Z-axis sensitive mechanical structure with beizer curve short beam and parameter design method thereof

Abstract

The application discloses a Z-axis sensitive mechanical structure adopting a Bessel curve short beam and a parameter design method thereof, belongs to the technical field of micro electro mechanical system and inertial sensor mechanical structure design, and the structure comprises a mass block, a closed anchoring frame and at least two groups of center-symmetric or axis-symmetric arranged support beams, each support beam comprises a long straight beam and a short beam located between the mass block and a local transition area of the long straight beam, the upper boundary and the lower boundary of the short beam are respectively defined by a first second-order Bessel curve and a second second-order Bessel curve, and the horizontal coordinates of corresponding control points are the same; the parameter design method comprises the following steps: establishing a short beam parameterized model; setting a width distribution variable, an outline envelope constraint and a process constraint; performing statics analysis and modal analysis; and performing optimization solving on the variable based on a target function and a constraint condition. The application can realize continuous adjustment of local rigidity, stress distribution and modal characteristics of the Z-axis sensitive mechanical structure without increasing modeling complexity.

Description

Technical Field

[0001] This invention relates to the field of microelectromechanical systems and mechanical structure technology of inertial sensors, and in particular to a Z-axis sensitive mechanical structure using a short beam with a Bézier curve and its parameter design method. Background Technology

[0002] Z-axis sensitive mechanical structures are key elastic support units in inertial devices such as microelectromechanical systems (MEMS) accelerometers. The configuration of its local beam segments directly affects the Z-axis displacement response, the frequency interval between working and non-working modes, cross-axis coupling, and the local stress level in the connection area.

[0003] In existing Z-axis sensitive mechanical structures, the short beam between the mass block and the long straight beam typically uses a straight boundary, and the connection between the short beam and the mass block or long straight beam uses regular geometric transitions such as fixed arcs or fillets. Although the above scheme facilitates layout drawing, the adjustable degrees of freedom of the local contour and width distribution of the short beam are usually low. Under the same external shape envelope and established process rules, it is difficult to continuously adjust the local bending stiffness and stress distribution at different positions of the short beam.

[0004] If the local short beam profile is described as a continuous curved boundary, the continuously changing geometric shape can be expressed with fewer parameters, which is also more conducive to finite element analysis and optimization solutions. However, there is currently no feasible technical solution for using free curves for short beams. Summary of the Invention

[0005] The technical problem to be solved by this invention is that in inertial devices, the existing Z-axis sensitive mechanical structure has limited freedom of adjustment of the geometric profile of the short beam, and the local width variation along the length of the short beam is limited, making it difficult to continuously adjust the local bending stiffness and the overall equivalent stiffness distribution at different positions under a given shape envelope and process rules.

[0006] Another technical problem that this invention aims to solve is that some connections have large geometric abrupt changes, which can easily lead to local stress concentration.

[0007] The principle of this invention: The short beam between the mass block and the long straight beam is described by a Bézier curve. The boundary of the short beam is defined by two second-order Bézier curves. The corresponding control points have the same horizontal coordinate and the corresponding vertical coordinates differ. , , Characterizing the width distribution, where , and These represent the longitudinal spacing between the starting, intermediate, and ending control points of two second-order Bézier curves, respectively; and the positional parameters along the length direction. This represents the distance along the short beam length between the intermediate control point pair and the starting control point pair, expressed as bending offset. This indicates the degree of longitudinal offset of the midpoint of the intermediate control point relative to the line connecting the midpoints of the two end control points. (By...) , , , and The combined adjustment can continuously adjust the local stiffness, stress distribution and modal characteristics while maintaining the overall shape envelope constraint.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0009] A Z-axis sensitive mechanical structure using a Bézier curve short beam includes a mass block disposed inside a closed anchoring frame and connected to the anchoring frame via a support beam; the support beam includes a long straight beam and a Bézier short beam, one end of the long straight beam is connected to the Bézier short beam and the other end is connected to the anchoring frame, and the other end of the Bézier short beam is connected to the mass block;

[0010] The upper boundary of the Bezier short beam is formed by the first and second order Bezier curves. By definition, the lower boundary is defined by the second-order Bézier curve. Define, where, Let be the parameters of the second-order Bézier curve, and ;

[0011] The first and second order Bézier curves can be represented as:

[0012] (1)

[0013] The second-order Bézier curve can be represented as:

[0014] (2)

[0015] Among them, control points Control points and control points These are the starting control point, intermediate control point, and ending control point of the first and second order Bézier curves, respectively. Control points and control points These are the starting control point, intermediate control point, and ending control point of the second-order Bézier curve, respectively.

[0016] Set control points With control points The x-coordinates are the same, control points With control points The x-coordinates are the same, control points With control points The x-coordinates are the same.

[0017] The aforementioned Z-axis sensitive mechanical structure employing a short beam with a Bézier curve is designed as follows: , and Control points With control points Control points With control points Control points With control points The vertical spacing between them is expressed as:

[0018] (3)

[0019] Control points and control points As the reference endpoint of the main structure, let point... ,point ,point Control points With control points Control points With control points Control points With control points The midpoint, This represents the length-direction position parameter of the intermediate control point pair relative to the starting control point pair. and satisfy ;

[0020] With point and points The line connecting the ends is used as the center reference line for the bending offset. For point The end center reference line is in the same The vertical directional distance between coordinates;

[0021] Through the vertical spacing one Longitudinal spacing two Three distances between longitudinal sections Length direction position parameters and bending offset The positions of six control points are determined, thereby uniquely determining the upper and lower boundary shapes of the Bessel short beam.

[0022] The aforementioned Z-axis sensitive mechanical structure using a short beam with a Bézier curve, under the same parameters The next two second-order Bézier curves have the same x-coordinate, and the Bézier short beam is in Local width of direction ( ) is represented as:

[0023] (4)

[0024] As can be seen from equation (4), by adjusting the longitudinal spacing... Longitudinal spacing two Vertical spacing three The relative size allows for continuous adjustment of the width distribution of the Bessel short beam along its length; by adjusting the position parameters along the length direction... The position of the intermediate control point pair relative to the starting control point pair in the length direction can be changed by adjusting the bending offset. The longitudinal offset of the intermediate control point relative to the end center reference line can be changed, thereby further adjusting the overall bending shape of the Bessel short beam.

