A mechanical model establishment and optimization design method for airborne equipment vibration isolation system

Abstract

The present invention relates to a method for establishing a mechanical model of an airborne equipment vibration isolation system and an optimization design method thereof. The method for establishing a mechanical model of an airborne equipment vibration isolation system introduces parameters α and β into a normalized Bouc-Wen model, which can effectively describe the mechanical characteristics of a wire rope vibration isolation system under different load conditions. On the basis of the model, the transmissibility curves of a wire rope vibration isolation system and a high-static-low-dynamic wire rope vibration isolation system under different load conditions are calculated by the fourth-order Runge-Kutta method, and the number of wire rope vibration isolation components is adjusted to obtain optimized parameters α and β. The force F(x) generated by a negative stiffness device is added to the normalized Bouc-Wen model under the optimized parameters to obtain a normalized Bouc-Wen model that can describe a high-static-low-dynamic wire rope vibration isolation system. The force F(x) generated by the negative stiffness device is changed to obtain the transmissibility curves of the high-static-low-dynamic wire rope vibration isolation system under different negative stiffness sizes. Based on the transmissibility curves under different negative stiffness sizes, the optimal negative stiffness size can be optimized.

Description

Technical Field

[0001] The present invention relates to the technical field of airborne equipment vibration isolation, and in particular to a mechanical model establishment and optimization design method of an airborne equipment vibration isolation system. Background Art

[0002] Vibration problems are common in fields such as automobiles, civil engineering, and aerospace. In rotorcraft systems, vibration problems are mainly caused by the main rotor, tail rotor, and engine. The vibration caused by the main rotor is usually between 16Hz and 40Hz, the vibration caused by the tail rotor is between 50Hz and 150Hz, and the vibration caused by the engine occurs above 200Hz. These vibrations can significantly affect the accuracy of onboard electronic equipment, computer acquisition systems, and tracking systems, resulting in measurement and data acquisition errors. In addition, high-frequency vibrations can blur aerial photography images, and low-frequency vibrations can distort them. In view of these challenges, it is necessary to take appropriate measures to simultaneously eliminate the adverse effects of high-frequency and low-frequency vibrations on airborne equipment.

[0003] Nonlinear vibration isolation systems with high static and low dynamic stiffness characteristics, composed of negative and positive stiffness devices, can effectively improve low-frequency vibration isolation performance while maintaining high-frequency vibration isolation performance. Therefore, high static and low dynamic vibration isolation systems are the preferred device for eliminating the adverse effects of high- and low-frequency vibrations on airborne equipment. Due to the limited space available for aircraft payloads, the design of high static and low dynamic vibration isolation systems requires that both the negative and positive stiffness devices be compact, efficient, and lightweight.

[0004] Wire rope vibration isolation systems are widely used in marine engineering, civil engineering, and electronic equipment due to their ease of installation, excellent durability, and lightweight design. However, their inherent stiffness is excessive, limiting their low-frequency vibration isolation performance in airborne equipment. Therefore, it is necessary to incorporate negative stiffness devices into the wire rope vibration isolation system to create a high-static, low-dynamic wire rope vibration isolation system to improve its low-frequency vibration isolation performance. High static, low-dynamic stiffness is a unique stiffness design concept that combines the characteristics of high static stiffness with low dynamic stiffness. Under static loads, a structure or material exhibits high stiffness to control static displacement; under dynamic loads, it exhibits low stiffness to reduce dynamic response. This design effectively resolves the contradiction in low-frequency vibration isolation found in traditional designs: the difficulty in effectively isolating low-frequency vibrations while ensuring load-bearing capacity.

[0005] In the existing vibration isolation system, the mechanical models of the wire rope vibration isolation system under no-load state and different loads need to be fitted separately, which makes the fitting and subsequent transmissibility curve calculation complicated. Therefore, it is necessary to carry out reasonable mechanical modeling and optimization design of the high-static and low-dynamic wire rope vibration isolation system. Summary of the Invention

[0006] The purpose of the present invention is to overcome the problem in the prior art that the mechanical models of the wire rope vibration isolation system under no-load state and under different loads need to be fitted separately, which leads to complex fitting and subsequent calculation of the transmissibility curve, and to provide a method for establishing a mechanical model of an airborne equipment vibration isolation system and its optimization design.

[0007] In one aspect, the present invention provides a method for establishing a mechanical model of an airborne equipment vibration isolation system, comprising the following steps:

[0008] S1. Identify the low-frequency interference frequency w to which the airborne equipment is subjected u , mass of airborne equipment m t , the layout space of airborne equipment and the payload of the aircraft;

[0009] S2, according to the low-frequency interference frequency w u , mass of airborne equipment m t , the layout space of airborne equipment, the payload of the aircraft, the nominal load of the wire rope vibration isolation assembly and the average stiffness of the wire rope vibration isolation assembly under static load conditions to preliminarily determine the model and quantity Q1 of the wire rope vibration isolation assembly in the wire rope vibration isolation system;

[0010] S3. Based on the wire rope vibration isolation components of the model and quantity Q1 preliminarily determined in S2, a wire rope vibration isolation system is obtained. Then, a dynamic test is performed on the wire rope vibration isolation system to obtain a dynamic test curve. Based on the dynamic test curve, a normalized Bouc-Wen model of the wire rope vibration isolation system is obtained.

[0011] S4. Effective stiffness k of the wire rope vibration isolation system under different load conditions eff and the effective stiffness k without initial load eff The parameter α is introduced into the normalized model in S3 according to the ratio of the single-loop energy dissipation area E under different load conditions of the wire rope vibration isolation system to the single-loop energy dissipation area E without initial load. The improved normalized Bouc-Wen model is obtained and used as the hysteresis model of the wire rope vibration isolation system without negative stiffness device, thus completing the establishment of the mechanical model.

[0012] Among them, the effective stiffness k eff The calculation formula (1) is as follows:

[0013]

[0014] In formula (1), It represents the maximum positive displacement during a tension-compression cycle of the wire rope isolation system; Indicates the minimum negative displacement of the wire rope vibration isolation system during a tension and compression cycle; F + Indicates the force corresponding to the maximum positive displacement; F - Indicates the force corresponding to the minimum negative displacement;

[0015] The single-loop energy consumption area E represents the area enclosed by the hysteresis curve under one tension and compression cycle of the wire rope vibration isolation system.

[0016] The method for establishing the mechanical model of the airborne equipment vibration isolation system of the present invention is to obtain the normalized Bouc-Wen model of the wire rope vibration isolation system and then calculate the effective stiffness k of the wire rope vibration isolation system under different load conditions. eff and the effective stiffness k without initial load eff The parameter α is introduced into the normalized model according to the ratio of the single-loop energy dissipation area E of the wire rope vibration isolation system under different load conditions and the single-loop energy dissipation area E without initial load. The parameter β is introduced into the normalized model to obtain the improved normalized Bouc-Wen model. The improved normalized Bouc-Wen model is used as the hysteresis model of the wire rope vibration isolation system without a negative stiffness device. This mechanical model can effectively describe the mechanical characteristics of the wire rope vibration isolation system under different load conditions. There is no need to fit the mechanical models of the wire rope vibration isolation system under no load and different loads separately, which makes the fitting of the mechanical model and the subsequent calculation of the transmissibility curve simpler.

[0017] Preferably, the force F(x) generated by the negative stiffness device is superimposed on the improved normalized Bouc-Wen model to obtain a mechanical model of a high static and low dynamic wire rope vibration isolation system with a negative stiffness device.

[0018] The vibration isolation effect of the wire rope vibration isolation system can be optimized by introducing a negative stiffness device.

