meters having multiple flow tubes or a single flow tube. A drive coil and magnet 20 are mounted in a region of the mid-point between the upper portion 130 and 130 'of the flow tubes 12, 14 to oscillate the flow tubes 12, 14 out of phase around the axes -W and '-W. Vibration is referred to herein as a "bending" or simply "bending mode" vibration mode. Figure 3 is a perspective view of a single flow tube 14 attached to a manifold body 30 which vibrates in the bending mode around the W axis. A pair of drive coils and associated magnets 21R and 21L are mounted on the right and left sides, respectively, of the flow tubes 12, 14 to oscillate the flow tubes 12, 14 about the central axis of each flow tube, ie, T and T ', respectively, out of phase with respect to to the sides left and right of the flow tubes. This vibration is referred to herein as "torsion" vibration mode or simply "torsion mode". Those of ordinary skill in the art will readily recognize that the drive coil and magnet 20 positioned on the upper portions 130 and 130 'can be eliminated if the drive coils and magnets 2IR and 21L are capable of driving the flow tubes 12 and 14. to vibrate in both modes. Fig. 4 is a top view of a single flow tube 12 attached to a manifold body 30 which vibrates in the torsion mode about the axis T. As indicated in Fig. 1, each flow tube 12 and 14 is driven to vibrate in the torsion mode around its own axis T and T 'respectively. The left detector 16 and the right detector 18 are mounted near the respective ends of the upper portions of the flow tubes 12, 14 to detect the relative movement of the flow tubes 12, 14. This detection is preferably carried out by means of techniques well known that apply speed detectors. The flow tubes 12 and 14 have left side legs 131 and 131 'and right side legs 134 and 134'. The side legs converge downwards towards each other and are fixed to the surfaces 120 and 120 'of the manifold elements 121 and 121'. Cross bars 140R and 140L are welded to the legs of the flow tubes 12, 14 and serve to define the axes -W and W'-W ', around which the flow tubes oscillate out of phase when the impeller 20 is energized on the path 156. The position of the shafts WW and WW 'is determined by the placement of the crossbars 140R and 140L on the lateral legs of the flow tube 131, 131' and 134, 134 '. The temperature sensor 22 is mounted on the side leg 131 of the flow 14 to measure the temperature of the flow tube and the approximate temperature of the material influencing it. This temperature information is used to determine the changes in the spring constant of the flow tubes. The impellers 20, 21R and 21L, the detectors 16 and 18 and the temperature sensor 22 are connected to the mass flow instrumentation 24 via the paths 156., 161, 160, 157, 158 and 159 respectively. The mass flow instrumentation 24 includes at least one microprocessor that processes the signals received from the detectors 16, 18 and 22 to determine the mass flow rate of the material flowing through the flow meter 10, as well as other measurements such as the density and temperature of the material. The mass flow instrumentation 24 also applies a drive signal on the path 156 to the driver or actuator 20 to oscillate the tubes flow 12 and 14 in the out-of-phase bending mode around the axes W-W and W'-W '. Additionally, the instrumentation 24 applies a drive signal on the paths 160 and 161 to the impellers 21L and 21R respectively, to oscillate the flow tubes 12 and 14 in the torsion mode about the axis W. "Those of ordinary experience in the art will readily recognize that the driver or actuator 20 can be eliminated if the impellers 21L and 21R are physically and electronically capable of simultaneously driving the flow tubes 12 and 14 in the two desired modes of vibration.Alternatively, the actuators can drive the Flow tubes sequentially in the two different modes - one mode at a time Those of ordinary skill in the art will readily recognize that, depending on the geometrical configurations of the flow tube, a single driver circuit, properly positioned on the flow tubes , it may be able to drive the flow tubes to vibrate in both modes. molding 150, 150 'is formed. The molding elements 150, 150 'can be attached to a feed conduit and outlet conduit (not shown) by the flanges 103, 103'. The body 30 of the manifold deflects the material flow from the conduit of Feed the flow tubes 12, 14 and then back to an outlet duct. When the flanges 103 and 103 'of the manifold are joined via the inlet end 104 and the outlet end 104' to a conduit system (not shown) carrying the process material to be measured, the material enters the body 30 of the manifold and the manifold member 110 through the inlet 101 in the flange 103 and is joined by a channel (not shown) having a gradually changing transverse section in the molding element 150 to the flow tubes 12, 14 The material is divided and channeled by the manifold element 121 to the left legs 131, 131 'of the flow tubes 12, 14 respectively. Then, the material flows through the upper tube elements 130, 130 'and through the right side legs 134 and 134' and is recombined into a single stream within the manifold 121 'of the flow tube. After this, the fluid is channeled to a channel (not shown) in the outlet molding element 150 'and then to the output manifold element 110'. The output end 104 'is connected by the flange 103', which has holes 102 'for bolts, to the conduit system (not shown). The material exits through the exit hole 101 'to return to the flow in the conduit system (not shown).

The mass flow instrumentation 24 analyzes the signals received on the paths 157, 158 and 159 and generates standard output signals on the path 155 to indicate the mass flow rates used by a control or operator system to verify and control the speed of the flow. mass flow through the associated conduit system (not shown). The mass flow instrumentation 24 also generates output signals on the pressure indicating path 162 within the mass flow meter. As indicated above, the pressure thus determined is used in the mass flow instrumentation to correct the mass flow rate calculations and can be used independently for other control purposes that require pressure measurements.

Overview - Effects of pressure on flow tube vibrations It is known that the mass flow rate in a Coriolis mass flow meter is proportional to Δt (the measurement of the time difference discussed above). Therefore, the mass flow rate can be expressed as: m = CF? T where CF is the calibration factor and m is the flow velocity. However, as the pressure increases or decreases within the flow tubes of the Coriolis effect mass flow meter, the stiffness of the flow tubes can change. A change in the stiffness of the flow tube affects the sensitivity of the mass flow rate of the flow meter. A change in the stiffness of the flow tube also affects the vibration frequencies of the flow tubes. The ratio or ratio between the vibration frequencies of the bending mode and the vibration mode of the flow tubes changes in response to pressure changes in the flow tubes. Accordingly, the ratio or proportion of frequencies is related to the pressure within the flow tubes (also as a variety of other factors). Figures 13 and 14 are graphs of empirical mass flow meter data of Coriolis effect in operation, illustrating the effects described above. Figure 13 is a graph illustrating the typical effects of pressure on the calibration factor of the flow meter. Graph 1300 shows the calibration factor of the meter on the y-axis as a function of the pressure inside the flow tubes on the x-axis. The plotted data points 1302, 1304 and 1306 are measured data from a Micro Motion D300 flow meter in operation (modified to provide additional drive coils for the application of torque drive force also as bending actuation force). It can be seen in graph 1300 that the calibration factor increases as the pressure in the D300 flow tubes increases. Figure 14 is a graph illustrating the typical effects of pressure on the ratio or frequency ratio of the flow tubes. Graph 1400 shows the ratio or proportion of vibration frequencies of the torsion mode with respect to the vibration of the bending mode on the y-axis as a function of the pressure within the flow tubes on the x-axis. Curves 1402 and 1404 are adjusted to the measured data points of a CMF300 Micro Motion mass flow meter in operation (modified to provide additional drive coils for the application of torsion drive force also as bending drive force). Specifically, curve 1402 is adjusted with measured data points as water is flowed through the flow meter CMF300 and curve 1404 is adjusted with measured data points as corn syrup is flowed through the meter of flow CMF300. It can be seen in curves 1402 and 1404 of graph 1400 that the frequency relationship is affected by the pressure within the flow tubes (also as by the density of the material flowing therein).

As shown in Figure 14, the density of the material affects the ratio or proportion of frequencies. Also, it can be shown that the temperature and mounting parameters of the flow tubes can affect the determination of the frequency ratio. These factors can be easily characterized and compensated by the mass flow meter calibration, as used in a particular application. The proportion of frequencies with these compensations applied to them is therefore usable as an indirect measure of the pressure in the flow tubes of the mass flow meter in operation. The details of the required compensation are provided later herein. Once the frequency ratio has been adjusted properly it is used to determine the corresponding pressure inside the flow tubes. Curve adjustment techniques or table consultation and interpolation numerical techniques can be applied to calculate the pressure given the compensated frequency ratio. The pressure thus determined can be used, per se, as a direct pressure measurement for applications requiring such pressure determinations. In addition, the pressure thus determined is used to correct the calibration factor of the mass flow meter to correct by this the measurements of mass flow velocity thereof. The pressure is used to determine a pressure correction factor that is then applied to correct the mass flow determination. Therefore, the mass flow rate within the vibratory flow tubes is determined as: m = CF CP? T where CF and? T are as described above and CP is a pressure correction factor. This pressure correction factor is determined in the calibration of the mass flow meter and is calculated as a function of the pressure calculated as follows: CP = 1 + ((Kp / 100) (P + Po)) where Kp is a pressure calibration factor (expressed as a percentage per psi (pounds / square inch) of pressure), P is the pressure (determined as indicated above) within the flow tubes and P0 is the pressure in the line calibration (that is, the nominal pressure used to calibrate the flow meter for normal operation in your proposed application). The calibration factor of the pressure Kp and the pressure of the calibration line P0 are determined by means of standard or in situ factory calibration techniques, well known to those of ordinary skill in the art.

General view - Mass flow instrumentation The present invention comprises digital signal processing methods that can be put into operation in a digital signal processor chip (DSP) to carry out the calculation functions in the mass flow instrumentation 24. Discrete samples of the analog signals generated as output or result of each of the detectors of the flow tube are taken. The discrete samples of the left and right detectors are digitized by the use of standard analogue to digital (A / D) conversion devices. Once digitized, additional processing of the samples is carried out by means of digital signal processing methods on the DSP chip. The digital signal processing programming elements (discussed later herein) can be put into operation in the instrumentation 24 of the mass flow shown in greater detail in Fig. 12. The digital signal processor 1200 of Fig. 12 is a device of calculation very similar to any common microprocessor, but with functions of special purposes tuned for the application to tasks of signal processing. Many such DSP processor devices are known to those skilled in the art. An example of such a device is the TMS 320C31 from Texas Instruments. This device includes a floating point processing unit based on physical elements to improve the performance of the signal processing calculations. Those skilled in the art will readily recognize that fixed point signal processing devices can be employed in conjunction with programming element emulation libraries for precision floating point calculations where, for example, application cost conditions In particular, they are more important than performance considerations. The processor 1200 reads the program instructions from the program ROM 1202 in the distribution bar 1252 and manipulates temporary and intermediate data and memories in the RAM 1204 in the distribution bar 1254. The skilled artisan will recognize that, depending on the various cost and performance factors, it may be preferable under certain circumstances to copy the program instructions from ROM 1202 to RAM 1204 to improve the performance of processor 1200 in search instructions. Each of the A / D converters 200 receives an analogous signal from their respective output signals from the flow tube detector applied to the paths 157 and 158 respectively. The processor 1200 applies signals of control to the A / D converters 200 on the paths 250 and 252 respectively and receive values of digitized samples of the A / D converters 200 on the paths 250 and 252 respectively. One skilled in the art will readily recognize that the synchronization or clock signals required by the various components can be generated by any of the well-known timing or clock generation techniques, such as crystal controlled oscillators or any of the various integrated circuits. of commercially available synchronization or clock generation. In the preferred embodiment, the A / D converters 200 are implemented in a single integrated circuit with multiple converters and a single communication busbar connection to the DSP processor. This helps to ensure that the phase relationship between the two sampled signals is due to the Coriolis effects of the vibratory flow tubes, rather than the effects of channeling the signal traces on a printed circuit board to physically separate the circuits of the A / D converter. Many such stereo A / D converter chips are known to those skilled in the art. An example of such a chip is the Crystal Semiconductors CS5329, a two-channel stereo A / D converter device.

