Modelica-based digital vibration isolation system design optimization method

Abstract

The invention discloses a digital vibration isolation system design optimization method based on Modelica, and the method sequentially comprises the steps: determining the overall layout of each vibration isolation element of a vibration isolation system, constructing the dynamic performance mapping from the rigidity k of the vibration isolation element and the damping c of a damping element to the vibration isolation system, constructing a vibration isolation element rigidity and damping and structural parameter mapping model, and carrying out the design optimization of the vibration isolation system. Structural parameters of the vibration isolation element are optimized based on methods such as sensitivity analysis, a particle swarm optimization algorithm and a genetic algorithm, and structural finite element simulation verification and vibration isolation system performance simulation verification of a three-dimensional model are carried out according to the structural parameters of the vibration isolation element. According to the method, a digital forward design method is adopted, mapping among the vibration isolation system, rigidity and damping of the vibration isolation elements and structural parameters of the vibration isolation elements can be accurately established, and index decomposition completeness and accuracy of the vibration isolation system can be guaranteed.

Description

Technical Field

[0001] The invention belongs to the technical field of computer modeling and simulation, and in particular relates to a digital vibration isolation system design optimization method based on Modelica, which is particularly suitable for parameter design and optimization of vibration isolation systems for optoelectronic equipment. Background Art

[0002] As the requirements for the stability and accuracy of optoelectronic equipment are increasing across generations, the impact of the vibration environment on the stability and accuracy of optoelectronic equipment cannot be ignored. In a vibration environment, the optomechanical system produces rigid displacement, and the stability accuracy of each optical system is significantly reduced due to the vibration of its installation position. In order to improve the stability of the optomechanical system in a complex environment, it is necessary to isolate the shipboard environment excitation from the optomechanical system through a vibration isolation system.

[0003] Therefore, introducing a vibration isolation system into optoelectronic equipment has important practical significance for improving the stability of the optical axis and alleviating the impact of shock.

[0004] At present, the vibration isolation system and vibration isolation components are constructed through engineering experience and applied based on previous equipment. This method has the following shortcomings: the design parameters of the vibration isolation system are tried and true, and the design lacks a basis; it is difficult to establish a correlation between the performance of the vibration isolation system and the design parameters of the vibration isolation components; there is a lack of effective optimization methods and directions for the design parameters of the vibration isolation system and vibration isolation components. Summary of the invention

[0005] The purpose of the present invention is to design a digital vibration isolation system design optimization method based on Modelica according to the deficiencies of the prior art.

[0006] The technical solution adopted by the present invention to solve the technical problem is: a digital vibration isolation system design optimization method based on Modelica, comprising the following steps:

[0007] S1, decompose the performance index of the vibration isolation system of the optoelectronic equipment to obtain the performance model of the vibration isolation system;

[0008] S2, mathematical modeling of the vibration isolation system based on Modelica, constructing the mapping of the stiffness k of the vibration isolation element and the damping c of the damping element to the dynamic performance of the vibration isolation system;

[0009] S3, optimize the performance parameters such as stiffness k and damping c of the vibration isolation element based on sensitivity analysis, particle swarm optimization, genetic algorithm and other methods;

[0010] S4, construct a mapping model of the stiffness k and damping c of the vibration isolation element to the structural parameters;

[0011] S5, optimize the structural parameters of the vibration isolation elements based on sensitivity analysis, particle swarm algorithm and genetic algorithm.

[0012] Further, the step S1 is specifically as follows: determining the required layout form of the vibration isolation system, that is, the number of elastic elements and damping elements of stiffness required in the optoelectronic device and the layout restrictions, and taking the restrictions as the boundary conditions for optimization; based on the layout form of the vibration isolation system of the optoelectronic device, dynamically modeling the vibration isolation system through the Newton-Euler equation or the Lagrange equation, and obtaining the mapping relationship between the comprehensive performance of the vibration isolation system and the stiffness k and damping c of each vibration isolation element; obtaining the dynamic equation containing the stiffness k and damping c of the vibration isolation element and the mass and moment of inertia of the object supported by the vibration isolation system Where M, C, and K are the mass matrix, damping matrix, and stiffness matrix of the object supported by the vibration isolation system, respectively; x and u are the center of mass motion vector and base excitation vector of the object supported by the vibration isolation system; the transfer function of the vibration isolation system can be solved by Laplace transform Where s is the Laplace operator, and finally the vibration isolation system performance model including the stiffness and damping of the vibration isolation elements is obtained.