[0019] Preferably, the mechanical model of the high static and low dynamic wire rope vibration isolation system with a negative stiffness device includes equations (2) and (3):

[0020]

[0021] In equations (2) and (3), φ(x, t) is the restoring force generated by the high-static-low-dynamic wire rope vibration isolation system; N is the order of the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; i is the degree of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; α is the effective stiffness k of the wire rope vibration isolation system under different load conditions. eff and the effective stiffness k without initial load eff ratio; k eiis the coefficient of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system under no load; x represents the deformation of the high-static-low-dynamic wire rope vibration isolation system; M is the order of the polynomial corresponding to the amplification coefficient of the high-static-low-dynamic wire rope vibration isolation system; j is the degree of the monomial in the polynomial corresponding to the amplification coefficient of the high-static-low-dynamic wire rope vibration isolation system; k nj is the coefficient of the monomial in the polynomial corresponding to the amplification factor of the high static and low dynamic wire rope vibration isolation system; β is the ratio of the single-loop energy dissipation area E under different load conditions of the wire rope vibration isolation system to the single-loop energy dissipation area E without initial load; z is a hysteresis component that satisfies equation (3); F(x) represents the force generated by the negative stiffness device; t represents time; represents the derivative of z with respect to time t; represents the derivative of the deformation x with respect to time t; sgn() represents the step function; σ, ρ, and n are the parameters of the standardized Bouc-Wen model.

[0022] Preferably, in step S4, parameters α and β of at least two load conditions are obtained through experiments, and then parameters α and β of intermediate adjacent load conditions are obtained by interpolation based on parameters α and β of adjacent load conditions.

[0023] The at least two load conditions include a no initial load condition.

[0024] It is possible to avoid the need to obtain the parameters α and β for each load condition through experiments.

[0025] Preferably, the values ​​of parameters α and β under three different load conditions are obtained through experiments and are assigned as follows:

[0026]

[0027] Among them, I represents the serial number, K effI and E I They respectively represent the effective stiffness and single-turn energy dissipation area of ​​the wire rope vibration isolation system under different loads when the amplitude is 5 mm.

[0028] In another aspect, the present invention provides a method for optimizing the design of a mechanical model of an airborne equipment vibration isolation system, comprising the following steps:

[0029] S01: Based on the improved normalized Bouc-Wen model established by the method for establishing a mechanical model of an airborne equipment vibration isolation system, the transmissibility curve of the wire rope vibration isolation system is calculated using the fourth-order Runge-Kutta method; the low-frequency interference w is determined based on the transmissibility curve. u Transmissibility T u Is it less than T targ If T u <T targ, it can be determined that the model and quantity of the wire rope vibration isolation components can meet the target vibration isolation requirements, and the optimization design is completed; if T u >T targ , enter S02;

[0030] S02: Optimize and adjust the number of wire rope vibration isolation components, and ensure that the static load deformation Ds of the adjusted new wire rope vibration isolation system is ≤ 5mm, and then proceed to S03; if the number of wire rope vibration isolation components cannot be adjusted to ensure that the static load deformation Ds of the new wire rope vibration isolation system is less than or equal to 5mm, skip S03 and proceed directly to S04;

[0031] S03: Calculate new α and β based on the ratio of the number of wire rope vibration isolation components Q2 after adjustment to the number of wire rope vibration isolation components Q1 before adjustment, then obtain the new improved normalized Bouc-Wen model, and then calculate the transmissibility curve of the new wire rope vibration isolation system through the fourth-order Runge-Kutta method. According to the transmissibility curve of the new wire rope vibration isolation system, determine the low-frequency interference w u Transmissibility T u Is it less than T targ If T u <T targ , it can be determined that the model and quantity of the wire rope vibration isolation components can meet the target vibration isolation requirements, and the optimization design is completed; if T u >T targ , proceed to step S04;

[0032] S04: Optimize the parameters of the negative stiffness device, calculate the transmissibility curve of the high static and low dynamic wire rope vibration isolation system by the fourth-order Runge-Kutta method, and judge the low-frequency interference w according to the transmissibility curve of the high static and low dynamic wire rope vibration isolation system. u Transmissibility T u Is it less than T targ If T u <T targ , it can be determined that the model, quantity and parameters of the optimized negative stiffness device of the wire rope vibration isolation assembly can meet the target vibration isolation requirements, and the optimization design is completed; if T u >T targ , enter S05;

[0033] S05: Select a new model of wire rope vibration isolation assembly and repeat steps S01-S05 until the low-frequency interference w u Transmissibility T u <T targ .

[0034] Based on a model established using a mechanical modeling method for airborne equipment vibration isolation systems, the transmissibility curves of a wire rope vibration isolation system and a high-static-low-dynamic wire rope vibration isolation system under different load conditions were calculated using the fourth-order Runge-Kutta method. Based on the transmissibility curves under different loads, the optimal parameters α and β were optimized. The force F(x) generated by the negative stiffness device was added to the normalized Bouc-Wen model under the optimal parameters, resulting in a normalized Bouc-Wen model that describes the high-static-low-dynamic wire rope vibration isolation system. By varying the force F(x) generated by the negative stiffness device, transmissibility curves for the high-static-low-dynamic wire rope vibration isolation system under different negative stiffness values ​​were obtained. Based on the transmissibility curves under different negative stiffness values, the optimal negative stiffness value was optimized.

[0035] Preferably, the method for calculating the transmissibility curve of the high-static and low-dynamic wire rope vibration isolation system using the fourth-order Runge-Kutta method is:

[0036] First, use formula (4) to give the basic excitation x g , and use formula (5) to calculate the deformation x of the wire rope vibration isolation system, and then according to the deformation x of the wire rope vibration isolation system and the foundation excitation x g Obtain the absolute response x of the isolated object under external excitation at different frequencies abs , and then use formula (6) to get the transmissibility T at different frequencies. According to the transmissibility T at different frequencies, the transmissibility curve of the high static and low dynamic wire rope vibration isolation system can be obtained;

[0037] x g =A g cos(2πft) (4)

[0038]

[0039] T=Amp[x abs ] / Amp[x g ] (6)

[0040] In formula (4), formula (5) and formula (6): x g Indicates basic incentive; A g represents the excitation amplitude; f is the excitation frequency; t represents time; x represents the deformation of the high-static and low-dynamic wire rope vibration isolation system; represents the derivative of deformation x with respect to time t; represents the second-order derivative of the deformation x with respect to time t; N is the order of the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; i is the degree of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; α is the effective stiffness k of the wire rope vibration isolation system under different load conditions eff and the effective stiffness k without initial load eff ratio; kei is the coefficient of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system under no load; x represents the deformation of the high-static-low-dynamic wire rope vibration isolation system; M is the order of the polynomial corresponding to the amplification coefficient of the high-static-low-dynamic wire rope vibration isolation system; j is the degree of the monomial in the polynomial corresponding to the amplification coefficient of the high-static-low-dynamic wire rope vibration isolation system; k nj is the coefficient of the monomial in the polynomial corresponding to the amplification factor of the high static and low dynamic wire rope vibration isolation system; β is the ratio of the single-loop energy dissipation area E under different load conditions of the wire rope vibration isolation system to the single-loop energy dissipation area E without initial load; z is a hysteresis component that satisfies equation (3); F(x) represents the force generated by the negative stiffness device; m represents the mass of the object to be isolated; represents the second-order derivative of the fundamental excitation with respect to time; represents the derivative of z with respect to time t; sgn() represents the step function; σ, ρ, and n are the parameters of the standardized Bouc-Wen model; T represents the transmissibility; Amp[·] represents the amplitude of the steady-state response; x abs Indicates the absolute response of the object being isolated.

[0041] Preferably, in step S03, the steps of calculating new α and β according to the ratio of the number Q2 of the wire rope vibration isolation assemblies after adjustment to the number Q1 of the wire rope vibration isolation assemblies before adjustment are:

[0042] The equivalent load of the new wire rope vibration isolation system is obtained based on the ratio of the number of wire rope vibration isolation components Q2 after adjustment to the number of wire rope vibration isolation components Q1 before adjustment -m eq g, equivalent load-m eq The conversion formula (7) of g is as follows:

[0043] -m eq g=-m t gQ1 / Q2 (7)

[0044] Where: -m eq g represents the equivalent load; g represents the acceleration of gravity; Q1 is the number of wire rope vibration isolation components in the preliminary design, and Q2 is the number of wire rope vibration isolation components after optimization;

[0045] Based on equivalent load-m eq g, according to the parameters α and β under different initial states, the equivalent load -m is interpolated eq α under g eq and β eq , based on α eq and β eq The two parameters α2 and β2 of the improved normalized Bouc-Wen of the new wire rope vibration isolation system are obtained. The calculation formulas of α2 and β2 are as follows:

[0046] α2=Q2α eq / Q1;β2=Q2β eq / Q1.

