Numerical simulation method for linear-angular coupled vibration response of optical equipment vibration isolation system

Abstract

The present application provides a numerical simulation method for the line-angular coupling vibration response of an optical device vibration isolation system, and belongs to the technical field of optical vibration isolation system design. The present application derives the rigid body dynamics equation of the optical device vibration isolation system by treating the optical device vibration isolation system as a rigid body, and obtains the frequency response function according to the rigid body dynamics equation; based on this, by inputting the design parameters of the optical device vibration isolation system, the mass matrix of the optical device, the damping matrix of the optical device, the stiffness matrix of the optical device, the basic damping matrix and the basic stiffness matrix are calculated according to the rigid body dynamics equation, and the calculation results are substituted into the frequency response function to solve the angular displacement vibration response caused by the linear vibration excitation. In the above manner, the present application can quickly calculate the angular displacement vibration response caused by the environmental lateral linear vibration excitation without the need for fine modeling of the vibration isolator, and provide guidance for the design of the vibration isolation system.

Description

Technical Field

[0001] The invention relates to the technical field of optical vibration isolation system design, and in particular to a numerical simulation method for line-angle coupled vibration response of an optical device vibration isolation system. Background Art

[0002] Since precision optical detection equipment is very sensitive to vibration environment, it is necessary to design a vibration isolation system to suppress and isolate the impact and high-frequency vibration input from the external environment. In actual engineering environments, due to the limitation of installation space, the vibration isolator can only be installed at the bottom of the equipment, which will cause a large vertical center of mass rigidity deviation in the vibration isolation system. The larger the vertical mass deviation, the stronger the coupling effect of the translational and rotational modes of the system, and the greater the angular displacement response around the pitch axis caused by the lateral linear vibration disturbance. The sensitivity of optical detection equipment to angular vibration is much greater than that to linear vibration. The accuracy error of 1mrad angular displacement disturbance can reach 1m at 1km away. In addition, compared with lightweight equipment, the layout of vibration isolators for large-mass and large-size optical equipment is more complicated, and the difference in vibration isolator stiffness and layout design will also significantly affect the angular vibration response of the system. Therefore, under the premise of ensuring impact resistance and high-frequency vibration isolation performance, reducing the angular displacement disturbance caused by environmental vibration is the key to the design of vibration isolation system for optical equipment.

[0003] Compared with general vibration isolation systems, the design of large-load, vertical large-mass eccentric vibration isolation systems is more difficult, and the number of iterations in the design stage is greater and the iteration cycle is longer. Therefore, improving the iteration speed of the design of large-load, vertical large-mass eccentric vibration isolation systems is of great significance to shortening the R&D cycle of the entire product and reducing R&D costs.

[0004] In the early stage of vibration isolation system design, it is necessary to use numerical simulation methods to analyze the angular displacement disturbances to the equipment. In the prior art, the finite element method is usually used to study such problems. For example, the patent with publication number CN115292833A provides a system-level optimization method for the dynamic parameters of micro-vibration isolators for optical remote sensing satellites. The patent optimizes the isolator parameters by establishing a finite element model of the entire satellite and the isolator, and performing analysis and fitting based on the corresponding finite element model. Although this method can be used to simulate the line-angle coupled vibration response of the optical device vibration isolation system, it is necessary to establish a finite element model for the optical device and the isolator. Whenever the stiffness and layout of the isolator need to change, it needs to be remodeled, and the remodeling process requires huge time and computational costs.

[0005] In view of this, in order to achieve high efficiency of numerical simulation, it is necessary to provide an improved numerical simulation method for line-angle coupled vibration response of optical device vibration isolation system to solve the above problems. Summary of the invention

[0006] In view of the technical problems existing in the background technology, the present application provides a numerical simulation method for the line-angular coupled vibration response of an optical device vibration isolation system. By regarding the entire system as a rigid body, the rigid body dynamics equation of the optical device vibration isolation system containing a vibration isolator is derived, and the frequency response function is solved. In this way, the angular displacement vibration response caused by the environmental lateral line vibration excitation can be quickly calculated without the need for detailed modeling of the vibration isolator, thereby providing guidance for the design of the vibration isolation system.

