Hemispherical harmonic oscillator anchor rod size optimization method and device

Abstract

The invention discloses a hemispherical harmonic oscillator anchor rod size optimization method and device, and the method comprises the steps: S1, obtaining the size and attribute parameters of a hemispherical harmonic oscillator, S2, sampling the parameters of an anchor rod, and obtaining the parameter sampling value of the anchor rod; s3, calculating the frequency of the hemispherical harmonic oscillator to obtain a calculation frequency value of the hemispherical harmonic oscillator, judging whether the calculation frequency value is smaller than or equal to a set frequency upper limit value or not, if yes, turning to step S4, and if not, turning to step S2; and S4, constructing a two-dimensional axisymmetric finite element model of the hemispherical harmonic oscillator, performing two-dimensional thermal field transient simulation after obtaining simulated boundary conditions, judging whether the temperature difference between the lip edge of the hemispherical harmonic oscillator and the center of the top end of the anchor rod meets the requirement within specified time or not after simulation is completed, if yes, outputting a specific parameter value of the anchor rod, and if not, turning to the step S2. The anchor rod is optimized, and the performance of the hemispherical resonator gyroscope can be comprehensively improved while the strength requirement is met.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation technology, specifically to a method and apparatus for optimizing the dimensions of a hemispherical resonator anchor. Background Technology

[0002] The core component of a hemispherical resonant gyroscope is a resonator made of fused silica. During startup or operation, temperature changes in the base are conducted to the hemispherical shell via anchor bolts. Since there is no convection cooling within the vacuum encapsulation of the gyroscope, heat can only diffuse along the meridian via conduction. This process generates a temperature gradient on the shell. Because the Young's modulus of quartz varies with temperature, this temperature gradient leads to uneven stiffness distribution of the resonator, causing frequency fragmentation and zero-point drift.

[0003] Since the thermodynamic component of the drift rate of a hemispherical resonant gyroscope is one of its error sources, the thermodynamic component... ,in, Let T be the constant component of the rotational speed of the hemispherical resonant gyroscope base about its axis of symmetry; T is the time constant, which can be expressed as a fixed value sequence T1, T2, ..., T N .

[0004] Furthermore, the linear dimensions of the gyroscope element change non-uniformly when a temperature gradient exists, causing a displacement of the resonator's center of mass. During the resonator's principal mode vibration, this displacement generates radial and axial reaction forces on the support structure, transferring some of the resonator's energy to the support system through the fixed shaft. This energy is then dissipated due to damping within the support, resulting in a decrease in the resonator's quality factor (Q). Since this Q decrease is related to the wave's orientation, it exacerbates the inconsistency of the quality factor in different directions. The drift is proportional to the difference between the reciprocals of the maximum and minimum Q values. Therefore, temperature gradient control is necessary.

[0005] As the only physical channel connecting the resonator to the base, the hemispherical resonator anchor is not only a heat flow channel but also a mechanical boundary condition for the resonator's vibration. Its structural design involves multi-physics coupling contradictions. The contradiction lies in the relationship between mechanics and energy dissipation: the anchor must be thick and short enough to provide stiffness, resist overload and vibration, and prevent the resonator from impacting the electrodes. However, the thicker the anchor, the faster the vibrational energy leaks to the base, and the more severe the decrease in the quality factor Q, which directly affects the gyroscope's angular random walk and bias stability.

[0006] The contradiction lies in heat conduction: the base connects to the control circuit and is the main heat source. The resonator is in a vacuum environment with no convective heat dissipation. If the thermal resistance of the anchor rod is too small, heat will rush into the pole region but will not have time to diffuse to the lip, forming a significant temperature gradient on the shell. This will lead to uneven thermal stress, asymmetry between the stiffness field and the mass field, and thermal drift.

[0007] Geometric parameters have an impact: the diameter and length of the anchor bolt directly affect the temperature field distribution, stress concentration, and natural frequency. Excessively high frequencies reduce mechanical sensitivity, which is detrimental to signal detection.

[0008] Existing technologies typically rely on engineering experience and repeated experiments to determine the geometric parameters of anchor bolts, lacking a systematic design method, resulting in long design cycles, high costs, and difficulty in achieving optimal performance. Summary of the Invention

[0009] To address the problems in the background technology, this invention proposes a method for optimizing the anchor size of a hemispherical resonator. By optimizing the anchor, the temperature gradient is suppressed, energy leakage is reduced, and a reasonable frequency and high sensitivity are obtained while meeting strength requirements, thereby comprehensively improving the performance of the hemispherical resonator gyroscope.

