Resonant frequency simulation method for multi-physics-field coupled piezoelectric vibration sensor

Abstract

The invention provides a resonant frequency simulation method for a multi-physics-field coupled piezoelectric vibration sensor, and the method comprises the steps: building a geometric model of the piezoelectric vibration sensor, and setting the structural form, material mechanical properties, electrical properties and polarization direction of the piezoelectric vibration sensor; a solid mechanical physical field and an electrical physical field of the piezoelectric vibration sensor are added in finite element simulation software, piezoelectric multi-physical field coupling is added, and solid mechanics and static electricity are used as interfaces of the piezoelectric multi-physical field coupling; and performing grid division on the geometric model, and analyzing and resolving the response of the sensor at different frequency points through a multi-physics coupling simulation method of material mechanics and electrical characteristics to obtain the resonant frequency of the piezoelectric vibration sensor. According to the method, the mechanical and electrical characteristics of the sensor structure are introduced into the simulation model of the sensor, the resonant frequencies of the sensors of different structures can be intuitively reflected, and the frequency domain output of the sensor under the multi-physics coupling condition is intuitively reflected by introducing multi-physics simulation into the model.

Description

Technical Field

[0001] The present invention relates to the field of measurement and testing technology, and in particular to a multi-physical field coupled piezoelectric vibration sensor resonant frequency simulation method. Background Art

[0002] Uncontrolled vibration typically causes noise, mechanical stress, and potentially structural failure. Therefore, vibration sensors are indispensable in harsh mechanical environments such as aerospace, shipbuilding, and nuclear power. Vibration sensors based on the direct piezoelectric effect have become indispensable in vibration monitoring due to their excellent annual stability, high sensitivity, simple structure, wide applicable temperature range, wide applicable frequency band, and compatibility with complex thermal and mechanical environments. The resonant frequency range of a vibration sensor determines the upper limit of its operating frequency band; therefore, designing the resonant frequency specification for a vibration sensor has always been a key element in its design.

[0003] Currently established methods for designing the resonant frequency of piezoelectric vibration sensors primarily rely on a theoretical model that simplifies the sensor into a mass-spring inertia system. This simplified model can roughly estimate the sensor's resonant frequency. However, this simplified model cannot directly reflect the impact of the material properties of the sensor's structural components and the actual assembly scheme on the sensor's resonant frequency. Therefore, existing approaches to designing the resonant frequency of piezoelectric vibration sensors based on theoretical simplifications have significant limitations.

[0004] After analysis, it was found that the resonant frequency of the piezoelectric vibration sensor is related to the overall structure of the sensor, the weight of the inertial mass, the type of sensitive element, and the level of pre-applied bolt preload.

[0005] Existing simulation solutions primarily focus on sensitive components and are unable to determine the sensor's true resonant frequency. Therefore, simulating the entire sensor is more valuable. The rapid development of COMSOL, a multi-physics coupled finite element software, in recent years has enabled modular sensor analysis, providing a more accurate method for resonant frequency simulation of piezoelectric vibration sensors. This, in turn, improves the sensor's resonant frequency design from the ground up. Summary of the Invention

[0006] The present invention aims to solve the problem of obtaining the true resonant frequency level of the sensor and provides a multi-physical field coupled piezoelectric vibration sensor resonant frequency simulation method. The mechanical and electrical characteristics of the sensor structure are introduced into the simulation model of the sensor, which can intuitively reflect the resonant frequency of sensors with different structures. By introducing multi-physical field simulation into the model, the frequency domain output of the sensor under multi-physical field coupling conditions can be intuitively reflected.

[0007] The present invention provides a multi-physical field coupled piezoelectric vibration sensor resonant frequency simulation method, establishes a geometric model of the piezoelectric vibration sensor, the piezoelectric vibration sensor includes a structural material and a piezoelectric material, sets the structural form of the piezoelectric vibration sensor, and sets the mechanical properties, electrical properties, and polarization direction of the structural material and the piezoelectric material;

[0008] Add the solid mechanics and electrical physics fields of the piezoelectric vibration sensor to the finite element simulation software. Set the applied bolt preload in the solid mechanics physics field, set the inter-domain contact mode to contact pair, and set the electric potential and grounding parameters in the electrical physics field.

