Method and device for determining steady-state frequency response of MHD angular velocity sensor element

Abstract

The present application provides a method and device for determining the steady-state frequency response of an MHD angular velocity sensor element. The method comprises: obtaining structural dimension parameters and material property parameters of the MHD angular velocity sensor element in response to a modeling instruction; generating an average magnetic induction intensity of a radial magnetic circuit in a conductive fluid ring in the MHD angular velocity sensor element based on the Maxwell equations according to the structural dimension parameters and the material property parameters; generating an average circumferential velocity of the conductive fluid relative to the magnetic field based on a low magnetic Reynolds number incompressible equation group according to the structural dimension parameters and the material property parameters; generating a frequency response characteristic function of the MHD angular velocity sensor element based on the average magnetic induction intensity and the circumferential average velocity based on the Faraday motional electromotive force method; and solving the frequency response characteristic function to obtain amplitude-frequency response data and phase-frequency response data of the MHD angular velocity sensor element.

Description

Technical Field

[0001] The present application relates to the field of sensor technology, and more specifically, to a method and device for determining a steady-state frequency response of an MHD angular velocity sensor element. Background Art

[0002] With the continuous development of space science and technology, space technologies such as high-resolution earth observation, deep space exploration, and laser communication have continuously increased the requirements for the attitude stability and pointing accuracy of spacecraft payloads. However, the payload platform is extremely sensitive to the disturbance effect of micro-angular vibration and is easily affected by the micro-angular vibration of the space structure. The micro-angular vibration of the space structure limits the further improvement of the attitude and pointing control accuracy of high-precision spacecraft payloads.

[0003] Magnetohydrodynamics (MHD) angular velocity sensor has the characteristics of low noise, wide bandwidth, miniaturization, long life, etc. It is insensitive to acceleration shock and is currently one of the most direct, effective and reliable sensors for measuring broadband micro-angular vibrations of spacecraft payload platforms.

[0004] The steady-state frequency response is the response of the MHD angular velocity sensor to the sinusoidal angular velocity input, including the amplitude-frequency response and the phase-frequency response. The steady-state frequency response describes the linear correspondence of the sensor converting the input angular velocity into the output voltage signal, and is one of the key technical indicators that need to be considered first in sensor design.

[0005] In the process of implementing the concept of the present application, it was found that the related technology could not accurately determine the steady-state frequency response characteristics of the MHD angular velocity sensor element. Summary of the invention

[0006] In view of this, the present application provides a method and a device for determining the steady-state frequency response of an MHD angular velocity sensor element.

[0007] One aspect of the present application provides a method for determining a steady-state frequency response of an MHD angular velocity sensor element, comprising:

[0008] In response to the modeling instruction, obtaining the structural dimension parameters and material property parameters of the MHD angular velocity sensor element;

[0009] Based on Maxwell's equations, according to the structural dimension parameters and the material property parameters, an average magnetic induction intensity of the radial magnetic circuit in the conductive fluid ring in the MHD angular velocity sensor element is generated;

[0010] Based on the low magnetic Reynolds number incompressible equations, the circumferential average velocity of the conductive fluid relative to the magnetic field is generated according to the above structural size parameters and material physical property parameters;

[0011] Based on the Faraday motional electromotive force method, according to the average magnetic induction intensity and the average circumferential velocity, a frequency response characteristic function of the MHD angular velocity sensor element is generated;

[0012] The frequency response characteristic function is solved to obtain the amplitude-frequency response data and the phase-frequency response data of the MHD angular velocity sensor element.

[0013] According to an embodiment of the present application, the method for determining the steady-state frequency response further includes:

[0014] Generate cutoff frequency data according to the amplitude-frequency response data or the phase-frequency response data;

[0015] When the cutoff frequency data does not meet the design threshold, the structural dimension parameters and the material property parameters are adjusted to obtain new structural dimension parameters and new material property parameters, so as to generate new amplitude-frequency response data and new phase-frequency response data according to the new structural dimension parameters and the new material property parameters.

[0016] According to an embodiment of the present application, the average magnetic induction intensity of the radial magnetic circuit in the conductive fluid ring in the MHD angular velocity sensor element is generated according to the structural size parameters and the material property parameters, including:

[0017] Generate a first target curve and a second target curve according to the magnetic induction intensity and magnetic field intensity inside the material, wherein the first target curve is a BH function curve, and the second target curve represents the relationship between the residual magnetic flux density and the recoil permeability;

[0018] Substituting the first target curve and the second target curve into the Maxwell equations under the condition of a constant magnetic field to obtain a first set of equations to be solved;

[0019] Solving the first set of equations to be solved based on the finite element method to obtain multiple target magnetic induction intensities of the MHD angular velocity sensor element at multiple positions within the magnetic circuit structure area;

[0020] The average magnetic flux density is generated based on the plurality of target magnetic flux densities.

[0021] According to an embodiment of the present application, the first set of equations to be solved is shown in formula (1):

[0022] (1)

[0023] in, is the magnetic induction intensity inside the material, is the magnetic field strength, is the BH function curve, is the second target curve, is the vacuum permeability, is the residual flux density, is the recovery permeability, is the magnetic scalar potential, The boundary element vector of the magnetic circuit solution domain is: is any point within the magnetic circuit structure area of ​​the MHD angular velocity sensor element.

[0024] According to an embodiment of the present application, the circumferential average velocity of the conductive fluid relative to the magnetic field is generated according to the above-mentioned structural dimension parameters and material property parameters, including:

[0025] Substituting the above structural dimension parameters and the above material property parameters into the above low magnetic Reynolds number incompressible equation group, a second equation group to be solved is obtained;

[0026] Solving the second set of equations to be solved to obtain the velocity field of the conductive fluid;

[0027] The circumferential average velocity is generated based on the conductive fluid velocity field.

[0028] According to an embodiment of the present application, the above structural dimension parameters and the above material property parameters are substituted into the above low magnetic Reynolds number incompressible equation group to obtain a second set of equations to be solved, including:

[0029] Substituting the above structural dimension parameters and the above material property parameters into the above low magnetic Reynolds number incompressible equation group, the initial equation group to be solved is obtained;

[0030] The above-mentioned initial set of equations to be solved is simplified based on boundary conditions and initial conditions to obtain the above-mentioned second set of equations to be solved.