[0010] The present invention adopts the following technical solution: A method for optimizing the dimensions of a hemispherical resonator anchor includes the following steps: S1: Obtain the design dimensions of the hemispherical shell of the hemispherical resonator, the number of anchor segments of the hemispherical resonator, the range of values ​​for the anchor parameters of the hemispherical resonator, and the property parameters of the material of the hemispherical resonator. S2: Based on the range of values ​​for the anchor bolt parameters of the hemispherical harmonic oscillator, the parameters of the anchor bolt are sampled to obtain the sampled values ​​of the anchor bolt parameters; S3: Calculate the frequency of the hemispherical harmonic oscillator based on the sampled values ​​of the anchor bolt parameters and the property parameters of the hemispherical harmonic oscillator material. Obtain the calculated frequency value of the hemispherical harmonic oscillator and determine whether the calculated frequency value is less than or equal to the set upper limit value of the frequency. If yes, proceed to step S4; otherwise, proceed to step S2. S4: Based on the specific values ​​of the anchor rod parameters corresponding to the calculated frequency value of the hemispherical harmonic oscillator and the hemispherical design dimensions of the hemispherical harmonic oscillator, construct a two-dimensional axisymmetric finite element model of the hemispherical harmonic oscillator. After obtaining the boundary conditions for simulation, perform a two-dimensional transient thermal field simulation. After the simulation is completed, determine whether the temperature difference between the lip of the hemispherical harmonic oscillator and the center of the top of the anchor rod meets the requirements within a specified time. If yes, output the specific values ​​of the anchor rod parameters; otherwise, proceed to step S2.

[0011] Optionally, in step S2, the parameters of the anchor bolt include the radius and length of each anchor bolt segment.

[0012] Optionally, in step S2, the parameters of the anchor bolt are sampled using Latin hypercube sampling. The specific sampling process includes: For an n-segment anchor bolt, N samples are drawn, and the N samples have M variables ( , … … , , … … ),in, Let x represent the radius of the x-th anchor segment. This represents the length of the x-th anchor segment. First, divide the distribution interval of each variable into N equal intervals, with each interval having an equal probability. Within each interval of each variable, randomly select one value. Then, randomly shuffle the N selected values ​​for each variable, ensuring they do not interfere with each other. Combine the shuffled data columns of each variable to form an N×M matrix, where each row of the matrix forms a complete set of anchor bolt geometric parameters. ; ;...; ;...; ; ; ;...; ;...; },in, This represents the radius of the anchor rod in the x-th segment of the m-th row. This represents the length of the anchor rod in the x-th segment of the m-th row.

[0013] Optionally, in step S3, the frequency calculation formula for the hemispherical harmonic oscillator is as follows: ,in, The calculated frequency value of the hemispherical harmonic oscillator. For coupling efficiency, The frequency is calculated based on the Rayleigh method principle for thin shells; ,in, Take 1E10 experience points. For stiffness factor, ,in, This refers to the total length of the anchor bolt; The anchor bolt moment of inertia factor. , Let m be the length of the m-th anchor segment. Let be the moment of inertia factor of the m-th anchor segment. , Let be the radius of the m-th anchor segment, ∈ (1, 2, ..., n-1, n); ,in, Let be the radius of the hemisphere of the hemispherical harmonic oscillator. The thickness of the hemispherical wall of the hemispherical harmonic oscillator. Young's modulus of hemispherical harmonic oscillator material. The density of the hemispherical harmonic oscillator material is given. The Poisson's ratio of the hemispherical harmonic oscillator material. It is a dimensionless frequency coefficient.

[0014] Optionally, in step S4, the process of constructing the two-dimensional axisymmetric finite element model of the hemispherical harmonic oscillator is as follows: A two-dimensional axisymmetric geometric model of the hemispherical harmonic oscillator is constructed using a cylindrical coordinate system. The two-dimensional axisymmetric geometric model is then discretized to obtain a two-dimensional axisymmetric finite element model of the hemispherical harmonic oscillator.

[0015] Optionally, the two-dimensional axisymmetric geometric model is discretized, specifically including spatial discretization and temporal discretization of the two-dimensional axisymmetric geometric model.

[0016] Optionally, the two-dimensional axisymmetric geometric model is spatially discretized, specifically including: The anchor bolt section is discretized in two dimensions using linear discretization, while the hemispherical shell section is discretized along the meridian angle. For the node with index i, the volume of the node is... The heat capacity of this node ,in, Let i be the effective radius of node i. , Let i be the actual radius of node i. This represents the radius increment between node i and the next node in the radial direction in cylindrical coordinates. This represents the height increment between node i and the next node along the axis in cylindrical coordinates. The density of the hemispherical harmonic oscillator material is given. The specific heat of the hemispherical harmonic oscillator material; Axial node heat transfer coefficient Radial internode heat transfer coefficient ,in It is the radius at the intersection of node i and the next radial node; The time discretization of the two-dimensional axisymmetric geometric model specifically includes: Construct the following linear equations: ; In the formula, External heat source; Let J be the temperature of the next node j, which is axially adjacent to node i, at time n+1. Let j be the temperature of the next node j radially adjacent to node i at time n+1. Let i be the temperature of node i at time n+1. Let i be the temperature of node i at time n. For node heat capacity, It represents the time increment between the current time n and the next time n+1.

[0017] Optionally, in step S4, the boundary conditions for simulation include: using the hemispherical resonant gyroscope base as a constant-temperature heat source, conducting solid-state heat from the base to the hemispherical resonator, treating the heat conduction cross section of the hemispherical shell region as a circle, and setting the heat conduction interface where the anchor rod and the hemispherical shell intersect as a solid circle.

[0018] Optionally, in step S4, a two-dimensional Laplace governing equation is used to perform a two-dimensional transient thermodynamic field simulation on the two-dimensional axisymmetric finite element model. The calculation formula for the two-dimensional Laplace governing equation is as follows: ; in, The density of the hemispherical harmonic oscillator material is given. The specific heat of the hemispherical harmonic oscillator material. is the thermal conductivity of the hemispherical harmonic oscillator material.