[0025] A parametric design method for a Z-axis sensitive mechanical structure employing a short beam with a Bézier curve includes:

[0026] S1: The Z-axis sensitive mechanical structure model includes a mass block (1), which is located inside the closed anchor frame (3) and connected to the anchor frame (3) through a support beam (2); the support beam includes a long straight beam (22) and a Bessel short beam (21), one end of the long straight beam is connected to the Bessel short beam and the other end is connected to the anchor frame, and the other end of the Bessel short beam is connected to the mass block;

[0027] A parametric geometric model of the Z-axis sensitive mechanical structure is established based on equations (1) and (2). Control points are used in the parametric geometric model. To control point Construct the upper and lower boundaries of the Bessel short beam;

[0028] The first and second order Bézier curves can be represented as:

[0029] (1)

[0030] The second-order Bézier curve can be represented as:

[0031] (2)

[0032] in, Let be the parameters of the second-order Bézier curve, and Control points Control points and control points These are the starting control point, intermediate control point, and ending control point of the first and second order Bézier curves, respectively. Control points and control points These are the starting control point, intermediate control point, and ending control point of the second-order Bézier curve, respectively.

[0033] Set control points With control points The x-coordinates are the same, control points With control points The x-coordinates are the same, control points With control points The x-coordinates are the same;

[0034] S2: Adjust the vertical spacing... Longitudinal spacing two Vertical spacing three and length direction position parameters and bending offset Together they serve as geometric design variables for the width distribution of Bessel short beams;

[0035] Simultaneously, set geometric constraints, shape envelope constraints, minimum linewidth constraints, minimum gap constraints, maximum stress constraints, working mode frequency range, and non-sensitive direction coupling response constraints for the corresponding control points with the same abscissa;

[0036] S3: Based on the parametric geometric model, establish a finite element model and perform static analysis, modal analysis, and harmonic response analysis to obtain the performance parameters of the Z-axis sensitive mechanical structure. These performance parameters include the Z-axis displacement response sensitivity. Maximum equivalent stress Operating mode frequency Frequency interval between operating mode and non-operating mode and cross-axis sensitivity ;

[0037] S4: Based on the performance parameters obtained in step S3, an optimization solution method is used to calculate the longitudinal spacing. Longitudinal spacing two Vertical spacing three Length direction position parameters and bending offset Perform iterative updates to obtain the target structure parameters that satisfy the objective function and constraints.

[0038] In the aforementioned parametric design method for a Z-axis sensitive mechanical structure using a short beam with a Bézier curve, in step S2, the design variable vector is set as follows: The geometric constraints that correspond to the same x-coordinate of the control points are: and satisfy , , ,and ,in and The bending offset is defined as follows, assuming that the upper and lower boundaries of the Bessel short beam do not exceed the preset shape envelope area. The minimum and maximum allowed values.

[0039] In the aforementioned parametric design method for a Z-axis sensitive mechanical structure using a short beam with a Bézier curve, the minimum linewidth constraint of the short beam in step S2 is expressed as: ,in The minimum local width of the short beam is obtained from the parametric geometric model. The minimum structural linewidth allowed by the process;

[0040] Shape envelope constraint is represented as ,in This refers to the pre-defined allowable shape envelope area for the short beam;

[0041] The minimum clearance constraint of the structure is ;

[0042] Maximum stress constraint is ;

[0043] Operating mode frequency Range constraints are ;

[0044] Frequency interval between operating mode and non-operating mode ;

[0045] The coupling response in the non-sensitive direction is achieved using cross-axis sensitivity. Indicate, and set ;

[0046] in To minimize the gap in the structure, To achieve the minimum clearance required by the process, For maximum stress, This is the allowable value for the material. and These are the lower and upper limits of the preset range for the operating modal frequencies, respectively. For the preset frequency interval threshold, Set a preset threshold for cross-axis sensitivity.

[0047] In the aforementioned parametric design method for a Z-axis sensitive mechanical structure using a short beam with a Bézier curve, in step S3, static analysis is used to obtain the Z-direction displacement response sensitivity, maximum equivalent stress, and cross-axis sensitivity; modal analysis is used to obtain the working modal frequency and the frequency interval between the working mode and the non-working mode; harmonic response analysis is used to obtain the Z-direction displacement frequency response curve, resonance frequency, and corresponding displacement amplitude of the mass block within a preset frequency range, as well as the Z-direction steady-state displacement amplitude within the working frequency range, in order to evaluate the dynamic characteristics of the candidate solution or the target structure.

[0048] The aforementioned parametric design method for a Z-axis sensitive mechanical structure using a short beam with a Bézier curve, in step S3, during static analysis, pre-set base accelerations in the Z, X, and Y directions are applied respectively. Under linear small deformation conditions, for any base acceleration input in any direction, the finite element equilibrium relationship is expressed as:

[0049] (5)

[0050] In equation (5), Here is the structural stiffness matrix. For the quality matrix, Let be the nodal displacement vector. This is the equivalent inertial load vector. The direction affects the vector. For the base acceleration, Take respectively , or ;

[0051] Under the action of the Z-axis base acceleration, the Z-axis displacement response sensitivity can be obtained based on the average Z-axis displacement of mass block 1:

[0052] (6)

[0053] In equation (6), Indicates the application of Z-axis base acceleration The average Z-direction displacement generated by mass block 1, where |.| represents the absolute value;

[0054] Under the same displacement amplitude base acceleration conditions in the Z, X, and Y directions, the equivalent stress distribution of the Bessel short beam and the region connecting the Bessel short beam with the long straight beam and the mass block were obtained. For each condition, the maximum equivalent stress in the aforementioned connection region was taken, and the maximum value of the maximum equivalent stress among the three conditions was defined as the maximum equivalent stress. To characterize the most unfavorable local stress level of the Z-axis sensitive mechanical structure under different directions of base acceleration;

[0055] Under the same base acceleration condition, X-axis and Y-axis accelerations are applied respectively, and the average Z-axis displacement of the mass block caused by the acceleration inputs in the two insensitive directions of X and Y is extracted to evaluate the cross-axis sensitivity. The cross-axis sensitivity can be expressed as:

[0056] (7)

[0057] In equation (7), and These represent the average Z-direction displacement of the mass block when X- and Y-direction base accelerations are applied, respectively. and The Z-axis cross-response sensitivity corresponds to the X-axis and Y-axis acceleration inputs, respectively. This refers to the cross-axis sensitivity.