[0047] Preferably, in step S04 , the parameters of the negative stiffness device are optimized to obtain the maximum negative stiffness.

[0048] Preferably, the method for optimizing the parameters of the negative stiffness device to obtain the maximum negative stiffness is:

[0049] The elastic restoring force R(x) of the high static and low dynamic wire rope vibration isolation system can be obtained by adding the nonlinear elastic restoring force of the new wire rope vibration isolation system and the force F(x) generated by the negative stiffness device. The calculation formula of R(x) is as follows (8):

[0050]

[0051] The optimization criterion for the parameters of the negative stiffness device is that the total stiffness R'(x) is the maximum relative displacement response D rmax There are no negative numbers in the equation, and the optimization standard is the following formula (9):

[0052]

[0053] Based on formula (9), the parameters of the negative stiffness device are iterated to obtain the maximum negative stiffness, while ensuring that the total stiffness meets the conditions in formula (10), which is:

[0054] R'(x)>0where,x∈[-D rmax ,D rmax ] (10)

[0055] Where R(x) is the elastic restoring force of the high static and low dynamic wire rope vibration isolation system; the total stiffness R'(x) is obtained by taking the derivative of the elastic restoring force R(x) with respect to x; D rmax is the maximum relative displacement during the vibration process; α2 is the new wire rope vibration isolation system under a load of -m t g condition; x represents the deformation of the high-static-low-dynamic wire rope vibration isolation system; N is the order of the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; i is the degree of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; α is the effective stiffness k of the wire rope vibration isolation system under different load conditions eff and the effective stiffness k without initial load eff ratio; k ei It is the coefficient of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high static and low dynamic wire rope vibration isolation system under no load; F(x) represents the force generated by the negative stiffness device.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] 1. The present invention provides a method for establishing a mechanical model of an airborne equipment vibration isolation system, according to the effective stiffness k of the wire rope vibration isolation system under different load conditions. eff and the effective stiffness k without initial load eff The parameter α is introduced into the normalized model according to the ratio of the single-loop energy dissipation area E of the wire rope vibration isolation system under different load conditions and the single-loop energy dissipation area E without initial load. The parameter β is introduced into the normalized model to obtain the improved normalized Bouc-Wen model. The improved normalized Bouc-Wen model is used as the hysteresis model of the wire rope vibration isolation system without a negative stiffness device. This mechanical model can effectively describe the mechanical characteristics of the wire rope vibration isolation system under different load conditions. There is no need to fit the mechanical models of the wire rope vibration isolation system under no load and different loads separately, which makes the fitting of the mechanical model and the subsequent calculation of the transmissibility curve simpler.

[0058] 2. The present invention provides an optimization design method for the mechanical model of the airborne equipment vibration isolation system, so that the number, model, and negative stiffness device parameters of the optimized wire rope vibration isolation components meet the airborne equipment vibration isolation target and provide sufficient gain effect without compromising the system stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a schematic diagram of the layout of the onboard equipment;

[0060] Figure 2 This is a schematic diagram of a high-static, low-dynamic wire rope vibration isolation system;

[0061] Figure 3 This is a calculation diagram of a high-static, low-dynamic wire rope vibration isolation system;

[0062] Figure 4 is the cross-sectional view of the negative stiffness device;

[0063] Figure 5 It is a schematic diagram of the calculation of the negative stiffness device;

[0064] Figure 6 is the force-displacement curve of the negative stiffness device;

[0065] Figure 7 It is a comparison chart of the test results and the improved normalized Bouc-Wen model fitting results;

[0066] Figure 8 This is the optimization flow chart of the high static and low dynamic wire rope vibration isolation system;

[0067] Figure 9 is the quasi-static test curve of the wire rope isolator;

[0068] Figure 10 This is a schematic diagram of the optimized high-static and low-dynamic wire rope vibration isolation system;

[0069] Figure 11 It is a diagram of vibration isolation effects in different states during the optimization process.

[0070] Markings in the figure: 1. Aircraft; 2. Airborne equipment; 3. High-static, low-dynamic wire rope vibration isolation system; 4. Negative stiffness device; 31. Wire rope vibration isolation assembly; 32. Upper aluminum part; 33. Lower aluminum part; 34. Bolt; 41. Ring-shaped NdFeB permanent magnet; 42. Acrylic tube; 43. Center movable rod; 44. Round aluminum plate. DETAILED DESCRIPTION

[0071] The present invention will be further described in detail below with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments, as all technologies implemented based on the present invention fall within the scope of the present invention.

[0072] Unless otherwise specified, in the description of the specific embodiments of the present invention, the terms indicating the orientation or positional relationship, such as "upper", "lower", "left", "right", "center", "inside", and "outside", are based on the expressions of the orientation or positional relationship shown in the accompanying drawings, or are the orientation or positional relationship in which the invented product / device / apparatus is placed when it is conventionally used. These terms of orientation or positional relationship are merely for the purpose of facilitating the description of the scheme of the present invention or simplifying the description of the specific embodiments to facilitate the rapid understanding of the scheme by technicians, and do not indicate or imply that a specific device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship, and therefore should not be understood as limiting the present invention.

[0073] In addition, if the terms "horizontal", "vertical", "overhanging", "parallel" and the like appear, it does not mean that the corresponding devices / components / elements are required to be absolutely horizontal or vertical or overhanging or parallel, but may be slightly tilted or have deviations. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but may be slightly tilted. Alternatively, it can be simply understood that the corresponding devices / components / elements are set in directions such as "horizontal", "vertical", "overhanging", and "parallel", and can have an error / deviation of ±10% relative to the corresponding direction setting, more preferably an error / deviation within ±8%, more preferably an error / deviation within ±6%, more preferably an error / deviation within ±5%, and more preferably an error / deviation within ±4%. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its role in the solution of the present invention.

[0074] In addition, the expressions “first”, “second”, “third”, etc. in the terms are merely used to distinguish the description of the same or similar components, and should not be understood as emphasizing or implying the relative importance of specific components.

[0075] In addition, in the description of the embodiments of the present invention, "several," "plurality," and "a number" represent at least two. It can also be any number such as two, three, four, five, six, seven, eight, nine, or even more than nine.

[0076] In addition, in the description of the technical solution of the present invention, unless otherwise clearly specified / defined / restricted, the terms "set", "install", "connect", "connected", "provided with", "laid", and "arranged" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection, and can be welding, riveting, bolting, threaded connection, and other commonly used connection means in the field.

[0077] Example 1

[0078] like Figure 1 As shown, the airborne equipment vibration isolation system employs a wire rope vibration isolation system, which is installed between airborne equipment 2 and aircraft 1. Aircraft 1 carries airborne equipment 2. The wire rope vibration isolation system includes a wire rope vibration isolation assembly 31, an upper aluminum component 32, a lower aluminum component 33, and several bolts 34. The upper and lower ends of the wire rope vibration isolation assembly 31 are connected to the upper and lower aluminum components 32, 33 via bolts 34. The upper aluminum component 32 is connected to aircraft 1, and the lower aluminum component 33 is connected to airborne equipment 2. The wire rope vibration isolation assembly 31 is each individual wire rope vibration isolator in the wire rope vibration isolation system and can be a butterfly-shaped wire rope vibration isolator, a T-shaped wire rope vibration isolator, or the like.

[0079] The airborne equipment vibration isolation system may also include a negative stiffness device 4, such as Figure 2 As shown, the negative stiffness device 4 is arranged between the upper aluminum part 32 and the lower aluminum part 33. The negative stiffness device 4 can reduce the stiffness of the wire rope vibration isolation system. Figure 2 As shown in , the steel wire rope of the steel wire rope vibration isolation system can be deformed and isolated in the vertical direction, and the negative stiffness device 4 can reduce the difficulty of the steel wire rope being deformed and isolated in the vertical direction.