[0007] The present application provides a method for numerically simulating the line-angle coupled vibration response of an optical device vibration isolation system, comprising the following steps:

[0008] S1. The optical device vibration isolation system is regarded as a rigid body, a rigid body dynamics equation of the optical device vibration isolation system is derived, and a frequency response function is obtained according to the rigid body dynamics equation;

[0009] S2. Input the design parameters of the optical device vibration isolation system, calculate the mass matrix of the optical device, the damping matrix of the optical device, the stiffness matrix of the optical device, the damping matrix of the foundation and the stiffness matrix of the foundation according to the rigid body dynamics equation, substitute the calculation results into the frequency response function, solve the angular displacement vibration response caused by the linear vibration excitation, and output the results.

[0010] In some embodiments, the rigid body dynamics equation is:

[0011] ;

[0012] in, M represents the mass matrix of the optical device, C represents the damping matrix of the optical device, K represents the stiffness matrix of the optical device, C B represents the damping matrix of the basis, K B represents the stiffness matrix of the foundation, D C represents the displacement of the optical device, represents the speed of the optical device, represents the acceleration of the optical device, D B represents the displacement of the foundation, Indicates the basic speed, Indicates the base acceleration.

[0013] In some embodiments, the step of obtaining the frequency response function according to the rigid body dynamics equation includes:

[0014] Performing Laplace transformation on both ends of the rigid body dynamics equation, we obtain the following equation:

[0015] ;

[0016] make , and obtain the frequency response function , as shown below:

[0017] ;

[0018] in, S represents the frequency domain signal, j represents the imaginary unit, represents frequency domain variables.

[0019] In some embodiments, the optical device vibration isolation system includes an optical device, a vibration isolator and a foundation, wherein the upper end surface of the vibration isolator is connected to the lower end surface of the optical device, and the lower end surface of the vibration isolator is connected to the upper end surface of the foundation.

[0020] In some embodiments, the mass matrix of the optical device is expressed as follows:

[0021] ;

[0022] in, m 0 Indicates the quality of the optical device, J xx represents the moment of inertia of the isolator relative to the X direction, J yy represents the moment of inertia of the isolator relative to the Y direction, J zz represents the moment of inertia of the isolator relative to the Z direction, J xy and J yx Both represent the inertia product of the isolator relative to the X and Y directions. J xz and J zx Both represent the inertia product of the isolator relative to the X and Z directions. J yz and J zy They all represent the inertia product of the isolator relative to the Y direction and the Z direction; the X direction, Y direction and Z direction are perpendicular to each other.

[0023] In some embodiments, the damping matrix of the optical device is as follows:

[0024]

[0025] in, c 1n Indicatesn The damping coefficient of the isolator along the X direction is, c 2n Indicates n The damping coefficient of the isolator along the Y direction is, c 3n Indicates n The damping coefficient of the isolator along the Z direction is, X Csn Indicates n The distance between the center of the upper end surface of the isolator and the center of mass of the optical device in the X direction, Y Csn Indicates n The distance between the center of the upper end surface of the isolator and the center of mass of the optical device in the Y direction, Z Csn Indicates n The distance between the center of the upper end surface of the isolator and the center of mass of the optical device in the Z direction, Indicates the sum of the corresponding data of all vibration isolators.

[0026] In some embodiments, the stiffness matrix of the optical device is shown as follows:

[0027]

[0028] in, k 1n Indicates n The stiffness of the isolator along the X direction, k 2n Indicates n The stiffness of the isolator along the Y direction, k 3n Indicates n The stiffness of the isolator along the Z direction.

[0029] In some embodiments, the basic damping matrix is ​​shown as follows:

[0030]

[0031] in, X Bxn Indicates n The distance between the center of the lower end surface of each isolator and the excitation center of the foundation in the X direction, Y Bxn Indicates n The distance between the center of the lower end surface of each isolator and the excitation center of the foundation in the Y direction, Z Bxn Indicates n The distance between the center of the lower end surface of the isolator and the excitation center of the foundation in the Z direction.

[0032] In some embodiments, the stiffness matrix of the foundation is as follows:

[0033] .

[0034] In some embodiments, the design parameters of the optical device vibration isolation system include the center of mass coordinates of the optical device, the excitation center coordinates of the foundation, and the upper end surface center coordinates, lower end surface center coordinates, load, natural frequency and damping coefficient of the vibration isolator.