[0058] The aforementioned parametric design method for a Z-axis sensitive mechanical structure using a short beam with a Bézier curve, in step S3, involves solving the characteristic equations of the Z-axis sensitive mechanical structure under the same constraint boundary conditions as in the static analysis during modal analysis, and obtaining the natural frequencies of each order:

[0059] (8)

[0060] In equation (8), For the first First natural angular frequency, The eigenvectors corresponding to the natural frequencies are used to characterize the relative displacement distribution of each node in the structure under that mode, i.e., the corresponding mode shape. For the first The natural frequencies of the first and second orders are determined; based on the mode shapes, the mode in which the Z-axis motion component of the mass block is dominant is identified as the working mode, and the natural frequencies corresponding to the working modes are determined as the working mode frequencies. The remaining modes are considered as non-operating modes. The frequency interval between the operating mode and the non-operating mode can be expressed as:

[0061] (9)

[0062] In equation (9), For the selected set of non-working modes, The first non-working mode in the set The natural frequency of each mode.

[0063] The aforementioned parameter design method for a Z-axis sensitive mechanical structure using a short beam with a Bézier curve, in step S3, involves setting a sweep point and damping parameters within a preset frequency range during harmonic response analysis, and applying a Z-axis simple harmonic base acceleration that varies sinusoidally with time to obtain the steady-state harmonic response of the Z-axis sensitive mechanical structure at different excitation frequencies. Under the steady-state harmonic response conditions, the structural dynamic equations are transformed to the frequency domain to obtain the frequency domain dynamic equations used to solve the reset displacement response at different excitation frequencies.

[0064] (10)

[0065] In equation (10), For the excitation angular frequency, Here is the damping matrix. ( ) is the reset shift response vector. ( ) represents the corresponding harmonic load vector;

[0066] The reset displacement response vector under different excitation frequencies is obtained from equation (10). ( The Z-axis reset displacement of the mass block is extracted from the mass block region, and the Z-axis reset displacement of the mass block region is spatially averaged to obtain the average Z-axis reset displacement of the mass block. Based on the relationship between the amplitude of the average Z-axis reset displacement and the excitation frequency, the Z-axis displacement frequency response curve within the preset sweep frequency range is obtained. Based on the frequency response curve, the resonance frequency and its corresponding displacement amplitude are determined, and the steady-state Z-axis displacement amplitude within the working frequency range is extracted.

[0067] The aforementioned parameter design method for a Z-axis sensitive mechanical structure using a short beam with a Bézier curve, in step S4, the optimization solution method includes a global search method, an approximate model-assisted optimization method, a local optimization method, or a combination of the above methods.

[0068] The beneficial effects achieved by this invention are as follows: The Z-axis sensitive mechanical structure of this invention can simultaneously describe the width distribution and overall bending shape of the short beam along its length direction with fewer design variables, thereby improving the efficiency and adjustability of the parametric description of the geometry of the local transition zone between the mass block and the long straight beam; by describing the upper and lower boundary parameters simultaneously, and then performing geometric modeling, finite element analysis, and parameter optimization, the performance indicators of the Z-axis sensitive mechanical structure are improved; by forming a continuous or smooth transition between the short beam and adjacent beam segments, it is beneficial to reduce the degree of geometric abrupt change in the connection area between the short beam and the long straight beam, and reduce local stress concentration; under the same shape envelope and process constraints, incorporating process requirements such as minimum linewidth and minimum gap as constraints into the optimization process improves the Z-axis sensitivity of the structure, increases the modal interval, reduces local stress, and also meets the predetermined MEMS processing conditions. Attached Figure Description

[0069] Figure 1 This is a top view of a Z-axis sensitive mechanical structure using a short beam with a Bézier curve, as described in Embodiment 1 of the present invention.

[0070] Figure 2 This is a schematic diagram illustrating the geometric definition and parametric relationship of the Bézier curve short beam in Embodiment 1 of the present invention;

[0071] Figure 3 This is a flowchart of the parameter design method in Embodiment 1 of the present invention.

[0072] Reference numerals: 1. Mass block, 2. Support beam, 3. Anchoring frame. Detailed Implementation

[0073] The present invention will be further described below with reference to the accompanying drawings and embodiments. It should be understood that the following embodiments are only for explaining the present invention and are not intended to limit the scope of protection of the present invention. Equivalent substitutions or modifications made by those skilled in the art to the structural form, parameter settings, and solution steps without departing from the concept of the present invention should all fall within the scope of protection of the present invention.

[0074] Example 1

[0075] like Figure 1 As shown, this embodiment provides a Z-axis sensitive mechanical structure using a short beam with a Bézier curve, including a mass block 1, a support beam 2, and an anchoring frame 3. The mass block 1 is disposed inside the closed anchoring frame 3 and is connected to the anchoring frame 3 through the support beam 2.

[0076] The top view of the mass block 1 and the anchoring frame 3 is square, and the support beams 2 are L-shaped, arranged in four sets symmetrically. Each set of support beams 2 includes a long straight beam 22 and a Bessel short beam 21. One end of the long straight beam 22 is connected to the Bessel short beam 21, and the other end is connected to the anchoring frame 3. The other end of the Bessel short beam 21 is connected to the mass block 1.

[0077] The Bessel short beam 21 is located in the local transition zone between the mass block 1 and the long straight beam 22, and is used to replace short beam structures with straight boundaries or fixed arcs and rounded corners. In this embodiment, the primary sensing direction of the Z-axis sensitive mechanical structure is the Z-direction perpendicular to the plane where the mass block 1 is located. The primary sensing direction refers to the acceleration input direction that the structure is designed to detect and generate the main displacement response. When an external acceleration input is generated in the Z-direction, the mass block 1 generates a corresponding displacement under the elastic constraint of the supporting beam 2. The local geometry of the Bessel short beam 21 affects the equivalent stiffness of the local transition zone, the stress distribution in the connection area between the Bessel short beam 21 and the long straight beam 22, and the mass block 1, as well as the relationship between the working and non-working modes.

[0078] like Figure 2 As shown, the upper boundary of the Bezier short beam 21 is formed by the first and second order Bezier curves. By definition, the lower boundary is defined by the second-order Bézier curve. Define, where, Let be the parameters of the second-order Bézier curve, and ;when When, it indicates the starting end of the Bessel short beam 21, when When, it indicates the end of the Bessel short beam 21.