[0080] This embodiment provides a method for establishing a mechanical model of an airborne equipment vibration isolation system, comprising the following steps:

[0081] S1. Identify the low-frequency interference frequency w to which the airborne equipment is subjected u , mass of airborne equipment m t , the layout space of airborne equipment and the payload of the aircraft;

[0082] S2, according to the low-frequency interference frequency w u, mass of airborne equipment m t , the layout space of airborne equipment, the payload of the aircraft, the nominal load of the wire rope vibration isolation assembly and the average stiffness of the wire rope vibration isolation assembly under static load conditions to preliminarily determine the model and quantity Q1 of the wire rope vibration isolation assembly in the wire rope vibration isolation system;

[0083] S3, based on the wire rope vibration isolation components of the model and quantity Q1 preliminarily determined in S2, a wire rope vibration isolation system is obtained, and then a dynamic test is performed on the wire rope vibration isolation system to obtain a dynamic test curve. The dynamic test curve is as follows: Figure 6 As shown in the figure, the normalized Bouc-Wen model of the wire rope vibration isolation system is obtained according to the dynamic test curve;

[0084] S4. Effective stiffness k of the wire rope vibration isolation system under different load conditions eff and the effective stiffness k without initial load eff The parameter α is introduced into the normalized model in S3 according to the ratio of the single-loop energy consumption area E under different load conditions of the wire rope vibration isolation system to the single-loop energy consumption area E without initial load. The improved normalized Bouc-Wen model is obtained and the improved normalized Bouc-Wen model is used as the hysteresis model of the wire rope vibration isolation system without negative stiffness device to complete the establishment of the mechanical model. The hysteresis model of the wire rope vibration isolation system without negative stiffness device includes the following formula:

[0085]

[0086] In the hysteresis model, φ(x, t) is the restoring force generated by the wire rope vibration isolation system; N is the order of the polynomial corresponding to the nonlinear elastic restoring force of the wire rope vibration isolation system; i is the degree of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the wire rope vibration isolation system; α is the effective stiffness k of the wire rope vibration isolation system under different load conditions. eff and the effective stiffness k without initial load eff ratio; k ei is the coefficient of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the wire rope vibration isolation system under no load; x represents the deformation of the wire rope vibration isolation system; M is the order of the polynomial corresponding to the amplification coefficient of the wire rope vibration isolation system; j is the degree of the monomial in the polynomial corresponding to the amplification coefficient of the wire rope vibration isolation system; k nj is the coefficient of the monomial in the polynomial corresponding to the amplification coefficient of the wire rope vibration isolation system; β is the ratio of the single-loop energy dissipation area E under different load conditions of the wire rope vibration isolation system to the single-loop energy dissipation area E without initial load; z is a hysteresis component that satisfies equation (3); t represents time; represents the derivative of z with respect to time t; represents the derivative of the deformation x with respect to time t; sgn() represents the step function; σ, ρ, and n are the parameters of the standardized Bouc-Wen model.

[0087] Among them, the effective stiffness k eff The calculation formula (1) is as follows:

[0088]

[0089] In formula (1), It represents the maximum positive displacement during a tension-compression cycle of the wire rope isolation system; Indicates the minimum negative displacement of the wire rope vibration isolation system during a tension and compression cycle; F + Indicates the force corresponding to the maximum positive displacement; F - Indicates the force corresponding to the minimum negative displacement;

[0090] The single-loop energy consumption area E represents the area enclosed by the hysteresis curve of a wire rope vibration isolation system under a tension and compression cycle, such as Figure 7 Each area enclosed by the same color and line type is the corresponding single-circle energy consumption area E.

[0091] In step S4, parameters α and β of at least two load conditions are obtained through experiments, and then parameters α and β of intermediate adjacent load conditions are obtained by interpolation based on parameters α and β of adjacent load conditions.

[0092] The at least two load conditions include a no initial load condition, which can avoid the need to obtain the parameters α and β for each load condition through experiments.

[0093] For example, the values ​​of parameters α and β under three different load conditions are obtained through experiments and are assigned to the following Table 1:

[0094] Table 1. Parameters α and β under different load conditions

[0095]

[0096] Among them, I represents the serial number, K effI and E I They respectively represent the effective stiffness and single-turn energy dissipation area of ​​the wire rope vibration isolation system under different loads when the amplitude is 5 mm.

[0097] That is, by interpolating between -50 and -80, the values ​​of α and β of the wire rope vibration isolation system under a -65N load condition when the amplitude is 5mm can be obtained. Therefore, there is no need to conduct experiments to obtain the values ​​of α and β of the wire rope vibration isolation system under a -65N load condition when the amplitude is 5mm. By substituting the values ​​of α and β of the wire rope vibration isolation system under a -65N load condition when the amplitude is 5mm into the hysteresis model, the mechanical model under the -65N load condition can be obtained. This method avoids refitting the mechanical model under the -65N load condition.

[0098] The method for establishing the mechanical model of the airborne equipment vibration isolation system in this embodiment is to obtain the normalized Bouc-Wen model of the wire rope vibration isolation system according to the effective stiffness k of the wire rope vibration isolation system under different load conditions. eff and the effective stiffness k without initial load eff The parameter α is introduced into the normalized model based on the ratio of the single-loop energy dissipation area E under different load conditions of the wire rope vibration isolation system to the single-loop energy dissipation area E without initial load. The parameter β is also introduced into the normalized model to obtain the improved normalized Bouc-Wen model. The improved normalized Bouc-Wen model is used as the hysteresis model of the wire rope vibration isolation system without a negative stiffness device. This mechanical model can effectively describe the mechanical characteristics of the wire rope vibration isolation system under different load conditions. There is no need to fit the mechanical models of the wire rope vibration isolation system under no load and different loads separately, which makes the fitting of the mechanical model and the subsequent calculation of the transmissibility curve simpler. Based on the above mechanical model, the transmissibility curve of the wire rope vibration isolation system can be calculated using the fourth-order Runge-Kutta method.

[0099] In some embodiments, the force F(x) generated by the negative stiffness device is superimposed on the improved normalized Bouc-Wen model to obtain a mechanical model of the high static and low dynamic wire rope vibration isolation system 3 with the negative stiffness device.

[0100] The mechanical model of the high static and low dynamic wire rope vibration isolation system 3 with a negative stiffness device includes equations (2) and (3):

[0101]

[0102] In equations (2) and (3), φ(x, t) is the restoring force generated by the high-static-low-dynamic wire rope vibration isolation system; N is the order of the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; i is the degree of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; α is the effective stiffness k of the wire rope vibration isolation system under different load conditions. eff and the effective stiffness k without initial load eff ratio; k eiis the coefficient of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system under no load; x represents the deformation of the high-static-low-dynamic wire rope vibration isolation system; M is the order of the polynomial corresponding to the amplification coefficient of the high-static-low-dynamic wire rope vibration isolation system; j is the degree of the monomial in the polynomial corresponding to the amplification coefficient of the high-static-low-dynamic wire rope vibration isolation system; k nj is the coefficient of the monomial in the polynomial corresponding to the amplification factor of the high static and low dynamic wire rope vibration isolation system; β is the ratio of the single-loop energy dissipation area E under different load conditions of the wire rope vibration isolation system to the single-loop energy dissipation area E without initial load; z is a hysteresis component that satisfies equation (3); F(x) represents the force generated by the negative stiffness device; t represents time; represents the derivative of z with respect to time t; represents the derivative of the deformation x with respect to time t; sgn() represents the step function; σ, ρ, and n are the parameters of the standardized Bouc-Wen model.

[0103] Example 2

[0104] The initial design of the wire rope vibration isolation system ignored the effects of varying loads and the differences between dynamic and static stiffness. Therefore, there is room for optimization. If the negative stiffness provided by the negative stiffness device is too small, the added benefit to the vibration isolation performance will be minimal. Conversely, if the negative stiffness provided by the negative stiffness device is too large, the high-static, low-dynamic wire rope vibration isolation system will become unstable and ineffective in isolating vibrations. Therefore, there exists an optimal negative stiffness value that provides sufficient gain without compromising system stability.