[0035] The beneficial effects of this application are:

[0036] The numerical simulation method for the line-angle coupled vibration response of the optical device vibration isolation system provided in the present application can derive the rigid body dynamics equation and frequency response function by treating the optical device vibration isolation system as a rigid body, and quickly and efficiently calculate the angular vibration response of the system based on the relevant parameters of the optical device vibration isolation system. Based on this, even if the stiffness and layout of the vibration isolator change, there is no need to re-model, and only the changed design parameters need to be substituted into the corresponding rigid body dynamics equation and frequency response function for solution. Compared with the traditional finite element method, it achieves two orders of magnitude acceleration, effectively shortens the time cost and calculation cost, and can provide timely results with certain guiding significance in the early design stage of the vibration isolation system, provide a basis for subsequent fine analysis or model optimization, improve the iterative efficiency of the vibration isolation system design, and shorten the product development cycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solution of the present application, the following is a brief introduction to the drawings used in the present application. Obviously, the drawings described below are only some embodiments of the present application, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0038] Figure 1 This is a schematic diagram of the structure of the optical device vibration isolation system in the embodiment of the present application;

[0039] Figure 2 This is a schematic diagram of the layout of the vibration isolator in the embodiment of the present application from a top view;

[0040] Figure 3 This is a schematic diagram of the layout of the vibration isolator in the embodiment of the present application from a frontal perspective;

[0041] Figure 4 A schematic diagram of a finite element model established in the comparative example of the present application;

[0042] Figure 5 This is a comparison diagram of the angular displacement PSD spectra obtained in the examples and comparative examples of the present application.

[0043] Explanation of reference numerals: 100, optical device vibration isolation system; 10, optical device; 11, center of mass; 20, vibration isolator; 30, foundation. DETAILED DESCRIPTION

[0044] The following embodiments of the technical solution of the present application are described in detail in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present application, and are therefore only used as examples, and cannot be used to limit the scope of protection of the present application.

[0045] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by technicians in the technical field to which this application belongs; the terms used herein are only for the purpose of describing specific embodiments and are not intended to limit this application; the terms "including" and "having" in the specification and claims of this application and the above-mentioned figure descriptions and any variations thereof are intended to cover non-exclusive inclusions.

[0046] Reference to "embodiments" herein means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present application. The appearance of the phrase in various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0047] The existing finite element method requires re-modeling every time the stiffness and layout of the vibration isolator 20 change, and the re-modeling process requires huge time and computational costs, resulting in a long R&D cycle and high R&D cost for the optical device vibration isolation system 100. Based on the problems existing in the finite element method, the present application provides a numerical simulation method for the line-angle coupled vibration response of the optical device vibration isolation system 100. By treating the entire system as a rigid body, the rigid body dynamics equation of the optical device vibration isolation system 100 containing the vibration isolator 20 is derived, and the frequency response function is solved, thereby quickly calculating the angular displacement vibration response caused by the environmental lateral line vibration excitation without the need for detailed modeling of the vibration isolator 20, providing guidance for the design of the vibration isolation system.

[0048] The embodiment of the present application provides a method for numerically simulating the line-angle coupled vibration response of an optical device vibration isolation system 100, comprising the following steps:

[0049] S1. The optical device vibration isolation system 100 is regarded as a rigid body, the rigid body dynamics equation of the optical device vibration isolation system 100 is derived, and the frequency response function is obtained according to the rigid body dynamics equation;

[0050] S2. Input the design parameters of the optical device vibration isolation system 100, calculate the mass matrix of the optical device 10, the damping matrix of the optical device 10, the stiffness matrix of the optical device 10, the damping matrix of the foundation 30 and the stiffness matrix of the foundation 30 according to the rigid body dynamics equation, substitute the calculation results into the frequency response function, solve the angular displacement vibration response caused by the linear vibration excitation, and output the results.

[0051] Through the above method, the present application can derive the rigid body dynamics equation and frequency response function, and quickly and efficiently calculate the angular vibration response of the system according to the relevant parameters of the optical device vibration isolation system 100. Based on this, even if the stiffness and layout of the vibration isolator 20 change, there is no need to re-model, and only the changed design parameters need to be substituted into the corresponding rigid body dynamics equation and frequency response function for solution. This method has a simple principle and fast calculation speed, and can quickly and efficiently calculate the angular vibration response of the system. Compared with the traditional finite element method, it achieves two orders of magnitude acceleration, effectively shortens the time cost and calculation cost, and can provide timely results with certain guiding significance in the early design stage of the vibration isolation system, provide a basis for subsequent fine analysis or model optimization, improve the iterative efficiency of vibration isolation system design, and shorten the product development cycle.