[0079] The first and second order Bézier curves can be represented as:

[0080] (1)

[0081] The second-order Bézier curve can be represented as:

[0082] (2)

[0083] To ensure a clear one-to-one correspondence between the upper and lower boundaries of the Bessel short beam 21 and to reduce the number of independent variables, this embodiment sets control points. With control points The x-coordinates are the same, control points With control points The x-coordinates are the same, control points With control points The x-coordinates are the same. Among them, the control points Control points and control points These are the starting control point, intermediate control point, and ending control point of the first and second order Bézier curves, respectively. Control points and control points These are the starting control point, intermediate control point, and ending control point of the second-order Bézier curve, respectively.

[0084] Each control point at Figure 2 The coordinates in the coordinate system shown are: Wherein, the first coordinate component and the second coordinate component in the coordinate pair represent the corresponding control points at... Figure 2 The x and y coordinates in the coordinate system shown.

[0085] , and Control points With control points Control points With control points Control points With control points The longitudinal spacing between them can be expressed as:

[0086] (3)

[0087] To characterize the overall bending shape of the Bessel short beam 21, excluding its width distribution, control points are used in this embodiment. and control points As the reference endpoint of the main structure, let point... ,point ,point Control points With control points Control points With control points Control points With control points The midpoint, This represents the length-direction position parameter of the intermediate control point pair relative to the starting control point pair. That is, control point to control point Control points Control point to control point Control points Between along Distance in direction, and satisfying With points and points The line connecting the ends is used as the center reference line for the bending offset. For point The end center reference line is in the same The longitudinal directional distance between coordinates.

[0088] Then there is At control points Control points Given a fixed location, control points and control points According to the longitudinal spacing and longitudinal spacing Confirm; Click The longitudinal position depends on the bending offset. Determine, and use points Set the midpoint and ,make Therefore, by using a longitudinal spacing of one Longitudinal spacing two Three distances between longitudinal sections Length direction position parameters and bending offset The positions of the six control points can be determined, thereby uniquely determining the upper and lower boundary shapes of the Bessel short beam 21.

[0089] Since the control points of the two Bézier curves have the same x-coordinate, under the same parameters... The two second-order Bézier curves have the same x-coordinate, and the Bézier short beam 21 is in Local width of direction ( This can be represented as:

[0090] (4)

[0091] As can be seen from equation (4), by adjusting the longitudinal spacing... Longitudinal spacing two Vertical spacing three The relative size allows for continuous adjustment of the width distribution of the Bessel short beam 21 along its length; by adjusting the position parameters along the length direction... The position of the intermediate control point pair relative to the starting control point pair in the length direction can be changed by adjusting the bending offset. The longitudinal offset of the intermediate control point relative to the end center reference line can be changed, thereby further adjusting the overall bending shape of the Bessel short beam 21.

[0092] Longitudinal spacing 1, longitudinal spacing 2, and longitudinal spacing 3 can also take the same or different values, thus forming different types of width distributions; the positional parameters in the length direction and the bending offset can be taken within the allowable range of the shape envelope. By setting the above parameters, the local stiffness, stress distribution of the short beam and its connection area, and modal characteristics can be adjusted under the constraints of the shape envelope.

[0093] Example 2

[0094] like Figure 3 As shown, this embodiment provides a parametric design method for a Z-axis sensitive mechanical structure using a short beam with a Bézier curve, including the following steps:

[0095] S1: Based on equations (1) and (2), establish a parametric geometric model of the Z-axis sensitive mechanical structure, and use control points in the parametric geometric model. To control point Construct the upper and lower boundaries of the Bessel short beam 21, and combine it with the mass block 1, the long straight beam 22 and the anchoring frame 3 to form a sensitive mechanical structure model;

[0096] S2: Set design variables and constraints. Adjust the longitudinal spacing... Longitudinal spacing two Vertical spacing three and length direction position parameters and bending offset Together, they serve as geometric design variables for the width distribution of the Bessel short beam 21; among which, the longitudinal spacing is... Longitudinal spacing two Vertical spacing three Used to control width distribution and position parameters in the length direction. Used to control the length distance between intermediate control point pairs and starting control point pairs, bending offset. Used to control the longitudinal bending offset of intermediate control point pairs.

[0097] At the same time, set geometric constraints with the same abscissa for the corresponding control points, as well as conditions such as shape envelope constraints, minimum linewidth constraints, minimum gap constraints, maximum stress constraints, working mode frequency range, and non-sensitive direction coupling response constraints.

[0098] Let the design variable vector be The geometric constraints that correspond to the same x-coordinate of the control points are: and satisfy , , ,and ,in and The bending offset is defined as follows, assuming that the upper and lower boundaries of the Bessel short beam do not exceed the preset shape envelope area. The minimum and maximum values ​​allowed; the minimum and maximum values ​​can be determined by moving the intermediate control point pair along the longitudinal direction until any Bézier curve boundary reaches the preset shape envelope boundary.

[0099] The minimum linewidth constraint for short beams can be expressed as: ,in The minimum local width of the short beam is obtained from the parametric geometric model. This is the minimum structural linewidth allowed by the process.

[0100] Shape envelope constraint is represented as ,in This refers to the pre-defined allowable shape envelope area for the short beam.

[0101] The minimum clearance constraint of the structure is ;

[0102] Maximum stress constraint is ;

[0103] Operating mode frequency Range constraints are .

[0104] Frequency interval between operating mode and non-operating mode ;

[0105] The coupling response in the non-sensitive direction is achieved using cross-axis sensitivity. Indicate, and set .

[0106] in To minimize the gap in the structure, To achieve the minimum clearance required by the process, For maximum stress, This is the allowable value for the material. and These are the lower and upper limits of the preset range for the operating modal frequencies, respectively. For the preset frequency interval threshold, Set a preset threshold for cross-axis sensitivity.

[0107] S3: Based on the parametric geometric model, establish a finite element model and perform static analysis, modal analysis, and harmonic response analysis to obtain the performance parameters of the Z-axis sensitive mechanical structure. These performance parameters include the Z-axis displacement response sensitivity. Maximum equivalent stress Operating mode frequency Frequency interval between operating mode and non-operating mode and cross-axis sensitivity .