[0031] According to an embodiment of the present application, the initial set of equations to be solved is shown in formula (2), the second set of equations to be solved is shown in formula (3), and the velocity field of the conductive fluid is As shown in formula (4), the average circumferential velocity As shown in formula (5):

[0032] (2)

[0033] in, is the electric field strength in the conductive fluid, is the current density in the conducting fluid, is the absolute velocity of the conductive fluid, is the conductivity of the conducting fluid, Is the conductive fluid relative The relative speed of motion, is the electric potential of the conducting fluid, is the density of the conducting fluid, It's time. is the static pressure inside the conductive fluid, is the kinematic viscosity of the conductive fluid, Except for the Laplace force The volume force on the conductive fluid outside is is the circumferential base coordinate vector of the cylindrical coordinate system where the conductive fluid ring is located, yes exist The weight in direction, is the radial coordinate component of the cylindrical coordinate system where the conductive fluid ring is located, It is the angular velocity of the external input to the sensor element;

[0034] (3)

[0035] in, yes of Directional component, is the height direction base coordinate vector of the cylindrical coordinate system where the conductive fluid ring is located, yes The coordinate component of the direction, yes of Directional component, yes of Directional component, is the inner radius of the conductive fluid ring, is the outer radius of the conductive fluid annulus, is the average magnetic induction intensity;

[0036] (4)

[0037] (5)

[0038] in, Represents complex number The real part of , is the input angular velocity The angular frequency, It is half the width of the air gap in the conductive fluid ring. is the Hartmann number, is the average radius of the conductive fluid annulus, , and They are The hyperbolic cosine, sine and tangent functions of is an imaginary unit, yes The corresponding amplitude when is a sinusoidal quantity, that is , is the amplitude of the sine function, , is a natural constant.

[0039] According to an embodiment of the present application, the above frequency response characteristic function is shown in formula (6):

[0040] (6)

[0041] in, is the height of the conductive fluid ring, Representation function The Fourier transform of .

[0042] According to an embodiment of the present application, the above amplitude-frequency response data As shown in formula (7), the above phase-frequency response data As shown in formula (8):

[0043] (7)

[0044] (8)

[0045] in, Indicates plural The model, Indicates plural exist The angle within the interval.

[0046] Another aspect of the present application provides a device for determining a steady-state frequency response of an MHD angular velocity sensor element, characterized in that it comprises:

[0047] An acquisition module, used for acquiring structural dimension parameters and material property parameters of the MHD angular velocity sensor element in response to a modeling instruction;

[0048] A first generating module is used to generate an average magnetic induction intensity of a radial magnetic circuit in a conductive fluid ring in the MHD angular velocity sensor element based on Maxwell equations, the structural dimension parameters and the material property parameters;

[0049] The second generation module is used to generate the circumferential average velocity of the conductive fluid relative to the magnetic field based on the low magnetic Reynolds number incompressible equations and the above-mentioned structural size parameters and material physical property parameters;

[0050] A third generating module is used to generate a frequency response characteristic function of the MHD angular velocity sensor element according to the average magnetic induction intensity and the circumferential average velocity based on the Faraday motional electromotive force method;

[0051] The solving module is used to solve the frequency response characteristic function to obtain the amplitude-frequency response data and the phase-frequency response data of the MHD angular velocity sensor element.

[0052] Another aspect of the present application provides an electronic device, comprising:

[0053] one or more processors;

[0054] a memory for storing one or more programs,

[0055] When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described above.

[0056] Another aspect of the present application provides a computer-readable storage medium storing computer-executable instructions, which are used to implement the method described above when executed.

[0057] Another aspect of the present application provides a computer program product, which includes computer executable instructions, and the instructions are used to implement the method as described above when executed.

[0058] According to the embodiments of the present application, the average magnetic induction intensity and the circumferential average velocity can be determined by using the structural dimension parameters and material property parameters of the MHD angular velocity sensor element, and the Maxwell equations and the low magnetic Reynolds number incompressible equations. After that, the frequency response characteristic function of the MHD angular velocity sensor element can be obtained by processing the average magnetic induction intensity and the circumferential average velocity using the Faraday motional electromotive force method. The amplitude-frequency response data and the phase-frequency response data of the MHD angular velocity sensor element can be obtained by solving it. Since the present application considers the radial magnetic circuit inside the conductive fluid ring in the MHD angular velocity sensor element in the process of determining the steady-state frequency response, it can accurately and conveniently describe the steady-state frequency response characteristics of the sensor element, thereby accurately guiding the design of the structure and material parameters of the sensor element, which can greatly shorten the research and development cycle of the MHD angular velocity sensor and significantly reduce the research and development cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The above and other objects, features and advantages of the present application will become more apparent through the following description of the embodiments of the present application with reference to the accompanying drawings, in which:

[0060] Figure 1 An exemplary system architecture to which a method for determining a steady-state frequency response according to an embodiment of the present application can be applied is shown;

[0061] Figure 2 A flow chart showing a method for determining a steady-state frequency response according to an embodiment of the present application is shown;

[0062] Figure 3 A schematic diagram of the magnetic circuit structure of an MHD angular velocity sensor element according to an embodiment of the present application is shown;

[0063] Figure 4 A schematic diagram of a grid division result according to an embodiment of the present application is shown;

[0064] Figure 5 A schematic diagram of the velocity field and frequency response of a conductive fluid according to an embodiment of the present application is shown;

[0065] Figure 6 A structural block diagram of a device for determining a steady-state frequency response according to an embodiment of the present application is shown;

[0066] Figure 7 A block diagram of an electronic device suitable for implementing the method described above according to an embodiment of the present application is shown. DETAILED DESCRIPTION

[0067] Below, embodiments of the present application will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the present application. In the following detailed description, for ease of explanation, many specific details are set forth to provide a comprehensive understanding of the embodiments of the present application. However, it is apparent that one or more embodiments may also be implemented without these specific details. In addition, in the following description, descriptions of known structures and technologies are omitted to avoid unnecessary confusion of the concepts of the present application.

[0068] The terms used herein are only for describing specific embodiments and are not intended to limit the present application. The terms "include", "comprising", etc. used herein indicate the existence of the features, steps, operations and / or components, but do not exclude the existence or addition of one or more other features, steps, operations or components.

[0069] All terms (including technical and scientific terms) used herein have the meanings commonly understood by those skilled in the art unless otherwise defined. It should be noted that the terms used herein should be interpreted as having a meaning consistent with the context of this specification and should not be interpreted in an idealized or overly rigid manner.

[0070] When using expressions such as "at least one of A, B, and C, etc.", they should generally be interpreted according to the meaning of the expression commonly understood by those skilled in the art (for example, "a system having at least one of A, B, and C" should include but is not limited to a system having A alone, B alone, C alone, A and B, A and C, B and C, and / or A, B, C, etc.).