[0009] Add piezoelectric multiphysics coupling to the finite element simulation software. The interfaces for piezoelectric multiphysics coupling are solid mechanics and electrostatics.

[0010] The geometric model is meshed in the finite element simulation software, and the response of the sensor at different frequencies is analyzed and solved through the multi-physics field coupling simulation method of material mechanics and electrical properties to obtain the resonant frequency of the piezoelectric vibration sensor.

[0011] The multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method described in the present invention, as a preferred embodiment, includes the following steps:

[0012] S1. Establish a geometric model of a piezoelectric vibration sensor and set the material properties, structural form, and combination / assembly method. The piezoelectric vibration sensor includes a base, a piezoelectric sensitive element, an inertial mass block, and a pre-tightening bolt connected sequentially from bottom to top. The pre-tightening bolt passes through the inertial mass block, the piezoelectric sensitive element, and the base to be tightened. The piezoelectric vibration sensor has a compression structure.

[0013] S2. Add physical fields in the finite element software COMSOL, which includes solid mechanics modules and electrostatic modules;

[0014] In the Solid Mechanics module, set the base, inertial mass, and pre-tightening bolts to elastic materials, define contact between the structural components, set the contact method between the contact pairs, and set the bolt preload for the pre-tightening bolts.

[0015] In the electrostatic module, set the initial potential, assumed equations, grounding structure, and grounding equation of the piezoelectric vibration sensor.

[0016] S3. Add multiphysics in the finite element software COMSOL and set the multiphysics coupling interface to solid mechanics and electrostatics, and set the coupling domain to the piezoelectric sensitive element;

[0017] S4. Add meshing in the finite element software COMSOL. The meshing includes presetting the mesh size, shape, and scanning mode. The mesh size of the piezoelectric sensor is smaller than that of the base, inertial mass block, and preload bolts.

[0018] S5. Perform parameter scanning in the preset frequency domain in the finite element software COMSOL, and obtain the resonant frequency of the piezoelectric vibration sensor model under the multi-physics field coupling condition. A multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method is completed.

[0019] In the multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method described in the present invention, as a preferred embodiment, in step S1, the material properties of the base and the pre-tightening bolt include density, Young's modulus, Poisson's ratio, thermal conductivity, resistivity, thermal expansion coefficient, constant pressure heat capacity, electrical conductivity, bulk modulus and shear modulus;

[0020] The material properties of the inertial mass include density, Young's modulus, thermal conductivity, resistivity, coefficient of thermal expansion, heat capacity at constant pressure, electrical conductivity, bulk modulus, and shear modulus;

[0021] The material properties of piezoelectric sensitive elements include density, compliance matrix, coupling matrix, relative dielectric constant, loss factor of each matrix and elastic matrix;

[0022] The piezoelectric vibration sensor combination / assembly method comprises forming an assembly;

[0023] In step S1 , the polarization directions of the base, the piezoelectric sensitive element, the inertial mass block and the pre-tightening bolts are also set.

[0024] In the multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method described in the present invention, as a preferred embodiment, the base and the pre-tightening bolts are made of stainless steel, the inertial mass block is made of tungsten alloy, and the piezoelectric sensitive element is made of PZT-5A piezoelectric ceramic material;

[0025] There are two piezoelectric sensitive elements stacked one on top of the other.

[0026] The multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method described in the present invention is preferably configured such that, in step S2, in the solid mechanics module, the base, the inertial mass block, and the pre-tightening bolt all use a global coordinate system;

[0027] The initial displacement field and structural velocity field of the piezoelectric vibration sensor are both 0;

[0028] The pair types among the base, piezoelectric sensitive element, inertial mass block and pre-tightening bolt are all contact pairs, and the mapping type of the contact pairs is deformation configuration;

[0029] In the Solid Mechanics module, the contact formula for the contact pair is the augmented Lagrangian formula. In the Solid Mechanics physics field, add boundary continuity, select the contact pair, design the preload force type for the preload bolts as preload stress, and set the preload force magnitude.

[0030] The present invention describes a multi-physical field coupled piezoelectric vibration sensor resonant frequency simulation method, as a preferred method, in step S2, in the electrostatic module, the initial value potential of the structure is 0, the assumption equation and the grounding equation are both frequency domain equations, and the selected domain is the piezoelectric sensitive element.

