Design method of improved X-type connecting rod vibration isolation structure with large-stroke quasi-zero stiffness and full-band vibration isolation characteristics

Abstract

The invention discloses a design method of an improved X-type connecting rod vibration isolation structure with large-stroke quasi-zero stiffness and full-band vibration isolation characteristics. The method comprises the following steps that 1, the design of the improved X-type connecting rod vibration isolation structure and the deformation relation of the improved X-type connecting rod vibration isolation structure are explicitly defined; 2, establishing a mechanical model of the improved X-type connecting rod vibration isolation structure; and step 3, constructing a nonlinear motion differential equation of the improved X-type connecting rod vibration isolation structure. The structure is simple and compact in design layout and does not contain any sliding guide rail, meanwhile, the superior quasi-zero rigidity performance is kept through connection between the connecting rod and the spring, and the ultralow-frequency vibration isolation and full-frequency-band vibration isolation characteristics are achieved. The mechanism that the vibration isolation structure achieves the ultra-low-frequency vibration isolation and full-band vibration isolation characteristics is explored, and a new thought is provided for design of quasi-zero-stiffness passive vibration isolators in the engineering field.

Description

Technical Field

[0001] The invention relates to a design method of an X-type vibration isolation structure, and in particular to a design method of an improved X-type connecting rod vibration isolation structure with large stroke quasi-zero stiffness and full-band vibration isolation characteristics. Background Art

[0002] Vibration describes the oscillation or reciprocating motion of an object, which is characterized by periodic motion around a central equilibrium point. In engineering applications such as aerospace, automotive and shipbuilding industries, a certain degree of vibration is inevitable, but harmful vibration can lead to a shortened service life and fatigue damage of mechanical equipment. Therefore, it is very important to control harmful vibration within a reasonable and acceptable range.

[0003] At present, different vibration control methods, including passive, semi-active and active control, have been used in engineering practice to meet different vibration isolation requirements. Active and semi-active control strategies can easily obtain the required control force. However, it requires complex control algorithms and precise sensors, which increases the complexity and cost of the system. In addition, control system failure or malfunction can lead to unexpected consequences and potential safety risks. Passive vibration isolation systems have excellent stability and economy and have been widely used in engineering practice to address the limitations of semi-active and active control methods.

[0004] In a linear passive vibration isolation system, only frequencies exceeding The excitation of the multiple resonant frequency can be effectively attenuated. Although the resonant frequency can be reduced by reducing the stiffness of the linear system, doing so will also increase the deviation from the equilibrium point and reduce the bearing capacity of the system. In order to address the shortcomings of the linear isolation system, quasi-zero stiffness isolation systems with high static and low dynamic stiffness characteristics are widely used in engineering practice. However, the realization of high static and low dynamic characteristics of most existing nonlinear vibration isolators is limited to a specific working range, and their quasi-zero stiffness range is significantly smaller than the entire stroke of the vibration isolation system, which greatly limits the realization of its ultra-low frequency vibration isolation characteristics and reduces the stability of the system. In addition, the traditional X-type vibration isolation structure requires the design of sliding guides during movement, which increases the complexity of the vibration isolation structure. Summary of the invention

[0005] The present invention aims to solve the problems that the realization of high static and low dynamic characteristics of existing nonlinear vibration isolators is limited to a specific working range, resulting in a quasi-zero stiffness range that is significantly smaller than the entire stroke of the vibration isolation system, and that the traditional X-type vibration isolation structure needs to design a sliding guide rail during movement, which increases the complexity of the vibration isolation structure. The present invention provides a design method for an improved X-type connecting rod vibration isolation structure with large-stroke quasi-zero stiffness and full-band vibration isolation characteristics. The structural design layout is simple and compact and does not contain any sliding guide rails. At the same time, the connection between the connecting rod and the spring maintains superior quasi-zero stiffness performance, achieving ultra-low frequency vibration isolation and full-band vibration isolation characteristics. The present invention explores the mechanism by which the vibration isolation structure achieves ultra-low frequency vibration isolation and full-band vibration isolation characteristics, providing new ideas for the design of quasi-zero stiffness passive vibration isolators in the engineering field.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] A design method for an improved X-type connecting rod vibration isolation structure with large stroke quasi-zero stiffness and full-band vibration isolation characteristics comprises the following steps:

