Method for optimizing kinetic parameters of metal rubber two-stage multidirectional vibration isolation system

Abstract

The invention discloses a method for optimizing kinetic parameters of a metal rubber two-stage multidirectional vibration isolation system, and relates to the field of metal rubber vibration isolation. S2, constructing a random vibration signal, and converting the random vibration signal into a stage Fourier coefficient; s3, solving the nonlinear dynamic model; s4, dispersing the internal metal wires into countless equivalent micro-spring units; s5, constructing an optimization objective function; s6, constructing constraint conditions; s7, optimizing parameters; s8, judging whether vibration isolation design requirements are met or not, if yes, determining that the optimized parameters are optimal design parameters, otherwise, returning to S6, and reconstructing the constraint conditions; the method comprises the following steps: constructing a metal rubber two-stage multidirectional vibration isolation system by utilizing the characteristics of anisotropy of a metal rubber material, establishing a system dynamic model, and solving system response under random vibration by utilizing a harmonic balance method; according to the relation between axial and radial mechanical properties of a metal rubber material, kinetic parameters are optimally designed, and rapid design of the metal rubber two-stage multidirectional vibration isolation system is achieved.

Description

Technical Field

[0001] The invention relates to the field of metal rubber vibration isolation, and in particular to a method for optimizing dynamic parameters of a metal rubber secondary multi-directional vibration isolation system. Background Art

[0002] The design of metal rubber vibration isolation mostly adopts a primary vibration isolation strategy, but the primary vibration isolation system cannot meet the wide-band vibration isolation requirements of the aircraft during service, and it is also prone to cause local amplification effects. A secondary vibration isolation system is often used to make up for the shortcomings of the primary vibration isolation system. However, when designing a secondary vibration isolation system, it is necessary to consider parameters such as stiffness, damping, mass distribution, and the material and structure of the mounting plate, which makes the dynamic design of the secondary vibration isolation system more complicated than that of the primary vibration isolation system. Existing research is mainly limited to the stiffness and damping properties of the metal rubber material itself or the design method of the primary vibration isolation system under simple harmonic excitation. Therefore, it is urgent to develop a design method for a metal rubber secondary multi-directional vibration isolation system under random vibration excitation. Summary of the invention

[0003] The purpose of the present invention is to design a method for optimizing the dynamic parameters of a metal rubber two-level multi-directional vibration isolation system in order to solve the above problems.

[0004] The present invention achieves the above-mentioned purpose through the following technical solutions:

[0005] The dynamic parameter optimization method of the metal rubber two-stage multi-directional vibration isolation system includes:

[0006] S1. Construct the dynamic model of the metal rubber two-level multi-directional vibration isolation system;

[0007] S2, constructing a random vibration signal, and converting the random vibration signal into a phase Fourier coefficient having a basic frequency;

[0008] S3. Use the extended harmonic balance method to solve the nonlinear dynamic model of the metal rubber multi-directional vibration isolation system under random vibration;

[0009] S4, discretize the metal wire inside the metal rubber into countless equivalent micro-spring units;

[0010] S5. Constructing the optimization objective function of metal rubber vibration isolation according to the vibration isolation efficiency and the resonance peak magnification factor;

[0011] S6. According to the relationship between the axial and radial mechanical performance parameters of metal rubber, the constraint conditions of the metal rubber two-level multi-directional vibration isolation system are constructed;

[0012] S7. Optimize the parameters of the metal rubber two-stage multi-directional vibration isolation system using a particle swarm optimization algorithm;

[0013] S8. Calculate the fitness according to the optimized parameters and determine whether they meet the vibration isolation design requirements. If so, the optimized parameters are the optimal design parameters. Otherwise, return to S6 and rebuild the constraint conditions.

[0014] The beneficial effects of the present invention are: utilizing the anisotropic characteristics of metal rubber materials, constructing a metal rubber secondary multi-directional vibration isolation system, establishing a system dynamics model, and using the harmonic balance method to solve the system response under random vibration. According to the relationship between the axial and radial mechanical properties of the metal rubber material, and using this as the boundary condition and optimization target of the particle swarm algorithm, the dynamic parameters of the metal rubber secondary multi-directional vibration isolation system are optimized and designed, the optimal vibration isolation efficiency and resonance peak amplification of the secondary vibration isolation system are obtained, and the rapid design of the metal rubber secondary multi-directional vibration isolation system is realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic diagram of a method for optimizing dynamic parameters of a metal rubber two-stage multi-directional vibration isolation system of the present invention;