[0052] For details, please refer to Figure 1 In some embodiments of the present application, the optical device vibration isolation system 100 includes an optical device 10, a vibration isolator 20 and a base 30, the upper end surface of the vibration isolator 20 is connected to the lower end surface of the optical device 10, and the lower end surface of the vibration isolator 20 is connected to the upper end surface of the base 30.

[0053] The optical device vibration isolation system 100 is regarded as a rigid body as a whole, and the rigid body dynamics equation of the optical device vibration isolation system 100 can be derived. The specific derivation process is as follows:

[0054] First, establish an XYZ rectangular coordinate system (the X direction, Y direction, and Z direction are perpendicular to each other) and determine the coordinates of the center of mass 11 of the optical device 10 ( X C , Y C , Z C ), the coordinates of the excitation center of base 30 ( X B , Y B , Z B ), the coordinates of the center of the upper end surface of each vibration isolator 20 ( X sn , Y sn , Zsn ), the coordinates of the center of the lower end surface of each vibration isolator 20 ( X xn , Y xn , Z xn ).

[0055] According to the movement of the optical device 10, the following equation can be derived:

[0056] .

[0057] in, Indicates n The movement speed of the upper end surface of the vibration isolator 20 along the X direction is, Indicates n The movement speed of the upper end surface of the vibration isolator 20 along the Y direction is, Indicates n The movement speed of the upper end surface of each vibration isolator 20 along the Z direction; represents the speed of the optical device 10 moving in the X direction, represents the speed of the optical device 10 moving in the Y direction, represents the translation speed of the optical device 10 along the Z direction, represents the speed at which the optical device 10 rotates around the X direction, represents the speed of the optical device 10 rotating around the Y direction, represents the speed at which the optical device 10 rotates around the Z direction; X Csn Indicates n The distance between the center of the upper end surface of each vibration isolator 20 and the center of mass 11 of the optical device 10 in the X direction is, X Csn = X sn - X C ; Y Csn Indicates n The distance between the center of the upper end surface of each vibration isolator 20 and the center of mass 11 of the optical device 10 in the Y direction is, Y Csn = Y sn - Y C ; Z Csn Indicates n The distance between the center of the upper end surface of each vibration isolator 20 and the center of mass 11 of the optical device 10 in the Z direction is, Z Csn = Zsn - Z C .

[0058] Similarly, the following equation can be derived based on the movement of the base 30:

[0059] .

[0060] in, Indicates n The movement speed of the lower end surface of the vibration isolator 20 along the X direction is, Indicates n The movement speed of the lower end surface of the vibration isolator 20 along the Y direction is, Indicates n The movement speed of the lower end surface of each vibration isolator 20 along the Z direction; represents the speed of the base 30 moving in the X direction, represents the speed of the base 30 moving in the Y direction, represents the speed of the base 30 moving in the Z direction, represents the speed of the base 30 rotating around the X direction, represents the speed of the base 30 rotating around the Y direction, represents the speed of the base 30 rotating around the Z direction; X Bxn Indicates n The distance between the center of the lower end surface of the vibration isolator 20 and the excitation center of the foundation 30 in the X direction, that is, X Bxn = X xn - X B ; Y Bxn Indicates n The distance between the center of the lower end surface of the vibration isolator 20 and the excitation center of the foundation 30 in the Y direction, that is, Y Bxn = Y xn - Y B ; Z Bxn Indicates n The distance between the center of the lower end surface of the vibration isolator 20 and the excitation center of the foundation 30 in the Z direction is, Z Bxn = Z xn - Z B .

[0061] According to the movement of the upper and lower end surfaces of the vibration isolator 20, the relative displacement of the upper and lower end surfaces of the vibration isolator 20 along the X, Y, and Z directions can be derived, which is specifically expressed as follows:

[0062]

[0063] in, R 1n Indicates n The relative displacement of the upper and lower end surfaces of the vibration isolator 20 along the X direction, R 2n Indicates n The relative displacement of the upper and lower end surfaces of the vibration isolator 20 along the Y direction, R 3n Indicates n The relative displacement of the upper end surface and the lower end surface of each vibration isolator 20 along the Z direction.

[0064] Based on this, the translational motion equation of the optical device vibration isolation system 100 can be derived, which is specifically expressed as follows:

[0065] .

