Mechanical model establishment and optimization design method of airborne equipment vibration isolation system

Abstract

The invention relates to an airborne equipment vibration isolation system mechanical model establishment and optimization design method. According to the mechanical model building method of the airborne equipment vibration isolation system, parameters alpha and beta are introduced into a normalized Bouc-Wen model, and the mechanical characteristics of the steel wire rope vibration isolation system under different load conditions can be effectively described. On the basis of the model, transmissibility curves of a steel wire rope vibration isolation system and a high-static and low-dynamic steel wire rope vibration isolation system under different load conditions are calculated through a fourth-order Runge-Kutta method, the number of steel wire rope vibration isolation assemblies is adjusted, and optimized parameters alpha and beta can be obtained. And adding a force F (x) generated by a negative stiffness device into the normalized Bouc-Wen model under the optimized parameters to obtain the normalized Bouc-Wen model capable of describing the high-static and low-dynamic steel wire rope vibration isolation system. The force F (x) generated by the negative stiffness device is changed to obtain a transmissibility curve of the high-static low-dynamic steel wire rope vibration isolation system under different negative stiffness, and based on the transmissibility curve under different negative stiffness, the optimal negative stiffness can be obtained through optimization.

Description

Technical Field

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

[0002] Vibration problems are common in the automotive, civil engineering, aerospace and other fields. 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] The nonlinear vibration isolation system with high static and low dynamic stiffness characteristics is composed of negative stiffness devices and positive stiffness devices. It can effectively improve the performance of the low-frequency vibration isolation system while maintaining the high-frequency vibration isolation performance. Therefore, the vibration isolation system with high static and low dynamic characteristics is the preferred device to eliminate the adverse effects of high-frequency and low-frequency vibrations on airborne equipment. Due to the limited layout space for the payload of the aircraft, the design process of the high static and low dynamic vibration isolation system requires that the negative stiffness device and the positive stiffness system are compact, efficient and lightweight.

[0004] Wire rope vibration isolation systems are widely used as vibration isolation systems in the fields of marine engineering, civil engineering and electronic equipment due to their advantages of easy installation, excellent durability and lightweight design. However, their inherent stiffness is too large, which limits their low-frequency vibration isolation performance in airborne equipment vibration isolation. Therefore, it is necessary to add a negative stiffness device to the wire rope vibration isolation system to construct a high static and low dynamic wire rope vibration isolation system to improve its low-frequency vibration isolation performance. High static and low dynamic stiffness is a special stiffness design concept that combines the characteristics of high static stiffness and low dynamic stiffness. Under static load, the structure or material exhibits higher stiffness to control static displacement; under dynamic load, it exhibits lower stiffness to reduce dynamic response. This design can effectively solve the contradiction of low-frequency vibration isolation in traditional design, that is, it is difficult to effectively isolate low-frequency vibration under the premise of ensuring bearing capacity.

[0005] In the existing vibration isolation system, the mechanical models of the wire rope vibration isolation system under no-load state and under different loads need to be fitted separately, which makes the fitting and subsequent calculation of the transmissibility curve 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 complicated fitting and subsequent calculation of the transmission rate 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 subject 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 assembly of the model preliminarily determined in S2 and the quantity Q1, 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, and a normalized Bouc-Wen model of the wire rope vibration isolation system is obtained according to the dynamic test curve;

[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-turn energy dissipation area E of the wire rope vibration isolation system under different load conditions and the single-turn energy dissipation area E without initial load, and the parameter β is introduced into the normalized model in S3; 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, and the establishment of the mechanical model is completed;

[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 phase displacement during a tension and compression cycle of the wire rope vibration isolation system; It represents 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-turn energy dissipation area E represents the area enclosed by the hysteresis curve under a tension-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-turn energy consumption area E of the wire rope vibration isolation system under different load conditions and the single-turn energy consumption 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 negative stiffness device. The mechanical model can effectively describe the mechanical properties of the wire rope vibration isolation system under different load conditions, and 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 comprises equations (2) and (3):

[0020]

[0021] In formula (2) and formula (3), φ(x, t) is the restoring force generated by the high static and 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 and 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 eiis 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; x represents the deformation of the high static and low dynamic wire rope vibration isolation system; M is the order of the polynomial corresponding to the amplification coefficient of the high static and 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 and 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-turn energy dissipation area E of the wire rope vibration isolation system under different load conditions to the single-turn energy dissipation area E without initial load; z is the pure hysteresis restoring force; 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 according to parameters α and β of adjacent load conditions.