The processor 1200 determines a value of τ from the phase difference between the sampled channels and applies a signal proportional to τ to the path 1256. The D / A converter 1206 converts the value of the digital signal applied to the path 1256 to an analogous signal proportional to the mass flow rate applied to the path 155. The processor 1200, according to the present invention, also determines the pressure in the mass flow meter of Coriolis effect from the sampled channels and applies a signal proportional to the pressure to the path 1260. The D / A converter 1210 converts the value of the digital signal applied to the path 1260 to an analogous signal proportional to the pressure applied to the path 162. The signals in the paths 155 and 162 they are applied to the means of use (not shown) appropriate to the particular flow meter measurement application. The driving circuit 1208 receives the analog signals applied to the paths 157 and 158 generated by the detectors of the left and right channel. The driving circuit 1208 isolates the frequency of the bending mode and the frequency of the torsion mode. The drive circuit 1208 determines the sum of the left and right channel signals, as well as the difference between the left and right channel signals to isolate the frequency of bending mode of the torsion mode frequency. The signals applied to the left and right channel signal paths induced by the bending mode vibrations are substantially in phase while the signals induced thereon by the torsion mode vibrations of the flow tubes are substantially out of phase. phase (approximately 180 °). Accordingly, the sum of the left and right channel signals therefore has a strong frequency component in the bending frequency and a frequency component significantly decreased in the torsional frequency. Conversely, the difference between the signals of the left and right channel has a strong frequency component in the frequency of the torsion mode and a frequency component significantly decreased in the frequency of the bending mode. Figures 10 and 11 describe the driver circuit 1208 in further detail. The balanced op-amp circuit 1008 of FIG. 10 combines the signals of the left and right channels to produce the sum and difference of the signals as described above. Graphs 1000 and 1004 on path 157 illustrate the superposition of the vibrations of the bending mode and the bending mode respectively on path 157. Likewise, graphs 1002 and 1006 illustrate the superposition of the bending mode and bending mode vibrations respectively in path 158. It will be noted that graphs 1000 and 10002, which illustrate the signals induced by vibration in the bending mode are substantially in phase, while graphs 1004 and 1006, which illustrate the signals induced by the vibration in the torsion mode are substantially out of phase. The graph 1010 illustrates the sum of the left and right channel signals produced by the op-amp circuit 1008 and applied to the path 156, while the graph 1012 illustrates the difference of the right and left channel signals produced by the circuit balanced op-amp 1008 and applied to paths 160 and 161. The skilled artisan will recognize that the signals applied to paths 156, 160 and 161 must be amplified and conditioned before being applied as signals from the driver or actuator to the meter. flow 10. It will be noted that the frequency illustrated in graph 1010 is the frequency component of the bending mode, of the signals of the left and right channels, while the frequency illustrated in graph 1012 is the frequency component of the mode torsion of the same signals. The sum / difference method of the circuit 1008 isolates the two components of the superimposed signals in each of the channels. The Figure 11 shows the cascaded op-amps comprising the balanced op-amp circuit 1008 of Figure 10. Those skilled in the art will readily recognize digital processing techniques equivalent to the driving or driving circuit 1208 discussed above. The overall design of the driving or actuator circuit 1208 discussed above depends on the fact that the detector output signals from the flow tube detectors are 180 ° out of phase with respect to one another with respect to the vibrations of the mode. of torsion, while the signals of the detector are in phase with respect to the vibrations in the bending mode. This fact allows the use of the analog sum / difference circuit design discussed above to isolate the two vibration mode frequencies superimposed on the output signals of the detector. Digital variants of the analog circuit will be apparent to those of ordinary skill in the art. In addition, other modes of vibration can be employed by the methods of the present invention, in which the phase relationships of 0 ° and 180 ° indicated above may not exist. In such cases, well-known digital signal processing techniques can be employed to provide the isolation of the various vibration mode frequencies and for the generation of appropriate drive signals.

Signal Processing Methods - Frequency Determination: Figure 2 illustrates the general structure of and associated flow of information in the instrumentation 24 of the flow meter of the present invention and in particular the flow of information and calculations in the DSP 1200. The electronic components of the meter of the present invention consist of two essentially identical "channels": a first channel for processing the output signal of the detector of the left flow flow tube and a second channel for processing the output signal of the tube detector of right flow. The two "channels" are fundamentally symmetrical, except with respect to the adaptation of the weight of the notch filters as discussed hereinafter. The following discussion is presented in terms of a typical Coriolis flow meter application in which the fundamental frequency of the vibratory flow tubes in the bending mode is approximately 100 Hz. A frequency of the typical torsion mode corresponding to this exemplary bending mode frequency may be, for example, about 250 Hz. Other flow tube configurations may vibrate at other frequencies corresponding to other proportions which may be similarly useful for determining the pressure and correct the measurements of the mass flow rate of the same. Accordingly, it will be readily recognized by those of ordinary skill in the art that the apparatuses and methods of the present invention can be applied to many combinations of vibration modes and frequencies. The calculations carried out by the DSP 1200 are shown as elementary calculation blocks in the DSP 1200 in Figure 2. Many of the calculation elements discussed hereinafter operate in synchronization with the synchronization or clock signals associated with the various samples of the output signals of the flow tube detector. CLOCK 214 of Figure 2 provides synchronization signals associated with the various sampling rates of the calculation elements discussed hereinafter. It will be understood that the clock or synchronization signals required for the operation of the signal processing methods in the mass flow instrumentation 24 are fed as appropriate by the CLOCK 214. Timing or synchronization of the various calculations in the illustrated elements in figure 2 they can be "synchronized" (or combined in gate) additionally by the availability of signals from a previous calculation stage. In other words, each calculation block illustrated in the DSP 1200 of Figure 2 can operate synchronized with respect to the data availability of a previous calculation. Therefore, CLOCK 214 conceptually feeds synchronization or timing for all calculations, since all the calculation elements depend on previous intermediate calculations, which in turn depend on the precisely synchronized digitized samples generated by the A / A converters. D 200. The data paths indicated in FIG. 2 that join the various calculation elements to the interior of the DSP 1200 represent the passage of data from one calculation element or stage to another. Those of ordinary skill in the art will readily recognize that equivalent calculations can be factored in a variety of similar ways, so that different intermediate stages of the calculations can be shown as they pass between the various calculation elements. The particular decomposition of the calculations in the elements shown as blocks in Figure 2 is a matter of choice for discussion clarity. The precise methods are discussed later in the present with respect to the flow diagrams of Figures 7-9. The CLOCK 214 feeds a periodic pulsed signal synchronization to the A / D converters 200 on the path 270, to determine the speed of taking of samples of the raw (unprocessed) signals generated by the flow tube detectors. Each A / D converter 200 samples its corresponding analog signal and converts the sampled value to a digital form once for each signal pulse applied to the path 270 by the CLOCK 214. This clock or synchronization signal applied to the A / D converters 200 on path 270 must have a highly accurate frequency to allow sampling of output signals from the flow tube detector at a fixed sampling rate, as required for the processing of the sample. present invention. This accuracy of clock pulse or synchronization is preferably obtained by the use of a crystal-controlled clock. To the extent that the CLOCK 214 is programmable by nature, the DSP 1220 schedules the operation parameters of the CLOCK 214 by means of appropriate registers of the CLOCK 214. The output signal of the detector 18 of the right flow tube of Figure 1 is applied to the A / D converter 200 on the path 158 of FIG. 1. The output signal of the detector 16 of the left flow tube of FIG. 1 is applied to the A / D converter 200 on the path 157 of FIG. 1. The A / D converter 200 samples and converts the analog signals of the flow tube detectors to digital values. The A / D converters 200 operate in response to the fixed frequency periodic clock signal defined in the path 270 fed by a broad CLOCK 214 of the system. The converted digital value, corresponding to the detector output of the right channel, is applied on the path 252 to the decimation filter element 202: 48: 1. The 48: 1 decimation filter elements 202 are operable in the DSP 1200 in response to each sample received from the A / D 200 converters in the channels. The decimation filter elements 202 reduce the number of samples by a factor of 48, while providing significant anti-alias filtration of the values of the sampled signal. Those of ordinary skill in the art will recognize that the particular decimation ratio of 48: 1 is a matter of design choice that depends on the particular application environment. The decimation filter element 202 of 48: 1 is made in two stages, a step of 8: 1 followed by a step of 6: 1. Both stages of the decimation filter element 202 are preferably implemented as finite impulse response (FIR) antialias filters. Preferably, FIR filters are designed and implemented through the use of the well-known Remez algorithm, which generates an optimal filter. Those of ordinary experience in the art will recognize that an infinite impulse response filter (IIR) can also be used for the decimation stages.