[0066] in, m 0 represents the quality of the optical device 10; represents the acceleration of the optical device 10 in the X direction, represents the acceleration of the optical device 10 in the Y direction, represents the acceleration of the optical device 10 in translation along the Z direction; c 1n Indicates n The damping coefficient of the isolator 20 along the X direction is, c 2n Indicates n The damping coefficient of the isolator 20 along the Y direction is, c 3n Indicates n The damping coefficient of the vibration isolator 20 along the Z direction; Indicates n The relative speed of the upper and lower end surfaces of the vibration isolator 20 moving in the X direction, Indicates n The relative speed of the upper and lower end surfaces of the vibration isolator 20 moving in the Y direction, Indicates n The relative speed of the upper and lower end surfaces of the vibration isolator 20 moving in the Z direction; k 1n Indicates n The stiffness of the isolator 20 along the X direction, k2n Indicates n The stiffness of the isolator 20 along the Y direction, k 3n Indicates n The stiffness of the vibration isolator 20 along the Z direction; It represents the sum of the corresponding data of all the vibration isolators 20 .

[0067] Similarly, the rotational motion equation of the optical device vibration isolation system 100 can also be derived, which is specifically expressed as follows:

[0068] .

[0069] in, J xx represents the moment of inertia of the vibration isolator 20 with respect to the X direction, J yy represents the moment of inertia of the vibration isolator 20 relative to the Y direction, J zz represents the moment of inertia of the vibration isolator 20 with respect to the Z direction, J xy and J yx Both represent the inertia product of the vibration isolator 20 relative to the X direction and the Y direction, J xz and J zx Both represent the inertia product of the vibration isolator 20 relative to the X direction and the Z direction, J yz and J zy Both represent the inertia products of the vibration isolator 20 relative to the Y direction and the Z direction; represents the acceleration of the optical device 10 rotating along the X direction, represents the acceleration of the optical device 10 rotating along the Y direction, represents the acceleration of the optical device 10 rotating along the Z direction.

[0070] After combining the translational motion equation and the rotational motion equation of the optical device vibration isolation system 100, the rigid body dynamics equation of the optical device vibration isolation system 100 including the vibration isolator 20 can be obtained, which is specifically expressed as follows:

[0071] ;

[0072] in, M represents the mass matrix of the optical device 10, C represents the damping matrix of the optical device 10, K represents the stiffness matrix of the optical device 10, C Brepresents the damping matrix of foundation 30, K B represents the stiffness matrix of foundation 30, D C represents the displacement of the optical device 10, represents the speed of the optical device 10, represents the acceleration of the optical device 10, D B represents the displacement of the foundation 30, Indicates the speed of base 30, represents the acceleration of the base 30 .

[0073] More specifically, in the rigid body dynamics equation, the mass matrix of the optical device 10 is specifically shown as follows:

[0074] ;

[0075] In the above matrix, the blank values ​​are all 0.

[0076] The damping matrix of the optical device 10 is specifically shown in the following formula:

[0077] .

[0078] The stiffness matrix of the optical device 10 is specifically shown in the following formula:

[0079] .

[0080] The damping matrix of the foundation 30 is specifically shown as follows:

[0081] .

[0082] The stiffness matrix of the foundation 30 is specifically shown as follows:

[0083] .

[0084] Displacement of the optical device 10 D C and displacement of base 30 D B The specific formula is as follows:

[0085] , .

[0086] in, D C1 represents the translation displacement of the optical device 10 along the X direction, D C2 represents the translation displacement of the optical device 10 along the Y direction, D C3represents the translation displacement of the optical device 10 along the Z direction, D C4 represents the displacement of the optical device 10 rotating around the X direction, D C5 represents the displacement of the optical device 10 rotating around the Y direction, D C6 represents the displacement of the optical device 10 rotating around the Z direction; D B1 represents the translational displacement of the foundation 30 along the X direction, D B2 represents the displacement of the foundation 30 in the Y direction, D B3 represents the translational displacement of the foundation 30 along the Z direction, D B4 represents the displacement of the base 30 rotating around the X direction, D B5 represents the displacement of the base 30 rotating around the Y direction, D B6 It represents the displacement of the base 30 rotating around the Z direction.

[0087] Through the above-mentioned method, the present application can derive the rigid body dynamics equation of the optical device vibration isolation system 100. Based on this, the design parameters of the optical device vibration isolation system 100 are obtained and substituted into the corresponding rigid body dynamics equation. When the stiffness and layout of the vibration isolator 20 need to be changed, only the parameters need to be replaced, and no re-modeling is required, which effectively improves the calculation rate. Specifically, in some embodiments of the present application, the design parameters of the optical device vibration isolation system 100 include the coordinates of the center of mass 11 of the optical device 10, the coordinates of the center of the upper end face, the coordinates of the center of the lower end face, the load, the natural frequency and the damping coefficient of the vibration isolator 20; in other embodiments of the present application, the corresponding design parameters can also be adjusted as needed, and the values ​​in each matrix in the rigid body dynamics equation can be calculated, which all belong to the protection scope of the present application.