[0016] Figure 2 It is a schematic flow chart of the method for optimizing the dynamic parameters of the metal rubber two-stage multi-directional vibration isolation system of the present invention;

[0017] Figure 3 It is a schematic diagram of random vibration test;

[0018] Figure 4 It is the experimental PSD response curve of random vibration before the first-order mode. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0020] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0021] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0022] In the description of the present invention, it should be understood that the terms "upper", "lower", "inside", "outside", "left", "right", etc. indicate directions or positional relationships based on the directions or positional relationships shown in the accompanying drawings, or are directions or positional relationships in which the product of the invention is usually placed when in use, or are directions or positional relationships commonly understood by those skilled in the art. These directions or positional relationships are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore should not be understood as a limitation on the present invention.

[0023] Furthermore, the terms “first”, “second”, etc. are merely used for distinguishing descriptions and are not to be understood as indicating or implying relative importance.

[0024] In the description of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, the terms such as "setting" and "connection" should be understood in a broad sense. For example, "connection" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or an indirect connection through an intermediate medium, or it can be the internal communication of two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0025] The specific implementation modes of the present invention are described in detail below in conjunction with the accompanying drawings.

[0026] The dynamic parameter optimization method of the metal rubber two-stage multi-directional vibration isolation system includes:

[0027] S1. Using the multi-directional vibration isolation characteristics of the metal rubber vibration isolator, according to the nonlinear functional constitutive model of the metal rubber vibration isolator, the dynamic parameters of the upper and lower vibration isolators are solved respectively, and the dynamic model of the metal rubber two-level multi-directional vibration isolation system is constructed, which is expressed as:

[0028] Among them, u a is the axial excitation displacement, a p is the absolute displacement of the mounting plate, a e is the absolute displacement of the instrument cabin, u r is the radial excitation displacement, and r is the radial response displacement of the entire shock absorber. ma11 is the first-order stiffness of the lower metal rubber isolator, k ma13 is the third-order stiffness of the lower metal rubber isolator, c ma1 is the damping of the lower metal rubber isolator, k a11 is the total linear stiffness of the lower isolator in the vibration isolation system, k a13 is the third-order total stiffness of the lower vibration isolator in the vibration isolation system, c a1 is the total damping of the lower isolator in the vibration isolation system.

[0029] S1', transform the kinetic model into matrix form, expressed as: in

[0030]

[0031] S2. Construct random vibration signals and process them by inverse fast Fourier transform, which is expressed as:

[0032]

[0033] Among them, f c Nyquist frequency, is a random phase set, is the frequency resolution, f0 is the first-order resonance frequency, is the relevant damping ratio, where Q is the quality factor, x N (t) is a discrete random vibration signal.

[0034] And the random vibration signal is converted into the phase Fourier coefficient with the fundamental frequency, which is expressed as:

[0035]

[0036] Among them, (A0, (A k ,B k )),(C0,(C k ,D k )),(C k,excit ,D k,excit ) is the Fourier coefficient, the coefficient C0 depends on the coefficient A0 and (A0, (A k ,B k )) k∈[1,p] .They can be calculated using the alternating frequency-time method (AFT).

[0037] S3. Use the extended harmonic balance method to solve the nonlinear dynamic model of the metal rubber multi-directional vibration isolation system under random vibration; specifically:

[0038] Since the random excitation is chosen to be transposed into an equivalent deterministic excitation with one fundamental pulsation and a large number of harmonics, the number of harmonics is extremely high, so the extended harmonic balance method is adjusted using the fast Fourier transform algorithm. The nonlinearity is calculated in the time domain and then converted back to the frequency domain using the fast Fourier transform algorithm, which is expressed as: The discretized equilibrium equation is transformed into the form of a minimum optimization problem and solved as: H(X,Ω,F NL )=||AX-BB NL (X)||<ε, in

[0039] S4. Discretize the metal wire inside the metal rubber into countless equivalent microspring units. The axial stiffness K of the equivalent microspring unit is α and radial stiffness K r It is expressed as:

[0040]

[0041] Among them, ΔZ is the axial compression deformation; ΔR is the radial shear deformation; F a is the axial load; F r is the radial load; E is the elastic modulus of the wire; r is the Poisson's ratio of the wire; D is the diameter of the spiral coil; α is the helical angle of the microspring unit; r is the wire diameter of the wire; K a is the axial stiffness of the microspring unit; K r is the radial stiffness of the microspring unit.