[0071] In the MHD angular velocity sensor, the structural component that can convert the external angular velocity input into the motional electromotive force output is called the MHD angular velocity sensor element, hereinafter referred to as the sensor element. The steady-state frequency response of the MHD angular velocity sensor is composed of the frequency responses of the sensor element and the detection circuit. Therefore, accurate modeling of the steady-state frequency response of the sensor element is a necessary prerequisite for the precise design of the sensor.

[0072] The existing technology cannot quantitatively and accurately describe the flow characteristics of conductive fluids, and thus cannot accurately model the steady-state frequency response characteristics of MHD angular velocity sensor elements, and cannot accurately guide the design of the structure and material parameters of the sensor elements.

[0073] In view of this, an embodiment of the present application provides a method and device for determining the steady-state frequency response of an MHD angular velocity sensor element, the method comprising obtaining structural dimension parameters and material property parameters of the MHD angular velocity sensor element in response to a modeling instruction; based on the Maxwell equations, generating the average magnetic induction intensity of the radial magnetic circuit in the conductive fluid ring in the MHD angular velocity sensor element according to the structural dimension parameters and material property parameters; based on the low magnetic Reynolds number incompressible equations, generating the circumferential average velocity of the conductive fluid relative to the magnetic field according to the structural dimension parameters and material property parameters; based on the Faraday motional electromotive force method, generating the frequency response characteristic function of the MHD angular velocity sensor element according to the average magnetic induction intensity and the circumferential average velocity; solving the frequency response characteristic function to obtain the amplitude-frequency response data and phase-frequency response data of the MHD angular velocity sensor element.

[0074] In the embodiments of this application, the collection, updating, analysis, processing, use, transmission, provision, disclosure, storage, etc. of the data involved (for example, including but not limited to user personal information) are in compliance with the provisions of relevant laws and regulations, are used for legitimate purposes, and do not violate public order and good morals. In particular, necessary measures are taken for user personal information to prevent illegal access to user personal information data and maintain the security of user personal information and network security.

[0075] Figure 1 An exemplary system architecture 100 to which a method for determining a steady-state frequency response according to an embodiment of the present application can be applied is shown. It should be noted that: Figure 1 What is shown is merely an example of a system architecture to which the embodiments of the present application can be applied, in order to help those skilled in the art understand the technical content of the present application, but it does not mean that the embodiments of the present application cannot be used in other devices, systems, environments or scenarios.

[0076] like Figure 1As shown, the system architecture 100 according to this embodiment may include a first terminal device 101, a second terminal device 102, a third terminal device 103, a network 104, and a server 105. The network 104 is used to provide a medium for a communication link between the first terminal device 101, the second terminal device 102, the third terminal device 103, and the server 105. The network 104 may include various connection types, such as wired and / or wireless communication links, etc.

[0077] The user may use the first terminal device 101, the second terminal device 102, and the third terminal device 103 to interact with the server 105 through the network 104 to receive or send messages, etc. Various communication client applications may be installed on the first terminal device 101, the second terminal device 102, and the third terminal device 103, such as shopping applications, web browser applications, search applications, instant messaging tools, email clients, and / or social platform software, etc. (only for example).

[0078] The first terminal device 101, the second terminal device 102, and the third terminal device 103 may be various electronic devices having display screens and supporting web browsing, including but not limited to smart phones, tablet computers, laptop computers, desktop computers, and the like.

[0079] The server 105 may be a server that provides various services, such as a background management server (only as an example) that provides support for websites browsed by users using the first terminal device 101, the second terminal device 102, and the third terminal device 103. The background management server may analyze and process the received data such as user requests, and feed back the processing results (such as web pages, information, or data obtained or generated according to user requests) to the terminal device.

[0080] It should be noted that the method for determining the steady-state frequency response provided in the embodiment of the present application can generally be executed by the server 105. Accordingly, the device for determining the steady-state frequency response provided in the embodiment of the present application can generally be set in the server 105. The method for determining the steady-state frequency response provided in the embodiment of the present application can also be executed by a server or server cluster that is different from the server 105 and can communicate with the first terminal device 101, the second terminal device 102, the third terminal device 103 and / or the server 105. Correspondingly, the device for determining the steady-state frequency response provided in the embodiment of the present application can also be set in a server or server cluster that is different from the server 105 and can communicate with the first terminal device 101, the second terminal device 102, the third terminal device 103 and / or the server 105. Alternatively, the method for determining the steady-state frequency response provided in the embodiment of the present application can also be performed by the first terminal device 101, the second terminal device 102 or the third terminal device 103, or can also be performed by other terminal devices that are different from the first terminal device 101, the second terminal device 102 or the third terminal device 103. Correspondingly, the steady-state frequency response determination device provided in the embodiment of the present application may also be arranged in the first terminal device 101, the second terminal device 102 or the third terminal device 103, or in other terminal devices different from the first terminal device 101, the second terminal device 102 or the third terminal device 103.

[0081] It should be understood that Figure 1 The number of terminal devices, networks and servers in the embodiment is only . According to the implementation requirements, there can be any number of terminal devices, networks and servers.

[0082] Figure 2 A flow chart of a method for determining a steady-state frequency response according to an embodiment of the present application is shown.

[0083] like Figure 2 As shown, the method for determining the steady-state frequency response of the MHD angular velocity sensor element includes operations S201 to S205.

[0084] In operation S201, in response to a modeling instruction, structural dimension parameters and material property parameters of an MHD angular velocity sensor element are acquired;

[0085] In operation S202, based on Maxwell's equations, according to structural dimension parameters and material property parameters, an average magnetic induction intensity of a radial magnetic circuit in a conductive fluid ring in an MHD angular velocity sensor element is generated;

[0086] In operation S203, based on the low magnetic Reynolds number incompressible equations, according to the structural size parameters and the material property parameters, the circumferential average velocity of the conductive fluid relative to the magnetic field is generated;

[0087] In operation S204, based on the Faraday motional electromotive force method, a frequency response characteristic function of the MHD angular velocity sensor element is generated according to the average magnetic induction intensity and the circumferential average velocity;

[0088] In operation S205, the frequency response characteristic function is solved to obtain amplitude-frequency response data and phase-frequency response data of the MHD angular velocity sensor element.

[0089] According to an embodiment of the present application, the modeling instruction may be generated by the electronic device after the staff performs corresponding operations on the electronic device.