[0088] Furthermore, in some embodiments of the present application, the step of obtaining a frequency response function according to the rigid body dynamics equation includes:

[0089] Performing Laplace transformation on both ends of the rigid body dynamics equation, we obtain the following equation:

[0090] ;

[0091] make , and obtain the frequency response function , as shown below:

[0092] ;

[0093] in,S represents the frequency domain signal, j represents the imaginary unit, represents frequency domain variables.

[0094] The frequency response function expresses the relationship between the input and output of the system in the frequency domain. The first a Line b Elements of a column Reflects the b The degree of freedom incentive a The contribution of the response of the degrees of freedom is Indicates that the system is only affected by b When the degree of freedom is stimulated, the a The ratio of the response of a degree of freedom to the exciting force. a , b The value of is an integer between 1 and 6. The first degree of freedom represents translation in the X direction, the second degree of freedom represents translation in the Y direction, the third degree of freedom represents translation in the Z direction, the fourth degree of freedom represents rotation in the X direction, the fifth degree of freedom represents rotation in the Y direction, and the sixth degree of freedom represents rotation in the Z direction.

[0095] In the above manner, even if the stiffness or layout of the vibration isolator 20 changes, the angular vibration response of the optical device 10 when excited by the linear vibration of the base 30 can be quickly calculated, and then the influence of the vibration isolator 20 on the angular vibration of the optical device under different stiffness and different layouts can be analyzed.

[0096] A specific embodiment is listed below. It should be noted that the embodiment described below is exemplary and is only used to explain the present application, and should not be understood as a limitation to the present application.

[0097] Example 1

[0098] The optical device vibration isolation system 100 in this embodiment adopts a four-point vibration isolation model. The layout of the vibration isolator 20 at different viewing angles is as follows: Figure 2-3 As shown. The coordinates of the center of mass 11 of the optical device 10 are set to (0, 0, 500), the four vibration isolators 20 are symmetrically distributed relative to the center of mass 11 of the optical device 10, the spacing between adjacent vibration isolators 20 is 1000 mm, and the height of the vibration isolators 20 is 160 mm. Then, the center coordinates of the upper end surfaces of the four vibration isolators 20 are (500, 500, 80), (500, -500, 80), (-500, -500, 80), (-500, 500, 80), and the center coordinates of the lower end surfaces of the four vibration isolators 20 are (500, 500, -80), (500, -500, -80), (-500, -500, -80), (-500, 500, -80).

[0099] Based on the above setting, the deviation between the mass center 11 and the rigid center of the optical device vibration isolation system 100 in the horizontal direction is 0, and the deviation in the vertical direction is set to 500mm. The rated load of a single vibration isolator 20 is set to 1t, and the vertical natural frequency and the lateral natural frequency are f If the frequency is set to 10 Hz, the vibration isolator 20 can load the mass of the optical device 10. m 0 =4t, from which the stiffness of each vibration isolator 20 can be calculated , moment of inertia , J xy , J yx , J xz , J zx , J yz , J zy The damping ratio of the system is set to 0.07, with an amplitude of 1E-6 (g 2 / Hz), the horizontal linear acceleration power density flat spectrum with a starting frequency of 0.1Hz and an end frequency of 100Hz is used as input, and the coordinates of the excitation center are (0, 0, 0). According to the above design parameters, it can be obtained that:

[0100] ;

[0101] c 1n = c 2n = , c 3n = ;

[0102] X Cs1 =500mm, Y Cs1 =500mm, Z Cs1 =-420mm;

[0103] X Cs2 =500mm, Y Cs2 =-500mm, Z Cs2 =-420mm;

[0104] X Cs3 =-500mm, YCs3 =-500mm, Z Cs3 =-420mm;

[0105] X Cs4 =-500mm, Y Cs4 =500mm, Z Cs4 =-420mm;

[0106] X Bx1 =500mm, Y Bx1 =500mm, Z Bx1 =-80mm;

[0107] X Bx2 =500mm, Y Bx2 =-500mm, Z Bx2 =-80mm;

[0108] X Bx3 =-500mm, Y Bx3 =-500mm, Z Bx3 =-80mm;

[0109] X Bx4 =-500mm, Y Bx4 =500mm, Z Bx4 =-80mm.