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

[0024] The need to obtain the parameter α and the parameter β for each load condition through experiments can be avoided.

[0025] Preferably, the values ​​of the 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 fourth-order Runge-Kutta method is used to calculate the transmissibility curve of the wire rope vibration isolation system; the low-frequency interference w is determined according to the transmissibility curve. u The 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 enter S03; if the number of wire rope vibration isolation components is adjusted so that the static load deformation Ds of the new wire rope vibration isolation system cannot be less than or equal to 5mm, skip S03 and directly enter S04;

[0031] S03: Calculate new α and β according to 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, and then obtain the new improved normalized Bouc-Wen model. Then calculate the transmissibility curve of the new 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 new wire rope vibration isolation system. u The 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: Carry out the optimization of 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 The 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 The transmissibility T u <T targ .

[0034] On the basis of the model established by a method for establishing a mechanical model of an airborne equipment vibration isolation system, the transmissibility curves of the wire rope vibration isolation system and the high static low dynamic wire rope vibration isolation system under different load conditions are calculated by the fourth-order Runge-Kutta method. Based on the transmissibility curves under different loads, the optimal parameters α and β can be optimized. The force F(x) generated by the negative stiffness device is added to the normalized Bouc-Wen model under the optimal parameters to obtain a normalized Bouc-Wen model that can describe the high static low dynamic wire rope vibration isolation system. The transmissibility curves of the high static low dynamic wire rope vibration isolation system under different negative stiffness sizes are obtained by changing the force F(x) generated by the negative stiffness device. Based on the transmissibility curves under different negative stiffness sizes, the optimal negative stiffness size can be 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, the base excitation xg is given by equation (4), and the deformation x of the wire rope vibration isolation system is calculated by equation (5). Then, according to the deformation x of the wire rope vibration isolation system and the base excitation xg, g Obtain the absolute response x of the vibration-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(2πff) (4)

[0039]

[0040] T=Amp[x abs ] / Amp[x g ] (6)

[0042] In formula (4), formula (5) and formula (6): x g Represents basic incentive; A g represents the excitation amplitude; f is the excitation frequency; t represents the 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 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 and low-dynamic wire rope vibration isolation system; i is the order 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 loadeff ratio; k ei 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; x represents the deformation of the high static and low dynamic wire rope vibration isolation system; M is the order of the polynomial corresponding to the amplification coefficient of the high static and 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 and 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-turn energy dissipation area E of the wire rope vibration isolation system under different load conditions to the single-turn energy dissipation area E without initial load; z is the pure hysteresis restoring force; 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 Represents the absolute response of the object being isolated.

[0043] Preferably, 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:

[0044] The equivalent load of the new wire rope vibration isolation system is obtained according to 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. eq g, equivalent load - m eq The conversion formula (7) of g is as follows:

[0045] -m eq g=-m t Q1 / Q2 (7)

[0047] Where: -m eq g represents equivalent load; g represents gravitational acceleration; 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;

[0048] 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 eqThe 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:

[0049] α2=Q2α eq / Q1;β2=Q2β eq / Q1.

[0050] Preferably, in step S04, the parameters of the negative stiffness device are optimized to obtain the maximum negative stiffness.

[0051] Preferably, the method of optimizing the parameters of the negative stiffness device to obtain the maximum negative stiffness is:

[0052] 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):

[0053]

[0054] The optimization criterion for the parameters of the negative stiffness device is that the total stiffness R′(x) is at the maximum relative displacement response D rmax There are no negative numbers in the formula, and the optimization standard is as follows (9):

[0055]

[0056] 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 satisfies the conditions in formula (10), which is:

[0057] R′(x)>0 where x∈[-D rmax , D rmax ]

[0058]

[0059] 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 vibration; α2 is the load of the new wire rope vibration isolation system under -m t g condition; x represents the deformation of the high static and 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 and low dynamic wire rope vibration isolation system; i is the order 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 effratio; 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.