[0042] S5. The optimization objective function of metal rubber vibration isolation is constructed based on the vibration isolation efficiency and the resonance peak magnification factor, which is expressed as:

[0043]

[0044] Among them, η a is the axial vibration isolation efficiency, η r is the radial vibration isolation efficiency, Q a is the axial resonance peak magnification, Q r is the resonance peak magnification factor.

[0045] S6. According to the relationship between the axial and radial mechanical properties of metal rubber, the constraint conditions of the metal rubber two-level multi-directional vibration isolation system are constructed. The constraint conditions include the constraint equation of the vibration isolation system and the constraint equation of the vibration isolator, which are expressed as:

[0046]

[0047] S7. Optimize the parameters of the metal rubber two-stage multi-directional vibration isolation system using the particle swarm optimization algorithm; the number of initialization groups is set to 2000, the maximum number of iterations is 20, the particle adaptive weight and social adaptive weight are both set to 1.49, the group size is 200, and the function tolerance is 10 -6 ;

[0048] S8. Calculate the fitness according to the optimized parameters and determine whether they meet the vibration isolation design requirements. If so, the optimized parameters are the optimal design parameters. Otherwise, return to S6 and rebuild the constraint conditions.

[0049] Using this method, the optimal parameters of the secondary vibration isolation system are obtained, as shown in Table 1. The metal rubber is prepared using 304 stainless steel, and its preparation process is shown in Table 2. The dynamic model of high-order nonlinear friction is used for parameter identification, and the parameters of the dynamic model are shown in Table 3. The basic structure of the upper and lower metal rubber isolators in the secondary vibration isolation system is the same, which consists of a limit sleeve, a protective cover, a steel sleeve, a limit gasket, a hollow cylindrical metal rubber, and a fixing bolt. The limit sleeve and the limit gasket are to control the maximum vibration amplitude to 1.5mm. The force can be transmitted in the axial direction through the mounting plate, and in the radial direction through the steel sleeve. Therefore, the metal rubber isolator of this structure can achieve three-way vibration isolation capability. The main difference between the upper and lower vibration isolators is that the diameter of the lower vibration isolator is 6mm and the height is 40mm, while the diameter of the upper vibration isolator is 4mm and the height is 26mm. Figure 3 -a. The first-level vibration isolation consists of 6 primary vibration isolators, which are connected to the base through bolts, while the second-level vibration isolation has 3 devices that need to be isolated. Each device to be isolated is connected to the mounting plate through 4 M4 second-level metal rubber vibration isolators, as shown in the figure. Figure 3 -b. The random vibration test of the metal rubber secondary vibration isolation system is carried out on a vibration table, as shown in Figure 3 -c.

[0050] The numerical results of the system in the axial and radial directions under random vibration are basically consistent with the experimental PSD response, such as Figure 4 As shown in the figure. The first-order modal frequencies of the system in the axial and radial directions under the random vibration test are 45Hz and 65Hz, while the errors of the first-order natural modal frequencies in these two directions in the numerical calculation results are less than 5Hz. The experimental PSD response curve of the random vibration before the first-order mode is basically consistent with the theoretical calculation, as shown in the figure. Figure 4 Comparing the peak response and vibration isolation efficiency of the numerical results with those of the test results, as shown in Table 4, the errors between the numerical simulation values ​​and the test results are both around 10%, indicating that the numerical calculation results have a certain degree of accuracy and can meet the requirements of vibration isolation design.

[0051] Table 1 Parameter optimization results of the secondary vibration isolation system

[0052]

[0053] Table 2 Preparation parameters of metal rubber

[0054]

[0055] Table 3 Dynamic parameters of metal rubber vibration isolator

[0056]

[0057] Table 4 Comparison of numerical calculation results and test results

[0058]

[0059] The technical solution of the present invention is not limited to the above-mentioned specific embodiments. All technical variations made according to the technical solution of the present invention fall within the protection scope of the present invention.

