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AssigneeMicro Motion, Inc.
InventorDavid F. Normen
Estimating the term…
Abstract of Disclosure A calibration factor for a sensor including a material-containing conduit and a plurality of motion transducers operative to generate motion signals representing motion of the conduit is determined from a normal modal dynamic characterization of motion of the conduit. The calibration factor may be generated by generating a solution to a modal differential equation of motion in a modal domain including a plurality of normal modes of motion of the conduit, and by generating the calibration factor from this solution. The normal modal dynamic characterization may characterize motion of the conduit as a function of a modal Coriolis term that describes coupling among a plurality of normal modes of the conduit responsive to mass flow in the conduit. The modal Coriolis term may be determined from a mode shape function that describes modal motion of the conduit as a function of location on the conduit. The invention may be embodied as methods, apparatus and computer program products.
A method of characterizing a parameter sensor comprising a conduit configured to contain a material and a plurality of motion transducers operative to generate motion signals representing motion of the conduit, the method comprising:
A method according to Claim[Claim Reference] 1, wherein determining a calibration factor comprises:
A method according to Claim[Claim Reference] 1, wherein the calibration factor relates mass flow rate to a spatio-temporal relationship among the plurality of motion signals.
A method according to Claim[Claim Reference] 3, wherein the calibration factor relates mass flow rate to one of a time difference or a phase relationship.
A method according to Claim[Claim Reference] 1, wherein the normal modal dynamic characterization characterizes motion of the conduit as a function of a modal Coriolis term that describes coupling among a plurality of normal modes of the conduit responsive to mass flow in the conduit.
A method according to Claim[Claim Reference] 5, wherein determining a calibration factor is preceded by determining the modal Coriolis term from a mode shape function that describes motion of the conduit in a normal mode as a function of location on the conduit.
A method according to Claim[Claim Reference] 5, wherein determining a calibration factor is preceded by determining the modal Coriolis term from a spatial Coriolis characterization that describes motion of a plurality of discrete locations of the conduit in a spatial domain in response to a predetermined mass flow.
A method according to Claim[Claim Reference] 7, wherein determining the modal Coriolis term from a spatial Coriolis characterization that describes motion of a plurality of discrete locations of the conduit in a spatial domain in response to a predetermined mass flow comprises determining the modal Coriolis term from the spatial Coriolis characterization using a transformation that relates the spatial domain to the plurality of normal modes.
A method according to Claim [Claim Reference]8, wherein the plurality of motion transducers are operative to generate respective motion signals that represent motion at respective transducer locations of the conduit, wherein the plurality of discrete locations associated with the spatial Coriolis characterization includes locations other than the transducer locations, and wherein determining the modal Coriolis term from the spatial Coriolis characterization using a transformation that relates the spatial domain to the plurality of normal modes comprises:
A method according to Claim [Claim Reference]9, wherein determining a transformation that relates the spatial domain to the plurality of normal modes for the plurality discrete locations comprises determining the transformation that relates the spatial domain to the plurality of normal modes at the plurality of discrete locations from a mode shape function that describes motion of the conduit in a normal mode as a function of location on the conduit.
A method according to Claim [Claim Reference]10, wherein the mode shape function is a function of an eigenvalue and a boundary condition.
A method according to Claim [Claim Reference]10, further comprising determining the mode shape function.
A method according to Claim [Claim Reference]12, wherein determining the mode shape function comprises determining the mode shape function from a predetermined eigenvalue and a predetermined boundary condition.
A method according to Claim [Claim Reference]13, wherein determining the mode shape function from a predetermined eigenvalue and a predetermined boundary condition comprises assuming a homogenous boundary condition.
A method according to Claim [Claim Reference]6, wherein determining a calibration factor is preceded by determining an orthogonality of a mode shape function for a predetermined mass flow in the conduit, the mode shape function describing motion of the conduit in a normal mode as a function of location on the conduit.
A method according to Claim [Claim Reference]15, wherein the mode shape function is a function of an eigenvalue and a boundary condition.
A method according to Claim [Claim Reference]15, further comprising determining the mode shape function.
A method according to Claim [Claim Reference]17, wherein determining the mode shape function comprises determining the mode shape function from a predetermined eigenvalue and a predetermined boundary condition.
A method according to Claim [Claim Reference]18, wherein determining the mode shape function from a predetermined eigenvalue and a predetermined boundary condition comprises assuming a homogenous boundary condition.