[0019] As a general inventive concept, the present invention also provides an apparatus for implementing the above-mentioned method for optimizing the anchor rod size of a hemispherical resonator, comprising: The acquisition module is used to obtain the design dimensions of the hemispherical shell of the hemispherical resonator, the number of anchor segments of the hemispherical resonator, the range of values ​​for the anchor parameters of the hemispherical resonator, and the property parameters of the material of the hemispherical resonator. The sampling module is used to sample the parameters of the anchor rod according to the range of values ​​of the anchor rod parameters of the hemispherical harmonic oscillator, and obtain the sampled values ​​of the anchor rod parameters. The calculation module is used to calculate the frequency of the hemispherical harmonic oscillator based on the sampled parameters of the anchor bolt and the property parameters of the hemispherical harmonic oscillator material, obtain the calculated frequency value of the hemispherical harmonic oscillator, and determine whether the calculated frequency value is less than or equal to the set upper limit value of the frequency. If yes, the calculated frequency value of the hemispherical harmonic oscillator is transmitted to the simulation module; otherwise, the sampling module is triggered to perform the next round of sampling. The simulation module is used to construct a two-dimensional axisymmetric finite element model of the hemispherical resonator based on the specific parameter values ​​of the anchor corresponding to the calculated frequency value of the hemispherical resonator and the hemispherical design dimensions of the hemispherical resonator. After obtaining the boundary conditions for the simulation, a two-dimensional transient thermal field simulation is performed. After the simulation is completed, it is determined whether the temperature difference between the lip of the hemispherical resonator and the center of the top of the anchor meets the requirements within a specified time. If yes, the specific parameter values ​​of the anchor are output; otherwise, the sampling module is triggered to perform the next round of sampling.

[0020] Compared with the prior art, the advantages of the present invention are as follows: The hemispherical resonator anchor size optimization method of this invention comprehensively considers the coupling effects of multiple physical fields such as mechanics, thermodynamics, and vibration. It optimizes the anchor by combining classical frequency calculation with thermodynamic field modeling, integrating the physical quantity of "temperature field" with the drift rate of the gyroscope. By controlling the temperature difference on the shell surface, the drift rate of the gyroscope is suppressed. While meeting strength requirements, this method suppresses temperature gradients, reduces energy leakage, and achieves a reasonable frequency and high sensitivity, thereby comprehensively improving the performance of the hemispherical resonator gyroscope. Furthermore, this invention uses two-dimensional modeling and calculation to achieve optimization calculations, eliminating the need for complex three-dimensional model simulations, resulting in fast iterative calculation speeds that meet the needs of engineering applications. Attached Figure Description

[0021] To facilitate understanding of the invention, it will be described in more detail with reference to the specific embodiments shown in the accompanying drawings. These drawings depict only typical embodiments of the invention and should not be considered as limiting the scope of protection of the invention.

[0022] Figure 1 This is a flowchart of the method for optimizing the anchor rod size of a hemispherical harmonic oscillator according to an embodiment of the present invention.

[0023] Figure 2 This is a schematic diagram of the optimized space search in an embodiment of the present invention.

[0024] Figure 3 This is a schematic diagram showing the performance trade-off calculation results in an embodiment of the present invention, where minimizing the temperature gradient is the first priority.

[0025] Figure 4 The diagram shows the hemispherical meridian temperature distribution, representing the optimal result in this embodiment of the invention.

[0026] Figure 5 This is a schematic diagram of the 2D temperature field cloud representing the optimal result in the embodiments of the present invention.

[0027] Figure 6 This is a schematic diagram illustrating the temperature change over time for the optimal result in an embodiment of the present invention.

[0028] Figure 7 This is a schematic diagram illustrating the temperature gradient change over time for the optimal result in an embodiment of the present invention. Detailed Implementation

[0029] The embodiments of the present invention are described below with reference to the accompanying drawings to enable those skilled in the art to better understand and implement the present invention. However, the listed embodiments are not intended to limit the present invention. In the absence of conflict, the following embodiments and the technical features in the embodiments can be combined with each other, wherein the same components are indicated by the same reference numerals.

[0030] Example 1: like Figure 1 As shown, this embodiment provides a method for optimizing the dimensions of a hemispherical resonator anchor rod, including the following steps: S1: Obtain the design dimensions of the hemispherical shell of the hemispherical resonator, the number of anchor segments of the hemispherical resonator, the range of values ​​for the anchor parameters of the hemispherical resonator, and the property parameters of the material of the hemispherical resonator. S2: Based on the range of values ​​for the anchor bolt parameters of the hemispherical harmonic oscillator, the parameters of the anchor bolt are sampled to obtain the sampled values ​​of the anchor bolt parameters; S3: Calculate the frequency of the hemispherical harmonic oscillator based on the sampled values ​​of the anchor bolt parameters and the property parameters of the hemispherical harmonic oscillator material. Obtain the calculated frequency value of the hemispherical harmonic oscillator and determine whether the calculated frequency value is less than or equal to the set upper limit value of the frequency. If yes, proceed to step S4; otherwise, proceed to step S2. S4: Based on the specific values ​​of the anchor rod parameters corresponding to the calculated frequency value of the hemispherical harmonic oscillator and the hemispherical design dimensions of the hemispherical harmonic oscillator, construct a two-dimensional axisymmetric finite element model of the hemispherical harmonic oscillator. After obtaining the boundary conditions for the simulation, perform a two-dimensional transient thermal field simulation. After the simulation is completed, determine whether the temperature difference between the lip of the hemispherical harmonic oscillator and the center of the top of the anchor rod meets the requirements within a specified time. If yes, output the specific values ​​of the anchor rod parameters; otherwise, proceed to step S2.