Claims

1. A method for optimizing dynamic parameters of a metal rubber two-stage multi-directional vibration isolation system, characterized in that: include: S1. Construct the dynamic model of the metal rubber two-level multi-directional vibration isolation system; S2, constructing a random vibration signal, and converting the random vibration signal into a phase Fourier coefficient having a basic frequency; S3. Use the extended harmonic balance method to solve the nonlinear dynamic model of the metal rubber multi-directional vibration isolation system under random vibration; S4, discretize the metal wire inside the metal rubber into countless equivalent micro-spring units; S5. Constructing the optimization objective function of metal rubber vibration isolation according to the vibration isolation efficiency and the resonance peak magnification factor; S6. According to the relationship between the axial and radial mechanical performance parameters of metal rubber, the constraint conditions of the metal rubber two-level multi-directional vibration isolation system are constructed; S7. Optimize the parameters of the metal rubber two-stage multi-directional vibration isolation system using a particle swarm optimization algorithm; S8. Calculate the fitness according to the optimized parameters and determine whether they meet the vibration isolation design requirements. If so, the optimized parameters are the optimal design parameters. Otherwise, return to S6 and rebuild the constraint conditions.

2. The method for optimizing dynamic parameters of a metal rubber two-stage multi-directional vibration isolation system according to claim 1 is characterized in that: In S1, the multi-directional vibration isolation characteristics of the metal rubber isolator are used. According to the nonlinear functional constitutive model of the metal rubber isolator, the dynamic parameters of the upper and lower isolators are solved respectively, and the dynamic model of the metal rubber two-level multi-directional vibration isolation system is constructed, which is expressed as: Among them, u a is the axial excitation displacement, a p is the absolute displacement of the mounting plate, a e is the absolute displacement of the instrument cabin, u r is the radial excitation displacement, and r is the radial response displacement of the entire shock absorber. ma 11 is the first-order stiffness of the lower metal rubber isolator, k ma13 is the third-order stiffness of the lower metal rubber isolator, c ma1 is the damping of the lower metal rubber isolator, k a11 is the total linear stiffness of the lower isolator in the vibration isolation system, k a13 is the third-order total stiffness of the lower vibration isolator in the vibration isolation system, c a1 is the total damping of the lower isolator in the vibration isolation system.

3. The method for optimizing dynamic parameters of a metal rubber two-stage multi-directional vibration isolation system according to claim 2 is characterized in that: Between S1 and S2, S1' is also included, and the dynamic model is converted into a matrix form, which is expressed as: in 4. The method for optimizing dynamic parameters of a metal rubber two-stage multi-directional vibration isolation system according to claim 1, characterized in that: In S2, the random vibration signal is processed by inverse fast Fourier transform, which is expressed as: Among them, f c Nyquist frequency, is a random phase set, is the frequency resolution, f0 is the first-order resonance frequency, is the relevant damping ratio, where Q is the quality factor, x N (t) is a discrete random vibration signal The random vibration signal is converted into the phase Fourier coefficients with the fundamental frequency, expressed as: Among them, (A0, (A k ,B k )),(C0,(C k ,D k )),(C k,excit ,D k,excit ) is the Fourier coefficient, the coefficient C0 depends on the coefficient 5. The method for optimizing dynamic parameters of a metal rubber two-stage multi-directional vibration isolation system according to claim 1, characterized in that: In S3, the extended harmonic balance method is adjusted using the fast Fourier transform algorithm. The nonlinearity is first calculated in the time domain and then converted back to the frequency domain using the fast Fourier transform algorithm, expressed as: The discretized equilibrium equation is transformed into the form of a minimum optimization problem and solved as: H(X,Ω,F NL )=||AX-BB NL (X)||<ε, 6. The method for optimizing dynamic parameters of a metal rubber two-stage multi-directional vibration isolation system according to claim 1, characterized in that: In S4, the axial stiffness K of the equivalent microspring unit is α and radial stiffness K r It is expressed as: Among them, ΔZ is the axial compression deformation; ΔR is the radial shear deformation; F a is the axial load; F r is the radial load; E is the elastic modulus of the wire; r is the Poisson's ratio of the wire; D is the diameter of the spiral coil; α is the helical angle of the microspring unit; r is the wire diameter of the wire; K a is the axial stiffness of the microspring unit; K r is the radial stiffness of the microspring unit.

7. The method for optimizing dynamic parameters of a metal rubber two-stage multi-directional vibration isolation system according to claim 1, characterized in that: In S5, the optimization objective function is expressed as: Among them, η a is the axial vibration isolation efficiency, η r is the radial vibration isolation efficiency, Q a is the axial resonance peak magnification, Q r is the resonance peak magnification factor.

8. The method for optimizing dynamic parameters of a metal rubber two-stage multi-directional vibration isolation system according to claim 1, characterized in that: In S6, the constraints include the vibration isolation system constraint equation and the vibration isolator constraint equation, which are expressed as:

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