The use of FIR against IIR is a matter of design choice based on the calculation complexity and the relative power of the calculation elements used in a particular design. The first stage of the decimation filter element 202 performs a reduction of 8: 1 in the sampling rate from approximately 39.1 KHz to approximately 4.9 KHz. For this first stage, the pass band or passband ends at approximately 300 Hz and the suppressed band or blocking band (band of attenuated or non-transmitted frequencies) begins at approximately 2319 Hz. The pass band of the first stage has a weight of 1 and the suppressed or blocking band has a weight of approximately 104. The center has a length of 72. The second stage of the decimation filter element 202 carries out a reduction of 6: 1 at the sampling rate of approximately 4.9 KHz to approximately 814 Hz. For the second stage, the pass band ends at approximately 300 Hz, the suppressed or blocking band starts at approximately 400 Hz, the pass band has a weight of 1, the blocking band has a weight of 104 and the center has a length of 181. The coefficients of the center for the decimator filter of the first stage are preferably: -0.000000-817645.24630121 0.00000698245451987758 0.00001773963885136871 0.00003898240757193200 0.00007548672488844681 0.00013409289751968492 0.00022348636822400024 0.00035427612800655528 0.00053901217722666664 0.00079209847140532400 0.00112956940174060416 0.00156872083590591968 0.00212758437199228352 0.00282427204255895904 0.00367616275994291200 0.00469898731907314112 0.00590584018301447296 0.00730617267761646208 0.00890478563478318592 0.01070092291349931840 0.01268750876431035520 0.01485057644139987840 0.01716893380830959680 0.01961418511740982400 0.02215097935643592320 0. 02473769406056195200 0.02732738160877671360 0.02986905691870672640 0.03230924399368606080 5 0.03459371442646413440 0.03666937963516617600 0.03848619661702702080 0.03999905354911612160 0.04116950605355454720 0.04196728384459161600 0.04237150120084636160 0.04237150120084636160 0.04196728384459161600 0.04116950605355454720 0.03999905354911612160 0.03848619661702702080 0.03666937963516617600 0.03459371442646413440 0.03230924399368606080 0.02986905691870672640 0.02732738160877671360 0.02473769406056195200 0.02215097935643592320 0.01961418511740982400 0.01716893380830959680 0. 01485057644139987840 0.01268750876431035520 0.01070092291349931840 0.00890478563478318592 0.00730617267761646208 0.00590584018301447296 0.00469898731907314112 0.00367616275994291200 0.00282427204255895904 0.00212758437199228352 0.00156872083590591968 0.00112956940174060416 0.00079209847140532400 0.00053901217722666664 0.00035427612800655528 0.00022348636822400024 0.00013409289751968492 0.00007548672488844681 0.00003898240757193200 0.00001773963885136871 0.00000698245451987758 -0.00000081764524630121 center The coefficients for the decimating filter of the second stage are preferably: 0.00000442476810646958 0. 00000695183248940121 0.00000923764143759751 0.00000714413514201519 -0.00000492704497770928 - . 5 -0.00003489048179859716 -0.00009263530705114960 -0.00018905831520468072 -0.00033444730957182660 -0.00053626977796454416 10 -0.00079662003202712672 -0.00110972681566274544 -0.00146004062478959264 -0.00182142399675758176 -0.00215800240585865472 15 '-0.00242694602625900160 -0.00258321531356594560 -0.00258595488430649824 -0.00240572194854850240 -0.00203154744227315104 20 -0.00147645851005435168 -0.00078021447557776288 -0.00000817274057693339 0.00075426709707067504 0.00141150795697302464 0.00187095161052143488 0. 00205783908806485888 0.00192943571960413760 0.00148598692512453856 0.00077606363427304864 -0.00010548433903324906 -0.00102764398217807344 -0.00184078746460040160 -0.00239957337125188800 -0.00258787044696211360 -. 10 -. 10 -0.00234158106765920384 -0.00166505851114574304 -0.00063743956961237104 0.00059343304869999640 0.00182986089451760448 0.00285400415538192992 0.00346436214815012608 0.00351321839727078272 0.00293841932540287360 0.00178313427507570240 0.00019874998215256696 -0.00157142938076768256 -0.00322673006618933952 -0.00445756082164491968 -0.00500041373054022336 -. 25 -. 25 -. 25 -0.00469011227472791616 -0.00349953894849836288 -0.00155835913437617184 0.00085478554892281696 0.00334786697510189632 0.00547518370123789568 0.00681278906253363456 0.00703755587107394560 0.00599594663350389504 0.00374906069643158208 10 0.00058348227032761616 -0.00301740455601272832 -0.00644042362264125952 -0.00903974843902937216 -0.01024986918050410880 15 -0.00969589010450159232 -0.00728139494412460544 -0.00323617204253763328 0.00188855897383295168 0.00728184827350282496 0.01198668054361748960 0.01505134116424442240 0.01569656324736917120 0.01347199361008710720 0.00837503599972582272 25 0.00090911821339905088 -0.007933752759778378240 -0.01676840904279348800 -0.02398607719808193280 -0.02796978000715982080 - . 5 - . 5 -0.02733379993624548160 -0.02114770650772032640 -0.00911189426247965824 0.00834468626759415936 0.03006335482259185280 0.05425620094049752960 0.07869841218265049600 0.10098866498628454400 0.11884306255675470400 0.13038232897640233600 15 0.13437210128885929600 0.13038232897640233600 0.11884306255675470400 0.10098866498628454400 0.07869841218265049600 20 0.05425620094049752960 0.03006335482259185280 0.00834468626759415936 -0.00911189426247965824 -0.02114770650772032640 -0.02733379993624548160 -0.02796978000715982080 -0.02398607719808193280 -0.01676840904279348800 -0.00793352759778378240 5 0.00090911821339905088 0.00837503599972582272 0.01347199361008710720 0.01569656324736917120 0.01505134116424442240 10 0.01198668054361748960 0.00728184827350282496 0.00188855897383295168 -0.00323617204253763328 -0.00728139494412460544 fifteen - . fifteen - . 15 -0.00969589010450159232 -0.01024986918050410880 -0.00903974843902937216 -0.00644042362264125952 -0.00301740455601272832 20 0.00058348227032761616 0.00374906069643158208 0.00599594663350389504 0.00703755587107394560 0.00681278906253363456 25 0.00547518370123789568 0. 00334786697510189632 0.00085478554892281696 -0.00155835913437617184 -0.00349953894849836288 -0.00469011227472791616 -0.00500041373054022336 -0.00445756082164491968 -0.00322673006618933952 -0.00157142938076768256 10 0.00019874998215256696 0.00178313427507570240 0.00293841932540287360 0.00351321839727078272 0.00346436214815012608 15 0.00285400415538192992 0.00182986089451760448 0.00059343304869999640 -0.00063743956961237104 -0.00166505851114574304 twenty - . twenty - . 20 -0.00234158106765920384 -0.00258787044696211360 -0.00239957337125188800 -0.00184078746460040160 -0.00102764398217807344 25 -0.00010548433903324906 0. 00077606363427304864 0.00148598692512453856 0.00192943571960413760 0.00205783908806485888 0.00187095161052143488 0.00141150795697302464 0.00075426709707067504 -0.00000817274057693339 -0.00078021447557776288 -0.0014.7645851005435168 -0.00203154744227315104 -0.00240572194854850240 -0.00258595488430649824 -0.00258321531356594560 -0.00242694602625900160 -0.00215800240585865472 -0.00182142399675758176 -0.00146004062478959264 -0.00110972681566274544 -0.00079662003202712672 -0.0005362697779.6454416 -0.00033444730957182660 -0.00018905831520468072 -0.00009263530705114960 -0.00003489048179859716 -0.00000492704437770928 0.00000714413514201519 0.00000923764143759751 0.00000695183248940121 0.00000442476810646958 The left channel, comprising the A / D converter 200 and the decimation filter element 202 connected via path 250 operates identically to the right channel discussed above. The A / D converter 200 receives the signal generated by the left detector 16 on the path 157, converts the analog signal to digital form and applies the digital value on the path 250 to the decimation filter 202 for the left channel. The output of the decimation filter element 202 for the left channel applies its output signal to the path 254 for further processing and for the right channel to apply its output to the path 256 for further processing. The calculations of the decimation stages preferably use a floating-point arithmetic to maintain the required calculation accuracy. Subsequent calculations for notch filtration, phase calculations, t calculations and mass flow rate calculations, are also carried out in preference to using floating-point arithmetic due to the wide range of Calculation scaling involved with more complex functions. The digitized, decimated, anti-alias signal values for the right channel are applied on the path 256 to the frequency / phase calculation element 204. Also, the digitized, decimated, anti-alias signal values for the left channel are applied on the path 254 to the frequency / phase calculation element 204. The frequency / phase calculation element 204, discussed in detail later herein, improves the values of the signal. This process isolates the signals generated by the vibration movements of the bending mode of the flow tubes of the various harmonics, noise and of the vibration movements in torsion mode. The frequency / phase calculation element 204 removes a frequency band (a notch) centered around the fundamental frequency of the flow tubes vibrating in the bending mode. The resulting signal represents all the noise outside the notch centered around the fundamental frequency of the flow tubes vibrating in the bending mode. Then, this noise signal is subtracted from the signal applied as input to the frequency / phase calculation element 204 on the path 256, which is the sum of the fundamental frequency and all the noise not filtered by the decimation filter element 202. . He The result of the subtraction or subtraction, which represents the fundamental frequency of the filtered vibratory flow tubes of most of the noise signals, is then applied to the path 262 as the output or result of the frequency / phase calculation element 204. The indicator values of the phase of each of the output signals of the left and right channel are generated in the frequency / phase calculation element 204 and are applied to the trajectories 260 and 262 respectively to the calculation element 208 of? T. The parameters (factors or weighting coefficients and the depolarization parameter) of the frequency / phase calculation element 204 determine the characteristics of the notch, that is, the shape of the notch (bandwidth of the rejected frequencies) and the fundamental frequency at which the notch is centered. The parameters are calculated by means of weight adaptation or weighting elements in the frequency / phase calculation element 204. The calculations required for the adaptation of the notch filters are discussed in further detail later herein. The shape of the notch and the fundamental frequency around which the notch is centered can be adapted to track or track changes in the fundamental frequency. The shape of the notch determines the speed with which the notch filters can track or track changes in frequency fundamental. A wider notch provides less filtering, but can be adjusted more quickly to changes in the fundamental frequency. A narrower notch converges more slowly to changes in the fundamental frequency, but provides superior filtering of the detector's input signals. In the preferred embodiment, it is believed that the shape of the notch does not need to be altered. Empirical data reveal that programmable filters are capable of normal tracking of changes in their respective input signals, without the need to alter the shape of their respective notches. The weight adaptation parameters calculated in the frequency / phase calculation element 204 are applied to the left channel and the right channel such that both output channels of the detector signal are processed identically. The use of a single set of parameters applied to the left and right channels serves to maintain the critical phase relationship between the two channels. This relationship is used to calculate the value of? T that is proportional to the mass flow rate. The fundamental frequency of the vibrations of the flow tube in the bending mode is calculated by the frequency / phase calculation element 204 and is applied to the path 266 as an input to the calculation element 208. ? t. The improved signals are further processed by a Goertzel filter, in the frequency / phase calculation element 204, to determine the phase of the signals, as required for the calculation of? T unavoidable by the element 208. The indicator values of the phase of the tubes vibrating in the bending mode are generated in the element 204 of the frequency / phase calculation and applied to the paths 260 and 262 corresponding to the left and right channels respectively. The phase calculations in element 204 use Fourier transform techniques with two Hanning windows to determine the phase of the filtered signals. The length of a window is a function of the fundamental frequency of the nominal or expected flow tube. The length of a window determines a variety of oscillation cycles of the flow tubes in which the samples are collected and weighted to determine the phase of the flow tubes. The expected frequency of the flow tube can be programmed into the electronic components of the present invention at the time of manufacture or it can be entered as a parameter at the particular installation / application site or can be determined by the operation of the flow meter and the appropriate measurements. The length of a window represents an exchange between the response time and the rejection of noise due to leaks. A larger number of accumulated cycles to determine the phase provides additional rejection of noise, but requires additional delay and therefore slows the response to changes in the vibration phase relationship of the flow tube. Fewer samples reduce the delay and therefore improve the response speed to the vibration phase changes of the flow tube, but provide a lower rejection of the noise. Eight flow tube cycles are selected as the preferred length of the window, as measured in cycles. Assuming a given expected frequency, the preferred window size (2N) is determined as: window_length = 2 floor (3200 / tube_waiting_waiting) where floor (x) is the largest whole number less than or equal to x. The Hanning window is represented as a vector of weights to be applied to the discrete samples over the period of a Hanning window. Where 2N is the number of discrete samples within a period of the Hanning window, the weight for the k-th discrete sample, where k fluctuates from 0 to 2N-1 is determined as: h (k) = (1 - eos (2pk / (2N - 1))) A half-window signal condition is determined (in the methods of the programming elements of the present invention) each N shows discrete (where a complete Hanning window of the output signal of the sampled detector has 2N of discrete samples in a single period) for purposes discussed in more detail later in the present concerning the parallel calculations of overlapping Hanning windows. In addition, a countervariable (eg, called SAMPNO in the methods of the present invention) counts the index of the sample number in a currently sampled Hanning window (eg, as a function of modulo N from 0 to N-1). The SAMPNO counter-variable is increased with the processing of each improved sample of the frequency / phase calculation element 204. When SAMPNO reaches N-l, the next sample value resets SAMPNO to zero. The half-window signal corresponds to the fact that the SAMPNO counter is equal to zero. In the preferred embodiment of the present invention, the SAMPNO counter is implemented in programming elements that count the number of detector output values sampled, decimated, discrete, processed during a Hanning window. Those of ordinary skill in the art will recognize many equivalent structures and functions to implement this function, either in a design of programming elements or in equivalent circuit structures. The signal samples at the edges of each window are given smaller weights than those towards the middle part of the window. To use the available data more fully, two Fourier calculations are made simultaneously, in such a way that the windows overlap by one half of a window length. Therefore, new Fourier phase measurements are produced for each channel every half window of samples. The use of a constant window size in the present invention allows the Hanning window weights to be pre-calculated before the flow measurements begin. When used in conjunction with a discrete time Fourier transform (DTFT), as in the present invention, the size of the window determines the sharpness of the frequency discrimination characteristic of the DTFT filter output and thus the rejection of noise, pseudo-harmonics and leaks. A larger window size provides a slower filter response to phase changes. The size of the window, as determined above, represents the best known approximation suitable for balancing competing objectives of improved frequency discrimination and noise rejection, against rapid response to changes of phase. The preferred window size can be changed for different applications of the flow meter, to optimize certain environmental conditions. The phase calculations carried out in the frequency / phase calculation element 204 sum the sampled, discrete, filtered values to generate a complex number indicating the phase of the detector output signal, filtered, sampled. This complex number is used in subsequent calculations. Specifically, a Fourier transform of the Goertzel filter is applied to each Hanning window of sampled, discrete, filtered detector output signal values to determine the Fourier component in the frequency of the bending mode of both channels. left. The coefficients of the Goertzel filter are determined by the frequency calculations in the frequency / phase calculation element 204, based on the average of the RML bending frequency coefficient (discussed later herein) for the preceding Hanning half-window of improved signal values. The phase calculations for the left channel and for the right channel operate identically. The calculation element 208 of? T determines the time delay resulting from the phase difference between the output signals of the left and right detector, such as received from the element 204 via the paths 260 and 262. The time delay thus determined is used in conjunction with the frequency estimates of the vibrations in bending mode of the flow tubes received from the element 204, via the path 266 , to determine the mass flow rate of the material flowing through the flow tubes of the Coriolis flow meter. The Fourier component (a complex number phase indicator) of the left channel (received by the calculation element 208 of? T on the path 260) is multiplied by the conjugate of the Fourier component of the right channel (received by the element 208 of calculation of? t on trajectory 262). Then, the angle of the complex result is calculated. This angle of the phase difference is divided by the tube frequency of the flow tubes vibrating in bending mode (received by the calculation element 208 from? T on the path 266 and converted to appropriate units to correspond with the measurements phase) to produce a value of? t. The value of? T thus determined by the calculation element of? T 208 is applied to the mass flow calculation element 290 on the path 294. The mass flow calculation element 290 determines the mass flow rate of the material that flows through the flow meter in proportion to the value of? t applied to its input path 294. As is known in the art, the mass flow rate calculations can be corrected for temperature variations, as detected. by the detector 22 and transmitted to the mass flow calculation element 290, via the path 159. The mass flow rate determined by the mass flow calculation element 290 is further corrected by the measurement value of the pressure applied to its input path 162. Then, the corrected mass flow rate is applied, via the output path 155, to a utilization means 292 that uses the corrected mass flow rate for the control of the fundamental process. In addition to the determination of the mass flow rate from the vibration in flex mode of the flow tubes (as summarized above), the torsion mode vibration of the flow tubes is used by the calculation elements in the mass flow instrumentation 24 to determine the pressure in the flow meter. As indicated above, the pressure in the flow meter can affect the accuracy of flow rate measurements. The measurement of the pressure in the mass flow instrumentation 24 is used, therefore, to correct the mass flow rate calculations summarized above. The sampled, decimated values of the left and right channels are applied, via the paths 254 and 256 respectively, to the frequency / phase calculation element 204, as discussed above. The frequency / phase calculation element 204 improves the values of the sampled signal, decimated, of each channel, to isolate the signals generated by the vibration movements in torsion mode of the flux tubes of the various harmonics, noise and the vibration movements in bending mode. The frequency / phase calculation element 204 determines the fundamental frequency of the torsion mode vibrations of the flow tubes and applies that frequency to the path 264. Similarly, the frequency / phase calculation element 204 determines the fundamental frequency of the vibrations in bending mode of the flow tubes and applies that frequency to the path 266. The element 212 for calculating the frequency and pressure ratio receives the frequencies thus determined via the paths 264 and 266 and determines the pressure in the flow meter as a function of the proportion of the two frequencies.