[0031] The hemispherical resonator anchor size optimization method of this invention comprehensively considers the coupling effects of multiple physical fields such as mechanics, thermodynamics, and vibration. It optimizes the anchor by combining classical frequency calculation with thermodynamic field modeling, integrating the physical quantity of "temperature field" with the drift rate of the gyroscope. By controlling the temperature difference on the shell surface, the drift rate of the gyroscope is suppressed. While meeting strength requirements, this method suppresses temperature gradients, reduces energy leakage, and achieves a reasonable frequency and high sensitivity, thereby comprehensively improving the performance of the hemispherical resonator gyroscope. Furthermore, this invention uses two-dimensional modeling and calculation to achieve optimization calculations, eliminating the need for complex three-dimensional model simulations, resulting in fast iterative calculation speeds that meet the needs of engineering applications.

[0032] In this embodiment, in step S2, the parameters of the anchor bolt include the radius and length of each anchor bolt segment.

[0033] Specifically, in step S2, the parameters of the anchor bolt are sampled using Latin hypercube sampling. The specific sampling process includes: For an n-segment anchor bolt, N samples are drawn, and the N samples have M variables ( , … … , , … … ),in, Let x represent the radius of the x-th anchor segment. This represents the length of the x-th anchor segment. First, divide the distribution interval of each variable into N equal intervals, with each interval having an equal probability. Within each interval of each variable, randomly select one value. Then, randomly shuffle the N selected values ​​for each variable, ensuring they do not interfere with each other. Combine the shuffled data columns of each variable to form an N×M matrix, where each row of the matrix forms a complete set of anchor bolt geometric parameters. ; ;...; ;...; ; ; ;...; ;...; },in, This represents the radius of the anchor rod in the x-th segment of the m-th row. This represents the length of the anchor rod in the x-th segment of the m-th row.

[0034] Using Latin hypercubes to sample variable parameters can achieve high coverage of the sample space, improve the efficiency of high-dimensional and multivariate problems, and avoid the exponential growth of computation caused by traditional grid parameter scanning. This is especially true when anchor bolts are designed and evaluated using multi-segment structural parameters. In addition, it also avoids the focusing phenomenon of pure random sampling in high-dimensional sampling.

[0035] In this embodiment, the formula for calculating the frequency of the hemispherical harmonic oscillator in step S3 is as follows: ,in, The calculated frequency value of the hemispherical harmonic oscillator. For coupling efficiency, The frequency is calculated based on the Rayleigh method principle for thin shells; ,in, Take 1E10 experience points. For stiffness factor, ,in, This refers to the total length of the anchor bolt; The anchor bolt moment of inertia factor. , Let m be the length of the m-th anchor segment. Let be the moment of inertia factor of the m-th anchor segment. , Let be the radius of the m-th anchor segment, ∈ (1, 2, ..., n-1, n); ,in, Let be the radius of the hemisphere of the hemispherical harmonic oscillator. The thickness of the hemispherical wall of the hemispherical harmonic oscillator. Young's modulus of hemispherical harmonic oscillator material. The density of the hemispherical harmonic oscillator material is given. The Poisson's ratio of the hemispherical harmonic oscillator material. It is a dimensionless frequency coefficient.

[0036] In this embodiment, the construction process of the two-dimensional axisymmetric finite element model of the hemispherical harmonic oscillator in step S4 is as follows: A two-dimensional axisymmetric geometric model of the hemispherical harmonic oscillator is constructed using a cylindrical coordinate system. The two-dimensional axisymmetric geometric model is then discretized to obtain a two-dimensional axisymmetric finite element model of the hemispherical harmonic oscillator.

[0037] In this embodiment, the two-dimensional axisymmetric geometric model is discretized, specifically including spatial discretization and temporal discretization of the two-dimensional axisymmetric geometric model.

[0038] Furthermore, the two-dimensional axisymmetric geometric model is spatially discretized, specifically including: The anchor bolt section is discretized in two dimensions using linear discretization, while the hemispherical shell section is discretized along the meridian angle. For the node with index i, the volume of the node is... The heat capacity of this node ,in, Let i be the effective radius of node i. , Let i be the actual radius of node i. This represents the radius increment between node i and the next node in the radial direction in cylindrical coordinates. This represents the height increment between node i and the next node along the axis in cylindrical coordinates. The density of the hemispherical harmonic oscillator material is given. The specific heat of the hemispherical harmonic oscillator material; Axial node heat transfer coefficient Radial internode heat transfer coefficient ,in It is the radius at the intersection of node i and the next radial node; Furthermore, the two-dimensional axisymmetric geometric model is discretized in time, specifically including: Construct the following linear equations: ; In the formula, External heat source; Let J be the temperature of the next node j, which is axially adjacent to node i, at time n+1. Let j be the temperature of the next node j radially adjacent to node i at time n+1. Let i be the temperature of node i at time n+1. Let i be the temperature of node i at time n. For node heat capacity, It represents the time increment between the current time n and the next time n+1.