[0008] Step 1: Clarify the improved X-type connecting rod vibration isolation structure design and its deformation relationship

[0009] The improved X-type connecting rod vibration isolation structure includes four connecting rods and three springs, among which: the connecting rod length and assembly angle are L 1 and θ 1 , P 1 -P 4 , P 7 and P 8 is the hinge point of the connecting rod structure, P 5 and P 6 are two points on the connecting rod; along the vertical direction, the hinge point P 1 , P 3 and P 7 Collinear, hinge point P 2 , P 4 and P 8 Collinear; stiffness is k h The horizontal springs provide the main stiffness of the structure, and the two stiffnesses are k o The inclined spring is connected at point P 5 P 7 and P 6 P 8 To enhance the structural rigidity and bearing capacity; point P 5 With the hinge point P 8 The distance between the points P 6 With the hinge point P 7 The distance between them is L c ;

[0010] The rotation angle of the improved X-type connecting rod vibration isolation structure under the vertical load F is The vertical displacement of the bearing platform is y d , hinge point P 4 The horizontal displacement is x d , horizontal displacement x d and rotation angle Use vertical displacement y d It is expressed as:

[0011]

[0012] The original length of the horizontal spring is L 10 and the original length L of the two inclined springs 20 It is expressed as:

[0013] L 10 =L 1 cosθ 1 (3)

[0014]

[0015] The length L of the horizontal spring and the inclined spring after deformation 11 and L 21 It is expressed as:

[0016]

[0017] Deformation length ΔL of horizontal spring and inclined spring h and ΔL o It is expressed as:

[0018]

[0019] Step 2: Establish the mechanical model of the improved X-type connecting rod vibration isolation structure

[0020] According to the force analysis of the improved X-type connecting rod vibration isolation structure, the horizontal spring and the inclined spring are subjected to force F h and F o They are:

[0021] F h =k h ΔL h ,F o =k o ΔL o (9)

[0022] Based on the principle of virtual work, we get:

[0023] Fδy d -F h δΔL h -2F o δΔL o =0 (10)

[0024] Among them, δ is the symbol of variation;

[0025] According to formulas (2) and (7)–(10), the vertical bearing capacity is expressed as:

[0026]

[0027] in:

[0028]

[0029] Step 3: Construct the nonlinear motion differential equation of the improved X-type connecting rod vibration isolation structure

[0030] The vibration isolation mass is M, the base excitation and the platform vertical displacement are Y b and Y p , the relative displacement is Y=Y p -Y b Due to the effect of gravity, a new equilibrium point appears in the improved X-type connecting rod vibration isolation structure. When the improved X-type connecting rod vibration isolation structure is subjected to vibration from the base, the vibration isolation body vibrates vertically around the equilibrium position, introducing a new coordinate system (Y, F s ) represents relative motion, with the static equilibrium point as the origin, and the static displacement caused by gravity is y st , the nonlinear restoring force in the new coordinate system is F s According to the D'Alembert principle, the nonlinear motion equation of the improved X-type connecting rod vibration isolation structure is:

[0031]

[0032] Among them, c a is the structural damping coefficient;

[0033] In order to obtain its analytical solution, the nonlinear stiffness function F s (Y) Perform polynomial fitting:

[0034]

[0035] Among them, η 1 –η 4 is the polynomial fitting coefficient. Substituting formula (14) into (13), the nonlinear motion differential equation of the improved X-type connecting rod vibration isolation structure is further expressed as:

[0036]

[0037] in:

[0038]

[0039] Step 4: Obtain structural vibration transmissibility using the harmonic balance method