Frequency / phase filtering methods: The frequency / phase calculation element 204 of FIG. 2 is adapted to improve the signals generated by the left channel motion detector and the right channel movement detector attached to the flow tubes vibratory The shape of the notch (eg, the width of the notch frequencies) and the center frequency of the notch are adaptable by weighting or weight calculations in the frequency / phase calculation element 204 of FIG. 2. In FIG. Preferred embodiment of the present invention, the shape of the notch in the various notch filters (ie, the notch width or pitch width) need not be altered in order to ensure the tracking of reasonable changes which they can be expected in their respective entrance signs. Figures 5 and 6 show further details of two embodiments of the phase frequency calculation element 204 of Figure 2. The frequency / phase calculation element 204 of Figure 2 comprises a network of digital notch filters and pass filters. of digital bands together with appropriate adaptation calculation elements to adapt the various digital filters to the changes in the frequencies in the bending mode and the torsion mode. The various digital filters are arranged in cascade to allow a rapid convergence of the filter parameters in response to the changes in the central frequency of the respective filters, while maintaining a highly accurate digital filtering of the signals. In general, a notch filter is used that has a wide frequency response (the so-called "low Q") in conjunction with a fast conjugate gradient algorithm (FCG) to adapt the filter coefficients. This combination is referred to herein as an "FCG filter". The FCG filter processes the incoming signals from the left and right detector channels and quickly converges them to an estimated value of the fundamental frequencies (vibration frequencies, bending and torsion mode). The digital notch filters and the digital bandpass filters are then adapted to focus on the estimated fundamental frequencies derived from the digital processing of FCG, to improve each of the two fundamental frequencies. Then, the recursive maximum probability algorithm (RML) is used in conjunction with digital filters that have a narrower frequency response (the so-called "high Q") to further refine the response of digital notch filters and pass filters band to improve by this their respective input signals. RML filters accurately determine the frequencies of the bending and torsion mode of the flow tubes and apply these frequencies to the output paths of the frequency / phase calculation element 204 for further processing by the pressure calculation element 212 of FIG. 2. In addition, the frequencies of the bending mode of the output signals of the The left and right channel detector, as improved by digital filtering in the frequency / phase calculation element 204, are applied to a Goertzel filter in the element 204 for the phase measurement calculations. The phase values of the left and right channel detector output signals corresponding to the vibrations in the flexure mode of the flow tubes are applied to the output paths of the frequency / phase calculation element 204 for further processing by means of the calculation element 208 of? t of figure 2.