[0090] According to the embodiments of the present application, the structural dimension parameters refer to the magnetic conductive material area and the non-magnetic conductive material area of ​​the MHD angular velocity sensor element, and the material physical property parameters can be the material parameter characteristics of the magnetic conductive material area and the non-magnetic conductive material area (including conductive fluid and air) and the material parameter characteristics of the internal area of ​​the permanent magnet.

[0091] According to the embodiment of the present application, based on the Maxwell equations, according to the structural size parameters and material property parameters, the average magnetic induction intensity of the radial magnetic circuit in the conductive fluid ring in the MHD angular velocity sensor element is generated. Based on the low magnetic Reynolds number incompressible equations, the circumferential average velocity of the conductive fluid relative to the magnetic field is generated according to the structural size parameters and material physical properties. Then, based on the Faraday motional electromotive force method, the frequency response characteristic function of the MHD angular velocity sensor element is generated according to the average magnetic induction intensity and the average circumferential velocity. The frequency response characteristic function is solved to obtain the amplitude-frequency response data of the MHD angular velocity sensor element. and phase frequency response data .

[0092] According to the embodiments of the present application, the average magnetic induction intensity and the circumferential average velocity can be determined by using the structural dimension parameters and material property parameters of the MHD angular velocity sensor element, and the Maxwell equations and the low magnetic Reynolds number incompressible equations. After that, the frequency response characteristic function of the MHD angular velocity sensor element can be obtained by processing the average magnetic induction intensity and the circumferential average velocity using the Faraday motional electromotive force method. The amplitude-frequency response data and the phase-frequency response data of the MHD angular velocity sensor element can be obtained by solving it. Since the present application considers the radial magnetic circuit inside the conductive fluid ring in the MHD angular velocity sensor element in the process of determining the steady-state frequency response, it can accurately and conveniently describe the steady-state frequency response characteristics of the sensor element, thereby accurately guiding the design of the structure and material parameters of the sensor element, which can greatly shorten the research and development cycle of the MHD angular velocity sensor and significantly reduce the research and development cost.

[0093] According to an embodiment of the present application, the method for determining the steady-state frequency response further includes:

[0094] Generate cutoff frequency data according to the amplitude-frequency response data or the phase-frequency response data;

[0095] When the cutoff frequency data does not meet the design threshold, the structural dimension parameters and the material property parameters are adjusted to obtain new structural dimension parameters and new material property parameters, so as to generate new amplitude-frequency response data and new phase-frequency response data according to the new structural dimension parameters and the new material property parameters.

[0096] According to an embodiment of the present application, the preset amplitude threshold and the preset phase threshold can be specifically set according to actual needs, for example, the preset amplitude threshold can be -3dB, and the preset phase threshold can be 45°. The cutoff frequency data includes a first cutoff frequency or a second cutoff frequency.

[0097] In a specific embodiment, a first cutoff frequency is generated according to the amplitude-frequency response data and a preset amplitude threshold (-3dB); the first cutoff frequency is compared with the design threshold of the sensor element, and if the first cutoff frequency is less than the design threshold of the sensor element, the requirement is met and no adjustment is made; if the first cutoff frequency is greater than the design threshold of the sensor element, the structural dimension parameters and the material physical property parameters are adjusted to obtain new structural dimension parameters and new material physical property parameters, so as to generate new amplitude-frequency response data and new phase-frequency response data according to the new structural dimension parameters and the new material physical property parameters.

[0098] In another specific embodiment, a second cutoff frequency is generated according to the phase-frequency response data and a preset phase threshold (45°); the second cutoff frequency is compared with the design threshold of the sensor element, and if the second cutoff frequency is less than the design threshold of the sensor element, the requirement is met and no adjustment is made; if the second cutoff frequency is greater than the design threshold of the sensor element, the structural dimension parameters and the material physical property parameters are adjusted to obtain new structural dimension parameters and new material physical property parameters, so as to generate new amplitude-frequency response data and new phase-frequency response data according to the new structural dimension parameters and the new material physical property parameters.

[0099] It should be noted that the above adjustment method can be used to judge the threshold alone, or the two can be combined to judge. In this case, the cutoff frequency data needs to meet the design threshold of the sensor element.

[0100] According to the embodiments of the present application, by optimizing the design of the structural dimension parameters and material property parameters of the sensor element, the amplitude-frequency response and phase-frequency response of the sensor element are optimized, thereby further improving the accuracy and convenience of describing the steady-state frequency response characteristics of the sensor element.

[0101] Figure 3 A schematic diagram of the magnetic circuit structure of an MHD angular velocity sensor element according to an embodiment of the present application is shown. Figure 4 A schematic diagram of a grid division result according to an embodiment of the present application is shown.

[0102] According to an embodiment of the present application, the average magnetic induction intensity of the radial magnetic circuit in the conductive fluid ring in the MHD angular velocity sensor element is generated according to the structural size parameters and the material property parameters, including:

[0103] Generate a first target curve and a second target curve according to the magnetic induction intensity and magnetic field intensity inside the material, wherein the first target curve is a BH function curve, and the second target curve represents the relationship between the residual magnetic flux density and the recovery magnetic permeability;

[0104] Substituting the first target curve and the second target curve into the Maxwell equations under the condition of a constant magnetic field, to obtain a first set of equations to be solved;

[0105] The first set of equations to be solved is solved based on the finite element method to obtain multiple target magnetic induction intensities of the MHD angular velocity sensor element at multiple positions within the magnetic circuit structure area;

[0106] An average magnetic induction intensity is generated according to multiple target magnetic induction intensities.

[0107] According to an embodiment of the present application, the material parameter characteristics of the magnetic conductive material region and the non-magnetic conductive material region (including the conductive fluid and the air) are described using the BH curve of the material, that is, the first target curve is , the material parameters of the inner region of the permanent magnet are characterized using the residual flux density and the recoil permeability To describe, the second target curve is ,in is the magnetic permeability of vacuum.

[0108] According to an embodiment of the present application, the first target curve and the second target curve are substituted into the Maxwell equations under the condition of a constant magnetic field to obtain a first set of equations to be solved, and the first set of equations to be solved is solved using a finite element method (such as various software capable of performing finite element calculations) to obtain the MHD angular velocity sensor element at multiple positions (such as Figure 3 The magnetic induction intensity of multiple targets (in each point within the dotted box in . According to the magnetic induction intensity of multiple targets , generating the average magnetic induction intensity .

[0109] According to the embodiment of the present application, the finite element method is to perform grid division in the magnetic field solution domain, and the division result is as follows: Figure 4 As shown, the first set of equations to be solved is discretized and solved.