[0040] Assume that the external stimulus is Y b =Y 0 cos(ωt)=Y 0 cos(2πft), according to the harmonic balance method, the theoretical solution of formula (15) is assumed to be:

[0041]

[0042] Among them, Λ 0 is the bias term, Λ 1 and As amplitude and phase, transform equation (17) and Y b =Y 0 Substitute cos(ωt) into equation (15), ignore the higher-order terms, balance the coefficients of sin(ωt) and cos(ωt), and combine The characteristic equation is:

[0043]

[0044] The absolute displacement can be expressed as:

[0045]

[0046] The displacement transmissibility of the improved X-type connecting rod vibration isolation system is expressed as:

[0047]

[0048] Compared with the prior art, the present invention has the following advantages:

[0049] (1) The present invention develops a compact improved X-type connecting rod vibration isolation structure through the connection between the connecting rod and the spring. The structure does not need to design a sliding guide rail, thereby minimizing the influence of the friction caused by the sliding guide rail on the dynamic response of the system.

[0050] (2) By adjusting the design parameters, the improved X-type connecting rod vibration isolation structure designed by the present invention exhibits excellent high static and low dynamic characteristics, and its quasi-zero stiffness range can reach 90% of the total stroke of the structure.

[0051] (3) Compared with the mass-spring-damper linear isolator and the traditional quasi-zero stiffness isolator, the X-type connecting rod vibration isolation structure of the present invention achieves a lower vibration isolation frequency and resonance peak, and achieves a wider quasi-zero stiffness range while ensuring the load-bearing capacity and stability.

[0052] (4) When the stiffness of the improved X-type connecting rod vibration isolation structure of the present invention approaches zero, the structural stiffness exhibits weak nonlinear characteristics within a large range of motion; at the zero stiffness position, the improved X-type connecting rod vibration isolation structure can achieve full-band vibration isolation characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 To improve the X-type connecting rod vibration isolation structure;

[0054] Figure 2 It is a passive vibration isolation platform based on an improved X-type connecting rod vibration isolation structure;

[0055] Figure 3 Schematic diagram of the improved X-type connecting rod vibration isolation structure before and after deformation under the action of load F and the force analysis of the X-type connecting rod vibration isolation structure, (a) Schematic diagram of the improved X-type connecting rod vibration isolation structure before deformation (blue-green solid line) and after deformation (red dotted line) under the action of load F, (b) force analysis of the improved X-type connecting rod vibration isolation structure;

[0056] Figure 4 To improve the equivalent dynamic model of the X-type connecting rod vibration isolation structure and the static equilibrium position in the new coordinate system, (a) the equivalent dynamic model of the X-type connecting rod vibration isolation structure is improved, (b) the static equilibrium position in the new coordinate system;

[0057] Figure 5 Comparison of numerical simulation and theoretical calculation force-displacement curves under different oblique spring stiffness;

[0058] Figure 6 For different spring stiffness k o and k h The nonlinear force-displacement curve of the improved X-type connecting rod vibration isolation structure;

[0059] Figure 7 The amplitude-frequency response curve and displacement transmissibility curve based on direct numerical integration method and harmonic balance method, (a) amplitude-frequency response curve, (b) displacement transmissibility curve;

[0060] Figure 8 Static stiffness characteristics and vibration transmissibility curves of different vibration isolators. (a) Static stiffness characteristics of different vibration isolators, (b) Vibration transmissibility curve, M = 5.02 kg, c a =2Ns / m, Y 0 =0.01m;

[0061] Fig. 9 The displacement transmissibility curves of the improved X-type connecting rod vibration isolation structure at different static equilibrium positions. DETAILED DESCRIPTION

[0062] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0063] The present invention provides a design method for an improved X-type connecting rod vibration isolation structure with large stroke quasi-zero stiffness and full-band vibration isolation characteristics. The technical problems to be solved by the method mainly include:

[0064] (1) Design a compact X-type link vibration isolation structure consisting of linear springs and links with a large range of quasi-zero stiffness and without sliding guides, and analyze its ultra-low frequency and full-band vibration isolation characteristics;