A method according to Claim [Claim Reference]1, wherein determining a calibration factor comprises:
A method according to Claim [Claim Reference]20, wherein generating the calibration factor from the estimated spatial response comprises:
A method according to Claim [Claim Reference]21:
A method according to Claim [Claim Reference]1, further comprising processing a plurality of motion signals produced by the plurality of motion transducers according to the calibration factor to produce a mass flow estimate.
A method according to Claim [Claim Reference]1, wherein determining a calibration factor comprises generating the calibration factor from motion signals produced by the plurality of motion transducers.
A method of determining mass flow in a conduit configured to contain a material, the method comprising:
A method according to Claim [Claim Reference]25, wherein determining a calibration factor comprises:
A method according to Claim [Claim Reference]25, wherein processing the motion signals according to the calibration factor comprises:
A method according to Claim [Claim Reference]27:
A method according to Claim [Claim Reference]25, wherein the normal modal dynamic characterization includes a modal Coriolis term that describes coupling among a plurality of normal modes of the conduit responsive to mass flow in the conduit.
A method according to Claim [Claim Reference]29, wherein deriving a calibration factor comprises determining the calibration factor from a mode shape function that describes motion of the conduit in a normal mode as a function of location on the conduit.
A method according to Claim [Claim Reference]30, wherein the mode shape function is based on an assumed boundary condition for the conduit, and wherein the method further comprises constraining motion of the conduit to induce a boundary condition that approximates the assumed boundary condition.
A method according to Claim [Claim Reference]31, wherein constraining motion of the conduit comprises attaching the conduit to a structure.
A method according to Claim [Claim Reference]31, wherein constraining motion of the conduit comprises applying a force to the conduit responsive to motion of the conduit to thereby induce a boundary condition that approximates the assumed boundary condition.
An apparatus for calibrating a parameter sensor comprising a conduit configured to contain a material, a plurality of motion transducers operative to generate motion signals representing motion of the conduit and a mass flow estimator circuit operative to estimate mass flow from the motion signals according to a calibration factor, the apparatus comprising:
An apparatus according to Claim [Claim Reference]34, wherein the calibration factor generator circuit comprises:
An apparatus according to Claim [Claim Reference]35, wherein the normal modal characterization comprises a representation of a modal differential equation of motion in a modal domain comprising a plurality of normal modes of motion of the conduit, and wherein the calibration factor determiner circuit is operative to generate a solution of the modal differential equation of motion from the representation of the modal differential equation of motion and to generate the calibration factor from the solution of the modal differential equation of motion.
An apparatus according to Claim [Claim Reference]34, wherein the calibration factor relates mass flow rate to a spatio-temporal relationship among motion signals produced by the plurality of motion transducers.
An apparatus according to Claim [Claim Reference]37, wherein the calibration factor relates mass flow rate to one of a time difference or a phase relationship.
An apparatus according to Claim [Claim Reference]34, wherein the normal modal dynamic characterization characterizes motion of the conduit as a function of a modal Coriolis term that describes coupling among a plurality of normal modes of the conduit responsive to mass flow in the conduit.
An apparatus according to Claim [Claim Reference]39, wherein the calibration factor generator circuit is operative to determine the modal Coriolis term from a mode shape function that describes motion of the conduit in a normal mode as a function of location on the conduit.
An apparatus according to Claim [Claim Reference]39, wherein the calibration factor generator circuit is operative to determine the modal Coriolis term from a spatial Coriolis characterization that describes motion of a plurality of discrete locations of the conduit in a spatial domain in response to a predetermined mass flow.
An apparatus according to Claim [Claim Reference]41, wherein the calibration factor generator circuit is operative to determine the modal Coriolis term from the spatial Coriolis characterization using a transformation that relates the spatial domain to the plurality of normal modes.
An apparatus according to Claim [Claim Reference]42, wherein the plurality of motion transducers are operative to generate respective motion signals that represent motion at respective transducer locations of the conduit, wherein the plurality of discrete locations associated with the spatial Coriolis characterization includes locations other than the transducer locations, and wherein the calibration factor generator circuit is operative to determine a transformation that relates the spatial domain to the plurality of normal modes for the plurality of discrete locations and to determine the modal Coriolis term from the spatial Coriolis characterization according to the determined transformation that relates the spatial domain to the plurality of normal modes for the plurality of discrete locations.
An apparatus according to Claim [Claim Reference]43, wherein the calibration factor generator circuit is operative to determine the transformation that relates the spatial domain to the plurality of normal modes at the plurality of discrete locations from a mode shape function that describes motion of the conduit in a normal mode as a function of location on the conduit.
An apparatus according to Claim [Claim Reference]44, wherein the mode shape function is a function of an eigenvalue and a boundary condition.