Frequency / phase filtering methods - preferred mode of addition / difference Figure 5 is a block diagram describing the details of the frequency / phase calculation element 204. As illustrated in FIG. 5, second-order digital filters are used with a "sum / difference" method to isolate the signals induced by the bending mode vibration received from the detector detectors. left and right channel in the trajectories 254 and 256 respectively of the signals induced by the vibration in torsion mode superimposed. The sum / difference method uses the known symmetries of the bending mode vibrations and the torsion mode to separate the two vibration modes from the signals received in the paths 254 and 256. The vibrations of the torsion mode of the tubes of flow appear in the detectors of the left and right channel substantially out of phase, while the vibration in flex mode of the flow tubes appear substantially in phase in the two channels. Thus, when summing the corresponding sampled values of the left and right channels, the resulting signal is reinforced with respect to the vibrations of the bending mode, while the components of the vibrations of the torsion mode are diminished. It is said that the summed signal values have a strong component in the vibration components of the bending mode. Conversely, the difference between the output signals of the two channels (the signal of the left channel minus the signal of the right channel) has a strong component of the torsion mode and a component of the bending mode decreased. By thus separating the two superimposed sinusoids, an estimated value of the frequency of each vibration mode can be easily derived for the control of the various digital notch filters and filters of digital bandpass used to improve the signals. The signal values of the left channel detector are received on the path 254 in FIG. 5 and the values of the channel of the right detector are received on the path 256. The two values are summed by the union of sum 504 and the resulting sum ( also referred to herein as L + R) is applied to the path 554. In addition, the difference between the signal values is calculated by adding the junction 516 and the resulting difference (also referred to herein as LR) is applied to the trajectory 570. The sum of signals, L + R is applied to the path 554 to the fast conjugate gradient filter 511 (FCG) which estimates approximately the frequency of the vibrations of the flexure mode of the flow tubes. Although the estimate value is raw, due to the lack of filtering of the input signal, the estimated value of the FCG filter 512 converges rapidly in response to changes in the frequency of vibration in the bending mode. The estimated value of the frequency of the flexure mode of the FCG filter 512 is then applied to the path 560. The estimated values of the frequency, as calculated by the FCG and RML filters, are represented as a frequency coefficient "a" related to the frequency in the form: a = -2 eos (? Ts) where? is the frequency and T3 is the sampling period (decimated). These values are in the form necessary to tune the second-order and bandpass notch filters used in the preferred embodiment of Figure 5 and the modality of Figure 6. Use of this form avoids the frequent need for conversions. trigonometric complex calculation. The signal difference, LR is applied on the path 570 to the notch filter 518. The signal difference LR has a strong frequency component in the torsion mode of the flow tubes and has a significantly decreased frequency component in the mode of flexion. The notch filter 518 is adjusted to suppress the remnants of the vibration frequency in bending mode of the L-R signal applied to its input. The center frequency of the notch is fed as a parameter on the path 560 of the estimated frequency generated by the FCG filter 512. The vibration component of the isolated torsion mode of the flow tubes is applied as the outlet of the notch filter 518 to path 568. The sum of signals L + R in path 554 is also applied to the input of filter 506 of passage of band. The sum of L + R signals has a strong frequency component in the bending mode and a significantly reduced frequency torque component. The bandpass filter 506 passes a frequency range centered around the frequency of the bending mode estimated by the FCG filter 512 and applied to the bandpass filter 506 as a parameter on the path 560. The mode component The bending filter isolated from the flow tubes is applied as an output of the bandpass filter 506 to the path 556. The FCG filter 514 receives in the path 568 the isolated torque mode component generated by the notch filter 518. The FCG filter 514 estimates the vibration frequency of the torsion mode and applies the estimated value to the trajectory 562 as its output or result. This estimated value of the frequency of the torsion mode of the vibratory flow tubes is received via the path 562 as the central frequency parameter for the notch filter 508 and the bandpass filter 520. The notch filter 508 further improves the component of the bending mode received via the path 566 of the bandpass filter 506 by suppressing the remnants of the torque mode component in the enhanced signal. The bandpass filter 520 further improves the component of the torque mode received via the path 568 of the notch filter 518 by filtering the frequencies other than the narrow band centered around the estimated value of the torsion mode of the flow tubes. In other words, the filter chain comprising the band pass filter 506 and the notch filter 508 improves the vibration frequency component in bending mode in the sum of L + R signals, while the filter chain comprising the notch filter 518 and the bandpass filter 520 improves the frequency component of the torsion mode in the signal difference LR. All the filters in these filter chains (506, 508, 518 and 520) are quickly adapted to the changes in the frequencies of the vibratory flow tubes by FCG filters 512 and 514. The definition equation of all notch filters second order is preferably: y (k) = u (k) + au (kl) + u (k-2) - aay (kl) - a2y (k-2) where u is the input sample, and is the improved output sample, a is the depolarization parameter since it is the adaptation coefficient. The definition equation for all second-order bandpass filters is preferably: y (k) = (al) au (kl) + (cf-D u (k-2) - aay (kl) - c? y (k-2) The definition equation for second-order bandpass filters can also be described in equivalent matrix form. The matrix form is useful in the description (later in the present) of the FCG filter. For the unknown p coefficients, X and A (k) are vectors of p by 1. The matrix form of the second-order bandpass filters is therefore preferably: y (k) = A '(k) X - (c? -l) u (k-2) - c? Y (k-2) where: X = [a], A (k) = [(al) u (kD -ay (kl)] The algorithm of FCG adapts the coefficients of the bandpass and notch filters to tune the filters to the changes in the frequencies of the vibration modes.This algorithm is chosen due to its property of fast convergence, numerical stability and stability of calculation in comparison with other known existing algorithms The FCG algorithm adapts the weights to minimize an error function of the filter to be adapted.The error function expressed in matrix form is preferably: J (Xn) =? N "x (y (i) - u (i)) i = 0 where y (i) is calculated with the most recent coefficient Xn. The algorithm of FCG can be calculated by the following set of equations where the starting values are as follows: ^ n ^ p ^ n V - "" "" -, = * "+ YA In the previous FCG algorithm, for use in the second-order FCG filter, all parameters are scalar. For filters with p unknown coefficients, Qn is a matrix of p px p and dn, gn and Xn are vectors of p by 1. The e (epsilon) in the above equations is a small value added to avoid the numerical problems of division by zero in certain cases. As long as the value is small, the performance of the algorithm is not significantly degraded. The FCG filter generates an estimated value of the frequency at its output used to center the frequency of the notch and bandpass filters referred to above. The estimated value of the frequency is determined as: _ eos 1 (- / 2) 2p Then, the outputs of the torsion and bending improvement filter chains are applied to corresponding RML 510 and 522 filters to calculate more accurate estimates of the vibration frequencies of the bending mode and torsion mode of the flow tubes. In particular, the improved estimate value of the vibration component of the bending mode generated as the output of the notch filter 508 is applied to the RML filter 510 for the final estimation of the frequency. Similarly, the improved estimate value of the vibration component of the torsion mode generated as the output of the notch filter 520 is applied to the RML filter 522 for the final estimation of the frequency. The RML filters 510 and 522 provide higher frequency estimates of their respective input signals because their inputs have been improved by the filters to eliminate unrelated and undesirable signal components. The problems associated with the slower convergence of the RML filtering method are eliminated by the improvement of the fed signals as their respective signals. RML filters operate according to the following equations specified in scalar notation in where the starting values are p (0) = 0, f (0) 0, e (0) = 0, e F (0) = 0, uF (0) = 0, a (0) = 0, and the first N values of a are initialized or adjusted to initial values when using the estimated values of the FCG filter frequency and then when calculating: Then, the bending and torsion mode frequencies are applied as output values of the frequency / phase calculation element 204. Specifically, the frequency of the torsion mode of the flow tubes generated as output of the RML filter 522 is applied to the path 264 for further processing. In addition, the frequency of the flexure mode of the flow tubes generated as output of the RML filter 510 is applied to the path 266 for further processing. In addition to the isolation of the flexure against the torsion mode and the estimation of their respective frequencies, the frequency / phase calculation element 204 improves the bending mode signals for each channel to provide exact sinusoidal signal input values to the signals. phase calculations carried out by the element 528 of Goertzel filter. In particular, the estimated value of the frequency of the torsion mode generated by the RML filter 522 is applied on the path 566 as the central frequency parameter for adapting the notch filters 500 and 524. Similarly, the estimated value of the frequency of the bending mode generated by RML 510 is applied on the path 564 as the central frequency parameter for adapting the bandpass filters 502 and 526. The unimproved signal of the left channel received on the path 254 is applied to the notch filter 500 to eliminate a notch of the frequencies precisely centered around the estimated value of the frequency of the torsion mode. The output of the notch filter 500 is applied on the path 550 to the bandpass filter 502 which passes a narrow band of frequencies precisely centered around the estimated value of the frequency of the bending mode. The output of the bandpass filter 502 is applied to the path 552 and represents an improved version of the bending mode signal generated by the left channel detector. Similarly, for the right channel, the value of the signal of the right channel without improvement is received on the path 256, applied to the notch filter 524 to eliminate the frequencies of the torsion mode, then, applied on the path 574 to the filter 526 of step for further improve the signal by eliminating almost all narrow band frequencies centered precisely around the frequency of the bending mode. The output of the band pass filter 526 is applied to the path 576 and represents an improved version of the bending mode vibration signal generated by the right channel detector. The responses of the various filters illustrated in Figure 5 depend on the values of the specific parameters chosen for the filters according to the definition equations given above. Empirical studies have found that the following values are effective with the bending and torsional frequencies of the typical flow meter.

Item Type Parameters 500 notch filter 2nd. order a = 0.99 502 band pass filter of 2o. order = 0.99 506 bandpass filter of 2o. order a = 0.95 508 notch filter of 2o. order = 0.95 510 RML adaptive filter of 2o. order a = 0.99,? = 0.99 512 FCG adaptive filter of 2o. order a = 0.01,? = 0.99 514 FCG adaptive filter of 2o. order a = 0.01,? = 0.99 518 notch filter of 2o. order a = 0.95 520 bandpass filter of 2o. order = 0.95 522 RML adaptive filter of 2o. order a = 0.99,? 0.99 524 2nd notch filter. order a = 0.99 526 bandpass filter of 2o. order a = 0.99 The improved bending mode signals for the left and right channel detectors are applied via paths 522 and 576 respectively, to element 528 of phase calculation of Goertzel filter. The Goetzel filter also receives the estimated value of the frequency of the bending mode via the path 564 of the RML 510 filter and determines the average frequency with respect to the half-window period of previous samples. As indicated above, the Goertzel filter applies weighting values to each improved sample and adds the weighted values by means of the number of samples required for a Hanning window. The Goertzel filter calculations are carried out in parallel for each of the detector signal values of the left and right channel. The Goertzel filter calculations for each value of the channel detector result in a complex indicator number of the sinusoid phase represented by the enhanced signal values of the channel. The resulting complex numbers indicating the phase for the detector signals of the left and right channel are applied to the paths 260 and 262 respectively, as outputs or results of the element 528 of the phase calculation of the Goertzel filter. Figures 7-9 are flow diagrams showing the operation of the DSP 1200 to carry out the sum / difference filtering methods. The methods shown in the flowcharts of Figures 7-9 present another view of the functionality described above with respect to the block diagram of the Figure 5. The flow diagrams of Figures 7-9 describe the architecture of the training elements operable in the DSP 1200. The elements 700-720 of Figure 7 describe the operation of a first stage (first stage) of filtration in the frequency / phase calculation element 204. In particular, this first stage provides estimated values by using FCG filtration methods of the vibration frequencies of the bending and torsion mode. The FCG filtering method provides a rapid estimated value of the frequency given the sum / difference values calculated from the output values of the left and right channel detector. The elements 722-742 of figure 8 describe a second stage of the filtering processing in the DSP 1200. The second stage improves the estimated values of bending and torsional frequency provided by the first stage by means of the use of notch filters, filters bandpass and RML filtering methods. Finally, elements 744-754 of Figure 9 use the improved bending and torsional frequencies to provide improved filtering of the left and right channel detector output values to calculate the pressure in the Coriolis cash mass flow meter and to calculate and correct a given flow rate, the improved signal values for the left and right channels also as the improved frequencies of the bending and torsion mode. Finally, the third stage illustrated in Figure 9 uses the pressure value and the mass flow velocity value thus derived for the control of the specific application process. The element 700 initializes or adjusts to initial values two variables used to modify the filtering calculations of RML when the FCG filtering calculations determine that the estimated RML frequency values are outside a desirable range. It is known that RML filtering calculation techniques converge defectively to changes in the input frequency when the estimated value falls outside of an acceptable expected range. The variables are initialized or adjusted to initial values at a count of 100 samples to delay the filtering calculations of RML at the beginning of the filtration methods. Until 100 samples have been processed, the FCG filtering calculation that produces the estimated bending and torsion mode frequencies can not converge to a sufficiently accurate stabilized estimate to allow the use of the RML filter for the final improvement of the values estimates of frequency. During this period of time, the estimated value of the corresponding FCG filter frequency is used to adjust the RML filter to initial values. This characteristic of the present invention requires that the starting point of the RML adaptation be close to the correct frequency, to thereby ensure a rapid convergence of the RML adaptation. Next, element 702 is operable to obtain the pair of sampled signals from the left and right channel available. The sampled signals are applied to trajectories 254 and 256 as shown in Figure 2 by the decimation filters 202 of Figure 2. As will be recognized by those of ordinary skill in the art, the pair of signals sampled under the methods of the present invention, are retrieved from a 'FIFO or memory storage arrays in which the decimated sample values are stored. Next, the element 704 calculates the sum of the left and right channel sample values recovered by the element 702. As indicated above, since the vibrations of the bending mode between the left and right channel signals are generally in phase and the vibration frequency of the torsion mode is generally 180 ° out of phase, the sum of the left and right channel sample values substantially eliminates the frequency component of the torque mode of the summed signals while improving the component frequency of bending mode of the summed signals. Therefore, the sum of the two channel signals has a strong component of frequency in the frequency of the bending mode and a frequency component significantly decreased in the frequency of the torsion mode. Next, the element 706 is operable to estimate the bending frequency from the sum of the left and right channel signals through the use of a FCG filtering method. Next, item 708 is operable to determine if the frequency estimates of the FCG and RML filter are close enough to each other. The FCG adaptive filter converges much faster than the corresponding RML filter, especially when the frequency error is large. Thus, if the estimated frequency values differ widely, it can be assumed that the estimated value of FCG is a better approximation of the current frequency than the estimated value of improved RML. Under these conditions, the convergence of the RML filter can be accelerated by forcing the RML filter to track or track (use) the frequency estimate value of the FCG filter. The variable DELAY_RML__BEND is a value of the counter set to "suspend" the frequency estimates of the RML filter. While the estimated values of the RML filter are thus suspended, the estimates of RML filter frequency estimate remain close to the correct frequency due to the use of the estimated frequency of the FCG filter to initialize or adjust the RML filter calculations to initial values. When the RML filter processing is allowed to reassume (after the DELAY_RML_BEND counter decreases to zero) the estimated frequency, calculated by the RML filter will rapidly converge to a more accurate estimated frequency value. To determine if the estimated values of FCG and RML frequencies are close enough, it is found that the following test is useful: | 1 - (p + 2cos? FCG) (p + 2cos? RML) | = 0.01 It will be recognized by those of ordinary skill in the art that any value can be used to delay (suspend) the use of RML filtering calculations. Empirically, it has been found that the delay per 100 samples provides a sufficient time to ensure the stabilization of the estimated values of the FCG filtering calculation of the bending frequency before the RML filtration uses the estimated bending frequency as discussed below in the present. Additionally, those of ordinary experience will recognize that other inequality tests can be used to determine if the output of the RML filter is close enough to the estimated value of the FCG filter to be useful. Variations concerned with specific applications or flow meter designs will be recognized by those of ordinary experience in the art. Next, the element 712 is operable to calculate the difference between the signal values of the left and right channel. Again, due to the phase relationships of the bending and torsion mode frequencies as indicated above, the difference between the two sample signals will have a frequency component reinforced at the frequency of the torsion mode and a frequency component significantly decreased in the frequency of the bending mode. Then, the element 714 is operable to suppress the value of the difference signal to estimate any remaining frequency of the bending mode. In other words, the element 714 somewhat improves the value of the signal calculated as the difference between the values of the left and right channel signal. Next, the element 716 is operable to estimate the value of the frequency of the torsion mode by using a FCG filtering calculation applied to the difference value as improved by the notch filter of the element 714. The element 718 and the element 720 are operable in a manner analogous to element 708 and 710 discussed above. Specifically, the element 718 determines whether the estimated value of the frequency of the torsion mode produced by the FGC filtering calculation of the element 716 and the The estimated value of the frequency produced by the RML filtering calculation is too far apart for rapid convergence of the RML filter calculations. If so, the element 720 is operable immediately to reset or reset the delay counter variable to impose an additional delay in the use of the RML filtering calculations. Either in one case or another, the processing continues in Figure 8 with the second stage of filtering processing. Element 722 of Figure 8 applies a bandpass filtering calculation to the sum determined above by the operation of element 704. A frequency band centered around the estimated bending frequency produced by the operation of element 706 is passed through by the bandpass filtering operation. Next, the element 724 is operable to further improve the frequency of the bending mode by applying a notch filter to further eliminate the remnants of the torque mode frequency in the estimated value of the partially improved bending mode frequency by operation of element 722. Next, element 726 is operable to produce an improved estimate value of the bending mode frequency when using the RML filter technique. When using an improved version of the vibration signals of the mode of As input, the element 726 produces a more accurate estimate of the frequency of the bending mode than the element 706 discussed above. The elements 728-732 are operable to determine if the coefficient of the calculations applied in the RML filtering needs to be reset according to the value of the flag or delay flag set by the operation of the element 710 or the element 700. Specifically, the element 728 is operable to determine whether the value of the delay counter set by operation of elements 710 or 700 is not zero. If the value of the delay counter is not zero, the elements 730 and 732 are immediately operable to reset the filtering calculation coefficient of RML to the estimated coefficient provided by the filtering operation FCG in the above element 706. The element 732 is operable to decrease the value of the delay counter to indicate that the RML coefficient used in the RML filtering calculations has been delayed by a sample period. The elements 734-742 are operable in a manner similar to the above elements 722-732 to improve the torque mode component of the detected signals. In particular, the element 734 applies a bandpass filter to the difference value calculated by the above elements 712-714. Bandpass filtering makes passing a narrow band of frequencies, centered around the estimated torque frequency calculated by the operation of the previous element 716. Next, the element 736 is operable to produce an estimate value of the vibration frequency of the torsion mode when using the well-known RML filter technique. By using an improved version of the torque mode signal as input, element 736 produces a more accurate estimate value than element 716 discussed above. Then, the elements 738-742 are operable to determine if the filtering calculation coefficient of RML needs to be reset or adjusted according to the value of the delay counter established by the operation of the previous element 720 or 700. In particular, if the value of the delay counter is not zero, the element 740 is operable to set the RML setting calculation coefficient to the estimated coefficient provided with the operation of the FCG filtering calculation carried out by the operation of the element. 716 previous. Then, the element 742 is operable to decrease the value of the delay counter to indicate that the RML coefficient has been reset for an additional sample period. Either in one case or another, then, the processing continues with the third stage of the filtering operation illustrated in Figure 9.