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] 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-turn energy consumption area E of the wire rope vibration isolation system under different load conditions and the single-turn energy consumption 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 negative stiffness device. The mechanical model can effectively describe the mechanical properties of the wire rope vibration isolation system under different load conditions, and 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.

[0062] 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

[0063] Figure 1 It is a schematic diagram of the layout of the onboard equipment;

[0064] Figure 2 It is a schematic diagram of a high static and low dynamic wire rope vibration isolation system;

[0065] Figure 3 It is a calculation diagram of the high static and low dynamic wire rope vibration isolation system;

[0066] Figure 4 is the cross-sectional view of the negative stiffness device;

[0067] Figure 5 It is a schematic diagram of the calculation of the negative stiffness device;

[0068] Figure 6 is the force-displacement curve of the negative stiffness device;

[0069] Figure 7 It is a comparison chart between the test results and the improved normalized Bouc-Wen model fitting results;

[0070] Figure 8 It is the optimization flow chart of high static and low dynamic wire rope vibration isolation system;

[0071] Fig. 9 This is a schematic diagram of the optimized high static and low dynamic wire rope vibration isolation system;

[0072] Fig.10 This is a schematic diagram of the optimized high static and low dynamic wire rope vibration isolation system;

[0073] Fig.11 It is a diagram of vibration isolation effects in different states during the optimization process.

[0074] Markings in the figure: 1. Aircraft; 2. Airborne equipment; 3. High-static and 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. Central movable rod; 44. Round aluminum plate. DETAILED DESCRIPTION

[0075] The present invention is further described in detail below in conjunction with specific embodiments. However, this should not be understood as the scope of the above subject matter of the present invention being limited to the following embodiments, and all technologies realized based on the content of the present invention belong to the scope of the present invention.

[0076] Unless otherwise specified, in the description of the specific embodiments of the present invention, the terms indicating the orientation or position relationship such as "up", "down", "left", "right", "center", "inside", "outside", etc. are all expressions based on the orientation or position relationship shown in the drawings, or are the orientation or position relationship when the invented product / equipment / device is usually used. These terms of orientation or position relationship are only for the convenience of describing the scheme of the present invention or simplifying the description in the specific embodiments, so as to facilitate the technicians to quickly understand the scheme, 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 position relationship, and therefore cannot be understood as a limitation on the present invention.

[0077] 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 simplified to mean that the corresponding devices / components / elements are set in directions such as "horizontal", "vertical", "overhanging", "parallel", etc., 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 scheme of the present invention.

[0078] In addition, the expressions “first”, “second”, “third”, etc., which appear 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.

[0079] In addition, in the description of the embodiments of the present invention, "several", "plurality" and "a number" represent at least 2. It can be any number such as 2, 3, 4, 5, 6, 7, 8, 9, and even more than 9.

[0080] In addition, in the description of the technical solution of the present invention, unless otherwise clearly specified / defined / restricted, the terms "set", "installed", "connected", "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.

[0081] Example 1

[0082] like Figure 1 As shown, the airborne equipment vibration isolation system adopts a wire rope vibration isolation system, which is arranged between the airborne equipment 2 and the aircraft 1. The aircraft 1 carries the airborne equipment 2. The wire rope vibration isolation system includes a wire rope vibration isolation assembly 31, an upper aluminum part 32, a lower aluminum part 33 and a plurality of bolts 34. The upper and lower ends of the wire rope vibration isolation assembly 31 are connected to the upper aluminum part 32 and the lower aluminum part 33 by bolts 34. The upper aluminum part 32 is connected to the aircraft 1, and the lower aluminum part 33 is connected to the airborne equipment 2. The wire rope vibration isolation assembly 31 is each individual wire rope vibration isolator in the wire rope vibration isolation system. The wire rope vibration isolation assembly 31 can be a butterfly wire rope vibration isolator, a T-shaped wire rope vibration isolator, and the like.

[0083] The airborne equipment vibration isolation system may also include a negative stiffness device 4, such as Figure 2As shown, the negative stiffness device 4 is disposed between the upper aluminum member 32 and the lower aluminum member 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.