[0013] Furthermore, the step S2 performs sensitivity analysis on the stiffness k of the vibration isolation element and the damping c parameters of the damping element based on the MWorks Sysplorer sensitivity analysis toolbox, solves the contribution of each input factor to the output result, and helps determine which factors have a greater impact on the performance of the vibration isolation system. Within the appropriate value range of stiffness k and damping c, the Monte Carlo method is used to randomly sample and calculate the residuals of the natural frequency and amplification factor of the vibration isolation system under different parameters, and calculates various correlation coefficients.

[0014] Furthermore, the step S3 performs an optimization design on the stiffness k of the vibration isolation element and the damping c of the damping element based on the MWorks Sysplorer response optimization toolbox, optimizes the parameters of the vibration isolation element through a particle swarm algorithm and a genetic algorithm, takes the overall performance requirements of the vibration isolation system as the optimization target, uses the vibration isolation system layout in step S1 as a constraint boundary condition, and uses the sensitivity of the vibration isolation element in step S2 as an optimization reference, and finally obtains multiple sets of elastic element and damping element performance optimization parameters.

[0015] Furthermore, the step S4 carries out preliminary design of the geometric form of the vibration isolation element based on the layout constraints of the vibration isolation system, determines the structural boundary conditions of the vibration isolation element, and establishes the relationship between the elastic deformation of the material and the external force and external torque based on material mechanics. Where w is the deflection, M(x) is the external moment, E is the elastic modulus of the material, and I is the moment of inertia of the section. The relationship between the structural parameters of the elastic element and the external force is obtained by decomposing the parameters layer by layer, and multiple groups of optimizable structural parameters are obtained to complete the mathematical modeling of the vibration isolation element.

[0016] Furthermore, the step S5 is consistent with the steps S2 to S3 in that structural parameter sensitivity analysis and optimization are performed based on the MWorks Sysplorer sensitivity analysis and the MWorks Sysplorer response optimization toolbox, the optimization target is the performance parameters (stiffness, damping) optimized in step S3, and the optimization constraint is the vibration isolation system layout restriction determined in step S1; after completing the parameter optimization, the structural three-dimensional modeling is performed to confirm that the vibration isolation system layout constraints are met, and a finite element simulation model is generated at the same time.

[0017] Furthermore, it also includes step S6, finite element simulation verification: determine whether the vibration isolation element structure is feasible, otherwise repeat step S3, if so, perform finite element simulation analysis of the optomechanical system; determine whether the vibration isolation index requirements of the vibration isolation system are met, otherwise repeat step S3, if so, conduct digital-physical experimental verification based on the digital model to guide the development of subsequent engineering physical prototypes.

[0018] Furthermore, based on the three-dimensional finite element simulation model generated in step S5, the following two aspects of verification are carried out: (1) the finite element simulation is performed on the vibration isolation element designed according to the structural parameters after optimization in step five to obtain whether the stiffness and damping meet the performance indicators of the vibration isolation element in step S3; (2) the finite element simulation is performed on the vibration isolation system designed according to the structural parameters after optimization in step S5 to obtain the natural frequency and amplification factor to determine whether they meet the performance requirements of the vibration isolation system determined in step one.

[0019] The beneficial effects of the present invention are as follows: the method of the present invention adopts a digital forward design method, which can accurately establish the mapping between the vibration isolation system, the stiffness and damping of the vibration isolation element, and the structural parameters of the vibration isolation element, and can ensure the completeness and accuracy of the vibration isolation system index decomposition; the method of the present invention adopts a design method that combines design and engineering, which can accurately convert the analysis results of the theoretical vibration isolation element into an engineering design structure, and ensure the feasibility of the vibration isolation system; the method of the present invention adopts a digital optimization method to optimize the performance parameters and structural parameters of the vibration isolation element, avoiding the process of the traditional trial and error method, and improving the design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Design optimization method flow chart for the present invention;

[0021] Figure 2 It is the parameter sensitivity analysis process based on Modelica;

[0022] Figure 3 It is the result of parameter sensitivity analysis based on Modelica;

[0023] Figure 4 Set up for Modelica-based particle swarm and genetic optimization methods;

[0024] Figure 5The elastic element structure and optimizable parameters;

[0025] Figure 6 This is the finite element simulation result. DETAILED DESCRIPTION

[0026] The present invention will be further described in detail below in conjunction with the accompanying drawings. The following embodiments are only used to clearly illustrate the technical solutions of the present invention and are therefore only examples and cannot be used to limit the protection scope of the present invention.