The third filtering step, represented by the elements 744-762 of Figure 9 uses the vibration frequency values of the improved torsion mode and bending mode to improve the vibration frequency component of the bending mode of the signaling signals. left and right channel. Then, the various values of the improved signal are used in the third stage of the processing to determine the pressure in the Coriolis mass flow meter in operation and to determine the corrected mass flow rate as a function of the channel sample values. left and right and the calculated pressure in the Coriolis mass flow meter. In particular, the element 744 is operable first to suppress the torsional frequency signals of the signal values of the left channel and then to pass the band of flexural frequency signals of the improved left channel signal value. The operation of the element 744 corresponds to the notch filter 500 and the bandpass filter 502 illustrated in Figure 5. The element 746 is similarly operable to improve the frequency component of the bending mode of the signal mode of the right channel. The operation of the element 744 corresponds to the notch filter 524 and the bandpass filter 526 of Figure 5.

Although it may appear that the combination of bandpass filtration and notch filtration in the filter chains such as elements 500 and 502 of Figure 5 may be redundant in nature, the skilled artisan will readily recognize that simple filters of the Second order bandpass may be unable to reject enough noise and other signals outside of the selected band. In particular, it is difficult to obtain an efficient attenuation of the vibration frequency of the torsion mode with a reasonable filter bandwidth. For these reasons, the best currently known way to implement the invention requires the combination of bandpass filtering and notch filtering in filter chains to sufficiently improve the desired signals. Elements 748 and 705 update the Goertzel filter calculations and the averaging of the estimated frequencies for each discrete sample (decimated and improved). In particular, the element 748 updates the calculation of the Goertzel filter in progress for the samples in the window (average) of Hanning present by multiplying the sample values of the left and right channel enhanced by the appropriate Hanning window weight value. Then, this value is incorporated into the running DTFT calculation for the present (average) closing window to produce the value Indicator of the phase used in the subsequent calculations. The element 750 updates the running calculation of an average frequency for each release mode of the vibratory flow tubes. To minimize the use of complex inverse trigonometric functions from a calculation point of view, the actual bending and torsion mode frequencies are calculated only once every half window period, although the RML filters used to track the frequencies of the Torsion and bending produce estimated values for each sample (decimated). As indicated above, the RML filters represent their respective frequency estimate values in the form of filter coefficients that are related to the frequency by the formula: a = -2 eos (? Ts) where? is the frequency and Ts is the sample frequency decimated. The estimated values of the vibration frequencies, the bending and torsion mode are calculated every half window period of Hanning when calculating the average value of the coefficient "a" representative of the frequency over the previous half-window period and when feeding it to the formula :? = eos "1 (-a / 2) / T3 Therefore, element 750 determines the average value for this frequency coefficient representative for the estimated values of vibration frequency of bending and torsion mode. Element 752 is operable to determine if this particular sample (decimated and improved) completes the processing of the samples in the present half-window period of Hanning. If not, the processing proceeds to cycle back to element 702 (on the "A" label) to wait for the next sample. Otherwise, processing continues with elements 754-762 to consummate the processing of the present Hanning half-window period. Element 754 calculates the value of? T as a function ("f") of the values generated by the Goertzel filters on the (recently completed) Hanning window. As indicated above, the Goertzel filters produce a complex number indicator of the phase for each of the detector outputs for each of the left and right channels. As is known in the art, the phase of the sample signal values can be used to determine the value of? T which in turn is proportional to the mass flow signal of the material flowing in the flow tubes of the meter. mass flow of Coriolis effect. Next, element 756 determines the pressure within the flow tubes as a function ("g") of the frequency estimates, improved, averaged vibrations of the bending and torsion mode of the flow tubes. As indicated above, the relationship between the torsion frequency and the bending frequency is proportional to the pressure inside the flow tubes of a mass flow meter in operation. Then, element 758 is operable to calculate a corrected mass flow rate, averaged over the last Hanning window period (freshly accomplished) as a function ("h") of the values of Δt and pressure calculated above. As discussed in further detail hereinafter, the corrected mass flow rate is calculated as an iterative process based on the uncorrected mass flow rate and various correction factors (the main one among them is the pressure correction determined from according to the teachings of this invention). Then, the element 760 is representative of any processing that uses the corrected mass flow rate or pressure calculations per se to determine or control the state of a process. This use may represent any useful application of the mass flow rate or pressure corrected per se derived from the methods of the present invention.

Finally, the element 762 is operable to restore the calculations carried out previously by the elements 748 and 750 that are operable over the period of a Hanning window. Specifically, the weighted averaging of the Goertzel filter and the average frequency calculations are restored in preparation for the start of the next Hanning window period. Then, the processing is accomplished for this Hanning window and the methods continue to cycle back to element 702 (on the "A" label) to wait for the availability of another decimated sample.