An apparatus according to Claim [Claim Reference]44, wherein the calibration factor generator circuit is further operative to determine the mode shape function.
An apparatus according to Claim [Claim Reference]46, wherein the calibration factor generator circuit is operative to determine the mode shape function from a predetermined eigenvalue and a predetermined boundary condition.
An apparatus according to Claim [Claim Reference]47, wherein the calibration factor generator circuit determines the mode shape function assuming a homogenous boundary condition.
An apparatus according to Claim [Claim Reference]39, wherein the calibration factor generator circuit is operative to determine an orthogonality of a mode shape function for a predetermined mass flow in the conduit, the mode shape function describing motion of the conduit in a normal mode as a function of location on the conduit.
An apparatus according to Claim [Claim Reference]49, wherein the mode shape function is a function of an eigenvalue and a boundary condition.
An apparatus according to Claim [Claim Reference]49, wherein the calibration factor generator circuit is operative to determine the mode shape function.
An apparatus according to Claim [Claim Reference]51, wherein the calibration factor generator circuit is operative to determine the mode shape function from a predetermined eigenvalue and a predetermined boundary condition.
An apparatus according to Claim [Claim Reference]52, wherein the calibration factor generator circuit is operative to determine the mode shape function assuming a homogenous boundary condition.
An apparatus according to Claim [Claim Reference]34, wherein the calibration factor generator circuit is operative to generate an estimated spatial response for a plurality of locations of the conduit from the normal modal dynamic characterization and to generate the calibration factor from the estimated spatial response.
An apparatus according to Claim [Claim Reference]54, wherein the calibration factor generator circuit is operative to determine a spatio-temporal relationship among movements at the plurality of locations and to determine the calibration factor from the determined spatio-temporal relationship.
An apparatus according to Claim [Claim Reference]55, wherein the calibration factor generator circuit is operative to determine one of a time difference or a phase relationship and to determine the calibration factor from the determined one of a time difference or a phase relationship.
An apparatus according to Claim [Claim Reference]34, wherein the calibration factor generator circuit is configured to receive motion signals from the plurality of motion transducers of the parameter sensor and operative to generate the calibration factor from the received motion signals.
An apparatus according to Claim [Claim Reference]34, wherein the mass flow estimator circuit and at least a portion of the calibration factor generator circuit are co-located.
An apparatus according to Claim [Claim Reference]34, wherein the interface circuit is configured to be coupled and uncoupled to and from the mass flow estimator circuit.
An apparatus according to Claim [Claim Reference]34, wherein the calibration factor generator circuit comprises a data processor circuit.
An apparatus according to Claim [Claim Reference]34, wherein the mass flow estimator circuit and the calibration factor generator circuit are implemented in a common data processor circuit.
A mass flow sensor, comprising:
A mass flow sensor according to Claim [Claim Reference]62, wherein the mass flow estimator circuit is operative to determine a spatio-temporal relationship among the plurality of motion signals and to apply the calibration factor to the determined spatio-temporal relationship to generate a mass flow estimate.
A mass flow sensor according to Claim [Claim Reference]63, wherein the mass flow estimator circuit is operative to determine one of a time difference or a phase relationship and to apply the calibration factor to the determined one of a time difference or a phase relationship to generate an estimate of mass flow rate.
A mass flow sensor according to Claim [Claim Reference]62, wherein the normal modal dynamic characterization includes a modal Coriolis term that describes coupling among a plurality of normal modes of the conduit responsive to mass flow in the conduit.
A mass flow sensor according to Claim [Claim Reference]62, wherein means for constraining motion of the conduit comprises means for attaching the conduit to a structure.
A mass flow sensor according to Claim [Claim Reference]62, wherein the means for constraining motion of the conduit comprises means for applying a force to the conduit responsive to motion of the conduit to thereby induce a boundary condition that approximates the assumed boundary condition.
A mass flow sensor according to Claim [Claim Reference]67, wherein the means for applying a force to the conduit comprises:
A mass flow sensor according to Claim [Claim Reference]62:
A mass flow sensor according to Claim [Claim Reference]69:
A mass flow sensor according to Claim [Claim Reference]62:
A mass flow sensor according to Claim [Claim Reference]71, wherein the shape control circuit is operative to control the at least three actuators such that motion of the tube approximates a first bending mode.
A mass flow sensor according to Claim [Claim Reference]72, wherein the shape control circuit is operative to constrain motion of the tube such that first and second spaced apart locations of the tube exhibit approximately no relative motion.
A mass flow sensor according to Claim [Claim Reference]62, further comprising a calibration factor determiner circuit operative to generate the calibration factor responsive to motion signals produced by the plurality of motion transducers.