[0084] This embodiment provides a method for establishing a mechanical model of an airborne equipment vibration isolation system, comprising the following steps:

[0085] S1. Identify the low-frequency interference frequency w to which the airborne equipment is subject u 、Mass of airborne equipment m t , the layout space of airborne equipment and the payload of the aircraft;

[0086] 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;

[0087] S3, based on the wire rope vibration isolation components of the model preliminarily determined in S2 and the quantity Q1, 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, the normalized Bouc-Wen model of the wire rope vibration isolation system is obtained according to the dynamic test curve;

[0088] 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-turn energy consumption area E of the wire rope vibration isolation system under different load conditions and the single-turn energy consumption area E without initial load. The parameter β is introduced into the normalized model in S3. 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:

[0089]

[0090] In the formula of 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 order 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 factor of the wire rope vibration isolation system; β is the ratio of the single-turn energy dissipation area E of the wire rope vibration isolation system under different load conditions to the single-turn energy dissipation area E without initial load; z is the pure hysteresis restoring force; 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.

[0091] Among them, the effective stiffness k eff The calculation formula (1) is as follows:

[0092]

[0093] In formula (1), It represents the maximum positive phase displacement during a tension and compression cycle of the wire rope vibration isolation system; It represents 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;

[0094] The single-turn energy dissipation area E represents the area enclosed by the hysteresis curve of a tension-compression cycle of the wire rope vibration isolation system, such as Figure 7 Each area enclosed by the same color and line type is the corresponding single-circle energy consumption area E.

[0095] 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 according to parameters α and β of adjacent load conditions.

[0096] Wherein, at least two load conditions include a no initial load condition, which can avoid the need to obtain the parameter α and the parameter β of each load condition through experiments.

[0097] For example, the values ​​of parameters α and β under three different load conditions obtained through experiments are as follows:

[0098] Table 1. Parameters α and β under different load conditions

[0099]

[0100] 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.

[0101] That is, by interpolating between -50 and -80, the values ​​of α and β of the wire rope vibration isolation system under a load condition of -65N when the amplitude is 5mm can be obtained. There is no need to conduct experiments to obtain the values ​​of α and β of the wire rope vibration isolation system under a load condition of -65N when the amplitude is 5mm. By substituting the values ​​of α and β of the wire rope vibration isolation system under a load condition of -65N when the amplitude is 5mm into the formula of the hysteresis model, the mechanical model under the load condition of -65N can be obtained. This method avoids re-fitting the mechanical model under the load condition of -65N.

[0102] In the method for establishing the mechanical model of the airborne equipment vibration isolation system described in this embodiment, after obtaining the normalized Bouc-Wen model of the wire rope vibration isolation system, the effective stiffness k of the wire rope vibration isolation system under different load conditions is calculated. 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-turn energy dissipation area E of the wire rope vibration isolation system under different load conditions and the single-turn 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 negative stiffness device. This mechanical model can effectively describe the mechanical characteristics of the wire rope vibration isolation system under different load conditions, and 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 fourth-order Runge-Kutta method can be used to calculate the transmissibility curve of the wire rope vibration isolation system.

[0103] 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 a negative stiffness device.

[0104] 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):

[0105]

[0106] In formula (2) and formula (3), φ(x, t) is the restoring force generated by the high static and 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 and 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 and low dynamic wire rope vibration isolation system under no load; x represents the deformation of the high static and low dynamic wire rope vibration isolation system; M is the order of the polynomial corresponding to the amplification coefficient of the high static and 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 and 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-turn energy dissipation area E of the wire rope vibration isolation system under different load conditions to the single-turn energy dissipation area E without initial load; z is the pure hysteresis restoring force; 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.

[0107] Example 2

[0108] The preliminary design of the wire rope vibration isolation system ignores the influence of different loads and the difference between dynamic and static stiffness. Therefore, there is room for optimization in the preliminary designed wire rope vibration isolation system. For the negative stiffness generated by the negative stiffness device, if the negative stiffness provided by the negative stiffness device is too small, the gain effect provided on the vibration isolation performance is very small. On the contrary, if the negative stiffness provided by the negative stiffness device is too large, it will cause the high static and low dynamic wire rope vibration isolation system to be unstable and unable to effectively isolate vibration. Therefore, there is an optimal negative stiffness value that can provide sufficient gain effect without compromising the stability of the system.