[0039] In step S4, the boundary conditions for simulation include: using the hemispherical resonant gyroscope base as a constant-temperature heat source, conducting solid-state heat from the base to the hemispherical resonator, treating the heat conduction cross section of the hemispherical shell region as a circle, and setting the heat conduction interface where the anchor rod and the hemispherical shell intersect as a solid circle.

[0040] This embodiment uses the two-dimensional Laplace governing equation to perform a two-dimensional transient simulation of the thermodynamic field on a two-dimensional axisymmetric finite element model. The calculation formula for the two-dimensional Laplace governing equation is as follows: ; in, The density of the hemispherical harmonic oscillator material is given. The specific heat of the hemispherical harmonic oscillator material. is the thermal conductivity of the hemispherical harmonic oscillator material.

[0041] In summary, this invention employs a single-segment or multi-segment anchor design, incorporating both dimensional and vibration frequency constraints, resulting in a higher degree of design integrity for the hemispherical harmonic oscillator. Furthermore, based on the optimization strategy used in practical applications, this invention can select the optimal solution through trade-offs between frequency and temperature gradient.

[0042] The specific process of the hemispherical harmonic oscillator anchor size optimization method in this embodiment is as follows: (1) Construct the basic parameters of the hemispherical harmonic oscillator, including the radius of the hemisphere. hemispherical wall thickness The radius of the segmented anchor bolt and length The basic properties of fused silica materials, such as Young's modulus. ,density Poisson's ratio Specific heat and thermal conductivity; ; (2) Set the dimensional constraints on the radius and length of the anchor bolts, and the upper limit of the frequency required for actual vibration, based on experience or requirements; (3) Calculate the frequency using the empirical formula. The calculation process is as follows: For a hemispherical harmonic oscillator, the frequency approximation formula based on the thin-shell Rayleigh method is: , in It is a dimensionless frequency coefficient, which can be taken as 3.6.

[0043] The anchor bolt can be viewed as a torsion spring at the bottom of the shell, which corrects for the aforementioned frequency.

[0044] The anchor stiffness coupling correction is as follows: Support moment of inertia factor: , Where is the anchor bolt radius; When there are multiple anchor sections, set , ,…and These are the moment of inertia factors of the anchor rods for segments 1, 2, ..., and n, respectively. , ,…and Let be the lengths of the 1st, 2nd, ..., nth anchor segments, respectively. , ,…and These are the radii of anchor segments 1, 2, ..., and n, respectively. Total length. At this point, the moment of inertia factor of the support rod is calculated for each segment according to the above formula. , ,…,and Then, calculate the moment of inertia factor of the multi-segment anchor bolt according to the following formula. : .

[0045] For example: When the anchor bolt is segmented, the moment of inertia factor of the first segment is calculated according to the moment of inertia factor of the anchor bolt. Second segment support moment factor The calculation of the total length ;in This refers to the length of the first anchor bolt segment; This is the length of the second anchor bolt. and These are the radii of the first and second anchor sections, respectively; at this time... ; Stiffness factor: ; Coupling efficiency: , Take the experience value 1E10; System frequency: ; For multi-segment anchor bolt design, parameter initialization is performed by sampling geometrically constrained parameters using Latin hypercube, and the radius of the segmented anchor bolt is given for each calculation. and length If the anchor bolt is divided into n segments, that is, there are n anchor bolt radii ( , ,…and ) and the corresponding length ( , ,…and The definition and calculation are performed according to requirements. In multi-segment anchor bolts, the total length is usually defined, i.e. , ,…and Simultaneous independent sampling is not allowed, i.e., sampling , ,…and Then another The Latin hypercube matrix is ​​constructed as follows: N samples are drawn (e.g., N=50), and there are M variables ( , … … , , … … ),in, Let x represent the radius of the x-th anchor segment. This represents the length of the x-th anchor segment. In the Latin hypercube sampling process, the distribution interval (cumulative probability density CDF from 0 to 1) of each variable is first divided into N equal intervals, each with an equal probability of 1 / N. Within each subinterval of each variable, a value is randomly selected; then, the N selected values ​​for each variable are randomly shuffled without interference; the shuffled variable columns are combined to form an N×M matrix, where each row of the matrix (i.e., each sample point m) has a complete set of anchor geometric parameters { ; ;...; ;...; ; ; ;...; ;...; },in, This represents the radius of the anchor rod in the x-th segment of the m-th row. This represents the length of the anchor rod in the x-th segment of the m-th row.