[0031] The multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method of the present invention is preferably such that, in step S4, the meshing method of the piezoelectric sensitive element is cube sweeping, the mesh size is extremely fine, and the calibration method is ordinary physics;

[0032] The mesh shape of the base, inertial mass block and pre-tightening bolt is free tetrahedron, the mesh size is relatively fine, and the calibration method is ordinary physics.

[0033] The present invention provides a multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method, as a preferred method, in step S5, the finite element software COMSOL studies the output of the piezoelectric vibration sensor at different frequencies in the frequency domain and draws an output-frequency change curve to obtain the resonant frequency of the piezoelectric vibration sensor.

[0034] In the multi-physical field coupled piezoelectric vibration sensor resonant frequency simulation method described in the present invention, as a preferred embodiment, the frequency domain parameters include frequency range, start value, stop value and step size.

[0035] The present invention describes a multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method, as a preferred method, when the structure of the piezoelectric vibration sensor is changed or the size is fine-tuned, only the COMSOL finite element method changes the piezoelectric vibration sensor structure within the simulation software, and the simulation is performed again to obtain the changed resonant frequency.

[0036] The present invention first establishes a geometric model of a piezoelectric vibration sensor and assigns corresponding structural material properties; adds mechanical and electrical physical fields to the geometric model and defines the mechanical and electrical properties of a finite element model; determines the constitutive relationship of the piezoelectric material, the piezoelectric compliance matrix, the coupling matrix, and the relative dielectric constant; defines "pairs" between structural parts and determines the contact method between the "pairs"; adds bolts to the geometric model; determines the bolt preload; adds multi-physical fields to the geometric model to describe the coupling mechanism; meshes the structure; defines a research field using the finite element software COMSOL and obtains the resonant frequency information of the sensor;

[0037] The structural form of the piezoelectric vibration sensor is a compression structure, and the combination / assembly method of the piezoelectric vibration sensor is to form an assembly; the material parameters are defined according to the sensor model; the mechanical and electrical physical fields are the solid mechanics module and the electrostatic module; the solid mechanics module stipulates that the contact method of the physical field between the "pairs" is "continuity"; the solid mechanics module stipulates that the contact method between structural parts is "contact"; the constitutive relationship of the piezoelectric material is strain-charge type, and the flexibility matrix, coupling matrix, and relative dielectric constant are all material parameters; the contact surface of the contact structural parts is defined as a "contact pair"; the mapping method of the "contact pair" is defined as "deformation configuration";

[0038] The present invention adds bolts in geometry, adds bolt preload in the solid mechanics module, and specifies preload stress; adds piezoelectric effect in the multi-physics field, and the coupling interface of the piezoelectric effect is solid mechanics and electrostatics.

[0039] Meshing, with mesh size predefined as refinement and calibration as normal physics; cube sweeping for piezoelectric sensitive elements and free tetrahedron network sweeping for the remaining structure; defining the study area as frequency domain study; specifying the step size and scan range in the frequency domain study;

[0040] The finite element software COMSOL studies the sensor output at different frequencies in the frequency domain to draw the output-frequency change curve and determine the resonant frequency of the sensor.

[0041] The present invention provides a method for simulating the resonant frequency of a compression-type piezoelectric vibration sensor, comprising: establishing a geometric model of the piezoelectric vibration sensor; adding mechanical and electrical physical fields to the geometric model, and setting a multi-physics coupling-piezoelectric effect; defining the structural material, piezoelectric material properties, polarization direction, physical field, and multi-physics coupling interface; defining the applied bolt preload; defining the inter-domain contact mode as a contact pair; meshing the geometric model; and specifying the sensor's scanning frequency range and step size. The present invention aims to improve the defect that the resonant frequency of a vibration sensor can only be calculated theoretically and the actual results vary greatly by using a multi-physics coupling simulation method. By using COMSOL finite element simulation software, the material mechanical and electrical characteristics of the sensor are subjected to multi-physics coupling, the response of the sensor at different frequency points is analyzed and solved, and the resonant frequency of the piezoelectric vibration sensor is solved, thereby providing a theoretical basis and simulation data support for the design and improvement of the piezoelectric vibration sensor.