[0109] See also Figure 8 , an optimization design method for a mechanical model of an airborne equipment vibration isolation system, comprising the following steps:

[0110] 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 fourth-order Runge-Kutta method is used to calculate the transmissibility curve of the wire rope vibration isolation system; the low-frequency interference w is determined according to the transmissibility curve. u The 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;

[0111] The method of calculating the transmissibility curve of the high static and low dynamic wire rope vibration isolation system using the fourth-order Runge-Kutta method is:

[0112] 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 equation (5) (i.e., the 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 vibration-isolated object under external excitation at different frequencies abs , which is the base 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 made simpler; then the formula (6) is used to obtain the transmissibility T at different frequencies, and the transmissibility curve of the high static and low dynamic wire rope vibration isolation system can be obtained according to the transmissibility T at different frequencies;

[0113] x g =A g cos(2πft) (4)

[0115]

[0116] T=Amp[x abs ] / Amp[x g ] (6)

[0118] In formula (4), formula (5) and formula (6): x g Represents basic incentive; A grepresents the excitation amplitude; f is the excitation frequency; t represents the 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 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 and low-dynamic wire rope vibration isolation system; i is the order 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 and low dynamic wire rope vibration isolation system under no load; x represents the deformation of the high static and low dynamic wire rope vibration isolation system; M is the order of the polynomial corresponding to the amplification coefficient of the high static and 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 and 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-turn energy dissipation area E of the wire rope vibration isolation system under different load conditions to the single-turn energy dissipation area E without initial load; z is the pure hysteresis restoring force; 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 Represents the absolute response of the object being isolated.

[0119] 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 enter S03; if the number of wire rope vibration isolation components cannot be adjusted to make the static load deformation Ds of the new wire rope vibration isolation system less than or equal to 5mm, skip S03 and directly enter S04, that is, if the static load deformation Ds of the new wire rope vibration isolation system is greater than 5mm no matter how the number of wire rope vibration isolation components is adjusted, directly enter S04 to optimize the parameters of the negative stiffness device;

[0120] S03: Calculate new α and β according to 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, and then obtain the new improved normalized Bouc-Wen model. Then calculate the transmissibility curve of the new 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 new wire rope vibration isolation system. u The transmissibility Tu 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;

[0121] In step S03, the steps of calculating new α and β according to the ratio of the number Q2 of wire rope vibration isolation components after adjustment to the number Q1 of wire rope vibration isolation components before adjustment are:

[0122] The equivalent load of the new wire rope vibration isolation system is obtained according to 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. eq g, equivalent load - m eq The conversion formula (7) of g is as follows:

[0123] -m eq g=-m t Q1 / Q2 (7)

[0125] Where: -m eq g represents equivalent load; g represents gravitational acceleration; 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;

[0126] 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:

[0127] α2=Q2α eq / Q1;β2=Q2β eq / Q1. a2 and β2 are the update parameters of parameters α and β, respectively, which are used to substitute into the mechanical model.

[0128] S04: Carry out the optimization of 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 The transmissibility T u Is it less than T targ ; If T u <Ttarg , 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;

[0129] Negative stiffness devices such as Figure 4 As 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. The two ends of the acrylic tube 42 are provided with circular aluminum plates 44. 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. The two ends of the acrylic tube 42 are fixed with annular NdFeB permanent magnets 41. 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, and 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 annular NdFeB permanent magnets 41 and the middle annular NdFeB permanent magnet 41 are used to assist the axial movement of the central movable rod 43, thereby realizing the negative stiffness of the wire rope vibration isolation system.

[0130] In a preferred embodiment, in step S04, the parameters of the negative stiffness device are optimized to obtain the maximum negative stiffness.

[0131] The method to optimize the parameters of the negative stiffness device to obtain the maximum negative stiffness is:

[0132] 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):

[0133]

[0134] The optimization criterion for the parameters of the negative stiffness device is that the total stiffness R′(x) is at the maximum relative displacement response D rmax There are no negative numbers in the formula, and the optimization standard is as follows (9):

[0135]

[0136] 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 satisfies the conditions in formula (10), which is:

[0137] R′(x)>0 where x∈[-D rmax , Drmax ] (10)

[0139] 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 vibration; α2 is the load of the new wire rope vibration isolation system under -m t g condition; x represents the deformation of the high static and 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 and low dynamic wire rope vibration isolation system; i is the order 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 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.