[0046] The following explanation uses a two-section anchor bolt for Latin hypercube sampling: If the anchor bolt is divided into two sections, there are two anchor bolt radii ( , ) and the corresponding length ( , The definition and calculation are performed according to requirements. In a two-section anchor bolt, the total length is usually defined as... and Simultaneous independent sampling is not allowed, i.e., sampling , The Latin hypercube matrix is ​​constructed as follows: N samples are drawn (e.g., N=50), and there are M variables ( , , , (Total 4). In the Latin hypercube sampling process, the distribution interval (cumulative probability density CDF from 0 to 1) of each variable is first divided into N equal intervals, each with an equal probability of 1 / N. Within each small interval of each variable, a value is randomly selected; then, the N selected values ​​for each variable are randomly shuffled without interference; the shuffled variable columns are combined to form an N×M matrix, where each row of the matrix (i.e., each sample point m) has a complete set of anchor geometric parameters { ; ; ; }

[0047] (4) After sampling, the parameters are fed into the frequency calculation formula above for calculation. The calculated frequency value is compared with the maximum limit frequency. If the frequency does not meet the requirements, resampling is performed. If it meets the requirements, the hemispherical harmonic oscillator model is constructed according to the parameters. (5) Two-dimensional modeling is performed on the above geometric model. Due to the axisymmetric characteristics of the hemispherical harmonic oscillator, the coordinate system used for modeling is a cylindrical coordinate system. This ensures accurate geometric shape and reduces the size of the computational domain, enabling the two-dimensional thermal field simulation to accurately describe the real temperature changes. Therefore, the simulation can be achieved by using open-source Python programming instead of large and complex commercial simulation software.

[0048] The unsteady-state heat conduction equations are solved by discretizing and setting boundary conditions on the computational domain of a structured mesh using the finite difference method. The two-dimensional Laplace governing equations (unsteady-state heat conduction equations) for the constant temperature field T(r,z) of a harmonic oscillator in cylindrical coordinates (r,z) are as follows: .

[0049] Boundary conditions include spatial discretization settings on mesh properties: spatial discretization of the system includes: two-dimensional linear discretization of the anchor bolt part and discretization of the hemispherical shell part along the meridian angle; For the node with index i, the volume of the node is... , This is the actual radius of the node. This represents the radius increment between node i and the next radial node j in cylindrical coordinates. This represents the height increment between node i and the next node j along the axis in cylindrical coordinates; to avoid the issue of r=0, the program uses the effective radius. The effective radius is used in the calculation. Replace actual radius Perform calculations. Node heat capacity. .

[0050] inter-node heat transfer coefficient Proportional to the ratio of area to distance. Coefficient of heat transfer between axial nodes. Radial internode heat transfer coefficient ,in It is the radius at the intersection of these two nodes. When heat is transferred from node i in the axial direction, the following is used: Perform heat transfer capacity coefficient calculation; when heat transfer is radially from node i, use... Calculate the heat transfer coefficient.

[0051] The time discretization is established using the fully implicit backward Euler method, and the linear equations are constructed as follows: , In the formula, External heat source; Let J be the temperature of the next node j, which is axially adjacent to node i, at time n+1. Let j be the temperature of the next node j radially adjacent to node i at time n+1. Let i be the temperature of node i at time n+1. Let i be the temperature of node i at time n. For node heat capacity, It represents the time increment between the current time n and the next time n+1.

[0052] Boundary conditions for the transient simulation of the two-dimensional thermodynamic field: The hemispherical resonant gyroscope base is used as a constant-temperature heat source, and the hemispherical resonator anchor is fixed on the base. In terms of heat conduction mechanism, only solid heat conduction is considered, and radiation and convection are ignored because the hemispherical resonator operates in a vacuum environment; the heat conduction cross section of the thin shell region is treated as a circle, and the heat conduction interface where the anchor and the thin shell intersect is a solid circle.

[0053] (6) Calculate whether the temperature difference between the lip of the hemispherical harmonic oscillator and the center of the top of the anchor rod meets the requirements within a specified time. If it does not meet the requirements, resample the geometric parameters of the anchor rod until the temperature difference meets the requirements.

[0054] (7) Store the optimal geometric parameters and end the optimization calculation.

[0055] The following is an example calculation of optimizing the anchor size of a hemispherical harmonic oscillator using this invention. Table 1 shows the parameters and boundary conditions of the hemispherical harmonic oscillator: Table 1

[0056] like Figure 2 As shown, firstly, two-segment anchor sampling is performed to calculate the frequency value of the hemispherical harmonic oscillator to less than 5000 Hz. Then, a two-dimensional axisymmetric finite element model of the two-segment hemispherical harmonic oscillator is constructed and optimized through two-dimensional transient thermodynamic field simulation until the temperature difference between the top of the anchor and the edge of the hemispherical lip is ≤2 ℃ within 600 s. Multiple rounds of calculation can be performed, with minimizing the temperature gradient as the first priority, selecting the data result with the smallest temperature difference, such as... Figure 3 As shown.

[0057] The simulation results with the smallest temperature difference are as follows: Figures 4-7 As shown, the optimized calculation results are as follows: the lower section of the anchor rod has a radius of 1.8 mm and a length of 13 mm; the upper section of the anchor rod has a radius of 2.3 mm and a length of 10 mm; the distance between the bottom of the anchor rod and the center of the ball is 5 mm; the frequency is 4415.7 Hz; and the temperature difference between the midpoint of the upper section of the anchor rod and the lip edge after 600 s is 1.2 ℃, which meets the usage requirements.