[0105] See also Figure 8 , an optimization design method for a mechanical model of an airborne equipment vibration isolation system, comprising the following steps:

[0106] S01: Based on the improved normalized Bouc-Wen model established by the method for establishing a mechanical model of an airborne equipment vibration isolation system, the transmissibility curve of the wire rope vibration isolation system is calculated using the fourth-order Runge-Kutta method; the low-frequency interference w is determined based on the transmissibility curve. u Transmissibility T u Is it less than T targ If T u <T targ , it can be determined that the model and quantity of the wire rope vibration isolation components can meet the target vibration isolation requirements, and the optimization design is completed; if T u >T targ , enter S02;

[0107] The method for calculating the transmissibility curve of the high static and low dynamic wire rope vibration isolation system using the fourth-order Runge-Kutta method is as follows:

[0108] First, use formula (4) to give the basic excitation x g (Basic incentive x g is a time-varying variable), and the deformation x of the wire rope vibration isolation system is calculated using formula (5) (i.e., relative response, the deformation x is also a time-varying variable), and then the deformation x of the wire rope vibration isolation system is compared with the foundation excitation x. g Obtain the absolute response x of the isolated object under external excitation at different frequencies abs , which is the basic incentive x that changes over time g Added to the deformation x, the absolute response x of the isolated object under external excitation at different frequencies is obtained. abs ,like Figure 3 As shown, by connecting the wire rope vibration isolation system and the negative stiffness device to the ground to simulate the connection to the aircraft 1, the test process is simplified; then, the formula (6) is used to obtain the transmissibility T at different frequencies. According to the transmissibility T at different frequencies, the transmissibility curve of the high static and low dynamic wire rope vibration isolation system can be obtained;

[0109] x g =A g cos(2πft) (4)

[0110]

[0111] T=Amp[x abs ] / Amp[x g ] (6)

[0112] In formula (4), formula (5) and formula (6): x g Indicates basic incentive; A g represents the excitation amplitude; f is the excitation frequency; t represents time; x represents the deformation of the high-static and low-dynamic wire rope vibration isolation system; represents the derivative of deformation x with respect to time t; represents the second-order derivative of the deformation x with respect to time t; N is the order of the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; i is the degree of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; α is the effective stiffness k of the wire rope vibration isolation system under different load conditions eff and the effective stiffness k without initial load eff ratio; k ei is the coefficient of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system under no load; x represents the deformation of the high-static-low-dynamic wire rope vibration isolation system; M is the order of the polynomial corresponding to the amplification coefficient of the high-static-low-dynamic wire rope vibration isolation system; j is the degree of the monomial in the polynomial corresponding to the amplification coefficient of the high-static-low-dynamic wire rope vibration isolation system; k njis the coefficient of the monomial in the polynomial corresponding to the amplification factor of the high static and low dynamic wire rope vibration isolation system; β is the ratio of the single-loop energy dissipation area E under different load conditions of the wire rope vibration isolation system to the single-loop energy dissipation area E without initial load; z is a hysteresis component that satisfies equation (3); F(x) represents the force generated by the negative stiffness device; m represents the mass of the object to be isolated; represents the second-order derivative of the fundamental excitation with respect to time; represents the derivative of z with respect to time t; sgn() represents the step function; σ, ρ, and n are the parameters of the standardized Bouc-Wen model; T represents the transmissibility; Amp[·] represents the amplitude of the steady-state response; x abs Indicates the absolute response of the object being isolated.

[0113] S02: Optimize and adjust the number of wire rope vibration isolation components, and ensure that the static load deformation Ds of the adjusted new wire rope vibration isolation system is ≤ 5mm, and then proceed to S03; if the adjustment of the number of wire rope vibration isolation components cannot make the static load deformation Ds of the new wire rope vibration isolation system less than or equal to 5mm, skip S03 and proceed directly to S04. That is, if the static load deformation Ds of the new wire rope vibration isolation system is greater than 5mm regardless of the adjustment of the number of wire rope vibration isolation components, proceed directly to S04 to optimize the parameters of the negative stiffness device;

[0114] S03: Calculate new α and β based on the ratio of the number of wire rope vibration isolation components Q2 after adjustment to the number of wire rope vibration isolation components Q1 before adjustment, then obtain the new improved normalized Bouc-Wen model, and then calculate the transmissibility curve of the new wire rope vibration isolation system through the fourth-order Runge-Kutta method. According to the transmissibility curve of the new wire rope vibration isolation system, determine the low-frequency interference w u Transmissibility T u Is it less than T targ If T u <T targ , it can be determined that the model and quantity of the wire rope vibration isolation components can meet the target vibration isolation requirements, and the optimization design is completed; if T u >T targ , proceed to step S04;

[0115] In step S03, the steps of calculating new α and β according to the ratio of the number Q2 of wire rope vibration isolation assemblies after adjustment to the number Q1 of wire rope vibration isolation assemblies before adjustment are as follows:

[0116] The equivalent load of the new wire rope vibration isolation system is obtained based on the ratio of the number of wire rope vibration isolation components Q2 after adjustment to the number of wire rope vibration isolation components Q1 before adjustment -m eq g, equivalent load-m eq The conversion formula (7) of g is as follows:

[0117] -m eq g=-m t gQ1 / Q2 (7)

[0118] Where: -m eq g represents the equivalent load; g represents the acceleration of gravity; Q1 is the number of wire rope vibration isolation components in the preliminary design, and Q2 is the number of wire rope vibration isolation components after optimization;

[0119] Based on equivalent load-m eq g, according to the parameters α and β under different initial states, the equivalent load -m is interpolated eq α under g eq and β eq , based on α eq and β eq The two parameters α2 and β2 of the improved normalized Bouc-Wen of the new wire rope vibration isolation system are obtained. The calculation formulas of α2 and β2 are as follows:

[0120] α2=Q2α eq / Q1;β2=Q2β eq / Q1. Where α2 and β2 are the update parameters of parameters α and β, respectively, which are used to substitute into the mechanical model.

[0121] S04: Optimize the parameters of the negative stiffness device, calculate the transmissibility curve of the high static and low dynamic wire rope vibration isolation system by the fourth-order Runge-Kutta method, and judge the low-frequency interference w according to the transmissibility curve of the high static and low dynamic wire rope vibration isolation system. u Transmissibility T u Is it less than T targ If T u <T targ , it can be determined that the model, quantity and parameters of the optimized negative stiffness device of the wire rope vibration isolation assembly can meet the target vibration isolation requirements, and the optimization design is completed; if T u >T targ , enter S05;

[0122] Negative stiffness devices such as Figure 4As shown, the negative stiffness device includes an annular NdFeB permanent magnet 41, an acrylic tube 42, a central movable rod 43 and a circular aluminum plate 44. The central movable rod 43 is arranged along the axial direction of the acrylic tube 42. Circular aluminum plates 44 are provided at both ends of the acrylic tube 42. The circular aluminum plate 44 at the upper end has a through hole. The central movable rod 43 passes through the through hole of the circular aluminum plate 44 and enters the acrylic tube 42. An annular NdFeB permanent magnet 41 is fixed in both ends of the acrylic tube 42. The central movable rod 43 enters the acrylic tube 42. An annular NdFeB permanent magnet 41 is provided at one end, and the other end of the central movable rod 43 is connected to the deformed end of the wire rope vibration isolation system. The circular aluminum plate 44 at the lower end is connected to the other end of the deformed wire rope vibration isolation system. The axial movement of the central movable rod 43 is used to drive the middle annular NdFeB permanent magnet 41 to move, and the attraction and repulsion between the upper and lower ends of the annular NdFeB permanent magnet 41 and the middle annular NdFeB permanent magnet 41 assists the axial movement of the central movable rod 43, thereby realizing the negative stiffness of the wire rope vibration isolation system.

[0123] In a preferred embodiment, in step S04 , the parameters of the negative stiffness device are optimized to obtain the maximum negative stiffness.