[0042] The present invention has the following advantages:

[0043] (1) Existing theoretical methods for estimating the resonant frequency of piezoelectric vibration sensors can only infer the approximate range of the resonant frequency, which is not accurate enough. When the sensor structure is complex, the theoretically estimated data deviates greatly from the actual results. The piezoelectric vibration sensor resonant frequency simulation method proposed in this invention introduces the mechanical and electrical characteristics of the sensor structure into the sensor simulation model, which can intuitively reflect the resonant frequency of sensors with different structures.

[0044] (2) By introducing multi-physics field simulation into the model, the frequency domain output of the sensor under the multi-physics field coupling condition is intuitively reflected, which makes it easier for designers to observe the various effects of different design schemes on the sensor more intuitively.

[0045] (3) When the sensor structure is changed or the size is fine-tuned, there is no need to rebuild the three-dimensional model. It is only necessary to change the sensor structure within the simulation software to achieve sensor improvement and iterative optimization, which greatly saves the design time cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a flow chart of a multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method;

[0047] Figure 2 A multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method is shown. A structural diagram of a compressed piezoelectric vibration sensor.

[0048] Figure 3 A multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method and a compressed piezoelectric vibration sensor grid division diagram;

[0049] Figure 4 A multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method and a compression type piezoelectric vibration sensor simulation stress diagram;

[0050] Figure 5 A multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method and a compression type piezoelectric vibration sensor simulation potential diagram;

[0051] Figure 6 This is a multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method and a compression piezoelectric vibration sensor simulation result diagram.

[0052] Reference numerals:

[0053] 1. Base; 2. Piezoelectric sensitive element; 3. Inertial mass block; 4. Pre-tightening bolt. DETAILED DESCRIPTION

[0054] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0055] Example 1

[0056] like Figure 1 As shown, a multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method includes the following steps:

[0057] S1. The simulation of the resonant frequency of the compression piezoelectric vibration sensor involves the coupling relationship between the electric field, mechanical field and piezoelectric multi-physics field. The geometric model is as follows: Figure 2 shown.

[0058] S11. Geometric model construction

[0059] The geometric model in this example includes the base, piezoelectric sensor, inertial mass, and preload bolts. The piezoelectric vibration sensor is a compression-type structure. There are two piezoelectric sensors, and from bottom to top, they are the base, piezoelectric sensor, inertial mass, and preload bolts.

[0060] S12. Set material properties

[0061] In the Materials section, set the base and preload bolt material properties to stainless steel. Set the material properties, including density, Young's modulus, Poisson's ratio, thermal conductivity, resistivity, thermal expansion coefficient, heat capacity at constant pressure, conductivity, bulk modulus, and shear modulus. Set the inertial mass material to tungsten alloy. Set the material properties, including density, Young's modulus, thermal conductivity, resistivity, thermal expansion coefficient, heat capacity at constant pressure, conductivity, bulk modulus, and shear modulus. Set the piezoelectric sensor to PZT-5A piezoelectric ceramic material. Set the material properties, including density, compliance matrix, coupling matrix, relative dielectric constant, loss factors of each matrix, and elasticity matrix.

[0062] S2. Add physical fields in the finite element software COMSOL and set up each physical field.

[0063] S21. Setting up the physical fields of the Solid Mechanics module

[0064] Select the Physics Field - Solid Mechanics module in the menu bar. In the Solid Mechanics module, the base, inertial mass block, and pre-tightening bolts are linear elastic materials, and the global coordinate system is used; the initial displacement field and the structural velocity field of the structure are both 0. The "pair" type between the base, piezoelectric sensitive element, inertial mass block, and pre-tightening bolt is "contact pair", and the mapping type of "contact pair" is deformation configuration. In the Solid Mechanics module, the "contact" formula of the "contact pair" is the augmented Lagrangian formula. Add boundary continuity in the solid mechanics physics field and select "contact pair". The pre-tightening force type of the designed bolt pre-tightening force is pre-tightening stress, and the pre-tightening force magnitude is specified.