[0058] Example 2:

[0059] This embodiment provides an apparatus for implementing the hemispherical resonator anchor size optimization method of Embodiment 1, comprising: The acquisition module is used to obtain the design dimensions of the hemispherical shell of the hemispherical resonator, the number of anchor segments of the hemispherical resonator, the range of values ​​for the anchor parameters of the hemispherical resonator, and the property parameters of the material of the hemispherical resonator. The sampling module is used to sample the parameters of the anchor rod according to the range of values ​​of the anchor rod parameters of the hemispherical harmonic oscillator, and obtain the sampled values ​​of the anchor rod parameters. The calculation module is used to calculate the frequency of the hemispherical harmonic oscillator based on the sampled parameters of the anchor bolt and the property parameters of the hemispherical harmonic oscillator material, obtain the calculated frequency value of the hemispherical harmonic oscillator, and determine whether the calculated frequency value is less than or equal to the set upper limit value of the frequency. If yes, the calculated frequency value of the hemispherical harmonic oscillator is transmitted to the simulation module; otherwise, the sampling module is triggered to perform the next round of sampling. The simulation module is used to construct a two-dimensional axisymmetric finite element model of the hemispherical resonator based on the specific parameter values ​​of the anchor corresponding to the calculated frequency value of the hemispherical resonator and the hemispherical design dimensions of the hemispherical resonator. After obtaining the boundary conditions for the simulation, a two-dimensional transient thermal field simulation is performed. After the simulation is completed, it is determined whether the temperature difference between the lip of the hemispherical resonator and the center of the top of the anchor meets the requirements within a specified time. If yes, the specific parameter values ​​of the anchor are output; otherwise, the sampling module is triggered to perform the next round of sampling.

[0060] The embodiments described above are merely preferred embodiments of the present invention. The terms "in one embodiment," "in another embodiment," "in yet another embodiment," or "in still another embodiment" used in this specification all refer to one or more of the same or different embodiments according to this disclosure. Ordinary variations and substitutions made by those skilled in the art within the scope of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the dimensions of a hemispherical resonator anchor bolt, characterized in that, Includes the following steps: S1: Obtain the design dimensions of the hemispherical shell of the hemispherical resonator, the number of anchor segments of the hemispherical resonator, the range of values ​​for the anchor parameters of the hemispherical resonator, and the property parameters of the material of the hemispherical resonator. S2: Based on the range of values ​​for the anchor bolt parameters of the hemispherical harmonic oscillator, the parameters of the anchor bolt are sampled to obtain the sampled values ​​of the anchor bolt parameters; S3: Calculate the frequency of the hemispherical harmonic oscillator based on the sampled values ​​of the anchor bolt parameters and the property parameters of the hemispherical harmonic oscillator material. Obtain the calculated frequency value of the hemispherical harmonic oscillator and determine whether the calculated frequency value is less than or equal to the set upper limit value of the frequency. If yes, proceed to step S4; otherwise, proceed to step S2. S4: Based on the specific values ​​of the anchor rod parameters corresponding to the calculated frequency value of the hemispherical harmonic oscillator and the hemispherical design dimensions of the hemispherical harmonic oscillator, construct a two-dimensional axisymmetric finite element model of the hemispherical harmonic oscillator. After obtaining the boundary conditions for simulation, perform a two-dimensional transient thermal field simulation. After the simulation is completed, determine whether the temperature difference between the lip of the hemispherical harmonic oscillator and the center of the top of the anchor rod meets the requirements within a specified time. If yes, output the specific values ​​of the anchor rod parameters; otherwise, proceed to step S2.

2. The method for optimizing the size of a hemispherical harmonic oscillator anchor bolt according to claim 1, characterized in that, In step S2, the parameters of the anchor bolt include the radius and length of each anchor bolt segment.

3. The method for optimizing the size of a hemispherical harmonic oscillator anchor bolt according to claim 2, characterized in that, In step S2, the parameters of the anchor bolt are sampled using Latin hypercube sampling. The specific sampling process includes: For an n-segment anchor bolt, N samples are drawn, and the N samples have M variables ( , … … , , … … ),in, This represents the radius of the x-th anchor segment. This represents the length of the x-th anchor segment. First, divide the distribution interval of each variable into N equal intervals, with each interval having an equal probability. Within each interval of each variable, randomly select one value. Then, randomly shuffle the N selected values ​​for each variable, ensuring they do not interfere with each other. Combine the shuffled data columns of each variable to form an N×M matrix, where each row of the matrix forms a complete set of anchor bolt geometric parameters. ; ;...; ;...; ; ; ;...; ;...; },in, This represents the radius of the anchor rod in the m-th row and x-th segment. This represents the length of the anchor rod in the m-th row and x-th segment.

4. The method for optimizing the anchor size of a hemispherical harmonic oscillator according to claim 1, characterized in that, In step S3, the frequency of the hemispherical harmonic oscillator is calculated using the following formula: ,in, The calculated frequency value of the hemispherical harmonic oscillator. For coupling efficiency, The frequency is calculated based on the Rayleigh method principle for thin shells; ,in, Take 1E10 experience points. Stiffness factor ,in, This refers to the total length of the anchor bolt; The anchor bolt moment of inertia factor. , Let m be the length of the m-th anchor segment. Let be the moment of inertia factor of the m-th anchor segment. , Let be the radius of the m-th anchor segment, ∈ (1, 2, ..., n-1, n); ,in, Let be the radius of the hemisphere of the hemispherical harmonic oscillator. The thickness of the hemispherical wall of the hemispherical harmonic oscillator. Young's modulus of hemispherical harmonic oscillator material. The density of the hemispherical harmonic oscillator material is given. The Poisson's ratio of the hemispherical harmonic oscillator material. It is a dimensionless frequency coefficient.