[0110] Based on the above data, the quality matrix of the optical device 10 can be calculated as M , the damping matrix of the optical device 10 C , the stiffness matrix of the optical device 10 K , Damping matrix of base 30 C B and the stiffness matrix of foundation 30 K B , as shown below:

[0111] ;

[0112] ;

[0113] ;

[0114] ;

[0115] .

[0116] Substituting the above matrix into the frequency response function, the angular displacement response around the X direction caused by the line excitation in the Y direction can be solved, that is, The element in the 4th row and 2nd column of the matrix , which expresses the contribution of the second degree of freedom excitation to the fourth degree of freedom response. By calculating the angular displacement response corresponding to different input frequencies, the angular displacement PSD spectrum response diagram can be obtained.

[0117] Comparative Example 1

[0118] In order to verify the accuracy of the method provided in Example 1, this comparative example uses the existing finite element method to simulate the line-angle coupled vibration response of the optical device vibration isolation system 100 provided in Example 1. The finite element model established in this comparative example is as follows: Figure 4 As shown, the number of units of the finite element model is 6647, with a total of 10954 nodes, wherein the optical device 10 is simulated using the MASS unit (structural mass unit), the vibration isolator 20 is simplified into upper and lower mounting plates and a spring unit, and the MASS unit is rigidly connected to the upper mounting plate of the vibration isolator 20.

[0119] The calculation results of the methods provided in Example 1 and Comparative Example 1 are shown in Table 1. The comparison of the angular displacement PSD spectra obtained by the two methods is shown in Table 1. Figure 5 shown.

[0120] Table 1 Calculation results of the methods provided in Example 1 and Comparative Examples

[0121]

[0122] According to Table 1, compared with the finite element method in comparative example 1, the initial value and peak value calculated by the method provided in Example 1 of the present application are slightly higher. This is mainly because the entire vibration isolation system is regarded as a rigid body in the present application, and only the overall translation and rotation are considered. This simplification assumes that the structure has no deformation, ignoring the deformation and stress distribution inside the structure, which will make the overall stiffness of the system slightly higher, and thus make the angular displacement vibration response coupled by the transverse line vibration excitation slightly higher. However, the calculation time in Example 1 is only 0.2s, which is two orders of magnitude faster than 11.0s in comparative example 1. Moreover, when using the finite element method for calculation, if the layout of the vibration isolator 20 is changed, it is also necessary to remodel and set the boundary conditions, and then solve it. The actual time required is much longer than the calculation time of the solution process. In the design process of the vibration isolator 20, a large number of examples are required to preliminarily determine the stiffness transverse-vertical ratio range and layout form that can make the angular displacement response of the optical device 10 lower. If the finite element method is used, it will take a lot of time. The method adopted in this application not only has a fast calculation speed, but also has a simple and fast parameter change process. When processing large-scale data sets or scenarios that require real-time response, the calculation task can be completed in a short time.

[0123] In addition, according to Figure 5 It can be seen that although the angular displacement PSD spectrum obtained by the method of this article (i.e., the method provided in Example 1) is slightly different from that of the finite element method (i.e., the method provided in Comparative Example 1), the angular displacement PSD spectra calculated by the two have the same trend near the two response peaks, especially in the first response peak, the two curves basically overlap, proving that the method provided in this application has high accuracy. In the early design stage of the vibration isolation system, the accuracy requirements for the results are relatively low, and designers pay more attention to the ability to quickly screen out data subsets worthy of attention. Therefore, the method provided in the embodiment of the present application can greatly shorten the calculation time while ensuring that the structure is basically accurate, thereby quickly obtaining the required data, and can provide results with certain guiding significance in a timely manner, providing a basis for subsequent fine analysis or model optimization.

[0124] It should be noted that the present application is not limited to the above-mentioned embodiments. The above-mentioned embodiments are only examples, and the embodiments having the same structure as the technical idea and exerting the same effect within the scope of the technical solution of the present application are all included in the technical scope of the present application. In addition, without departing from the scope of the main purpose of the present application, various modifications that can be thought of by those skilled in the art to the embodiments and other methods of combining some of the constituent elements in the embodiments are also included in the scope of the present application.