[0110] According to the embodiments of the present application, the present application can effectively improve the accuracy and convenience of describing the steady-state frequency response characteristics of the sensor element by combining the finite element analysis method while considering the radial magnetic circuit inside the conductive fluid ring in the MHD angular velocity sensor element.

[0111] According to an embodiment of the present application, the first set of equations to be solved is shown in formula (1):

[0112] (1)

[0113] in, is the magnetic induction intensity inside the material, is the magnetic field strength, is the BH function curve, is the second target curve, is the vacuum permeability, is the residual flux density, is the recovery permeability, is the magnetic scalar potential, The boundary element vector of the magnetic circuit solution domain is: is any point within the magnetic circuit structure area of ​​the MHD angular velocity sensor element.

[0114] Figure 5 A schematic diagram of the velocity field and frequency response of a conductive fluid according to an embodiment of the present application is shown.

[0115] According to an embodiment of the present application, generating the circumferential average velocity of the conductive fluid relative to the magnetic field according to the structural size parameters and the material property parameters includes:

[0116] Substituting the structural dimension parameters and material property parameters into the low magnetic Reynolds number incompressible equation group, the second equation group to be solved is obtained;

[0117] Solving the second set of equations to be solved, obtaining the velocity field of the conductive fluid;

[0118] The circumferential average velocity is generated based on the conductive fluid velocity field.

[0119] According to the embodiment of the present application, the structural dimension parameters and material property parameters are substituted into the low magnetic Reynolds number incompressible equation group to obtain the second set of equations to be solved, and the second set of equations to be solved is solved by an analytical method to obtain the conductive fluid velocity field , according to the velocity field of the conductive fluid , generating the average circumferential velocity ,like Figure 5 shown.

[0120] According to an embodiment of the present application, the structural dimension parameters and the material property parameters are substituted into the low magnetic Reynolds number incompressible equation group to obtain the second equation group to be solved, including:

[0121] Substituting the structural dimension parameters and material property parameters into the low magnetic Reynolds number incompressible equations, the initial equations to be solved are obtained;

[0122] The initial set of equations to be solved is simplified based on boundary conditions and initial conditions to obtain a second set of equations to be solved.

[0123] According to an embodiment of the present application, the initial set of equations to be solved is shown in formula (2), the second set of equations to be solved is shown in formula (3), and the velocity field of the conductive fluid is As shown in formula (4), the average circumferential velocity As shown in formula (5):

[0124] (2)

[0125] in, is the electric field strength in the conductive fluid, is the current density in the conducting fluid, is the absolute velocity of the conductive fluid, is the conductivity of the conducting fluid, Is the conductive fluid relative The relative speed of motion, is the electric potential of the conducting fluid, is the density of the conducting fluid, It's time. is the static pressure inside the conductive fluid, is the kinematic viscosity of the conductive fluid, Except for the Laplace force The volume force on the conductive fluid outside is is the circumferential base coordinate vector of the cylindrical coordinate system where the conductive fluid ring is located, yes exist The weight in direction, is the radial coordinate component of the cylindrical coordinate system where the conductive fluid ring is located, It is the angular velocity of the external input to the sensor element;

[0126] (3)

[0127] in, yes of Directional component, is the height direction base coordinate vector of the cylindrical coordinate system where the conductive fluid ring is located, yes The coordinate component of the direction, yes of Directional component, yes of Directional component, is the inner radius of the conductive fluid ring, is the outer radius of the conductive fluid annulus, is the average magnetic induction intensity;

[0128] (4)

[0129] (5)

[0130] in, Represents complex number The real part of , is the input angular velocity The angular frequency, It is half the width of the air gap in the conductive fluid ring. is the Hartmann number, is the average radius of the conductive fluid annulus, , and They are The hyperbolic cosine, sine and tangent functions of is an imaginary unit, yes The corresponding amplitude when is a sinusoidal quantity, that is , is the amplitude of the sine function, , is a natural constant.

[0131] According to an embodiment of the present application, the frequency response characteristic function is shown in formula (6):

[0132] (6)

[0133] in, is the height of the conductive fluid ring, Representation function The Fourier transform of .

[0134] According to an embodiment of the present application, the amplitude-frequency response data As shown in formula (7), the phase-frequency response data As shown in formula (8):

[0135] (7)

[0136] (8)

[0137] in, Indicates plural The model, Indicates plural exist The angle within the interval.

[0138] According to an embodiment of the present application, when the cutoff frequency data does not meet the preset amplitude threshold and / or the phase frequency response data does not meet the preset phase threshold, the structural size parameters (including , , etc.) and material properties (including , , , , etc.) to obtain new structural size parameters and new material property parameters.

[0139] Figure 6 A structural block diagram of a device for determining a steady-state frequency response according to an embodiment of the present application is shown.

[0140] like Figure 6 As shown, the apparatus 600 for determining the steady-state frequency response of the MHD angular velocity sensor element includes an acquisition module 610 , a first generation module 620 , a second generation module 630 , a third generation module 640 and a solution module 650 .

[0141] An acquisition module 610 is used to acquire structural dimension parameters and material property parameters of the MHD angular velocity sensor element in response to the modeling instruction;

[0142] The first generating module 620 is used to generate the average magnetic induction intensity of the radial magnetic circuit in the conductive fluid ring in the MHD angular velocity sensor element based on the Maxwell equations, the structural size parameters and the material property parameters;

[0143] The second generating module 630 is used to generate the circumferential average velocity of the conductive fluid relative to the magnetic field based on the low magnetic Reynolds number incompressible equations according to the structural size parameters and the material property parameters;

[0144] The third generating module 640 is used to generate a frequency response characteristic function of the MHD angular velocity sensor element according to the average magnetic induction intensity and the circumferential average velocity based on the Faraday motional electromotive force method;

[0145] The solving module 650 is used to solve the frequency response characteristic function to obtain the amplitude-frequency response data and the phase-frequency response data of the MHD angular velocity sensor element.

[0146] According to the embodiments of the present application, the average magnetic induction intensity and the circumferential average velocity can be determined by using the structural dimension parameters and material property parameters of the MHD angular velocity sensor element, and the Maxwell equations and the low magnetic Reynolds number incompressible equations. After that, the frequency response characteristic function of the MHD angular velocity sensor element can be obtained by processing the average magnetic induction intensity and the circumferential average velocity using the Faraday motional electromotive force method. The amplitude-frequency response data and the phase-frequency response data of the MHD angular velocity sensor element can be obtained by solving it. Since the present application considers the radial magnetic circuit inside the conductive fluid ring in the MHD angular velocity sensor element in the process of determining the steady-state frequency response, it can accurately and conveniently describe the steady-state frequency response characteristics of the sensor element, thereby accurately guiding the design of the structure and material parameters of the sensor element, which can greatly shorten the research and development cycle of the MHD angular velocity sensor and significantly reduce the research and development cost.