[0027] In view of the problems of parameter trial and error, lack of design basis, and lack of optimization direction in the traditional design method of vibration isolation system, this patented method realizes forward design through digital design method, establishes the relationship between the overall performance of the vibration isolation system and the vibration isolation characteristics of each component of the vibration isolation system according to the performance requirements of the vibration isolation system, and optimizes the vibration isolation performance of the vibration isolation components to achieve the global optimization of the overall performance of the vibration isolation system. Further, the relationship between the structural parameters of the vibration isolation components and the vibration isolation performance is established, and the vibration isolation performance required by the vibration isolation components is achieved by optimizing the structural parameters of the vibration isolation components.

[0028] The method of the present invention uses a digital design optimization method in combination with the domestic modeling and simulation tool Modelica to digitally model the vibration isolation system, optimizes the parameters of multiple groups of vibration isolation elements through the optimization tool, and further optimizes the structure of the vibration isolation element based on the vibration isolation performance parameter optimization results of the vibration isolation element.

[0029] The vibration isolation system includes a stiffness damping system composed of multiple groups of vibration isolation elements; the vibration isolation elements mainly include elastic elements that provide stiffness and damping elements that provide damping; the performance parameters of the vibration isolation elements include the stiffness k of the vibration isolation elements and the damping c of the damping elements; the digital modeling optimization software is the domestically produced software MWorks Sysplorer.

[0030] A further technical solution based on the above solution is: determine the overall layout of each vibration isolation element of the vibration isolation system; mathematical modeling of the vibration isolation system, construct a mapping of the stiffness k of the vibration isolation element and the damping c of the damping element to the dynamic performance of the vibration isolation system, and optimize the performance parameters of the stiffness k and damping c of the vibration isolation element based on sensitivity analysis, particle swarm algorithm, genetic algorithm and other methods; mathematical modeling of the vibration isolation element, construct a mapping model of the stiffness k, damping c and structural parameters of the vibration isolation element; optimize the structural parameters of the vibration isolation element based on sensitivity analysis, particle swarm algorithm, genetic algorithm and other methods; carry out structural finite element simulation verification and vibration isolation system performance simulation verification based on a three-dimensional model of the structural parameters of the vibration isolation element.

[0031] Reference Figure 1As shown, the present invention discloses a digital vibration isolation system design optimization method based on Modelica, which involves five steps: mathematical modeling of the vibration isolation system based on Modelica, optimization of vibration isolation element performance parameters, mathematical modeling of the vibration isolation element, optimization of vibration isolation element structural parameters, and finite element simulation verification. The specific implementation is as follows.

[0032] Step 1: Decompose the performance indicators of the optoelectronic equipment vibration isolation system to obtain a vibration isolation system performance model.

[0033] Determine the required layout of the optoelectronic equipment vibration isolation system, that is, the required number of stiffness elastic elements and damping elements in the optoelectronic equipment and the layout restrictions. The above restrictions serve as the boundary conditions for optimization.

[0034] Based on the layout of the vibration isolation system of the optoelectronic equipment, the vibration isolation system is dynamically modeled by the Newton-Euler equation or the Lagrange equation, and the mapping relationship between the comprehensive performance of the vibration isolation system and the stiffness k and damping c of each vibration isolation element is obtained.

[0035] The dynamic equation including the stiffness k and damping c of the vibration isolation element and the mass and moment of inertia of the object supported by the vibration isolation system is obtained. Where M, C, and K are the mass matrix, damping matrix, and stiffness matrix of the object supported by the vibration isolation system, respectively; x and u are the center of mass motion vector and basic excitation vector of the object supported by the vibration isolation system.

[0036] The transfer function of the vibration isolation system can be solved by Laplace Where s is the Laplace operator, and finally the vibration isolation system performance model including the stiffness and damping of the vibration isolation elements is obtained.

[0037] Step 2: Based on the mathematical modeling (dynamic model) of the vibration isolation system using Modelica, a mapping of the stiffness k of the vibration isolation element and the damping c of the damping element to the dynamic performance of the vibration isolation system is constructed.

[0038] Based on the MWorks Sysplorer sensitivity analysis toolbox, a sensitivity analysis of the stiffness and damping parameters of the vibration isolation elements is carried out ( Figure 2 ), solve the contribution of each input factor to the output result, and help determine which factors have a greater impact on the performance of the vibration isolation system. In the appropriate range of stiffness k and damping c, the Monte Carlo method is used to randomly sample and calculate the residuals of the natural frequency and amplification factor of the vibration isolation system under different parameters, and calculate the correlation coefficients ( Figure 3 ).