[0108] Static analysis is used to obtain the Z-direction displacement response sensitivity, maximum equivalent stress, and cross-axis sensitivity; modal analysis is used to obtain the working mode frequency and the frequency interval between the working mode and the non-working mode; harmonic response analysis is used to obtain the Z-direction displacement frequency response curve, resonance frequency, and corresponding displacement amplitude of mass block 1 within the preset frequency range, as well as the Z-direction steady-state displacement amplitude within the working frequency range, in order to evaluate the dynamic characteristics of candidate solutions or target structures.

[0109] In the static analysis, the anchorage region corresponding to anchor frame 3 is set as a fixed boundary, and structural material parameters are assigned, including material density and elastic parameters describing the elastic mechanical properties of the material. For isotropic materials, the elastic parameters include elastic modulus and Poisson's ratio; for anisotropic materials, the elastic parameters are the corresponding elastic stiffness parameters. Preset base accelerations in the Z, X, and Y directions are applied respectively. These base accelerations refer to the external acceleration inputs applied to the device base connected to anchor frame 3, used to equivalently simulate the inertial response of mass block 1 when the entire device is subjected to acceleration in the corresponding directions. Under linear small deformation conditions, for any base acceleration input in any direction, the finite element equilibrium relationship can be expressed as:

[0110] (5)

[0111] In equation (5), Here is the structural stiffness matrix. For the quality matrix, Let be the nodal displacement vector. This is the equivalent inertial load vector. The direction affects the vector. For the base acceleration, Take respectively , or .

[0112] The linear small deformation refers to the displacement, rotation angle, and strain of the Z-axis sensitive mechanical structure being within a range where the geometric nonlinear effects are negligible and the material is within the linear elastic range.

[0113] Under the action of the Z-axis base acceleration, the Z-axis displacement response sensitivity can be obtained based on the average Z-axis displacement of mass block 1:

[0114] (6)

[0115] In equation (6), Indicates the application of Z-axis base acceleration The average Z-direction displacement generated by mass block 1 is given by |.|, where |.| represents the absolute value.

[0116] Under the same displacement amplitude base acceleration conditions in the Z, X, and Y directions, the equivalent stress distribution of the Bessel short beam 21 and the connection region between the Bessel short beam 21 and the long straight beam 22 and the mass block 1 were obtained. For each condition, the maximum equivalent stress in the connection region was taken, and the maximum value of the maximum equivalent stress among the three conditions was defined as the maximum equivalent stress. This is used to characterize the most unfavorable local stress level of the Z-axis sensitive mechanical structure under the action of base acceleration in different directions.

[0117] Under the same base acceleration condition, X-axis and Y-axis accelerations are applied respectively, and the average Z-axis displacement of mass block 1 caused by the acceleration inputs in the two insensitive directions of X and Y is extracted to evaluate the cross-axis sensitivity. The cross-axis sensitivity can be expressed as:

[0118] (7)

[0119] In equation (7), and These represent the average Z-direction displacement produced by mass block 1 when X-direction and Y-direction base accelerations are applied, respectively. and The Z-axis cross-response sensitivity corresponds to the X-axis and Y-axis acceleration inputs, respectively. This refers to the cross-axis sensitivity.

[0120] In modal analysis, the characteristic equations of the Z-axis sensitive mechanical structure are solved under the same constraint boundary conditions as in static analysis, and the natural frequencies of each order are obtained:

[0121] (8)

[0122] In equation (8), For the first First natural angular frequency, The eigenvectors corresponding to the natural frequencies are used to characterize the relative displacement distribution of each node in the structure under that mode, i.e., the corresponding mode shape. For the first The natural frequencies of each mode are determined. Based on the mode shapes, the mode in which the Z-axis motion component of mass block 1 is dominant is identified as the working mode, and the natural frequencies corresponding to the working modes are determined as the working mode frequencies. The remaining modes are considered as non-operating modes. The frequency interval between the operating mode and the non-operating mode can be expressed as:

[0123] (9)

[0124] In equation (9), For the selected set of non-working modes, The first non-working mode in the set The natural frequency of each mode.

[0125] In harmonic response analysis, sweep points and damping parameters are set within a preset frequency range, and a Z-axis simple harmonic base acceleration that varies sinusoidally with time is applied to obtain the steady-state harmonic response of the Z-axis sensitive mechanical structure at different excitation frequencies. Under steady-state harmonic response conditions, the structural dynamics equations are transformed to the frequency domain, yielding the frequency-domain dynamics equations for solving the reset displacement response at different excitation frequencies:

[0126] (10)

[0127] In equation (10), For the excitation angular frequency, Here is the damping matrix. ( ) is the reset shift response vector. ( ) represents the corresponding harmonic load vector.

[0128] The reset displacement response vector under different excitation frequencies is obtained from equation (10). ( The Z-axis reset displacement of mass block 1 is extracted from the mass block 1 region, and the Z-axis reset displacement of mass block 1 region is spatially averaged to obtain the Z-axis average reset displacement of mass block 1. Based on the relationship between the amplitude of the Z-axis average reset displacement and the excitation frequency, the Z-axis displacement frequency response curve within the preset sweep frequency range is obtained. Based on the frequency response curve, the resonance frequency and its corresponding displacement amplitude are determined, and the Z-axis steady-state displacement amplitude within the working frequency range is extracted.

[0129] In this embodiment, the harmonic response analysis results are used to evaluate the dynamic characteristics of candidate solutions or target structures. The core performance parameters obtained from the above static and modal analyses and used in step S4 include the Z-direction displacement response sensitivity. Maximum equivalent stress Operating mode frequency Frequency interval between operating mode and non-operating mode and cross-axis sensitivity The Z-axis displacement response sensitivity, frequency interval, and maximum equivalent stress were taken as the main optimization objectives, while the operating mode frequency and cross-axis sensitivity were taken as the main performance constraints.

[0130] S4: Based on the performance parameters obtained in step S3, an optimization solution method is used to calculate the longitudinal spacing. Longitudinal spacing two Vertical spacing three Length direction position parameters and bending offset The process involves iterative updates to obtain the target structural parameters that satisfy the objective function and constraints. These performance parameters include the Z-axis displacement response sensitivity. Maximum equivalent stress Operating mode frequency Frequency interval between operating mode and non-operating mode and cross-axis sensitivity .

[0131] The optimization solution method includes global search method, approximate model-assisted optimization method, local optimization method, or a combination of the above methods.

[0132] The global search method can employ a genetic algorithm or a particle swarm optimization algorithm, the approximate model-assisted optimization method can employ a response surface methodology, and the local optimization method can employ a gradient method.