[0147] According to an embodiment of the present application, the steady-state frequency response determination device 600 further includes:

[0148] A fourth generating module, used to generate cutoff frequency data according to the amplitude-frequency response data or the phase-frequency response data;

[0149] The adjustment module is used to adjust the structural dimension parameters and material property parameters when the cut-off frequency data does not meet the design threshold, so as to obtain new structural dimension parameters and new material property parameters, so as to generate new amplitude-frequency response data and new phase-frequency response data according to the new structural dimension parameters and the new material property parameters.

[0150] According to an embodiment of the present application, the first generation module 620 includes:

[0151] A first generating unit is used to generate a first target curve and a second target curve according to the magnetic induction intensity and the magnetic field intensity inside the material, wherein the first target curve is a BH function curve, and the second target curve represents the relationship between the residual magnetic flux density and the recoil permeability;

[0152] A first obtaining unit is used to substitute the first target curve and the second target curve into the Maxwell equations under the condition of a constant magnetic field to obtain a first set of equations to be solved;

[0153] A second obtaining unit is used to solve the first set of equations to be solved based on a finite element method to obtain a plurality of target magnetic induction intensities of the MHD angular velocity sensor element at a plurality of positions within the magnetic circuit structure area;

[0154] The second generating unit is used to generate an average magnetic induction intensity according to multiple target magnetic induction intensities.

[0155] According to an embodiment of the present application, the second generation module 630 includes:

[0156] The third unit is used to substitute the structural dimension parameters and the material property parameters into the low magnetic Reynolds number incompressible equation group to obtain the second equation group to be solved;

[0157] A solving unit, used for solving the second set of equations to be solved to obtain a velocity field of the conductive fluid;

[0158] The third generating unit is used to generate a circumferential average velocity according to the conductive fluid velocity field.

[0159] According to an embodiment of the present application, the third obtaining unit includes:

[0160] Obtaining subunits, which are used to substitute structural dimension parameters and material property parameters into the low magnetic Reynolds number incompressible equations, to obtain the initial equations to be solved;

[0161] The simplification subunit is used to simplify the initial set of equations to be solved based on boundary conditions and initial conditions to obtain a second set of equations to be solved.

[0162] According to the embodiments of the present application, any one or more of the modules, submodules, units, and subunits, or at least part of the functions of any one of them can be implemented in one module. According to the embodiments of the present application, any one or more of the modules, submodules, units, and subunits can be split into multiple modules for implementation. According to the embodiments of the present application, any one or more of the modules, submodules, units, and subunits can be at least partially implemented as hardware circuits, such as field programmable gate arrays (FPGAs), programmable logic arrays (PLAs), systems on chips, systems on substrates, systems on packages, application specific integrated circuits (ASICs), or can be implemented by hardware or firmware in any other reasonable way of integrating or packaging the circuit, or in any one of the three implementation methods of software, hardware, and firmware, or in any appropriate combination of any of them. Alternatively, according to the embodiments of the present application, one or more of the modules, submodules, units, and subunits can be at least partially implemented as computer program modules, and when the computer program modules are run, the corresponding functions can be executed.

[0163] For example, any of the acquisition module 610, the first generation module 620, the second generation module 630, the third generation module 640, and the solution module 650 can be combined in one module / unit / sub-unit for implementation, or any of the modules / units / sub-units can be split into multiple modules / units / sub-units. Alternatively, at least part of the functions of one or more of these modules / units / sub-units can be combined with at least part of the functions of other modules / units / sub-units and implemented in one module / unit / sub-unit. According to an embodiment of the present application, at least one of the acquisition module 610, the first generation module 620, the second generation module 630, the third generation module 640, and the solution module 650 can be at least partially implemented as a hardware circuit, such as a field programmable gate array (FPGA), a programmable logic array (PLA), a system on a chip, a system on a substrate, a system on a package, an application specific integrated circuit (ASIC), or can be implemented by hardware or firmware such as any other reasonable way of integrating or packaging the circuit, or by any one of the three implementation methods of software, hardware, and firmware, or by a suitable combination of any of them. Alternatively, at least one of the acquisition module 610, the first generation module 620, the second generation module 630, the third generation module 640 and the solution module 650 may be at least partially implemented as a computer program module, which may perform corresponding functions when executed.

[0164] It should be noted that the part of the device for determining the steady-state frequency response in the embodiment of the present application corresponds to the part of the method for determining the steady-state frequency response in the embodiment of the present application. The description of the part of the device for determining the steady-state frequency response specifically refers to the part of the method for determining the steady-state frequency response, which will not be repeated here.

[0165] Figure 7 A block diagram of an electronic device suitable for implementing the method described above according to an embodiment of the present application is shown. Figure 7 The electronic device shown is merely an example and should not bring any limitation to the functions and scope of use of the embodiments of the present application.

[0166] like Figure 7As shown, the electronic device 700 according to an embodiment of the present application includes a processor 701, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 702 or a program loaded from a storage part 708 to a random access memory (RAM) 703. The processor 701 may include, for example, a general-purpose microprocessor (such as a CPU), an instruction set processor and / or a related chipset and / or a special-purpose microprocessor (for example, an application-specific integrated circuit (ASIC)), etc. The processor 701 may also include an onboard memory for caching purposes. The processor 701 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of the present application.

[0167] In RAM 703, various programs and data required for the operation of electronic device 700 are stored. Processor 701, ROM 702 and RAM 703 are connected to each other via bus 704. Processor 701 performs various operations of the method flow according to the embodiment of the present application by executing the program in ROM 702 and / or RAM 703. It should be noted that the program can also be stored in one or more memories other than ROM 702 and RAM 703. Processor 701 can also perform various operations of the method flow according to the embodiment of the present application by executing the program stored in the one or more memories.