Frequency / phase filtering method - fourth order filter method Figure 6 illustrates a further detail of an alternative embodiment of the frequency / phase calculation element 204 that uses a fourth order FCG filter function to provide approximations of the vibration frequencies of the bending mode and the torsion mode of the flow tubes. In addition to generating estimated values of the frequency, the fourth order FCG filter provides some improvement of the input signal. The fourth order FCG mode has an advantage over the best known addition / difference methods presented above in that the fourth FCG filter The order is less sensitive to any imbalance between the detector output signals of the left and right channel. Nevertheless, the fourth-order FCG filter is somewhat more complex from the point of view of calculations. The results of the empirical tests have determined that in the practical application of the sum / difference methods presented above, the potential imbalance of the left and right channel detector signals does not affect the results of the estimated values of the frequency and the improvement of the the signal. Therefore, the additional complexity of the fourth-order FCG filter is not required to improve the measurement accuracy for the pressure or mass flow rates. The improved output of the fourth order FCG filter is applied to each of the two filter chains to further isolate and improve the vibration frequencies of the bending mode and torsion mode of the flow tubes. Each filter chain comprises a notch filter that receives the moderately improved output signal from the fourth order FCG filter and that output is applied to a chained bandpass filter. The output of the bandpass filter of each filter chain is applied to a second order RML filter to complete the improvement of each isolated frequency signal. An additional pair of filter chains is associated with the channels of left and right detector to improve the signals generated from it by the vibrations of the flex mode of the flow tubes. Then, the improved signal for each of the left and right channel detectors is applied to a Goertzel filter phase calculation element 528 as discussed above with respect to FIG. 5. A fourth order FCG filter 600 receives the signal values of the left channel of path 254. The fourth order FCG 600 calculates the estimated values of the frequency for the two strongest signals (highest-amplitude sinusoids) in its input data. It is assumed that the lower of the two estimated frequencies is the frequency of the bending mode and the higher of the two estimated frequencies is the frequency of the torsion mode. By this, the fourth order FCG 600 provides an estimated value of the frequency of the vibrations of the flexure mode of the flow tubes and applies that estimated value to the path 652. By this, the FCG 600 filter of fourth order also provides an estimated value of the frequency of the torsion mode and applies that estimate value to the path 654. Finally, the fourth order FCG 600 filter provides a moderate improvement of the path input signal 254 to eliminate the noise signals outside the two strong components and applies the improved signal to path 650. The definition equations of all the second-order bandpass and bandpass filters and RML filters are as indicated above. The definition equation for the fourth order bandpass filter in scalar form is preferably: y (k (al) x (I) u (kl) + (< Al) x (2) ?? (k-2) ) + (c? -l) x (l) u (k-3) + (c -l) u (k-4) -ax (l) y (k-lA < x (2) y (k -2Ac? X (l) and (k-3Aa4y (h-4) where u is the input signal, and is the improved output signal, a is the depolarization parameter, and x (l) and x (2) are the adaptation coefficients yx (l) = a + b, x (2) = 2 + ab.The definition equation can also be described in the form of an equivalent matrix as: y (k) = A '(k) X + ( a4-1) u (k-4) - CC4y (? - 4) where: -1) u (/ f-1) -ay (/ -1) + (a3-1) u (/ f-3) -a3y (/ f-3) (a2 -1) u (/ c-2) -a and (/ c-2) The fourth-order FCG 600 filter generates two estimated frequency values at its outputs used to center the frequency of the various notch and bandpass filters referenced in Figure 6. The estimated values of the frequency They are determined as: fí. eos-1 (-a2) (2p) f2_ c s- -b / 2) (2p) Alternatively, the fourth order FCG 600 filter can receive its input from the right channel detector values fed in path 256. Those of ordinary skill in the art will readily recognize the equivalence of the two input options with respect to the operation. of the fourth order FCG 600 filter. A first filter chain isolates and further improves the frequency component of the bending mode in the signal applied to the input path 650. First, the notch filter 602 suppresses the centered frequencies around the frequency of the estimated torque mode calculated by the element 612. The output of the notch filter 602 is applied via the path 656 to the bandpass filter 604 to pass a narrow frequency band centered around the frequency of the bending mode, estimated calculated by the element 600. The The output of the filter 604 of the bandpass is applied via the path 658 to the second order RML filter 606 to form the final estimated value of the frequency of the bending mode. Then, this final frequency estimate value is applied to the path 266.

A second filter chain isolates and further improves the vibration frequency component of the torsion mode in the signal applied to the input path 650. The notch filter 608 suppresses first the frequencies centered around the vibration frequency of the estimated vibration mode calculated by the element 606. The output of the notch filter 608 is applied via the path 660 to the bandpass filter 610 to pass a narrow frequency band centered around of the frequency of the estimated torque mode calculated by the element 600. The output of the bandpass filter 610 is applied via the path 662 to the second order RML filter 612 to form the final estimated value of the frequency of the torsion mode . Then, this estimated value of the final frequency is applied to the path 264. The estimated value of the frequency of the bending mode generated by the FCG 600 filter of fourth order and applied to the path 652 is received by the filter 604 of passage of band to adapt the center frequency of the filter pass band. Similarly, the estimated value of the frequency of the torsion mode generated by the FCG 600 filter of fourth order and applied to the path 654 is received by the band pass filter 610 to adapt the center frequency of the band of filter step. The precise frequency of the flexure mode of the flow tubes generated by the second order RML filter 606 and applied to the path 266 is received by the notch filter 608 to adapt the center frequency of the notch filter. Similarly, the frequency of the precise torsion mode of the flow tubes generated by the second order RML filter 612 and applied to the path 264 is received by the notch filter 602 to adapt the center frequency of the notch filter. A second pair of filter chains are used to isolate and improve the frequency of the bending mode for each of the left and right channel detector signals. The notch filter 614 receives the signal values from the detector of the left channel without improving on the path 254 and filters the frequencies with a notch centered on the precise frequency of the torque mode, supplied via the path 264 of the RML filter 612 of Second order. The improved signal generated by the notch filter 614 is applied on the path 664 to the bandpass filter 616. The bandpass filter 616 passes a narrow band of frequency centered around the frequency of vibration of precise bending mode, fed via the path 266 of the RML filter 606 of second order. The improved signal output by the band pass filter 616 represents the signal of the bending mode of the signal values of the detector of the left channel and is applied via the path 666 to the filter element 528 of Goertzel in a manner similar to that discussed above with respect to figure 5. A similar filter chain processes the detector signal values of the right channel. The notch filter 618 receives the signal values from the right channel detector without improving on the path 256 and filters the frequencies within a notch centered on the frequency of the precise torque mode, supplied via the path 264 of the RML filter 62 of Second order. The improved signal generated by the notch filter 618 is applied on the path 668 to the bandpass filter 620. The bandpass filter 620 passes a narrow band of frequencies centered around the precise bending mode frequency supplied via the trajectory 266 of the RML filter 606 of second order. The improved signal output by the band pass filter 620 represents the signal of the bending mode of the signal values of the right channel detector and is applied via the path 670 to the Goertzel filter element 528 in a manner similar to that discussed above with respect to Figure 5. The responses of the various filters illustrated in Figure 6, depend on the specific values of the parameters chosen for the filters according to the definition equations given above. Empirical studies have found that the following values are effective with the bending and torsional frequencies of the typical flow meter.

Element Type Parameters 600 FCG adaptive filter 4th order = 0.01,? = 0.99 602 2nd notch filter. order = 0.8 604 bandpass filter of 2o. order a = 0.5 606 adaptive RML filter of 2o. order a = 0.99,? = 0.99 608 2nd notch filter. order a = 0.8 610 bandpass filter of 2o. order a = 0.5 612 adaptive RML filter of 2o. order a = 0.99,? = 0.99 614 2nd notch filter. order = 0.99 616 bandpass filter of 2o. order a = 0.99 618 notch filter of 2o. order a = 0.99 620 bandpass filter of 2o. order a = 0.99 It is important to note that the estimated values of the frequency produced by the filter elements 606 and 612 of RML are used in a reciprocal feedback arrangement. In other words, the estimated value of the frequency produced by the RML filter element 606 is used to control the notch filter 608 that filters the input of the RML filter 612. Conversely, the estimated value of the frequency produced by the element 612 of the RML filter is used to control the notch filter 602 that filters the input to the filter 606 of RML.

The proper convergence of this cross-coupled system is ensured in two ways. First, the bandpass filters 604 and 610 are synchronized by using the output of the fourth order FCG filter 600. This provides a strong attenuation of the unwanted component for each filter chain (ie, removal of the torque mode frequency for the filter chain that includes the RML filter 606 and elimination of the bending mode frequency in the chain of filters that the RML filter 612 includes). The notch filters 602 and 608 further attenuate the unwanted components. Secondly, if the estimated values of the RML frequency differ significantly from the estimated values of the corresponding mode frequency produced by the fourth order FCG filter 600, the respective RML filter (606 or 612) is adjusted to values initials when using the estimated value of the corresponding FCG filter in a manner analogous to that described above with respect to the sum / difference methods. This adjustment to initial values is indicated by the dashed line extended to the RML filters (606 and 612) of FCG filter 460 of the fourth order. The phase calculation element 528 of the Goertzel filter, as discussed above with respect to FIG. 5, receives the improved signals representing the vibration movement of the bending mode of the left and right channel detectors and determines the sinusoid phase of each channel signal. The phase of each channel, represented by a given complex number when adding the sample values under Hanning window weight control, are applied to the paths 260 and 212 for further processing by means of the calculation element 212 of? T of Figure 2 Compensation of the frequency ratio: The methods of the present invention discussed above are applied to determine the frequency of bending mode and the frequency of the torsion mode of the vibratory flow tubes. The ratio of the torsion mode to the bending mode can be used to determine the pressure in the flow tubes as discussed above. However, as indicated above, the frequency ratio is affected by other parameters of the flow meter. These other factors can be used to compensate the proportion of frequencies by well-known calibration techniques. Then, the compensated frequency ratio can be used to accurately determine the pressure inside the flow tubes of the mass flow meter.

The proportion of raw frequency FRRAW is determined periodically as discussed above as the ratio of the frequency of the torsion mode to the frequency of the bending mode of the vibratory flow tubes. FRRA is corrected by applying compensation calculations in terms of physical assembly, temperature, density, and estimated mass flow rate (the mass flow rate is iteratively corrected by means of sampling periods) to determine FRCORR as follows: FRCORR = FRRAW -? FR0 -? FRT +? FRP +? FRm? FR0 is a compensation value that takes into account changes in the frequency response of the flow tubes in response to the physical assembly of the flow meter. The physical assembly of the flow meter in its proposed application can alter the vibration response of the flow tubes compared to the physical assembly used to calibrate the flow meter at the time of manufacture. ? FR0 is determined by measuring the frequency ratio in the installation or by resetting the flow meter (FRS mounted to the proposed application conduit) to zero and subtracting the frequency ratio by calibration (FR0 mounted on a calibration accessory ). The measured installation frequency ratio (FRS) is also adjusted for the differences in the installation temperature compared to the calibration temperature. ? FR0 is determined as follows: ? FRo = FRS - (ft (To) - ft (Ts)) - FRo where Ft (to) is a polynomial in T0 (calibration temperature of the flow tubes) appropriate to the particular flowmeter and ft (to) is a polynomial in Ts (installation temperature of the flow tubes) appropriate for the particular flow meter. ? FRT is a compensation factor that takes into account changes in the frequency ratio of the flow tubes in response to changes in the temperature of the flow tubes of the calibration temperatures.