[0124] The method for optimizing the parameters of the negative stiffness device to obtain the maximum negative stiffness is:

[0125] The elastic restoring force R(x) of the high static and low dynamic wire rope vibration isolation system can be obtained by adding the nonlinear elastic restoring force of the new wire rope vibration isolation system and the force F(x) generated by the negative stiffness device. The calculation formula of R(x) is as follows (8):

[0126]

[0127] The optimization criterion for the parameters of the negative stiffness device is that the total stiffness R'(x) is the maximum relative displacement response D rmax There are no negative numbers in the equation, and the optimization standard is the following formula (9):

[0128]

[0129] Based on formula (9), the parameters of the negative stiffness device are iterated to obtain the maximum negative stiffness, while ensuring that the total stiffness meets the conditions in formula (10), which is:

[0130] R'(x)>0where,x∈[-D rmax ,D rmax ] (10)

[0131] Where R(x) is the elastic restoring force of the high static and low dynamic wire rope vibration isolation system; the total stiffness R'(x) is obtained by taking the derivative of the elastic restoring force R(x) with respect to x; D rmaxis the maximum relative displacement during the vibration process; α2 is the new wire rope vibration isolation system under a load of -m t g condition; x represents the deformation of the high-static-low-dynamic wire rope vibration isolation system; N is the order of the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; i is the degree of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; α is the effective stiffness k of the wire rope vibration isolation system under different load conditions eff and the effective stiffness k without initial load eff ratio; k ei It is the coefficient of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high static and low dynamic wire rope vibration isolation system under no load; F(x) represents the force generated by the negative stiffness device.

[0132] The optimization method mentioned in this embodiment, such as Figure 8 As shown, the low-frequency interference w is determined according to the external excitation characteristics u ; Target transmission rate T at the interference frequency targ ; According to the mass m of the onboard equipment t , determine the initial state -m t g. Using equations (4), (5), and (6), the transmissibility curve of the wire rope vibration isolation system obtained in the preliminary design can be determined, which can be used to determine the low-frequency interference w u Is the transmission rate at less than T targ If T u1 <T targ , we can determine that the model and quantity of wire rope vibration isolation components can meet the target vibration isolation requirements. u1 >T targ , the number of wire rope vibration isolation components should be optimized while meeting the static load deformation requirements to achieve better isolation performance.

[0133] Adjust the number of wire rope vibration isolation components to Q2, and ensure that the adjusted wire rope vibration isolation system complies with the static load deformation (D s ≤5mm). The mechanical performance of the wire rope vibration isolation system is proportional to the number of wire rope vibration isolation components.

[0134] By reducing the number of wire rope vibration isolation components without changing the model of the components, the equivalent load (-m eq g). The conversion formula (7) is as follows:

[0135] -m eq g=-m t gQ1 / Q2 (7)

[0136] Where -m eq g represents the equivalent load; g represents the acceleration of gravity; Q1 is the number of wire rope vibration isolation components in the preliminary design, and Q2 is the number of wire rope vibration isolation components after optimization.

[0137] According to the equivalent load-m eq g, and the α and β parameter tables under different initial states to obtain α under the equivalent initial state eq and β eq After that, based on α eq and β eq The two important parameters of the improved normalized Bouc-Wen of the new wire rope vibration isolation system can be further obtained: α2 = Q2α eq / Q1 and β2 = Q2β eq / Q1.

[0138] Use equations (4), (5) and (6) to obtain the transmissibility curve of the new wire rope vibration isolation system to determine whether it meets the requirements. u2 <T targ , the model and quantity of the wire rope vibration isolation components in the new wire rope vibration isolation system can be confirmed. u2 >T targ , a negative stiffness device should be added to further improve the isolation performance.

[0139] As shown in formula (8), the elastic restoring force R(x) of the high static and low dynamic wire rope vibration isolation system can be obtained by adding the elastic restoring force of the new wire rope vibration isolation system and the force generated by the negative stiffness device.

[0140] The total stiffness R'(x) is obtained by differentiating the elastic restoring force R(x). The optimization criterion for the parameters of the negative stiffness device is that the total stiffness R'(x) is the maximum relative displacement response D rmax There are no negative numbers in , and the optimization standard is formula (9).

[0141] Based on the above principles, the parameters of the negative stiffness device can be iterated to obtain the maximum negative stiffness while ensuring that the total stiffness satisfies the conditions in equation (10).

[0142]

[0143] R'(x)>0where,x∈[-D rmax ,D rmax ] (10)

[0144] Where R(x) is the elastic restoring force of the high static and low dynamic wire rope vibration isolation system; the total stiffness R'(x) is obtained by taking the derivative of the elastic restoring force R(x) with respect to x; D rmax is the maximum relative displacement during the vibration process; α2 is the new wire rope vibration isolation system under a load of -mt g condition; x represents the deformation of the high-static-low-dynamic wire rope vibration isolation system; N is the order of the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; i is the degree of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; α is the effective stiffness k of the wire rope vibration isolation system under different load conditions eff and the effective stiffness k without initial load eff ratio; k ei It is the coefficient of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high static and low dynamic wire rope vibration isolation system under no load; F(x) represents the force generated by the negative stiffness device.

[0145] Calculate the transmissibility curve of the high static and low dynamic wire rope vibration isolation system. If T u3 <T targ , then the model and quantity of the wire rope vibration isolation assembly and the parameters of the negative stiffness device can be determined. u3 >T targ , you need to reselect a new wire rope vibration isolation assembly model. The new wire rope vibration isolation assembly model should have a lower average static load stiffness while meeting the aircraft payload and layout space requirements. After selecting a new wire rope vibration isolation assembly model, repeat the above steps until the optimized wire rope vibration isolation assembly quantity, model, and negative stiffness device parameters meet the airborne equipment vibration isolation target.

[0146] This embodiment also provides a practical optimization case. According to the previous research, it is confirmed that the low-frequency interference frequency w of the airborne equipment is u is 16Hz; the mass of the airborne equipment m t The weight of the wire rope vibration isolation system is 5kg. Considering the layout space of the airborne equipment and the payload of the aircraft, referring to the "Specifications for Wire Rope Vibration Isolation Systems for Ships", the number of wire rope vibration isolation components in the preliminary designed wire rope vibration isolation system is determined to be Q1, which is equal to 4. The model of the wire rope vibration isolation component is ALJ835400.

[0147] First, the improved normalized Bouc-Wen model is obtained according to the dynamic test curve. The improved normalized Bouc-Wen model includes the following formulas (2) and (3);

[0148]

[0149] where α and β are the effective stiffness k of the wire rope vibration isolation system under different load conditions. eff and the single-turn energy dissipation area E relative to the effective stiffness k in the no-load state effand the ratio of the single-loop energy dissipation area E; x represents the deformation of the high-static-low-dynamic wire rope vibration isolation system; t represents time; φ(x, t) is the restoring force generated by the high-static-low-dynamic wire rope vibration isolation system; N and M are the orders of the nonlinear elastic restoring force and the amplification coefficient, respectively; k ei and k nj are the parameters of the nonlinear elastic restoring force and amplification coefficient under no load, respectively; F(x) represents the force generated by the negative stiffness device. When F(x) is equal to 0, the above expressions (2) and (3) degenerate into the hysteresis model of the wire rope vibration isolation system; z is a hysteresis component that satisfies equation (3); σ, ρ, and n are the parameters of the standardized Bouc-Wen model. represents the derivative of z with respect to time t; Represents the derivative of deformation x with respect to time t; sgn() represents a step function.

[0150] First, the normalized Bouc-Wen model parameters of the improved wire rope vibration isolation system under no-load condition are as follows: N = 2; M = 1; k e0 =1.184;k e1 =13.896;k e2 =0.50; k n0 =45.413;k n1 =1.610; ρ=0.935; σ=1.698; n=1.300; α0=1; β0=1. Depend on Figure 7 It can be seen that the test curve and the model fitting curve are basically consistent, indicating that the model can well describe the mechanical properties of the wire rope vibration isolation system. eff and the single-turn energy dissipation area E relative to the effective stiffness k in the no-load state eff The ratio of the energy consumption area E of a single turn can be obtained as α1 = 0.979 and β1 = 0.984, as shown in Table 1.