[0065] S22. Setting up the physics field of the electrostatic module

[0066] Select Physics > Electrostatics from the menu bar. In the Electrostatics module, set the initial potential of the structure to 0. The assumed equations in the Electrostatics module are frequency-domain equations. Set the ground structure and select Frequency-domain for the Ground Equation. Select the domain as the piezoelectric sensor.

[0067] S3. Add multi-physics fields in the finite element software COMSOL and set up multi-physics field coupling interfaces.

[0068] Set the multiphysics field to piezoelectric effect, select Solid Mechanics and Electrostatics as the physics coupling interface, and select the piezoelectric sensor as the coupling domain.

[0069] S4. Add meshing in the finite element software COMSOL. The meshing model is as follows: Figure 3 shown.

[0070] Meshing includes presetting mesh size, shape, and scanning method.

[0071] S41. Set the calibration method to normal physics; the meshing method of the piezoelectric sensitive element to sweeping, and the mesh size to ultra-fine.

[0072] S42. Set the calibration method to normal physics; the mesh shape of the base, inertial mass block, and pre-tightening bolts to free tetrahedron, and the mesh size to relatively fine.

[0073] S5. Add a study in the finite element software COMSOL: Frequency Domain Study, preset parameters, complete a parameter sweep in the specified frequency domain, and determine the resonant frequency of the sensor model.

[0074] S51, frequency domain study, set the frequency range, including the start value, stop value and step size.

[0075] S52 , performing parameter scanning, reading the frequency domain curve output by the piezoelectric vibration sensor, and determining the resonant frequency of the piezoelectric vibration sensor.

[0076] The simulation results are as follows Figures 4-6As shown, it intuitively reflects the resonant frequency of sensors with different structures and the frequency domain output of the sensor under multi-physical field coupling conditions.

[0077] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method, characterized by: Establishing a geometric model of a piezoelectric vibration sensor, the piezoelectric vibration sensor including a structural material and a piezoelectric material, setting a structural form of the piezoelectric vibration sensor, and material mechanical properties, electrical properties, and polarization direction of the structural material and the piezoelectric material; Adding the solid mechanics physics field and electrical physics field of the piezoelectric vibration sensor in the finite element simulation software, setting the applied bolt preload force in the solid mechanics physics field, setting the inter-domain contact mode to contact pair, and setting the electric potential and grounding parameters in the electrical physics field; Add piezoelectric multi-physics coupling in finite element simulation software, where the interfaces of the piezoelectric multi-physics coupling are solid mechanics and electrostatics; The geometric model is meshed in the finite element simulation software, and the response of the sensor at different frequencies is analyzed and solved through the multi-physics field coupling simulation method of material mechanics and electrical properties to obtain the resonant frequency of the piezoelectric vibration sensor.

2. The method for simulating the resonant frequency of a piezoelectric vibration sensor coupled with multiple physical fields according to claim 1, wherein: The following steps are involved: S1. Establishing a geometric model of a piezoelectric vibration sensor and setting material properties, structural form, and a combination / assembly method, wherein the piezoelectric vibration sensor comprises a base (1), a piezoelectric sensitive element (2), an inertial mass block (3), and a pre-tightening bolt (4) connected sequentially from bottom to top, wherein the pre-tightening bolt (4) sequentially passes through the inertial mass block (3), the piezoelectric sensitive element (2), and is fastened to the base (1), and the structural form of the piezoelectric vibration sensor is a compression structure; S2. Adding a physical field in the finite element software COMSOL, wherein the physical field includes a solid mechanics module and an electrostatic module; In the solid mechanics module, the base (1), the inertial mass block (3) and the pre-tightening bolt (4) are set to elastic materials, contact is defined between structural parts and a contact method between contact pairs is set, and the bolt pre-tightening force of the pre-tightening bolt (4) is set; In the electrostatic module, the initial value potential, the assumed equation, the grounding structure and the grounding equation of the piezoelectric vibration sensor are set; S3, adding a multi-physics field in the finite element software COMSOL and setting the multi-physics field coupling interface to solid mechanics and electrostatics, and setting the coupling domain to the piezoelectric sensitive element (2); S4. Adding meshing in the finite element software COMSOL, wherein the meshing includes a preset mesh size, shape, and scanning mode, and the mesh size of the piezoelectric sensitive element (2) is smaller than that of the base (1), the inertial mass block (3), and the pre-tightening bolt (4); S5. Perform parameter scanning in the preset frequency domain in the finite element software COMSOL, and obtain the resonant frequency of the piezoelectric vibration sensor model under the multi-physics field coupling condition. A multi-physics field coupled piezoelectric vibration sensor resonant frequency simulation method is completed.