[0065] (2) Clarify the design method of the compact X-type connecting rod vibration isolation structure and reveal the mechanism by which the structure achieves quasi-zero stiffness characteristics over a long stroke;

[0066] (3) The nonlinear motion differential equation of the X-type connecting rod vibration isolation structure is established, and the displacement transmissibility curve of the vibration isolation system is obtained using the harmonic balance method;

[0067] (4) Reveal the influence of key design parameters on the quasi-zero stiffness range and ultra-low frequency vibration isolation characteristics of the X-type connecting rod vibration isolation structure;

[0068] (5) Verify the long-stroke quasi-zero stiffness characteristics of the X-type connecting rod vibration isolation structure and the effectiveness of the harmonic balance method in solving the vibration transmissibility. The vibration isolation structure achieves ultra-low frequency vibration isolation and full-band vibration isolation performance. The specific steps are as follows:

[0069] Step 1: Clarify the improved X-type connecting rod vibration isolation structure design and its deformation relationship

[0070] Figure 1 The improved X-type connecting rod vibration isolation structure is shown. The improved X-type connecting rod vibration isolation structure includes four connecting rods and three springs. The connecting rod length and assembly angle are L 1 and θ 1 The red dashed circle indicates the intersection point, corresponding to the midpoint of the green and blue rods. 1 -P 4 , P 7 and P 8 is the hinge point of the connecting rod structure, P 5 and P 6 are two points on the connecting rod; along the vertical direction, the hinge point P 1 , P 3 and P 7 Collinear, hinge point P 2 , P 4 and P 8 Also collinear. The stiffness is k h The horizontal springs provide the main stiffness of the structure, and the two stiffnesses are k o The inclined spring is connected at point P 5 P 7 and P 6 P 8 Point P 5 With the hinge point P8 The distance between the points P 6 With the hinge point P 7 The distance between them is L c The connecting rod is made of lightweight rigid material, and its elastic deflection is much smaller than the deformation of the spring and can be ignored.

[0071] Improved X-link isolators can be used to design vibration isolation systems to suit various application requirements, such as Figure 2 The vibration isolation platform shown in the figure. The vibration isolation platform includes an improved X-link structure connecting the upper and lower support platforms, as well as four external support rods to limit the rotation and translation movement of the platform. In addition, the passive vibration isolation platform does not require a vertical sliding guide like a traditional X-type vibration isolator, thereby minimizing the impact of the friction caused by the sliding guide on the dynamic response of the system.

[0072] Figure 3 The deformation and force analysis of the improved X-type connecting rod vibration isolation structure under the vertical load F are given. The rotation angle of the rod is The vertical displacement of the bearing platform is y d , hinge point P 4 The horizontal displacement is x d .according to Figure 3 Deformation analysis shown in (a), horizontal displacement x d and rotation angle The vertical displacement y d It is expressed as:

[0073]

[0074] The original length of the horizontal spring is L 10 and the original length L of the two inclined springs 20 It can be expressed as:

[0075] L 10 =L 1 cosθ 1 (twenty four)

[0076]

[0077] The length L of the horizontal spring and the inclined spring after deformation 11 and L 21 It can be expressed as:

[0078]

[0079] Therefore, the deformation length ΔL of the horizontal spring and the inclined spring is h and ΔL o It can be expressed as:

[0080]

[0081] Step 2: Establish the mechanical model of the improved X-type connecting rod vibration isolation structure

[0082] according to Figure 3 (b) The force analysis of the improved X-type connecting rod vibration isolation structure, where the horizontal spring and the inclined spring are subjected to force F h and F o They are:

[0083] F h =k h ΔL h ,F o =k o ΔL o (30)

[0084] Based on the principle of virtual work, we can get:

[0085] Fδy d -F h δΔL h -2F o δΔL o =0 (31)

[0086] Here, δ is the symbol of variation.