[0140] The optimization method mentioned in this embodiment is as follows: Figure 8 As shown, the low-frequency interference W is determined according to the external excitation characteristics. u ; The target transmission rate T at the interference frequency targ ; According to the mass of the onboard equipment m 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 , it can be determined that the model and quantity of the wire rope vibration isolation assembly 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.

[0141] Adjust the number of wire rope vibration isolation components to Q2, and ensure that the adjusted wire rope vibration isolation system meets the static load deformation (D s ≤5mm). The mechanical properties of the wire rope vibration isolation system are proportional to the number of wire rope vibration isolation components.

[0142] By reducing the number of wire rope vibration isolation components without changing the model of the wire rope vibration isolation components, the equivalent load (-m eq g). The conversion formula (7) is as follows:

[0143] -m eq g=-m t Q1 / Q2 (7)

[0145] Where -m eq g represents equivalent load; g represents gravitational acceleration; 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.

[0146] According to the equivalent load -m eq g, and the α and β parameter tables under different initial states to obtain the β under the equivalent initial state eq and β eq After that, based on α eq and β eq Two important parameters of the improved normalized Bouc-Wen of the new wire rope vibration isolation system can be further obtained: α2 = n2α eq / n1 and β2 = n2β eq / n1.

[0147] The transmissibility curve of the new wire rope vibration isolation system is obtained by using equations (4), (5) and (6) to determine whether it meets the requirements. u2 <T targ , the model and quantity of 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.

[0148] 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.

[0149] 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).

[0150] 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 condition in equation (10).

[0151]

[0152] R′(x)>0 where x∈[-D rmax , D rmax ] (10)

[0154] 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 vibration; α2 is the load of the new wire rope vibration isolation system under -m t g condition; x represents the deformation of the high static and 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 and low dynamic wire rope vibration isolation system; i is the order 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 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.

[0155] 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 type of wire rope vibration isolation assembly. The new type of wire rope vibration isolation assembly should have a lower average static load stiffness while meeting the aircraft payload and layout space. After selecting a new wire rope vibration isolation assembly model, repeat the above operation until the optimized wire rope vibration isolation assembly quantity, model, and negative stiffness device parameters meet the airborne equipment vibration isolation target.

[0156] 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 The frequency is 16Hz; the mass of the airborne equipment is 5kg. Considering the layout space of the airborne equipment and the payload of the aircraft, referring to the Specification for Wire Rope Vibration Isolation System for Ships, the number of wire rope vibration isolation components in the wire rope vibration isolation system obtained by the preliminary design is determined to be Q1, Q1 is equal to 4, and the model of the wire rope vibration isolation component is ALJ835400.

[0157] Firstly, 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);

[0158]

[0159] 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 eff and the ratio of the single-turn 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 factor 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 the pure hysteresis restoring force; 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 the deformation x with respect to time t; sgn() represents the step function.

[0160] Firstly, the parameters of the improved normalized Bouc-Wen model of the 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 single-turn energy consumption area E can be obtained as α1=0.979; β1=0.984, as shown in Table 1.

[0161] Table 1. Parameters α and β under different load conditions

[0162]

[0163]

[0164] 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.

[0165] Then according to Figure 8 The performance of the steel wire rope vibration isolation system is optimized and designed. The intermediate parameters obtained during the optimization process are listed in Table 2.

[0166] Table 2. Values ​​of various parameters during optimization

[0167]

[0168] In order to ensure effective isolation of low and high frequencies, the target transmission rate T is determined. targ Set to 50%. Fig.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 Fig. 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 of less than 5mm. The quasi-static test curve is used to verify whether the static load displacement of the vibration isolation system will be less than 5mm after optimizing the number of wire rope vibration isolation components.

[0169] like Fig.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 quantity is adjusted to Q2, where Q2 is equal to 3. u2 The value is 51.9%, which is also greater than T targ .

[0170] 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, see Figure 5 ; corresponds to Figure 3 , Figure 5 The figure shows three annular NdFeB permanent magnets 41, upper, middle and lower, and their parameters are listed in Table 3.