[0039] Step three, based on sensitivity analysis, particle swarm algorithm, genetic algorithm and other methods, the performance parameters such as stiffness k and damping c of the vibration isolation element are optimized.

[0040] Based on the MWorks Sysplorer response optimization toolbox, the stiffness k of the vibration isolation element and the damping c of the damping element are optimized, and the particle swarm algorithm and genetic algorithm are used to optimize the parameters of the vibration isolation element. Figure 4 ). The overall performance requirements of the vibration isolation system are taken as the optimization target, the layout of the vibration isolation system in step one is taken as the constraint boundary condition, and the sensitivity of the vibration isolation element in step two is taken as the optimization reference basis, and finally multiple groups of elastic element and damping element performance optimization parameters are obtained.

[0041] Step 4: Construct a mapping model of the stiffness k and damping c of the vibration isolation element to the structural parameters.

[0042] Based on the layout restrictions of the vibration isolation system, the geometric form of the vibration isolation element is preliminarily designed, the structural boundary conditions of the vibration isolation element are determined, and the relationship between the elastic deformation of the material and the external force and torque is established based on material mechanics. Where w is the deflection, M(x) is the external moment, E is the elastic modulus of the material, and I is the moment of inertia of the section. The relationship between the structural parameters of the elastic element and the external force is obtained by decomposing the parameters layer by layer, and multiple groups of optimizable structural parameters are obtained to complete the mathematical modeling of the vibration isolation element.

[0043] Parameterized vibration isolation elements ( Figure 5 ) as an example, its wall thickness and arc radius can be used as parameters to be optimized.

[0044] Step five: Optimize the structural parameters of the vibration isolation elements based on sensitivity analysis, particle swarm algorithm, genetic algorithm and other methods.

[0045] Consistent with steps 2 and 3, structural parameter sensitivity analysis and optimization are carried out based on MWorks Sysplorer sensitivity analysis and MWorks Sysplorer response optimization toolbox. The optimization target is the performance parameters (stiffness, damping) optimized in step 3, and the optimization constraint is the vibration isolation system layout restriction determined in step 1.

[0046] After completing parameter optimization, carry out structural three-dimensional modeling to confirm that the vibration isolation system layout constraints are met, and generate a finite element simulation model.

[0047] Step 6: Finite element simulation verification. Determine whether the vibration isolation component structure is feasible. If not, repeat step 3. If yes, perform finite element simulation analysis of the optical-mechanical system. Determine whether the vibration isolation index requirements of the vibration isolation system are met. If yes, repeat step 3. If yes, conduct digital-physical experimental verification based on the digital model to guide the development of subsequent engineering prototypes.

[0048] Based on the three-dimensional finite element simulation model generated in step five, the following two aspects of verification are carried out.

[0049] (1) Perform finite element simulation on the vibration isolation element designed based on the optimized structural parameters in step 5 to determine whether the stiffness and damping meet the vibration isolation element performance indicators in step 3 ( Figure 6 ).

[0050] (2) Whether the natural frequency and amplification factor obtained by finite element simulation of the vibration isolation system designed based on the structural parameters optimized in step 5 meet the performance requirements of the vibration isolation system determined in step 1.

[0051] The above embodiments are only illustrative of the principles and effects of the present invention, as well as some embodiments of its application. For those skilled in the art, several modifications and improvements may be made without departing from the creative concept of the present invention, and all of these belong to the protection scope of the present invention.

Claims

1. A digital vibration isolation system design optimization method based on Modelica, characterized by: The following steps are included S1, decompose the performance index of the vibration isolation system of the optoelectronic equipment to obtain the performance model of the vibration isolation system; S2, mathematical modeling of the vibration isolation system based on Modelica, constructing the mapping of the stiffness k of the vibration isolation element and the damping c of the damping element to the dynamic performance of the vibration isolation system; S3, optimize the stiffness k and damping c of the vibration isolation element; S4, construct a mapping model of the stiffness k and damping c of the vibration isolation element to the structural parameters; S5, optimizes the structural parameters of the vibration isolation elements based on sensitivity analysis, particle swarm algorithm and genetic algorithm.