[0133] The optimization process comprises improving the Z-axis displacement response sensitivity, increasing the frequency interval between the working and non-working modes, and reducing the maximum equivalent stress in the Bessel short beam 21 and its connection region with mass block 1 and long straight beam 22. When using a weighted single-objective approach, the multiple performance objectives are converted into dimensionless indices, multiplied by their respective weights, and then merged into a single scalar objective function. Dimensionlessness refers to normalization using reference quantities corresponding to each performance parameter, transforming performance parameters with different dimensions and orders of magnitude into comparable dimensionless indices. For example, the following objective function can be constructed:

[0134] (11)

[0135] In equation (11), , , These are non-negative weight coefficient one, weight coefficient two, and weight coefficient three, respectively. , and These are reference values ​​for the Z-axis displacement response sensitivity, frequency interval, and maximum equivalent stress, all of which are preset values ​​greater than 0. The corresponding performance parameters of the baseline structure before optimization can be used as reference values ​​to minimize the objective function. To optimize the objective, the constraints set in step S2—including the shape envelope constraint, process constraint, maximum stress constraint, operating mode frequency range constraint, and cross-axis sensitivity constraint—must be met simultaneously.

[0136] Alternatively, a multi-objective optimization approach can be directly adopted. This involves not weighting and merging the objectives, but instead treating improving the Z-axis displacement response sensitivity, increasing the frequency interval between the working and non-working modes, and reducing the maximum equivalent stress as independent optimization objectives. Target structural parameters are then selected from a set of non-dominated solutions that satisfy the constraints. A non-dominated solution is a feasible solution that satisfies the constraints and for which no other feasible solution can further improve at least one optimization objective without worsening the others. Multiple non-dominated solutions constitute a set of non-dominated solutions, and target structural parameters are selected from this set.

[0137] In step S4, during the parameter iterative solution process, firstly, at the longitudinal spacing... Longitudinal spacing two Vertical spacing three Length direction position parameters and bending offset Candidate design variables are generated within the preset value range. The positions of the six control points and the parametric geometric model of the Bessel short beam 21 are updated based on the candidate design variables. Static analysis and modal analysis in step S3 are then performed. Based on the finite element analysis results, the Z-direction displacement response sensitivity, maximum equivalent stress, working modal frequency, frequency interval between working and non-working modes, and cross-axis sensitivity are obtained. The performance evaluation and feasibility determination of the candidate design are performed based on the objective function and constraints. The design variables are updated according to the optimization solution method adopted. The above parametric geometric model update, finite element analysis, performance evaluation, constraint determination, and design variable update process are repeated until the preset convergence condition is met, and the optimal structural parameters are obtained.

[0138] The global search method is used to search for optimal structural parameters within a preset range of design variables. When using a genetic algorithm, an initial population is generated within the design variable range. Each individual is evaluated according to the objective function and constraints, and the population is updated through selection, crossover, and mutation. When using a particle swarm optimization algorithm, particles are initialized within the design variable range, and candidate structural parameters are updated based on the current evaluation results of each particle, its historical optimal position, and the population's optimal position. The above evaluation and update process is repeated until a preset convergence condition is met.

[0139] The approximate model-assisted optimization method can employ the response surface methodology. When using the response surface methodology, firstly, design test sample points are selected within the design variable space. Static and modal analyses are performed on each sample point in step S3 to obtain the objective function value and constraint response. Based on the sample data, an approximate response surface model is established between the design variables and the core performance parameters, and candidate structural parameters are searched on this approximate model. The obtained candidate solutions are substituted into the finite element model for finite element verification. If necessary, samples are supplemented and the response surface approximate model is updated based on the verification results. The approximate model-assisted optimization method helps reduce the number of times finite element analyses are performed on a large number of candidate designs during the optimization process.

[0140] The local optimization method can employ the gradient method. When using the gradient method, the preferred feasible solution satisfying the constraints is used as the initial design. The sensitivity of the objective function and constraints relative to each design variable is calculated. Based on the sensitivity, the search direction and step size are determined, and the design variables are updated. The updated design undergoes static and modal analysis in step S3, and the objective function is recalculated and constraints are re-determined until the change in design variables or the change in the objective function meets the preset convergence condition. The local optimization method is used to refine the obtained preferred feasible solution locally.

[0141] The combined approach can employ a multi-stage collaborative optimization solution method. First, design test sample points are selected within the design variable space, and static and modal analyses are performed in step S3 to obtain sample performance parameters, establishing an approximate response surface model. Second, a genetic algorithm or particle swarm optimization algorithm is used to perform a global search on the approximate response surface model to obtain multiple candidate solutions. Then, the candidate solutions are substituted into the finite element model of step S3 for verification, and samples are supplemented and the approximate response surface model is updated based on the verification results. Next, the preferred feasible solution verified by the finite element model is used as the initial design, and the gradient method is used for local refinement. Finally, the structural parameters obtained from the local refinement are substituted back into the finite element model of step S3 for final verification. When the verification results meet the preset constraints and the optimization results reach the preset convergence requirements, the target structural parameters are output; otherwise, the structural parameters are used as supplementary samples and iteration continues. By adopting the above combination, the number of direct finite element solutions for a large number of candidate designs can be reduced by using the response surface approximation model, the search range of the preferred structural parameters can be expanded by using the global search method, the impact of the approximation model error on the optimization results can be reduced by using finite element verification, and the solution accuracy and convergence efficiency in the preferred region can be improved by using the local optimization method. Thus, under the premise of satisfying the shape envelope constraint, process constraint, maximum stress constraint, working mode frequency range constraint and cross axis sensitivity constraint, the Z-direction displacement response sensitivity, the frequency interval between the working mode and the non-working mode, and the maximum equivalent stress of the Bessel short beam 21 and its connection area with the mass block 1 and the long straight beam 22 can be synergistically optimized.

[0142] S5: Generate micromachining layout files, geometric models, or pre-processing design data for Z-axis sensitive mechanical structures based on the optimized target parameters. These data describe the planar geometric contours of the MEMS structure and are used for subsequent mask layout design or processing data generation.

[0143] By adjusting the vertical spacing Longitudinal spacing two Vertical spacing three The relative size allows the short beam 21 to exhibit different local widths at one end near the mass block 1, one end near the long straight beam 22, or in the middle region. This enables a comprehensive evaluation of the Z-direction displacement response, the frequency interval between working and non-working modes, and the maximum equivalent stress under the same external envelope and predetermined process rules. The predetermined process rules include the minimum allowable structural linewidth, minimum structural gap, structural layer thickness, and manufacturing constraints related to release and etching in the employed MEMS process.