[0087] According to formulas (23) and (28)–(31), the vertical bearing capacity can be expressed as:

[0088]

[0089] in

[0090]

[0091] Step 3: Construct the nonlinear motion differential equation of the improved X-type connecting rod vibration isolation structure

[0092] The dynamic model of the improved X-type connecting rod vibration isolation structure is as follows Figure 4 As shown in (a), the structure is a single degree of freedom system designed to isolate the vibration caused by the base excitation. The vibration isolation mass is M, the base excitation and the platform vertical displacement are Y b and Y p , the relative displacement is Y=Y p -Y b Due to the effect of gravity, a new equilibrium point appears in the improved X-type connecting rod vibration isolation structure. When the improved X-type connecting rod vibration isolation structure is subjected to vibration from the base, the vibration isolation body vibrates vertically around the equilibrium position. Therefore, Figure 4 As shown in (b), a new coordinate system (Y, F s ) represents relative motion, with the static equilibrium point as the origin, and the static displacement caused by gravity is y st, the nonlinear restoring force in the new coordinate system is F s .

[0093] According to the D'Alembert principle, the nonlinear motion equation of the improved X-type connecting rod vibration isolation structure is:

[0094]

[0095] Among them, c a is the structural damping coefficient.

[0096] In order to obtain its analytical solution, the nonlinear stiffness function F s (Y) Perform polynomial fitting:

[0097]

[0098] Among them, η 1 –η 4 is the polynomial fitting coefficient. Substituting formula (35) into (34), the nonlinear motion differential equation of the improved X-type connecting rod vibration isolation structure can be further expressed as:

[0099]

[0100] in

[0101]

[0102] Step 4: Obtain structural vibration transmissibility using the harmonic balance method

[0103] Assume that the external stimulus is Y b =Y 0 cos(ωt)=Y 0 cos(2πft), according to the harmonic balance method, the theoretical solution of formula (36) can be assumed to be:

[0104]

[0105] Among them, Λ 0 is the bias term, Λ 1 and is the amplitude and phase. b =Y 0 Substitute cos(ωt) into equation (36), ignore the higher-order terms, balance the coefficients of sin(ωt) and cos(ωt), and combine The characteristic equation can be obtained as:

[0106]

[0107] Formulas (39) and (40) contain only two unknown variables Λ 0 and Λ 1, so for any given ω and Y 0 The corresponding solution can be obtained. The absolute displacement can be expressed as:

[0108]

[0109] The displacement transmissibility of the improved X-type link vibration isolation system can be expressed as:

[0110]

[0111] Example:

[0112] use Figure 4 The equivalent dynamic model of the improved X-type connecting rod vibration isolation structure shown in the figure is used to perform example calculation and analysis on the present invention. The relevant parameters are: L 1 =0.1m,θ 1 =80°, L c =L 1 cosθ 1 , k h =200N / m, k o =13000N / m,c a =2N·s / m, Y 0 =0.01m.

[0113] The calculation process is as follows:

[0114] (1) According to step 1 of the technical solution of the present invention, the design of the improved X-type connecting rod vibration isolation structure and its deformation relationship are clarified;

[0115] (2) According to step 2 of the technical solution of the present invention, a mechanical model of the improved X-type connecting rod vibration isolation structure is established;

[0116] (3) The nonlinear motion differential equation of the improved X-type vibration isolation system constructed according to step 3 of the technical solution of the present invention;

[0117] (4) The harmonic balance method proposed in step 4 of the technical solution of the present invention is used to obtain the structural vibration transmissibility and evaluate its vibration isolation performance.

[0118] The calculation benefits and vibration isolation performance evaluation are as follows:

[0119] (1) The compact X-type connecting rod vibration isolation structure designed in this embodiment does not require the design of a sliding guide rail, thereby minimizing the impact of the friction caused by the sliding guide rail on the system dynamic response.

[0120] (2) By adjusting the design parameters, the improved X-type connecting rod vibration isolation structure designed in this embodiment exhibits excellent high static and low dynamic characteristics, and its quasi-zero stiffness range can reach 90% of the total stroke of the structure.