5. The method for optimizing the dimensions of a hemispherical harmonic oscillator anchor bolt according to any one of claims 1-4, characterized in that, In step S4, the construction process of the two-dimensional axisymmetric finite element model of the hemispherical harmonic oscillator is as follows: A two-dimensional axisymmetric geometric model of the hemispherical harmonic oscillator is constructed using a cylindrical coordinate system. The two-dimensional axisymmetric geometric model is then discretized to obtain a two-dimensional axisymmetric finite element model of the hemispherical harmonic oscillator.

6. The method for optimizing the dimensions of a hemispherical harmonic oscillator anchor bolt according to claim 5, characterized in that, Discretizing the two-dimensional axisymmetric geometric model specifically includes spatial discretization and temporal discretization of the two-dimensional axisymmetric geometric model.

7. The method for optimizing the size of a hemispherical harmonic oscillator anchor bolt according to claim 6, characterized in that, Spatial discretization of the two-dimensional axisymmetric geometric model specifically includes: The anchor bolt section is discretized in two dimensions using linear discretization, while the hemispherical shell section is discretized along the meridian angle. For the node with index i, the volume of the node is... The heat capacity of this node ,in, Let i be the effective radius of node i. , Let i be the actual radius of node i. This represents the radius increment between node i and the next node in the radial direction in cylindrical coordinates. This represents the height increment between node i and the next node along the axis in cylindrical coordinates. The density of the hemispherical harmonic oscillator material is given. The specific heat of the hemispherical harmonic oscillator material; Axial node heat transfer coefficient Radial internode heat transfer coefficient ,in It is the radius at the intersection of node i and the next radial node; The time discretization of the two-dimensional axisymmetric geometric model specifically includes: Construct the following linear equations: ； In the formula, External heat source; Let J be the temperature of the next node j, which is axially adjacent to node i, at time n+1. Let j be the temperature of the next node j radially adjacent to node i at time n+1. Let i be the temperature of node i at time n+1. Let i be the temperature of node i at time n. For node heat capacity, It represents the time increment between the current time n and the next time n+1.

8. The method for optimizing the dimensions of a hemispherical harmonic oscillator anchor bolt according to any one of claims 1-4, characterized in that, In step S4, the boundary conditions for simulation include: using the hemispherical resonant gyroscope base as a constant-temperature heat source, conducting solid-state heat from the base to the hemispherical resonator, treating the heat conduction cross section of the hemispherical shell region as a circle, and setting the heat conduction interface where the anchor rod and the hemispherical shell intersect as a solid circle.

9. The method for optimizing the anchor size of a hemispherical harmonic oscillator according to any one of claims 1-4, characterized in that, In step S4, a two-dimensional Laplace governing equation is used to perform a two-dimensional transient thermodynamic field simulation on the two-dimensional axisymmetric finite element model. The calculation formula for the two-dimensional Laplace governing equation is as follows: ； in, The density of the hemispherical harmonic oscillator material is given. The specific heat of the hemispherical harmonic oscillator material. is the thermal conductivity of the hemispherical harmonic oscillator material.

10. An apparatus for implementing the method for optimizing the size of a hemispherical resonator anchor bolt as described in any one of claims 1-7, characterized in that, include: The acquisition module is used to obtain the design dimensions of the hemispherical shell of the hemispherical resonator, the number of anchor segments of the hemispherical resonator, the range of values ​​for the anchor parameters of the hemispherical resonator, and the property parameters of the material of the hemispherical resonator. The sampling module is used to sample the parameters of the anchor rod according to the range of values ​​of the anchor rod parameters of the hemispherical harmonic oscillator, and obtain the sampled values ​​of the anchor rod parameters. The calculation module is used to calculate the frequency of the hemispherical harmonic oscillator based on the sampled parameters of the anchor bolt and the property parameters of the hemispherical harmonic oscillator material, obtain the calculated frequency value of the hemispherical harmonic oscillator, and determine whether the calculated frequency value is less than or equal to the set upper limit value of the frequency. If yes, the calculated frequency value of the hemispherical harmonic oscillator is transmitted to the simulation module; otherwise, the sampling module is triggered to perform the next round of sampling. The simulation module is used to construct a two-dimensional axisymmetric finite element model of the hemispherical resonator based on the specific parameter values ​​of the anchor corresponding to the calculated frequency value of the hemispherical resonator and the hemispherical design dimensions of the hemispherical resonator. After obtaining the boundary conditions for the simulation, a two-dimensional transient thermal field simulation is performed. After the simulation is completed, it is determined whether the temperature difference between the lip of the hemispherical resonator and the center of the top of the anchor meets the requirements within a specified time. If yes, the specific parameter values ​​of the anchor are output; otherwise, the sampling module is triggered to perform the next round of sampling.

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