[0144] For example, when it is necessary to increase the local bending stiffness of the middle region of the short beam 21, the longitudinal spacing can be increased relatively. When it is necessary to alleviate end stress concentration, the longitudinal spacing can be coordinated. Vertical spacing three Tangential continuity at the connection point; when a trade-off needs to be struck between sensitivity and modal spacing, the longitudinal spacing can be jointly optimized while keeping the envelope size constant. Longitudinal spacing two Vertical spacing three And the length parameters of the long straight beam 22.

[0145] This invention can be used for the design of Z-axis sensitive mechanical structures in capacitive MEMS accelerometers, and can also be used for other micromechanical sensitive structures that require continuous adjustment of the stiffness distribution of local beam segments.

[0146] During the manufacturing process, this invention does not limit specific materials or micromachining routes. For platforms employing SOI, bulk silicon micromachining, DRIE release, or other compatible MEMS processes, as long as manufacturing constraints such as minimum linewidth, minimum gap, and structural layer thickness are met, the structural design can be completed based on the parametric expression of this invention.

[0147] It should be understood that the specific descriptions of the number of supporting beams, symmetry, optimization algorithm, objective function, and process constraints in the above embodiments are merely illustrative and do not constitute a limitation on the scope of protection of this invention. Any equivalent substitution, improvement, or combination of the short beam curve boundary, design variables, and solution process using the technical ideas disclosed in this invention should be considered to fall within the scope of protection of this invention.

[0148] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0149] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0150] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0151] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A Z-axis sensitive mechanical structure employing a short beam with a Bézier curve, characterized in that, Includes a mass block (1), which is located inside the closed anchor frame (3) and connected to the anchor frame (3) via a support beam (2); the support beam includes a long straight beam (22) and a Bessel short beam (21), one end of the long straight beam is connected to the Bessel short beam and the other end is connected to the anchor frame, and the other end of the Bessel short beam is connected to the mass block; The upper boundary of the Bezier short beam is formed by the first and second order Bezier curves. By definition, the lower boundary is defined by the second-order Bézier curve. definition, These are the parameters of the second-order Bézier curve; The first and second order Bézier curves are represented as follows: （1） The second-order Bézier curve is represented as: （2） Among them, control points Control points and control points These are the starting control point, intermediate control point, and ending control point of the first and second order Bézier curves, respectively. Control points and control points These are the starting control point, intermediate control point, and ending control point of the second-order Bézier curve, respectively. Set control points With control points The x-coordinates are the same, control points With control points The x-coordinates are the same, control points With control points The x-coordinates are the same.

2. The Z-axis sensitive mechanical structure using a short beam with a Bézier curve according to claim 1, characterized in that, set up , and Control points With control points Control points With control points Control points With control points The vertical spacing between them is expressed as: （3） Control points and control points As the reference endpoint of the main structure, let point... ,point ,point Control points With control points Control points With control points Control points With control points The midpoint, This represents the length-direction position parameter of the intermediate control point pair relative to the starting control point pair. and satisfy ; With point and points The line connecting the ends is used as the center reference line for the bending offset. For point The end center reference line is in the same The vertical directional distance between coordinates; Through the vertical spacing one Longitudinal spacing two Three distances between longitudinal sections Length direction position parameters and bending offset The positions of six control points are determined, thereby uniquely determining the upper and lower boundary shapes of the Bessel short beam (21).

3. A Z-axis sensitive mechanical structure employing a short beam with a Bézier curve according to claim 2, characterized in that, With the same parameters The two second-order Bézier curves have the same x-coordinate, and the Bézier short beam (21) is in Local width of direction ( ) is represented as: （4） As can be seen from equation (4), by adjusting the longitudinal spacing... Longitudinal spacing two Vertical spacing three The relative size of the Bessel short beam (21) is used to continuously adjust the width distribution along the length direction; the position parameters along the length direction are adjusted accordingly. By changing the lengthwise position of the intermediate control point pair relative to the starting control point pair, the bending offset can be adjusted. By changing the longitudinal offset of the intermediate control point relative to the end center reference line, the overall bending shape of the Bessel short beam (21) can be further adjusted.

4. A parametric design method for a Z-axis sensitive mechanical structure employing a short beam with a Bézier curve, characterized in that, include: S1: The Z-axis sensitive mechanical structure model includes a mass block (1), which is located inside the closed anchor frame (3) and connected to the anchor frame (3) through a support beam (2); the support beam includes a long straight beam (22) and a Bessel short beam (21), one end of the long straight beam is connected to the Bessel short beam and the other end is connected to the anchor frame, and the other end of the Bessel short beam is connected to the mass block; A parametric geometric model of the Z-axis sensitive mechanical structure is established based on equations (1) and (2). Control points are used in the parametric geometric model. To control point Construct the upper and lower boundaries of the Bessel short beam (21); The first and second order Bézier curves are represented as follows: （1） The second-order Bézier curve is represented as: （2） in, The parameters of the second-order Bézier curve; control points Control points and control points These are the starting control point, intermediate control point, and ending control point of the first and second order Bézier curves, respectively. Control points and control points These are the starting control point, intermediate control point, and ending control point of the second-order Bézier curve, respectively. Set control points With control points The x-coordinates are the same, control points With control points The x-coordinates are the same, control points With control points The x-coordinates are the same; S2: Adjust the vertical spacing... Longitudinal spacing two Vertical spacing three and length direction position parameters and bending offset Together they serve as geometric design variables for the width distribution of the Bessel short beam (21); Simultaneously, set geometric constraints, shape envelope constraints, minimum linewidth constraints, minimum gap constraints, maximum stress constraints, working mode frequency range, and non-sensitive direction coupling response constraints for the corresponding control points with the same abscissa; S3: Based on the parametric geometric model, establish a finite element model and perform static analysis, modal analysis, and harmonic response analysis to obtain the performance parameters of the Z-axis sensitive mechanical structure. These performance parameters include the Z-axis displacement response sensitivity. Maximum equivalent stress Operating mode frequency Frequency interval between operating mode and non-operating mode and cross-axis sensitivity ; S4: Based on the performance parameters obtained in step S3, an optimization solution method is used to calculate the longitudinal spacing. Longitudinal spacing two Vertical spacing three Length direction position parameters and bending offset Perform iterative updates to obtain the target structure parameters that satisfy the objective function and constraints.