2. According to claim 1, a digital vibration isolation system design optimization method based on Modelica is characterized in that: The step S1 is specifically as follows: Determine the number and layout restrictions of elastic elements and damping elements required for the stiffness of the vibration isolation system of the optoelectronic device in the optoelectronic device, and use the restrictions as boundary conditions for optimization; Based on the layout of the vibration isolation system of the optoelectronic equipment, the vibration isolation system is dynamically modeled to obtain the mapping relationship between the comprehensive performance of the vibration isolation system and the stiffness k and damping c of each vibration isolation element; The dynamic equation including the stiffness k and damping c of the vibration isolation element and the mass and moment of inertia of the object supported by the vibration isolation system is obtained. Where M, C, and K are the mass matrix of the object supported by the vibration isolation system, the damping matrix of the vibration isolation system, and the stiffness matrix of the vibration isolation system, respectively; x and u are the center of mass motion vector and the basic excitation vector of the object supported by the vibration isolation system; Solving the transfer function of the vibration isolation system by Laplace transform Where s is the Laplace operator, and finally the vibration isolation system performance model including the stiffness and damping of the vibration isolation elements is obtained.

3. The method for designing and optimizing a digital vibration isolation system based on Modelica according to claim 2, characterized in that: The step S2 performs sensitivity analysis on the stiffness k of the vibration isolation element and the damping c of the damping element based on the MWorks Sysplorer sensitivity analysis toolbox, solves the contribution of each input factor to the output result, and calculates the natural frequency and amplification factor residual of the vibration isolation system under different parameters by random sampling through the Monte Carlo method within the appropriate value range of stiffness k and damping c, and calculates various correlation coefficients.

4. The method for designing and optimizing a digital vibration isolation system based on Modelica according to claim 3 is characterized in that: The step S3 optimizes the stiffness k of the vibration isolation element and the damping c of the damping element based on the MWorks Sysplorer response optimization toolbox, optimizes the parameters of the vibration isolation element through particle swarm algorithm and genetic algorithm, takes the overall performance requirements of the vibration isolation system as the optimization target, uses the vibration isolation system layout in step S1 as the constraint boundary condition, and uses the sensitivity of the vibration isolation element in step S2 as the optimization reference basis, and finally obtains multiple groups of elastic element and damping element performance optimization parameters.

5. The method for designing and optimizing a digital vibration isolation system based on Modelica according to claim 4, characterized in that: The step S4 carries out preliminary design of the geometric form of the vibration isolation element based on the layout constraints of the vibration isolation system, determines the structural boundary conditions of the vibration isolation element, and establishes the relationship between the elastic deformation of the material and the external force and external torque based on material mechanics. Where w is the deflection, M(x) is the external moment, E is the elastic modulus of the material, and I is the moment of inertia of the section. The relationship between the structural parameters of the elastic element and the external force is obtained by decomposing the parameters layer by layer, and multiple groups of optimizable structural parameters are obtained to complete the mathematical modeling of the vibration isolation element.

6. The method for designing and optimizing a digital vibration isolation system based on Modelica according to claim 5, characterized in that: The step S5 performs structural parameter sensitivity analysis and optimization based on MWorks Sysplorer sensitivity analysis and MWorks Sysplorer response optimization toolbox, wherein the optimization target is the performance parameter optimized in step S3, and the optimization constraint is the vibration isolation system layout restriction determined in step S1; after completing the parameter optimization, the structural three-dimensional modeling is carried out to confirm that the vibration isolation system layout constraint conditions are met, and a finite element simulation model is generated at the same time.

7. The method for designing and optimizing a digital vibration isolation system based on Modelica according to claim 6, characterized in that: It also includes step S6, finite element simulation verification: determine whether the vibration isolation element structure is feasible, otherwise repeat step S3, if so, perform finite element simulation analysis on the optomechanical system; determine whether the vibration isolation index requirements of the vibration isolation system are met, otherwise repeat step S3, if so, conduct digital-physical experimental verification based on the digital model to guide the development of subsequent engineering prototypes.

8. The method for designing and optimizing a digital vibration isolation system based on Modelica according to claim 7, characterized in that: Based on the three-dimensional finite element simulation model generated in step S5, the following two aspects of verification are carried out: (1) the finite element simulation of the vibration isolation element designed according to the structural parameters after optimization in step five is performed to determine whether the stiffness and damping meet the performance indicators of the vibration isolation element in step three; (2) the finite element simulation of the vibration isolation system designed according to the structural parameters after optimization in step five is performed to determine whether the natural frequency and amplification factor meet the performance requirements of the vibration isolation system determined in step one.

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