[0171] Table 3 Parameters of permanent magnets in negative stiffness device

[0172] parameter <![CDATA[RPM1]]> <![CDATA[RPM2]]> <![CDATA[RPM3]]> Inner 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 magnetic 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]]>

[0173] 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. The optimized hz 47mm, Z a is 23.5 mm. Formula (11) is the force provided by the negative stiffness device, and its formula is as follows:

[0174] F(x)=k1x+k2x 2 +k3x 3 ; (11)

[0176] After optimization, the coefficients in expression (2) are: opt1 =-7.77, k opt2 =-0.0039, k opt3 =-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 It 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 Fig.10 .

[0177] This embodiment 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.

[0178] 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 protection scope 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 subject 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 effective load 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 assembly of the model preliminarily determined in S2 and the quantity Q1, 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, and a normalized Bouc-Wen model of the wire rope vibration isolation system is obtained according to the dynamic test curve; 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-turn energy dissipation area E of the wire rope vibration isolation system under different load conditions and the single-turn energy dissipation area E without initial load, and the parameter β is introduced into the normalized model in S3; 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, and the establishment of the mechanical model is completed; Among them, the effective stiffness k eff The calculation formula (1) is as follows: In formula (1), It represents the maximum positive phase displacement during a tension and compression cycle of the wire rope vibration isolation system; It represents 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-turn energy dissipation area E represents the area enclosed by the hysteresis curve under a tension-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 and 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 and 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 and low dynamic wire rope vibration isolation system under no load; x represents the deformation of the high static and low dynamic wire rope vibration isolation system; M is the order of the polynomial corresponding to the amplification coefficient of the high static and 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 and 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-turn energy dissipation area E of the wire rope vibration isolation system under different load conditions to the single-turn energy dissipation area E without initial load; z is the pure hysteresis restoring force; 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 according to 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. An optimization design method for a 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 The 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 assembly 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 enter S03; if the number of wire rope vibration isolation components is adjusted so that the static load deformation Ds of the new wire rope vibration isolation system cannot be less than or equal to 5mm, skip S03 and directly enter S04; S03: Calculate new α and β according to 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, and then obtain the new improved normalized Bouc-Wen model. Then calculate the transmissibility curve of the new 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 new wire rope vibration isolation system. u The 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 assembly can meet the target vibration isolation requirements, and the optimization design is completed; if T u >T targ , proceed to step S04; S04: Carry out the optimization of 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 The 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 The transmissibility T u <T targ .

7. The optimization design method of the mechanical model of the airborne equipment vibration isolation system according to claim 6 is characterized in that: The method of calculating the transmissibility curve of the high static and low dynamic wire rope vibration isolation system using the fourth-order Runge-Kutta method is: 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 vibration-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 Represents basic incentive; A g represents the excitation amplitude; f is the excitation frequency; t represents the 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 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 and low-dynamic wire rope vibration isolation system; i is the order 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 and low dynamic wire rope vibration isolation system under no load; x represents the deformation of the high static and low dynamic wire rope vibration isolation system; M is the order of the polynomial corresponding to the amplification coefficient of the high static and 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 and 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-turn energy dissipation area E of the wire rope vibration isolation system under different load conditions to the single-turn energy dissipation area E without initial load; z is the pure hysteresis restoring force; 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 Represents the absolute response of the object being isolated.

8. The optimization design method of the mechanical model of the airborne equipment vibration isolation system according to claim 7 is 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 components after adjustment to the number Q1 of wire rope vibration isolation components before adjustment are: The equivalent load of the new wire rope vibration isolation system is obtained according to 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. 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 equivalent load; g represents gravitational acceleration; 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 optimization design method of the mechanical model of the airborne equipment vibration isolation system according to claim 7 is characterized in that: In step S04 , the parameters of the negative stiffness device are optimized to obtain the maximum negative stiffness.

10. The optimization design method of the mechanical model of the airborne equipment vibration isolation system according to claim 9, characterized in that: The method to optimize 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 at the maximum relative displacement response D rmax There are no negative numbers in the formula, and the optimization standard is as follows (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 satisfies the conditions in formula (10), which is: R’(x)>0 where,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 vibration; α2 is the load of the new wire rope vibration isolation system under -m t g condition; x represents the deformation of the high static and 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 and low dynamic wire rope vibration isolation system; i is the order 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 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.

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