5. The parameter design method for a Z-axis sensitive mechanical structure using a short beam with a Bézier curve according to claim 4, characterized in that, In step S2, let the design variable vector be... The geometric constraints that correspond to the same x-coordinate of the control points are: and satisfy , , ,and ,in and The bending offset is defined as follows, assuming that the upper and lower boundaries of the Bessel short beam do not exceed the preset shape envelope area. The minimum and maximum allowed values.

6. The parameter design method for a Z-axis sensitive mechanical structure using a short beam with a Bézier curve according to claim 4, characterized in that, In step S2, the minimum linewidth constraint of the short beam is expressed as: ,in The minimum local width of the short beam is obtained from the parametric geometric model. The minimum structural linewidth allowed by the process; Shape envelope constraint is represented as , This refers to the pre-defined allowable shape envelope area for the short beam; The minimum clearance constraint of the structure is ; Maximum stress constraint is ; Operating mode frequency Range constraints are ; Frequency interval between operating mode and non-operating mode ; The coupling response in the non-sensitive direction is achieved using cross-axis sensitivity. Indicate, and set ; in, To minimize the gap in the structure, To achieve the minimum clearance required by the process, For maximum stress, This is the allowable value for the material. and These are the lower and upper limits of the preset range for the operating modal frequencies, respectively. For the preset frequency interval threshold, Set a preset threshold for cross-axis sensitivity.

7. The parameter design method for a Z-axis sensitive mechanical structure using a short beam with a Bézier curve according to claim 4, characterized in that, In step S3, static analysis is used to obtain the Z-direction displacement response sensitivity, maximum equivalent stress, and cross-axis sensitivity; modal analysis is used to obtain the working mode frequency and the frequency interval between the working mode and the non-working mode; harmonic response analysis is used to obtain the Z-direction displacement frequency response curve, resonance frequency, and corresponding displacement amplitude of the mass block (1) within the preset frequency range, as well as the Z-direction steady-state displacement amplitude within the working frequency range, in order to evaluate the dynamic characteristics of the candidate solution or the target structure.

8. The parameter design method for a Z-axis sensitive mechanical structure using a short beam with a Bézier curve according to claim 7, characterized in that, In step S3, during the static analysis, preset base accelerations in the Z, X, and Y directions are applied respectively. Under linear small deformation conditions, for any base acceleration input in any direction, the finite element equilibrium relationship is expressed as: （5） In equation (5), Here is the structural stiffness matrix. For the quality matrix, Let be the nodal displacement vector. This is the equivalent inertial load vector. The direction affects the vector. For the base acceleration, Take respectively , or ; Under the action of the Z-axis base acceleration, the Z-axis displacement response sensitivity can be obtained based on the average Z-axis displacement of the mass block (1): （6） In equation (6), Indicates the application of Z-axis base acceleration The average Z-direction displacement generated by the mass block (1) is |.|, where |.| represents the absolute value; Under the same displacement amplitude base acceleration conditions in the Z, X, and Y directions, the equivalent stress distribution of the Bessel short beam (21) and the connection area between the Bessel short beam (21) and the long straight beam (22) and the mass block (1) was obtained. For each condition, the maximum equivalent stress in the connection area was taken, and the maximum value of the maximum equivalent stress in the three conditions was defined as the maximum equivalent stress. To characterize the most unfavorable local stress level of the Z-axis sensitive mechanical structure under different directions of base acceleration; Under the same base acceleration condition, X-axis and Y-axis accelerations are applied respectively, and the average Z-axis displacement of the mass block (1) caused by the acceleration inputs in the two insensitive directions of X and Y is extracted to evaluate the cross-axis sensitivity, which is expressed as: （7） In equation (7), and These represent the average Z-direction displacements of the mass block (1) when X-direction and Y-direction base accelerations are applied, respectively. and The Z-axis cross-response sensitivity corresponds to the X-axis and Y-axis acceleration inputs, respectively. This refers to the cross-axis sensitivity.

9. The parameter design method for a Z-axis sensitive mechanical structure using a short beam with a Bézier curve according to claim 8, characterized in that, In step S3, during modal analysis, the characteristic equations of the Z-axis sensitive mechanical structure are solved under the same constraint boundary conditions as in the static analysis, and the natural frequencies of each order are obtained: （8） In equation (8), For the first First natural angular frequency, The eigenvectors corresponding to the natural frequencies are used to characterize the relative displacement distribution of each node in the structure under that mode, i.e., the corresponding mode shape. For the first The natural frequencies of each order are determined; based on the mode shapes, the mode in which the Z-axis motion component of the mass block (1) is dominant is identified as the working mode, and the natural frequencies corresponding to the working modes are determined as the working mode frequencies. The remaining modes are considered as non-operating modes, and the frequency interval between the operating mode and the non-operating mode is expressed as: （9） In equation (9), For the selected set of non-working modes, The first non-working mode in the set The natural frequency of each mode.

10. The parameter design method for a Z-axis sensitive mechanical structure using a short beam with a Bézier curve according to claim 9, characterized in that, In step S3, during harmonic response analysis, a sweep point and damping parameters are set within a preset frequency range, and a Z-axis simple harmonic base acceleration that varies sinusoidally with time is applied to obtain the steady-state harmonic response of the Z-axis sensitive mechanical structure at different excitation frequencies. Under the steady-state harmonic response conditions, the structural dynamic equations are transformed to the frequency domain to obtain the frequency domain dynamic equations used to solve the reset displacement response at different excitation frequencies. （10） In equation (10), For the excitation angular frequency, Here is the damping matrix. ( ) is the reset shift response vector. ( ) represents the corresponding harmonic load vector; The reset displacement response vector under different excitation frequencies is obtained from equation (10). ( The Z-axis reset displacement of the mass block (1) is extracted from it, and the Z-axis reset displacement of the mass block (1) region is spatially averaged to obtain the Z-axis average reset displacement of the mass block (1). According to the relationship between the amplitude of the Z-axis average reset displacement and the excitation frequency, the Z-axis displacement frequency response curve within the preset sweep frequency range is obtained. According to the frequency response curve, the resonance frequency and its corresponding displacement amplitude are determined, and the Z-axis steady-state displacement amplitude within the working frequency range is extracted.

Images