[0168] According to an embodiment of the present application, the electronic device 700 may further include an input / output (I / O) interface 705, which is also connected to the bus 704. The electronic device 700 may further include one or more of the following components connected to the input / output (I / O) interface 705: an input portion 706 including a keyboard, a mouse, etc.; an output portion 707 including a cathode ray tube (CRT), a liquid crystal display (LCD), etc., and a speaker, etc.; a storage portion 708 including a hard disk, etc.; and a communication portion 709 including a network interface card such as a LAN card, a modem, etc. The communication portion 709 performs communication processing via a network such as the Internet. A drive 710 is also connected to the input / output (I / O) interface 705 as needed. A removable medium 711, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 710 as needed, so that a computer program read therefrom is installed into the storage portion 708 as needed.

[0169] According to an embodiment of the present application, the method flow according to the embodiment of the present application can be implemented as a computer software program. For example, an embodiment of the present application includes a computer program product, which includes a computer program carried on a computer-readable storage medium, and the computer program includes a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 709, and / or installed from the removable medium 711. When the computer program is executed by the processor 701, the above-mentioned functions defined in the system of the embodiment of the present application are executed. According to an embodiment of the present application, the system, equipment, device, module, unit, etc. described above can be implemented by a computer program module.

[0170] The present application also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or may exist independently without being assembled into the device / apparatus / system. The above computer-readable storage medium carries one or more programs, and when the above one or more programs are executed, the method according to the embodiment of the present application is implemented.

[0171] According to an embodiment of the present application, the computer-readable storage medium may be a non-volatile computer-readable storage medium. For example, it may include, but is not limited to: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In the present application, a computer-readable storage medium may be any tangible medium containing or storing a program that may be used by or in combination with an instruction execution system, apparatus, or device.

[0172] For example, according to an embodiment of the present application, the computer-readable storage medium may include the ROM 702 and / or the RAM 703 described above and / or one or more memories other than the ROM 702 and the RAM 703 .

[0173] An embodiment of the present application also includes a computer program product, which includes a computer program, and the computer program contains program code for executing the method provided by the embodiment of the present application. When the computer program product runs on an electronic device, the program code is used to enable the electronic device to implement the method for determining the steady-state frequency response provided by the embodiment of the present application.

[0174] When the computer program is executed by the processor 701, the above functions defined in the system / device of the embodiment of the present application are executed. According to the embodiment of the present application, the system, device, module, unit, etc. described above can be implemented by a computer program module.

[0175] In one embodiment, the computer program may rely on tangible storage media such as optical storage devices, magnetic storage devices, etc. In another embodiment, the computer program may also be transmitted and distributed in the form of signals on a network medium, and downloaded and installed through the communication part 709, and / or installed from the removable medium 711. The program code contained in the computer program may be transmitted using any appropriate network medium, including but not limited to: wireless, wired, etc., or any suitable combination of the above.

[0176] According to an embodiment of the present application, the program code for executing the computer program provided by the embodiment of the present application can be written in any combination of one or more programming languages, and specifically, these computing programs can be implemented using high-level process and / or object-oriented programming languages, and / or assembly / machine languages. Programming languages ​​include, but are not limited to, such as Java, C++, python, "C" language or similar programming languages. The program code can be executed entirely on the user computing device, partially on the user device, partially on the remote computing device, or completely on the remote computing device or server. In the case of a remote computing device, the remote computing device can be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computing device (e.g., using an Internet service provider to connect through the Internet).

[0177] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architecture, functions and operations of the systems, methods and computer program products according to various embodiments of the present application. In this regard, each box in the flowchart or block diagram may represent a module, a program segment, or a part of a code, and the above-mentioned module, program segment, or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box may also occur in a different order from the order marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they may sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram or flowchart, and the combination of the boxes in the block diagram or flowchart, can be implemented with a dedicated hardware-based system that performs a specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions. It will be appreciated by those skilled in the art that the features recorded in the various embodiments of the present application can be combined and / or combined in a variety of ways, even if such a combination or combination is not clearly recorded in the present application. In particular, without departing from the spirit and teachings of the present application, the features described in the various embodiments of the present application may be combined and / or combined in a variety of ways. All of these combinations and / or combinations fall within the scope of the present application.

[0178] The embodiments of the present application are described above. However, these embodiments are only for the purpose of illustration, and are not intended to limit the scope of the present application. Although each embodiment is described above, this does not mean that the measures in each embodiment cannot be used in combination advantageously. The present application does not depart from the scope of the present application, and those skilled in the art may make various substitutions and modifications, which should all fall within the scope of the present application.

Claims

1. A method for determining the steady-state frequency response of an MHD angular velocity sensor element, characterized in that: include: In response to the modeling instruction, obtaining structural dimension parameters and material property parameters of the MHD angular velocity sensor element; Based on Maxwell's equations, according to the structural dimension parameters and the material property parameters, an average magnetic induction intensity of a radial magnetic circuit in a conductive fluid ring in the MHD angular velocity sensor element is generated; Based on the low magnetic Reynolds number incompressible equations, according to the structural size parameters and material property parameters, the circumferential average velocity of the conductive fluid relative to the magnetic field is generated; Based on the Faraday motional electromotive force method, generating a frequency response characteristic function of the MHD angular velocity sensor element according to the average magnetic induction intensity and the circumferential average velocity; Solving the frequency response characteristic function to obtain amplitude-frequency response data and phase-frequency response data of the MHD angular velocity sensor element; Wherein, generating the circumferential average velocity of the conductive fluid relative to the magnetic field according to the structural dimension parameters and the material property parameters includes: Substituting the structural dimension parameters and the material property parameters into the low magnetic Reynolds number incompressible equation group to obtain a second equation group to be solved; Solving the second set of equations to be solved to obtain a velocity field of the conductive fluid; generating the circumferential average velocity according to the conductive fluid velocity field; Wherein, the structural dimension parameters and the material property parameters are substituted into the low magnetic Reynolds number incompressible equation group to obtain the second equation group to be solved, including: Substituting the structural dimension parameters and the material property parameters into the low magnetic Reynolds number incompressible equation group to obtain an initial equation group to be solved; Simplifying the initial set of equations to be solved based on boundary conditions and initial conditions to obtain the second set of equations to be solved; The initial set of equations to be solved is shown in formula (2), the second set of equations to be solved is shown in formula (3), and the velocity field of the conductive fluid is As shown in formula (4), the average circumferential velocity As shown in formula (5): （2） in, is the electric field strength in the conductive fluid, is the current density in the conducting fluid, is the absolute velocity of the conductive fluid, is the conductivity of the conducting fluid, Is the conductive fluid relative The relative speed of motion, is the electric potential of the conducting fluid, is the density of the conducting fluid, It's time. is the static pressure inside the conductive fluid, is the kinematic viscosity of the conductive fluid, Except for the Laplace force The volume force on the conductive fluid outside is is the circumferential base coordinate vector of the cylindrical coordinate system where the conductive fluid ring is located, yes exist The weight in direction, is the radial coordinate component of the cylindrical coordinate system where the conductive fluid ring is located, It is the angular velocity of the external input to the sensor element; （3） in, yes of Directional component, is the height direction base coordinate vector of the cylindrical coordinate system where the conductive fluid ring is located, yes The coordinate component of the direction, yes of Directional component, yes of Directional component, is the inner radius of the conductive fluid annulus, is the outer radius of the conductive fluid annulus, is the average magnetic induction intensity; （4） （5） in, Represents complex number The real part of , is the input angular velocity The angular frequency, It is half the width of the air gap in the conductive fluid ring. is the Hartmann number, is the average radius of the conductive fluid annulus, , and They are The hyperbolic cosine, sine and tangent functions of is an imaginary unit, yes The corresponding amplitude when is a sinusoidal quantity, that is , is the amplitude of the sine function, , is a natural constant; Wherein, the frequency response characteristic function is shown in formula (6): （6） in, is the height of the conductive fluid ring, Representation function The Fourier transform of .