3. The method for simulating the resonant frequency of a piezoelectric vibration sensor coupled with multiple physical fields according to claim 2, wherein: In step S1, the material properties of the base (1) and the pre-tightening bolt (4) include density, Young's modulus, Poisson's ratio, thermal conductivity, resistivity, thermal expansion coefficient, constant pressure heat capacity, electrical conductivity, bulk modulus and shear modulus; The material properties of the inertial mass (3) include density, Young's modulus, thermal conductivity, resistivity, thermal expansion coefficient, constant pressure heat capacity, electrical conductivity, bulk modulus and shear modulus; The material properties of the piezoelectric sensitive element (2) include density, flexibility matrix, coupling matrix, relative dielectric constant, loss factor of each matrix and elastic matrix; The piezoelectric vibration sensor combination / assembly method action is to form an assembly; In step S1, the polarization directions of the base (1), the piezoelectric sensitive element (2), the inertial mass block (3) and the pre-tightening bolt (4) are also set.

4. The method for simulating the resonant frequency of a piezoelectric vibration sensor coupled with multiple physical fields according to claim 3, wherein: The base (1) and the pre-tightening bolt (4) are both made of stainless steel, the inertial mass block (3) is made of tungsten alloy, and the piezoelectric sensitive element (2) is made of PZT-5A piezoelectric ceramic material; The number of the piezoelectric sensitive elements (2) is two and they are stacked one above the other.

5. The method for simulating the resonant frequency of a piezoelectric vibration sensor coupled with multiple physical fields according to claim 2, wherein: In step S2, in the solid mechanics module, the base (1), the inertial mass block (3) and the pre-tightening bolt (4) all use a global coordinate system; The initial displacement field and structural velocity field of the piezoelectric vibration sensor are both 0; The pair types among the base (1), the piezoelectric sensitive element (2), the inertial mass block (3) and the pre-tightening bolt (4) are all contact pairs, and the mapping type of the contact pairs is a deformation configuration; In the solid mechanics module, the contact formula of the contact pair is the augmented Lagrangian formula; boundary continuity is added to the solid mechanics physical field, the contact pair is selected, the pre-tightening force type of the pre-tightening bolt (4) is designed to be pre-tightening stress, and the pre-tightening force size is set.

6. The method for simulating the resonant frequency of a piezoelectric vibration sensor coupled with multiple physical fields according to claim 2, wherein: In step S2, in the electrostatic module, the initial value potential of the structure is 0, the assumed equation and the grounding equation are both frequency domain equations, and the selected domain is the piezoelectric sensitive element (2).

7. The method for simulating the resonant frequency of a piezoelectric vibration sensor coupled with multiple physical fields according to claim 2, wherein: In step S4, the meshing method of the piezoelectric sensitive element (2) is cube sweeping, the mesh size is extremely fine, and the calibration method is ordinary physics; The mesh shapes of the base (1), the inertial mass block (3) and the pre-tightening bolt (4) are free tetrahedrons, the mesh size is relatively fine, and the calibration method is ordinary physics.

8. The method for simulating the resonant frequency of a piezoelectric vibration sensor coupled with multiple physical fields according to claim 2, wherein: In step S5, the finite element software COMSOL studies the output of the piezoelectric vibration sensor at different frequencies in the frequency domain to draw an output-frequency change curve to obtain the resonant frequency of the piezoelectric vibration sensor.

9. The method for simulating the resonant frequency of a piezoelectric vibration sensor coupled with multiple physical fields according to claim 2, wherein: Frequency domain parameters include frequency range, start value, stop value, and step size.

10. The method for simulating the resonant frequency of a piezoelectric vibration sensor coupled with multiple physical fields according to claim 2, wherein: When the structure of the piezoelectric vibration sensor is changed or the size is fine-tuned, only the COMSOL finite element method changes the structure of the piezoelectric vibration sensor in the simulation software, and performs simulation again to obtain the changed resonant frequency.

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