Claims

1. A numerical simulation method for the linear-angular coupled vibration response of an optical device vibration isolation system, characterized in that: The steps include: S1. The optical device vibration isolation system is regarded as a rigid body, the rigid body dynamics equation of the optical device vibration isolation system is derived, and the frequency response function is obtained according to the rigid body dynamics equation; the optical device vibration isolation system comprises an optical device, a vibration isolator and a foundation, the upper end surface of the vibration isolator is connected to the lower end surface of the optical device, and the lower end surface of the vibration isolator is connected to the upper end surface of the foundation; S2. Input the design parameters of the optical device vibration isolation system, calculate the mass matrix of the optical device, the damping matrix of the optical device, the stiffness matrix of the optical device, the damping matrix of the foundation and the stiffness matrix of the foundation according to the rigid body dynamics equation, substitute the calculation results into the frequency response function, solve the angular displacement vibration response caused by the linear vibration excitation, and output the results; Wherein, the mass matrix of the optical device is shown as follows: ； in, m 0 indicates the quality of the optical device, J xx represents the moment of inertia of the isolator relative to the X direction, J yy represents the moment of inertia of the isolator relative to the Y direction, J zz represents the moment of inertia of the isolator relative to the Z direction, J xy and J yx Both represent the inertia product of the isolator relative to the X and Y directions. J xz and J zx Both represent the inertia product of the isolator relative to the X and Z directions. J yz and J zy All represent the inertia product of the vibration isolator relative to the Y direction and the Z direction; the X direction, Y direction and Z direction are perpendicular to each other; The damping matrix of the optical device is shown below: in, c 1n Indicates n The damping coefficient of the isolator along the X direction is, c 2n Indicates n The damping coefficient of the isolator along the Y direction is, c 3n Indicates n The damping coefficient of the isolator along the Z direction is, X Csn Indicates n The distance between the center of the upper end surface of the isolator and the center of mass of the optical device in the X direction, Y Csn Indicates n The distance between the center of the upper end surface of the isolator and the center of mass of the optical device in the Y direction, Z Csn Indicates n The distance between the center of the upper end surface of the isolator and the center of mass of the optical device in the Z direction, It means to sum the corresponding data of all vibration isolators; The stiffness matrix of the optical device is shown as follows: in, k 1n Indicates n The stiffness of the isolator along the X direction, k 2n Indicates n The stiffness of the isolator along the Y direction, k 3n Indicates n The stiffness of the isolator along the Z direction.

2. The method for numerically simulating the linear-angular coupled vibration response of the optical device vibration isolation system according to claim 1, characterized in that: The rigid body dynamics equation is: ； in, M represents the mass matrix of the optical device, C represents the damping matrix of the optical device, K represents the stiffness matrix of the optical device, C B represents the damping matrix of the basis, K B represents the stiffness matrix of the foundation, D C represents the displacement of the optical device, represents the speed of the optical device, represents the acceleration of the optical device, D B represents the displacement of the foundation, Indicates the basic speed, Indicates the base acceleration.

3. The method for numerically simulating the linear-angular coupled vibration response of the optical device vibration isolation system according to claim 2, characterized in that: The step of obtaining the frequency response function according to the rigid body dynamics equation comprises: Performing Laplace transformation on both ends of the rigid body dynamics equation, we obtain the following equation: ； make , and obtain the frequency response function , as shown below: ； in, S represents the frequency domain signal, j represents the imaginary unit, represents frequency domain variables.

4. The method for numerically simulating the linear-angular coupled vibration response of the optical device vibration isolation system according to claim 1, characterized in that: The damping matrix of the foundation is shown below: in, X Bxn Indicates n The distance between the center of the lower end surface of each isolator and the excitation center of the foundation in the X direction, Y Bxn Indicates n The distance between the center of the lower end surface of each isolator and the excitation center of the foundation in the Y direction, Z Bxn Indicates n The distance between the center of the lower end surface of the isolator and the excitation center of the foundation in the Z direction.

5. The method for numerically simulating the linear-angular coupled vibration response of the optical device vibration isolation system according to claim 1, characterized in that: The stiffness matrix of the foundation is shown below: 。 6. The method for numerically simulating the linear-angular coupled vibration response of the optical device vibration isolation system according to claim 1, characterized in that: The design parameters of the optical device vibration isolation system include the center of mass coordinates of the optical device, the excitation center coordinates of the foundation, and the upper end surface center coordinates, lower end surface center coordinates, load, natural frequency and damping coefficient of the vibration isolator.

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