2. The method according to claim 1, characterized in that Also includes: Generate cutoff frequency data according to the amplitude-frequency response data or the phase-frequency response data; When the cutoff frequency data does not meet the design threshold, the structural dimension parameters and the material property parameters are adjusted to obtain new structural dimension parameters and new material property parameters, so as to generate new amplitude-frequency response data and new phase-frequency response data according to the new structural dimension parameters and the new material property parameters.

3. The method according to claim 1, characterized in that: According to the structural dimension parameters and the material property parameters, an average magnetic induction intensity of a radial magnetic circuit in a conductive fluid ring in the MHD angular velocity sensor element is generated, including: Generate a first target curve and a second target curve according to the magnetic induction intensity and magnetic field intensity inside the material, wherein the first target curve is a BH function curve, and the second target curve represents the relationship between the residual magnetic flux density and the recovery magnetic permeability; Substituting the first target curve and the second target curve into the Maxwell equations under the constant magnetic field condition to obtain a first set of equations to be solved; Solving the first set of equations to be solved based on a finite element method to obtain a plurality of target magnetic induction intensities of the MHD angular velocity sensor element at a plurality of positions within a magnetic circuit structure region; The average magnetic flux density is generated according to the plurality of target magnetic flux density.

4. The method according to claim 3, characterized in that The first set of equations to be solved is shown in formula (1): （1） in, is the magnetic induction intensity inside the material, is the magnetic field strength, is the BH function curve, is the second target curve, is the vacuum permeability, is the residual flux density, is the recovery permeability, is the magnetic scalar potential, The boundary element vector of the magnetic circuit solution domain is: is any point within the magnetic circuit structure area of ​​the MHD angular velocity sensor element.

5. The method according to claim 1, characterized in that The amplitude frequency response data As shown in formula (7), the phase-frequency response data As shown in formula (8): （7） （8） in, Indicates plural The model, Indicates plural exist The angle within the interval.

6. A device for determining the steady-state frequency response of an MHD angular velocity sensor element, characterized in that: include: An acquisition module, configured to acquire structural dimension parameters and material property parameters of the MHD angular velocity sensor element in response to a modeling instruction; A first generating module is used to generate an average magnetic induction intensity of a radial magnetic circuit in a conductive fluid ring in the MHD angular velocity sensor element based on the Maxwell equations, the structural size parameters and the material property parameters; A second generating module is used to generate a circumferential average velocity of the conductive fluid relative to the magnetic field based on a low magnetic Reynolds number incompressible equation group and according to the structural size parameters and material property parameters; A third generating module is used to generate a frequency response characteristic function of the MHD angular velocity sensor element according to the average magnetic induction intensity and the circumferential average velocity based on the Faraday motional electromotive force method; A solution module, used for solving the frequency response characteristic function to obtain amplitude-frequency response data and phase-frequency response data of the MHD angular velocity sensor element; Wherein, the second generation module includes: The third unit is used to substitute the structural dimension parameters and the material property parameters into the low magnetic Reynolds number incompressible equation group to obtain the second equation group to be solved; A solving unit, used for solving the second set of equations to be solved to obtain a velocity field of the conductive fluid; A third generating unit is used to generate a circumferential average velocity according to the velocity field of the conductive fluid; Wherein, the third obtaining unit comprises: Obtaining subunits, which are used to substitute structural dimension parameters and material property parameters into the low magnetic Reynolds number incompressible equations, to obtain the initial equations to be solved; A simplification subunit, used for simplifying the initial set of equations to be solved based on the boundary conditions and the initial conditions to obtain a second set of equations to be solved; The initial set of equations to be solved is shown in formula (9), the second set of equations to be solved is shown in formula (10), and the velocity field of the conductive fluid is As shown in formula (11), the average circumferential velocity As shown in formula (12): （9） in, is the electric field strength in the conductive fluid, is the current density in the conducting fluid, is the absolute velocity of the conductive fluid, is the conductivity of the conducting fluid, Is the conductive fluid relative The relative speed of motion, is the electric potential of the conducting fluid, is the density of the conducting fluid, It's time. is the static pressure inside the conductive fluid, is the kinematic viscosity of the conductive fluid, Except for the Laplace force The volume force on the conductive fluid outside is is the circumferential base coordinate vector of the cylindrical coordinate system where the conductive fluid ring is located, yes exist The weight in direction, is the radial coordinate component of the cylindrical coordinate system where the conductive fluid ring is located, It is the angular velocity of the external input to the sensor element; （10） in, yes of Directional component, is the height direction base coordinate vector of the cylindrical coordinate system where the conductive fluid ring is located, yes The coordinate component of the direction, yes of Directional component, yes of Directional component, is the inner radius of the conductive fluid annulus, is the outer radius of the conductive fluid annulus, is the average magnetic induction intensity; （11） （12） in, Represents complex number The real part of , is the input angular velocity The angular frequency, It is half the width of the air gap in the conductive fluid ring. is the Hartmann number, is the average radius of the conductive fluid annulus, , and They are The hyperbolic cosine, sine and tangent functions of is an imaginary unit, yes The corresponding amplitude when is a sinusoidal quantity, that is , is the amplitude of the sine function, , is a natural constant; Wherein, the frequency response characteristic function is shown in formula (13): （13） in, is the height of the conductive fluid ring, Representation function The Fourier transform of .

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