[0121] (3) Take the structural parameters as: L 1 =0.1m, L c =L 1 cosθ 1 ,θ 1 =80°, k h =200N / m. Figure 5 The structural force-displacement curve obtained based on the method provided by the present invention is given and compared with the ADAMS numerical simulation calculation results. Figure 5 It can be seen that the calculation results of the two methods are in good agreement (the error is less than 2%), which indicates the correctness of the theoretical analysis method and calculation program provided by the present invention.

[0122] (4) Consider the structural parameters: L 1 =0.1m, L c =L 1 cosθ 1 ,θ 1 =80°, k h =200N / m, k o =13000N / m. According to the analytical expression of bearing capacity established from step 1 to step 2, the nonlinear force-displacement curve of the structure under different spring stiffness is obtained, such as Figure 6 As shown. Figure 6 It can be observed that when k o =13000N / m and k h When =200N / m, the improved X-type connecting rod vibration isolation structure of this embodiment shows a quasi-zero stiffness area (0.02m-0.19m) in a very large range, and the proportion of the quasi-zero stiffness area in the total stroke of the structure reaches 90%, which is very beneficial for the structure to achieve ultra-low frequency vibration isolation characteristics.

[0123] (5) The structural parameters considered are: L 1 =0.1m,θ 1 =80°, L c =L 1 cosθ 1 , k h =200N / m, k o =13000N / m,c a =2N·s / m, Y 0 =0.01m. Figure 7 The amplitude-frequency response curve and displacement transmissibility curve obtained based on the direct numerical integration method and the harmonic balance method provided by the present invention are given. Figure 7 It can be seen that the direct numerical integration calculation results and the harmonic balance method structure are well consistent, which proves the effectiveness of the harmonic balance method provided by the present invention in solving this nonlinear motion differential equation.

[0124] (6) For the structural parameter k of the mass-spring-stiffness isolator v =310N / m; for traditional quasi-zero stiffness isolators, k h =335N / m, k v =1550N / m, L = 0.19m, Δh = 0.02m; for the improved X-type vibration isolator of the present invention, L 1 =0.1m,θ 1 =80°, L c =L 1 cosθ 1 , k h =200N / m, k o =13000N / m. Figure 8 The static stiffness curves and vibration transmissibility curves of three different vibration isolators are given. It can be observed that the vibration isolation frequency and resonance peak value of the X-type structure of the present invention are much lower than those of the mass-spring-damping linear vibration isolator and the traditional quasi-zero stiffness vibration isolator, and have a wider quasi-zero stiffness range. In addition, the X-type connecting rod structure of the present invention can achieve full-band vibration isolation characteristics at the zero stiffness position.

[0125] (7) In order to further verify that the structure can achieve ultra-low frequency and full-band vibration isolation characteristics, Fig. 9 It is clear that in S 1 (y st =0.08m), S 2 (y st =0.10m), S 3 (y st =0.13m) and S 4 (y st =0.16m) displacement transmissibility curve of the improved X-type vibration isolation structure at different equilibrium positions. It can be seen that at the zero stiffness position S 3 The improved X-type vibration isolator can achieve full-band vibration isolation characteristics. When the excitation frequency is 0.5Hz, its displacement transmission rate is 0.1, which means that the structure can isolate 90% of the vibration at this time.

[0126] (8) Compared with the traditional quasi-zero stiffness isolator, the X-type connecting rod vibration isolation structure designed in this embodiment has a wider quasi-zero stiffness range while ensuring the bearing capacity, and its quasi-zero stiffness area can be increased by 72%; in addition, the X-type vibration isolation structure designed in this embodiment has a better low-frequency vibration isolation effect. For example, when the external excitation frequency is 0.5Hz, the vibration isolation efficiency of this embodiment is increased by 76% compared with the traditional quasi-zero stiffness isolator.