A mass flow sensor, comprising:
A mass flow sensor according to Claim [Claim Reference]75, wherein the mass flow estimator circuit is operative to determine a spatio-temporal relationship among the plurality of motion signals and to apply the calibration factor to the determined spatio-temporal relationship to generate a mass flow estimate.
A mass flow sensor according to Claim [Claim Reference]76, wherein the mass flow estimator circuit is operative to determine one of a time difference or a phase relationship and to apply the calibration factor to the determined one of a time difference or a phase relationship to generate an estimate of mass flow rate.
A mass flow sensor according to Claim [Claim Reference]75, wherein the normal modal dynamic characterization includes a modal Coriolis term that describes coupling among a plurality of normal modes of the conduit responsive to mass flow in the conduit.
A mass flow sensor according to Claim [Claim Reference]75, wherein the shape control circuit is operative to control the plurality of actuators such that motion of the tube approximates a first bending mode.
A mass flow sensor according to Claim [Claim Reference]79, wherein the shape control circuit is operative to constrain motion of the tube such that first and second spaced apart locations of the tube exhibit approximately no relative motion.
A mass flow sensor according to Claim [Claim Reference]75, further comprising a calibration factor determiner circuit operative to generate the calibration factor responsive to motion signals produced by the plurality of motion transducers.
A computer program product for characterizing a parameter sensor comprising a conduit configured to contain a material and a plurality of motion transducers operative to generate motion signals representing motion of the conduit, the computer program product comprising computer-readable program code embodied in a computer-readable storage medium, the computer-readable program code comprising:
A computer program product according to Claim [Claim Reference]82, wherein the program code for determining a calibration factor comprises:
A computer program product according to Claim [Claim Reference]82, wherein the calibration factor relates mass flow rate to a spatio-temporal relationship among the plurality of motion signals.
A computer program product according to Claim [Claim Reference]84, wherein the calibration factor relates mass flow rate to one of a time difference or a phase relationship.
A computer program product according to Claim [Claim Reference]82, wherein the normal modal dynamic characterization characterizes motion of the conduit as a function of a modal Coriolis term that describes coupling among a plurality of normal modes of the conduit responsive to mass flow in the conduit.
A computer program product according to Claim [Claim Reference]86, where the computer readable program code further comprises program code for determining the modal Coriolis term from a mode shape function that describes motion of the conduit in a normal mode as a function of location on the conduit.
A computer program product according to Claim [Claim Reference]86, wherein the computer-readable program code further comprises program code for determining the modal Coriolis term from a spatial Coriolis characterization that describes motion of a plurality of discrete locations of the conduit in a spatial domain in response to a predetermined mass flow.
A computer program product according to Claim [Claim Reference]88, wherein the program code for determining the modal Coriolis term from a spatial Coriolis characterization that describes motion of a plurality of discrete locations of the conduit in a spatial domain in response to a predetermined mass flow comprises program code for determining the modal Coriolis term from the spatial Coriolis characterization using a transformation that relates the spatial domain to the plurality of normal modes.
A computer program product according to Claim [Claim Reference]89, wherein the plurality of motion transducers are operative to generate respective motion signals that represent motion at respective transducer locations of the conduit, wherein the plurality of discrete locations associated with the spatial Coriolis characterization includes locations other than the transducer locations, and wherein the program code for determining the modal Coriolis term from the spatial Coriolis characterization using a transformation that relates the spatial domain to the plurality of normal modes comprises:
A computer program product according to Claim [Claim Reference]90, wherein the program code for determining a transformation that relates the spatial domain to the plurality of normal modes for the plurality discrete locations comprises program code for determining the transformation that relates the spatial domain to the plurality of normal modes at the plurality of discrete locations from a mode shape function that describes motion of the conduit in a normal mode as a function of location on the conduit.
A computer program product according to Claim [Claim Reference]91, wherein the mode shape function is a function of an eigenvalue and a boundary condition.
A computer program product according to Claim [Claim Reference]91, wherein the computer-readable program code further comprises program code for determining the mode shape function.
A computer program product according to Claim [Claim Reference]93, wherein the program code for determining the mode shape function comprises program code for determining the mode shape function from a predetermined eigenvalue and a predetermined boundary condition.
A computer program product according to Claim [Claim Reference]93, wherein the program code for determining the mode shape function from a predetermined eigenvalue and a predetermined boundary condition comprises program code for assuming a homogenous boundary condition.
A computer program product according to Claim [Claim Reference]87, wherein the computer-readable program code further comprises program code for determining an orthogonality of a mode shape function for a predetermined mass flow in the conduit, the mode shape function describing motion of the conduit in a normal mode as a function of location on the conduit.