[0151] Table 1. Parameters α and β under different load conditions

[0152]

[0153] Among them, I represents the serial number, K effI and E I They respectively represent the effective stiffness and single-turn energy dissipation area of ​​the wire rope vibration isolation system under different loads when the amplitude is 5 mm.

[0154] Then according to Figure 8 The performance of the wire rope vibration isolation system was optimized. The intermediate parameters obtained during the optimization process are listed in Table 2.

[0155] Table 2. Values ​​of various parameters during optimization

[0156]

[0157] In order to ensure effective isolation of low and high frequencies, the target transmission rate T is determined. targ Set to 50%. Figure 11 It can be seen that in the preliminary design, u Transmissibility T of the lower wire rope vibration isolation system u1 is 89.5%, which is greater than T targ Therefore, it is necessary to combine Figure 9 The quasi-static test curve of the wire rope vibration isolation system is optimized. The optimization process needs to meet the static load displacement D s The requirement is less than 5mm. After optimizing the number of wire rope vibration isolation components, the static load displacement of the vibration isolation system will be less than 5mm through quasi-static test curve calculation.

[0158] like Figure 10 As shown in the figure, the model of the wire rope vibration isolation component in the optimized wire rope vibration isolation system remains unchanged, and the number is adjusted to Q2, which is equal to 3. u2 The value is 51.9%, which is also greater than T targ .

[0159] Therefore, it is necessary to add a negative stiffness device to the wire rope vibration isolation system to further optimize the performance of the wire rope vibration isolation system. The negative stiffness device used in the optimization process is based on three annular permanent magnets. Figure 5 ; corresponds to Figure 3 , Figure 5 The diagram shows three annular NdFeB permanent magnets 41, one in the upper, one in the middle, and one in the lower. The parameters of the three annular NdFeB permanent magnets 41 are listed in Table 3.

[0160] Table 3 Parameters of permanent magnets in negative stiffness device

[0161] parameter <![CDATA[RPM1]]> <![CDATA[RPM2]]> <![CDATA[RPM3]]> Internal radius <![CDATA[R1=0.01]]> <![CDATA[R3=0.01]]> <![CDATA[R5=0.01]]> External radius <![CDATA[R2=0.02]]> <![CDATA[R4=0.02]]> <![CDATA[R6=0.02]]> thickness 2b＝0.01 <![CDATA[2h2=0.01]]> <![CDATA[2h3=0.01]]> Residual flux density (T) <![CDATA[B r1 =1.42]]> <![CDATA[B r2 =1.42]]> <![CDATA[B r3 =1.42]]> Relative magnetic permeability <![CDATA[μ r1 =1.03]]> <![CDATA[μ r2 =1.03]]> <![CDATA[μ r3 =1.03]]>

[0162] After the size and performance parameters of the permanent magnet are determined, the center gap h of the permanent magnet in the negative stiffness device is mainly determined. z and Z a Just optimize it. z 47mm, Z a is 23.5 mm. Equation (11) is the force provided by the negative stiffness device, and its formula is as follows:

[0163] F(x)=k1x+k2x 2 +k3x 3 ; (11)

[0165] After optimization, the coefficients in expression (11) are: opt1 =-7.77, k opt2 =-0.0039, kopt3 =-0.0014, corresponding to k1, k2 and k3 respectively, and the negative stiffness device under these three parameters is optimal. u Under the value, the transmission rate T of the high static and low dynamic wire rope vibration isolation system u3 dropped to 36.7%, lower than T targ , which meets the target requirements. In summary, through optimization, w u The transmission rate can be reduced by 52.8%, see Figure 10 .

[0166] This embodiment provides a method for optimizing the design of a mechanical model of an airborne equipment vibration isolation system, so that the number, model, and negative stiffness device parameters of the optimized wire rope vibration isolation components meet the airborne equipment vibration isolation target and provide sufficient gain effect without compromising system stability.

[0167] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for establishing a mechanical model of an airborne equipment vibration isolation system, characterized in that: The following steps are involved: S1. Identify the low-frequency interference frequency w to which the airborne equipment is subjected u , mass of airborne equipment m t , the layout space of airborne equipment and the payload of the aircraft; S2, according to the low-frequency interference frequency w u , mass of airborne equipment m t , the layout space of airborne equipment, the payload of the aircraft, the nominal load of the wire rope vibration isolation assembly and the average stiffness of the wire rope vibration isolation assembly under static load conditions to preliminarily determine the model and quantity Q1 of the wire rope vibration isolation assembly in the wire rope vibration isolation system; S3. Based on the wire rope vibration isolation components of the model and quantity Q1 preliminarily determined in S2, a wire rope vibration isolation system is obtained. Then, a dynamic test is performed on the wire rope vibration isolation system to obtain a dynamic test curve. Based on the dynamic test curve, a normalized Bouc-Wen model of the wire rope vibration isolation system is obtained. S4. Effective stiffness k of the wire rope vibration isolation system under different load conditions eff and the effective stiffness k without initial load eff The parameter α is introduced into the normalized model in S3 according to the ratio of the single-loop energy dissipation area E under different load conditions of the wire rope vibration isolation system to the single-loop energy dissipation area E without initial load. The improved normalized Bouc-Wen model is obtained and used as the hysteresis model of the wire rope vibration isolation system without negative stiffness device, thus completing the establishment of the mechanical model. Among them, the effective stiffness k eff The calculation formula (1) is as follows: In formula (1), It represents the maximum positive displacement during a tension-compression cycle of the wire rope isolation system; Indicates the minimum negative displacement of the wire rope vibration isolation system during a tension and compression cycle; F + Indicates the force corresponding to the maximum positive displacement; F - Indicates the force corresponding to the minimum negative displacement; The single-loop energy consumption area E represents the area enclosed by the hysteresis curve under one tension and compression cycle of the wire rope vibration isolation system.

2. The method for establishing a mechanical model of an airborne equipment vibration isolation system according to claim 1, characterized in that: The force F(x) generated by the negative stiffness device is superimposed on the improved normalized Bouc-Wen model to obtain the mechanical model of the high-static and low-dynamic wire rope vibration isolation system with a negative stiffness device.

3. The method for establishing a mechanical model of an airborne equipment vibration isolation system according to claim 2, characterized in that: The mechanical model of the high static and low dynamic wire rope vibration isolation system with negative stiffness device includes equations (2) and (3): In equations (2) and (3), φ(x, t) is the restoring force generated by the high-static-low-dynamic wire rope vibration isolation system; N is the order of the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; i is the degree of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high static and low dynamic wire rope vibration isolation system; α is the effective stiffness k of the wire rope vibration isolation system under different load conditions eff and the effective stiffness k without initial load eff ratio; k ei is the coefficient of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system under no load; x represents the deformation of the high-static-low-dynamic wire rope vibration isolation system; M is the order of the polynomial corresponding to the amplification coefficient of the high-static-low-dynamic wire rope vibration isolation system; j is the degree of the monomial in the polynomial corresponding to the amplification coefficient of the high-static-low-dynamic wire rope vibration isolation system; k nj is the coefficient of the monomial in the polynomial corresponding to the amplification factor of the high static and low dynamic wire rope vibration isolation system; β is the ratio of the single-loop energy dissipation area E under different load conditions of the wire rope vibration isolation system to the single-loop energy dissipation area E without initial load; z is a hysteresis component that satisfies equation (3); F(x) represents the force generated by the negative stiffness device; t represents time; represents the derivative of z with respect to time t; represents the derivative of the deformation x with respect to time t; sgn() represents the step function; σ, ρ, and n are the parameters of the standardized Bouc-Wen model.

4. A method for establishing a mechanical model of an airborne equipment vibration isolation system according to any one of claims 1 to 3, characterized in that: In step S4, parameters α and β of at least two load conditions are obtained through experiments, and then parameters α and β of intermediate adjacent load conditions are obtained by interpolation based on parameters α and β of adjacent load conditions. The at least two load conditions include a no initial load condition.