Claims

1. A design method for an improved X-type connecting rod vibration isolation structure with large stroke quasi-zero stiffness and full-band vibration isolation characteristics, characterized in that The method comprises the following steps: Step 1: Clarify the improved X-type connecting rod vibration isolation structure design and its deformation relationship The improved X-type connecting rod vibration isolation structure includes four connecting rods and three springs, where the connecting rod length and assembly angle are L1 and θ1 respectively, P1-P4, P7 and P8 are the hinges of the connecting rod structure, and P5 and P6 are two points on the connecting rod; along the vertical direction, the hinges P1, P3 and P7 are collinear, and the hinges P2, P4 and P8 are collinear; the stiffness is k h The horizontal springs provide the main stiffness of the structure, and the two stiffnesses are k o The inclined springs are connected at points P5P7 and P6P8 to enhance the structural rigidity and bearing capacity; the distance between point P5 and hinge point P8 and the distance between point P6 and hinge point P7 are both L c ; The rotation angle of the improved X-type connecting rod vibration isolation structure under the vertical load F is The vertical displacement of the bearing platform is y d , the horizontal displacement of the hinge point P4 is x d , horizontal displacement x d and rotation angle Use vertical displacement y d It is expressed as: The original length of the horizontal spring is L 10 and the original length L of the two inclined springs 20 It is expressed as: L 10 =L1 cosθ1 (3) The length L of the horizontal spring and the inclined spring after deformation 11 and L 21 It is expressed as: Deformation length ΔL of horizontal spring and inclined spring h and ΔL o It is expressed as: Step 2: Establish the mechanical model of the improved X-type connecting rod vibration isolation structure According to the force analysis of the improved X-type connecting rod vibration isolation structure, the horizontal spring and the inclined spring are subjected to force F h and F o They are: F h =k h ΔL h ,F o =k o ΔL o (9) Based on the principle of virtual work, we get: Fδy d -F h δΔL h -2F o δΔL o =0 (10) Among them, δ is the symbol of variation; According to formulas (2) and (7)–(10), the vertical bearing capacity is expressed as: in: Step 3: Construct the nonlinear motion differential equation of the improved X-type connecting rod vibration isolation structure The vibration isolation mass is M, the base excitation and the platform vertical displacement are Y b and Y p , the relative displacement is Y=Y p -Y b Due to the effect of gravity, a new equilibrium point appears in the improved X-type connecting rod vibration isolation structure. When the improved X-type connecting rod vibration isolation structure is subjected to vibration from the base, the vibration isolation body vibrates vertically around the equilibrium position, introducing a new coordinate system (Y, F s ) represents relative motion, with the static equilibrium point as the origin, and the static displacement caused by gravity is y st , the nonlinear restoring force in the new coordinate system is F s According to the D'Alembert principle, the nonlinear motion equation of the improved X-type connecting rod vibration isolation structure is: Among them, c a is the structural damping coefficient; In order to obtain its analytical solution, the nonlinear stiffness function F s (Y) Perform polynomial fitting: Among them, η1–η4 are polynomial fitting coefficients. Substituting formula (14) into (13), the nonlinear motion differential equation of the improved X-type connecting rod vibration isolation structure is further expressed as: in: Step 4: Obtain structural vibration transmissibility using the harmonic balance method Assume that the external stimulus is Y b =Y0cos(ωt)=Y0cos(2πft), according to the harmonic balance method, the theoretical solution of formula (15) is assumed to be: Among them, Λ0 is the bias term, Λ1 and As amplitude and phase, transform equation (17) and Y b =Y0cos(ωt) Substitute into equation (15), ignore the higher-order terms, balance the coefficients of sin(ωt) and cos(ωt), and combine The characteristic equation is: The absolute displacement is expressed as: The displacement transmissibility of the improved X-type connecting rod vibration isolation system is expressed as:

2. The improved X-type connecting rod vibration isolation structure design method with large stroke quasi-zero stiffness and full-band vibration isolation characteristics according to claim 1 is characterized in that The connecting rod is made of a lightweight rigid material.

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