A computer program product according to Claim [Claim Reference]96, wherein the mode shape function is a function of an eigenvalue and a boundary condition.
A computer program product according to Claim [Claim Reference]96, wherein the computer-readable program code further comprises program code for determining the mode shape function.
A computer program product according to Claim [Claim Reference]98, wherein the program code for determining the mode shape function comprises program code for determining the mode shape function from a predetermined eigenvalue and a predetermined boundary condition.
A computer program product according to Claim [Claim Reference]99, wherein the program code for determining the mode shape function from a predetermined eigenvalue and a predetermined boundary condition comprises program code for assuming a homogenous boundary condition.
A computer program product according to Claim [Claim Reference]82, wherein the program code for determining a calibration factor comprises:
A computer program product according to Claim [Claim Reference]101, wherein the program code for generating the calibration factor from the estimated spatial response comprises:
A computer program product according to Claim [Claim Reference]102:
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Constructional details: means for influencing the flowmeter's motional or vibrational behaviour, e.g., conduit support or fixing means, or conduit…
Means for influencing the flowmeter's motional or vibrational behaviour, e.g., conduit support or fixing means, or conduit attachments: motion or…
Constructional details: signal processing
Vibrating measuring conduits: having straight measuring conduits
Term end not estimated
Coriolis sensors typically operate by detecting motion of a vibrating conduit that contains a flowing material. Properties associated with the material in the conduit, such as mass flow, density and the like, may be determined by processing signals from motion transducers associated with the conduit, as the vibrational modes of the vibrating material-filled system generally are affected by the combined mass, stiffness and damping characteristics of the containing conduit and the material contained therein.
A typical Coriolis mass flowmeter includes one or more conduits that are connected inline in a pipeline or other transport system and convey material, e.g., fluids, slurries and the like, in the system. Each conduit may be viewed as having a set of natural vibrational modes including, for example, simple bending, torsional, radial and coupled modes. In a typical Coriolis mass flow measurement application, a conduit is excited at resonance in one of its natural vibrational modes as a material flows through the conduit, and motion of the conduit is measured at points spaced along the conduit. Excitation is typically provided by an actuator, e.g., an electromechanical device, such as a voice coil-type driver, that perturbs the conduit in a periodic fashion. Mass flow rate may be determined by measuring time or phase differences between motion at the transducer locations. Exemplary Coriolis mass flowmeters are described in U.S. Patent Nos. 4,109,524 to Smith, 4,491,025 to Smith et al., and Re. 31,450 to Smith.
The accuracy of Coriolis mass flowmeters may be compromised by the mountings which constrain vibration of the conduit. The affects of these constraints may be reduced by using flowmeter designs that are balanced to reduce effects attributable to external vibration, and by using frequency domain filters, e.g., bandpass filters designed to filter out components of the motion signals away from the excitation frequency. However, mechanical filtering approaches are often limited by mechanical considerations, e.g., material limitations, mounting constraints, weight limitations, size limitations and the like, and frequency domain filtering may be ineffective at removing unwanted vibrational contributions near the excitation frequency.
FIG. 1 is a schematic diagram of a mass flow sensor apparatus according to embodiments of the present invention.
FIG. 2 is a schematic diagram of a mass flow sensor apparatus according to other embodiments of the present invention.
FIG. 3 is a schematic diagram of a calibration factor generator circuit according to embodiments of the present invention.
The present invention now will be described more fully hereinafter with reference to the accompanying drawings, in which embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Like numbers refer to like elements throughout. As will be appreciated by one of skill in the art, the present invention may be embodied as systems (apparatus), methods, or computer program products.
Embodiments of the present invention described herein relate to Coriolis mass flowmeters that utilize a single, substantially straight conduit that does not require, for example, a mechanically-tuned balance beam. The present invention may be particularly advantageous in such applications. However, those skilled in the art will appreciate that the present invention can be used with other types of flowmeter structures, including conventional curved tube structures and straight tube structures including mechanical balance beams.
As will be appreciated by one of skill in the art, the present invention may be embodied as an apparatus and/or method and/or computer program product. The present invention may be implemented in hardware or in a combination of hardware and software aspects. Furthermore, the present invention may also take the form of a computer program product including a computer-usable storage medium having computer-usable program code embodied in the medium. Any suitable computer readable medium may be utilized, including semiconductor memory devices (e.g., RAMs, ROMs, EEPROMs, and the like), hard disks, CD-ROMs, optical storage devices, and magnetic storage devices.