5. The method for establishing a mechanical model of an airborne equipment vibration isolation system according to claim 4, characterized in that: The values ​​of parameters α and β under three different load conditions obtained through experiments are as follows: Among them, I represents the serial number, K effI and E I They respectively represent the effective stiffness and single-turn energy dissipation area of ​​the wire rope vibration isolation system under different loads when the amplitude is 5 mm.

6. A method for optimizing the mechanical model of an airborne equipment vibration isolation system, characterized in that: The following steps are involved: S01: Based on the improved normalized Bouc-Wen model established by the method for establishing a mechanical model of an airborne equipment vibration isolation system according to any one of claims 1 to 5, the transmissibility curve of the wire rope vibration isolation system is calculated using the fourth-order Runge-Kutta method; the low-frequency interference w is determined according to the transmissibility curve. u Transmissibility T u Is it less than T targ If T u <T targ , it can be determined that the model and quantity of the wire rope vibration isolation components can meet the target vibration isolation requirements, and the optimization design is completed; if T u >T targ , enter S02; S02: Optimize and adjust the number of wire rope vibration isolation components, and ensure that the static load deformation Ds of the adjusted new wire rope vibration isolation system is ≤ 5mm, and then proceed to S03; if the number of wire rope vibration isolation components cannot be adjusted to ensure that the static load deformation Ds of the new wire rope vibration isolation system is less than or equal to 5mm, skip S03 and proceed directly to S04; S03: Calculate new α and β based on the ratio of the number of wire rope vibration isolation components Q2 after adjustment to the number of wire rope vibration isolation components Q1 before adjustment, then obtain the new improved normalized Bouc-Wen model, and then calculate the transmissibility curve of the new wire rope vibration isolation system through the fourth-order Runge-Kutta method. According to the transmissibility curve of the new wire rope vibration isolation system, determine the low-frequency interference w u Transmissibility T u Is it less than T targ If T u <T targ , it can be determined that the model and quantity of the wire rope vibration isolation components can meet the target vibration isolation requirements, and the optimization design is completed; if T u >T targ , proceed to step S04; S04: Optimize the parameters of the negative stiffness device, calculate the transmissibility curve of the high static and low dynamic wire rope vibration isolation system by the fourth-order Runge-Kutta method, and judge the low-frequency interference w according to the transmissibility curve of the high static and low dynamic wire rope vibration isolation system. u Transmissibility T u Is it less than T targ If T u <T targ , it can be determined that the model, quantity and parameters of the optimized negative stiffness device of the wire rope vibration isolation assembly can meet the target vibration isolation requirements, and the optimization design is completed; if T u >T targ , enter S05; S05: Select a new model of wire rope vibration isolation assembly and repeat steps S01-S05 until the low-frequency interference w u Transmissibility T u <T targ .

7. The method for optimizing the mechanical model of an airborne equipment vibration isolation system according to claim 6, characterized in that: The method for calculating the transmissibility curve of the high static and low dynamic wire rope vibration isolation system using the fourth-order Runge-Kutta method is as follows: First, use formula (4) to give the basic excitation x g , and use formula (5) to calculate the deformation x of the wire rope vibration isolation system, and then according to the deformation x of the wire rope vibration isolation system and the foundation excitation x g Obtain the absolute response x of the isolated object under external excitation at different frequencies abs , and then use formula (6) to get the transmissibility T at different frequencies. According to the transmissibility T at different frequencies, the transmissibility curve of the high static and low dynamic wire rope vibration isolation system can be obtained; x g =A g cos(2πft) (4) T=Amp[x abs ] / Amp[x g ] (6) In formula (4), formula (5) and formula (6): x g Indicates basic incentive; A g represents the excitation amplitude; f is the excitation frequency; t represents time; x represents the deformation of the high-static and low-dynamic wire rope vibration isolation system; represents the derivative of deformation x with respect to time t; represents the second-order derivative of the deformation x with respect to time t; N is the order of the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; i is the degree of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; α is the effective stiffness k of the wire rope vibration isolation system under different load conditions eff and the effective stiffness k without initial load eff ratio; k ei is the coefficient of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system under no load; x represents the deformation of the high-static-low-dynamic wire rope vibration isolation system; M is the order of the polynomial corresponding to the amplification coefficient of the high-static-low-dynamic wire rope vibration isolation system; j is the degree of the monomial in the polynomial corresponding to the amplification coefficient of the high-static-low-dynamic wire rope vibration isolation system; k nj is the coefficient of the monomial in the polynomial corresponding to the amplification factor of the high static and low dynamic wire rope vibration isolation system; β is the ratio of the single-loop energy dissipation area E under different load conditions of the wire rope vibration isolation system to the single-loop energy dissipation area E without initial load; z is a hysteresis component that satisfies equation (3); F(x) represents the force generated by the negative stiffness device; m represents the mass of the object to be isolated; represents the second-order derivative of the fundamental excitation with respect to time; represents the derivative of z with respect to time t; sgn() represents the step function; σ, ρ, and n are the parameters of the standardized Bouc-Wen model; T represents the transmissibility; Amp[·] represents the amplitude of the steady-state response; x abs Indicates the absolute response of the object being isolated.

8. The method for optimizing the mechanical model of an airborne equipment vibration isolation system according to claim 7, characterized in that: In step S03, the steps of calculating new α and β according to the ratio of the number Q2 of wire rope vibration isolation assemblies after adjustment to the number Q1 of wire rope vibration isolation assemblies before adjustment are as follows: The equivalent load of the new wire rope vibration isolation system is obtained based on the ratio of the number of wire rope vibration isolation components Q2 after adjustment to the number of wire rope vibration isolation components Q1 before adjustment -m eq g, equivalent load-m eq The conversion formula (7) of g is as follows: -m eq g=-m t gQ1 / Q2 (7) In formula (7): -m eq g represents the equivalent load; g represents the acceleration of gravity; Q1 is the number of wire rope vibration isolation components in the preliminary design, and Q2 is the number of wire rope vibration isolation components after optimization; Based on equivalent load-m eq g, according to the parameters α and β under different initial states, the equivalent load -m is interpolated eq α under g eq and β eq , based on α eq and β eq The two parameters α2 and β2 of the improved normalized Bouc-Wen of the new wire rope vibration isolation system are obtained. The calculation formulas of α2 and β2 are as follows: α2=Q2α eq / Q1;β2=Q2β eq / Q1.

9. The method for optimizing the mechanical model of an airborne equipment vibration isolation system according to claim 7, characterized in that: In step S04 , the parameters of the negative stiffness device are optimized to obtain the maximum negative stiffness.

10. The method for optimizing the mechanical model of an airborne equipment vibration isolation system according to claim 9, characterized in that: The method for optimizing the parameters of the negative stiffness device to obtain the maximum negative stiffness is: The elastic restoring force R(x) of the high static and low dynamic wire rope vibration isolation system can be obtained by adding the nonlinear elastic restoring force of the new wire rope vibration isolation system and the force F(x) generated by the negative stiffness device. The calculation formula of R(x) is as follows (8): The optimization criterion for the parameters of the negative stiffness device is that the total stiffness R'(x) is the maximum relative displacement response D rmax There are no negative numbers in the equation, and the optimization standard is the following formula (9): Based on formula (9), the parameters of the negative stiffness device are iterated to obtain the maximum negative stiffness, while ensuring that the total stiffness meets the conditions in formula (10), which is: R'(x)>0where,x∈[-D rmax ,D rmax ] (10) Where R(x) is the elastic restoring force of the high static and low dynamic wire rope vibration isolation system; the total stiffness R'(x) is obtained by taking the derivative of the elastic restoring force R(x) with respect to x; D rmax is the maximum relative displacement during the vibration process; α2 is the new wire rope vibration isolation system under a load of -m t g condition; x represents the deformation of the high-static-low-dynamic wire rope vibration isolation system; N is the order of the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; i is the degree of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high-static-low-dynamic wire rope vibration isolation system; α is the effective stiffness k of the wire rope vibration isolation system under different load conditions eff and the effective stiffness k without initial load eff ratio; k ei It is the coefficient of the monomial in the polynomial corresponding to the nonlinear elastic restoring force of the high static and low dynamic wire rope vibration isolation system under no load; F(x) represents the force generated by the negative stiffness device.

Images