Specifically,? FRT is determined as follows:? FRT = ft (TO) - ft (Tm) where ft (to) is a polynomial in T0 (calibration temperature of the flow tubes, appropriate to the particular flow meter and ft (tm) is a polynomial in Tm (currently measured temperature of the flow tubes) appropriate to the particular flow meter.? FRP is a compensation factor that takes into account changes in the frequency ratio of the flow tubes in response to changes in the density of the material flowing in the flow tubes the density of the calibration. Specifically,? FRP is determined as follows:? FRP = fp (pa) - fp (pm) where fp (p0) is a polynomial in p0 (material calibration density in the flow tubes) appropriate for the flow meter particular and fp (pa) is a polynomial in pm (currently measured density of the material in the flow tubes) appropriate for the particular flow meter. ? FRm is a compensation factor that takes into account changes in the frequency ratio of the flow tubes in response to changes in the mass flow rate through the flow tubes. Specifically? FRm is determined as follows:? FRm = fm (m) where fm (m) is a polynomial in m (the mass flow rate as it is iteratively corrected by means of sample periods) appropriate to the particular flow meter . The mass flow rate compensation factor is iterative in the sense that the correction factor is generated, in part, as a correction of the value previously corrected for the past sampling period. Therefore, this particular compensation factor provides feedback control over the correction of the mass flow rate based on previous correction calculations. Having thus calculated and corrected the proportion of frequencies, the pressure associated with it can be determined by standard calculations based on the calibration curve established in manufacturing that associates the pressure with the frequency ratio. A polynomial function corresponding to a curve adjusted to the calibration data of the frequency ratio as a function of the pressure can be applied to FRCORR. Alternatively, standard table and interpolation table query techniques can be applied to a table that represents the measured calibration data that correlates the frequency ratio with the pressure. Depending on the particular flow meter and its application, some or all of the above-described corrections of the FRRAW frequency ratio are not necessary to determine an appropriate accuracy pressure measurement. For example, if the frequencies of the vibration modes of interest for a given flow meter in a particular application are not affected by or subject to changes in mounting conditions, temperature, density and mass flow rate, then FRR may be used directly to calculate the pressure measurement as described above. If the frequencies of the Vibration modes of interest to a particular flow meter are affected only by certain mounting conditions, temperature, density or mass flow rate, so FRRAW needs to be corrected only for those factors that have an effect. It may be presented that several vibration modes used for a particular flow meter may not be affected by changes in pressure, conditions of assembly, temperature, density and speed of mass flow or that the effects due to changes in those parameters are negligible in the accuracy of pressure measurement required. Under these conditions, the pressure can be determined by measuring only one frequency. An example is a flow meter that has a bending mode frequency that is not affected, is affected negligibly, or is not subject to changes in the previously intended factors in which the pressure is included. The pressure is determined by measuring the frequency of the torsion mode and directly related the frequency of the torsion mode with the pressure. This is carried out by means of the methods of the present invention as described above but with the assumption that one of the frequencies used in the frequency relationship, be it the numerator or the denominator as appropriate, is a constant value . Where a flow meter has a bending frequency, for example, which is affected by the factors mentioned above but is affected to a relative degree substantially less than the frequency of the torsion mode for that flow meter, a lower pressure measurement performance could be accepted and only use the frequency of the mode torsion for its measurement of pressure and pressure compensation. It is obvious to those skilled in the art that the methods of the present invention are equally applicable to vibratory tube densitometers. The measuring tube of a vibratory tube densitometer is excited in two vibration modes as described above. The two frequencies are measured and processed as described above to produce a signal indicating the pressure inside the vibratory tube. Since the densitometers are not used to measure the mass flow rate, the pressure measurement is used as a pressure and compensation indication at the measured speed and is not used, as described above, to compensate for the velocity signal. mass flow. It will be expressly understood that the claimed invention will not be limited to the description of the preferred embodiment but covers other modifications and alterations in the spirit and scope of the concept of invention. In particular, the method and apparatus of the present invention can be applied to Coriolis mass flow meters with a variety of tube shapes including so-called "U" tubes, straight tubes and others. Many variables contribute to the calibration of the methods of the present invention to a particular flow meter configuration. Accordingly, the data shown in the various figures are only illustrative. Due to the many variables involved, it can not be assumed that the numerical values shown will be easily reproduced by others. It is noted that, with regard to this date, the best method known to the applicant to carry out the aforementioned invention is that which is clear from the present description of the invention.

Claims (23)

1. Claims Having described the invention as above, it is claimed as property, what is contained in the following: 1. A method for determining the pressure in a flow meter having vibratory flow tube means comprising the steps of: vibrating the means of flow tube the flow meter in a first mode of axial vibration; determining a first resonant frequency of the flow tube means in response to the first axial vibration mode of the flow tube; characterized in that it comprises: vibrating the flow tube means of the flow meter in a second mode of axial vibration; determining a second resonant frequency of the flow tube means in response to the second axial vibration mode; and determining the pressure inside the flow meter when calculating the ratio between the first resonant frequency and the second resonant frequency.
2. 2. The method according to claim 1, characterized in that the pressure is determined independently of the density of the material.
3. 3. The method according to claim 1, characterized in that the pressure is determined at a zero mass velocity of the material.
4. 4. The method according to claim 1, characterized in that the pressure is determined at the mass flow rates of the material greater than zero.
5. 5. The method according to claim 1, characterized in that the flow meter is a Coriolis mass flow meter.
6. 6. The method of compliance with the claim 1, characterized in that the flow meter is a vibration tube densitometer.
7. The method according to claim 1, characterized in that the first mode of axial vibration vibrates the flow tube means in a bending mode and wherein the second mode of axial vibration vibrates the flow tube means in a torsion mode.
8. The method according to claim 1, characterized in that it further comprises the steps of: determining an uncorrected mass flow velocity corresponding to the material flowing through the flow meter; and derive a corrected mass flow rate for the material flowing through the flow meter in response to the determination of uncorrected mass flow velocity and determination of pressure.
9. The method according to claim 1, characterized in that the step of determining the first resonant frequency includes the steps of: detecting a first signal generated by the movement of a first detector associated with the vibratory flow tube means of the meter flow; detecting a second signal generated by the movement of a second detector associated with the vibratory flow tube means of the flow meter; and filtering the first signal and the second signal to extract a signal component corresponding to the first resonant frequency.
10. 10. The method of compliance with the claim 1, characterized in that the first axial vibration mode vibrates the flow tubes in a bending mode.
11. The method according to claim 10, characterized in that the filtering step includes the steps of: adding the first signal to the second signal to produce an isolated signal having a strong frequency component in the frequency of the bending mode; Y improve the isolated signal to eliminate undesirable components in the isolated signal to produce an improved signal in the frequency of the bending mode.
12. The method according to claim 10, characterized in that it further comprises the steps of: determining an uncorrected mass flow rate corresponds to the material flowing through the flow meter in response to the vibrations of the flow tube means in the bending modes; and deriving a corrected mass flow rate for the material flowing through the flow meter in response to the determination of the uncorrected mass flow rate and the determination of the pressure.
13. The method according to claim 1, characterized in that the step of determining the second resonant frequency includes the steps of: detecting a first signal generated by the movement of a first detector attached to the vibratory flow tube means of the meter flow; detecting a second signal generated by the movement of a second detector attached to the vibratory flow tube means of the flow meter; and filtering the first signal and the second signal to extract a signal component corresponding to the second resonant frequency.
14. 14. The method in accordance with the claim 13, characterized in that the second axial vibration mode vibrates the flow tube means in a torsion mode.
15. 15. The method of compliance with the claim 14, characterized in that the step of filtering the first signal and the second signal includes the steps of: subtracting the second signal from the first signal to produce an isolated signal having a strong frequency component at the frequency of the torsion mode; and improving the isolated signal to eliminate undesirable components in the isolated signal to produce an improved torque mode frequency signal.
16. The method according to claim 1, characterized in that the flow tube means are vibrated concurrently in the first axial vibration mode and the second axial vibration mode.
17. The method according to claim 1, characterized in that the flow tube means are vibrated sequentially, one mode at a time, in the first axial vibration mode and the second axial vibration mode.
18. 18. The method according to claim 1, characterized in that the step of determining the pressure includes: determine a ratio between the first resonant frequency and the second resonant frequency; compensate for the proportion in terms of changes in proportion caused by changes in a flowmeter parameter; and where the pressure is determined in response to the compensated proportion.
19. The method according to claim 18, characterized in that the parameter is the mounting condition of the flow meter and wherein the compensation step comprises: determining a first calibration ratio when the flow meter is calibrated in a first condition of assembly; determining a second calibration ratio when the flow meter is installed in its proposed application in a second mounting condition; generate a proportion compensation value in response to the determination of the first calibration ratio and the second calibration ratio; compensate the proportion with the compensation value of the proportion; and where the pressure is determined in response to the compensated proportion.
20. 20. The method according to claim 18, characterized in that the parameter is the temperature of the vibratory flow tube means and wherein the compensation step comprises: determining a first calibration ratio when the flow meter is calibrated at a first temperature; determine a second calibration ratio when the flow meter is calibrated at a second temperature; generate a compensation value of the ratio in response to the determination of the first calibration ratio and the second calibration ratio; measure the temperature of the vibratory flow tube means; compensate the proportion with the compensation value of the proportion in response to the measured temperature; and where the pressure is determined in response to the compensated proportion.
21. The method according to claim 18, characterized in that the parameter is the density of the material in the vibratory flow tube means and wherein the compensation stage comprises: determining a first calibration ratio when the flow meter is calibrated with the material having a first density; determining a second calibration ratio when the flow meter is calibrated with the material having a second density; generate a compensation value of the ratio in response to the determination of the first calibration ratio and the second calibration ratio; measure the density of the material in the vibratory flow tube means; compensate the proportion with the compensation value of the proportion in response to the measured density; and where the pressure is determined in response to the compensated proportion.
22. The method according to claim 8, characterized in that the step of determining the proportion includes: determining a first calibration ratio when the flow meter is calibrated with the material having a first mass flow rate; determining a second calibration ratio when the flow meter is calibrated with the material having a second mass flow rate; generate a compensation value of the ratio in response to the determination of the first calibration ratio and the second calibration ratio; compensate the proportion with the compensation value of the proportion in response to the corrected mass flow rate; and where the pressure is determined in response to the compensated proportion.
23. 23. An apparatus for determining the pressure in a flow meter having vibratory tube means comprising: means for vibrating the flow tube means in a first mode of axial vibration; means for vibrating the flow tube means in a second mode of axial vibration; detector means attached to the vibratory flow tube means, operable to generate signals responsive to movement of the flow tube means; means responsive to the detector means for determining a first frequency of the first axial vibration mode; characterized in that it comprises: means responsive to the detector means for determining a second frequency of the second mode of axial vibration; means for determining a ratio between the first frequency and the second frequency; means for measuring the density of the material in the vibratory flow tube means; means for compensating the ratio in response to the measured density; and means for determining the pressure in response to the compensated proportion. SUMMARY OF THE INVENTION A method for determining the pressure in a Coriolis effect mass flow meter (10) in operation is described. The flow tubes (130, 130 ') of the Coriolis flow meter are vibrated in a bending mode (as is normal for the mass flow rate measurement) and in a torsion mode. The proportion of the fundamental frequencies at which the flow tubes vibrate in each of the two modes of vibration is proportional to the pressure inside the flow tubes. In the preferred embodiment, a sum / difference method initially isolates the overlapping sinusoids that represent the fundamental frequencies of the two vibration modes. Then, conjugate gradient digital filters (FCG) (512, 514) are used to quickly estimate the fundamental frequencies in each of the two vibration modes. Then, the estimated frequencies are used by filter chains that include digital notch filters (518, 508) and bandpass filters (506, 1520) also as recursive maximum likelihood digital filter (RML) techniques (510, 512). ) to improve the estimated values of the fundamental frequency of the bending mode and the torsion mode. The estimated values of the bending mode frequency and the improved torque mode are used to determine the pressure in the flow tubes as a function of the ratio or ratio of the two frequencies, also as to the center of the notch and the bandpass filter chains used to improve the frequency of the bending mode of the two channels of the vibration detector for flow rate calculations mass Then the pressure thus determined can be used to correct the calculations of the mass flow rate or for other purposes of pressure measurement per se.