Friction system stability analysis method and device, storage medium and electronic equipment

Abstract

The invention discloses a friction system stability analysis method and device, a storage medium and electronic equipment, and the method comprises the steps: building a fractal contact model of contact rigidity and contact damping based on a joint surface according to a fractal theory; constructing a linear system state equation according to the five-degree-of-freedom friction pair kinetic model; according to the fractal contact model and the linear system state equation, solving a characteristic value, and analyzing the stability and modal coupling of the friction system; and determining a fractal dimension D and a fractal scale coefficient G of an optimization target according to a dynamic response result of the friction system, and realizing prediction of stability, modal coupling and a scream risk area of the friction system. According to the embodiment of the invention, microstructure modeling and macrodynamics modeling are fused, the influence of the roughness of the contact surface on the vibration characteristics of the system can be described more accurately, and the method is suitable for design and optimization of friction pair structures of high-speed trains, automobile brakes and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to a friction system stability analysis method and device, a storage medium and an electronic equipment, and belongs to the technical field of friction vibration analysis and system modeling. BACKGROUND

[0002] In various high-performance mechanical systems, friction pairs, as an important part of energy transmission, braking and control, are widely used in rail transportation (such as high-speed trains), automobiles, aerospace, etc. However, in the actual operation process, the friction pair is often accompanied by vibration and noise problems to varying degrees, especially the friction-induced squeal, which has become an important bottleneck affecting the performance, comfort and reliability of the system.

[0003] In traditional friction modeling and vibration analysis methods, researchers often use simplified Hertz contact theory and ignore the influence of contact surface roughness, or give the normal stiffness and damping in the form of a constant. However, in real engineering, the contact interface shows obvious irregularity, self-similarity and statistical fluctuation, making it difficult for these simplified models to accurately predict the dynamic response of the friction system, especially in the generation of squeal vibration and modal coupling analysis.

[0004] To solve the above problems, some researchers have begun to introduce fractal theory to describe the non-stationary micro-characteristics of rough surfaces. The fractal theory can effectively characterize the geometric complexity and roughness amplitude characteristics of the contact surface through two core parameters: fractal dimension D and fractal scale coefficient G. However, existing researches are mostly limited to static contact performance modeling, such as contact stiffness, contact area or friction coefficient, and there is still a lack of systematic research on how to effectively couple the fractal contact modeling and structural dynamics model. In addition, the structural characteristics of the friction pair, such as the size, mass, stiffness configuration of the friction block, also directly determine the modal characteristics and vibration behavior of the system. For example, the thickness change of the friction block not only affects its natural frequency, but also changes its contact stiffness and friction force distribution with the friction disc, thereby triggering or suppressing modal coupling and Hopf bifurcation and other nonlinear phenomena. Therefore, there is a significant coupling relationship between the micro-topography parameters of the friction interface and the macro-structural parameters of the system, and if their mutual influence is ignored, it is difficult to fully reveal the dynamic characteristics and instability mechanism of the friction system.

[0005] The existing technology still lacks a cross-scale friction system modeling and analysis method that can consider the influence of micro-rough surface topography evolution and macro-structural parameter changes. If the fractal contact modeling and multi-degree-of-freedom structural dynamics model can be integrated to form a unified coupling analysis framework, it will help to: improve the accuracy of friction system stability prediction, identify the sensitive interval of friction squeal vibration, optimize the structure design of the friction pair, and reduce the probability of vibration and noise.

[0006] Therefore, it is urgent to propose a friction system analysis method considering the coupling effect of the fractal characteristics and structural parameters of the contact interface, so as to improve the modeling accuracy and engineering adaptability of the friction vibration problem. SUMMARY

[0007] Therefore, the application provides a friction system stability analysis method and device, a storage medium and an electronic equipment, which fuse micro-morphology modeling and macro-dynamics modeling, can more accurately depict the influence of the roughness of the contact surface on the vibration characteristics of the system, and are suitable for the design and optimization of the friction pair structure of high-speed trains, automobile brakes and the like.

[0008] A first object of the application is to provide a friction system stability analysis method.

[0009] A second object of the application is to provide a friction system stability analysis device.

[0010] A third object of the application is to provide an electronic equipment.

[0011] A fourth object of the application is to provide a storage medium.

[0012] The first object of the application can be achieved by adopting the following technical scheme:

[0013] A friction system stability analysis method comprises the following steps:

[0014] Based on the joint surface, a fractal contact model of contact stiffness and contact damping is constructed according to the fractal theory;

[0015] According to a five-degree-of-freedom friction pair dynamics model, a linear system state equation is constructed;

[0016] According to the fractal contact model and the linear system state equation, eigenvalues are solved, and the stability and modal coupling of the friction system are analyzed;

[0017] According to the dynamic response results of the friction system, the fractal dimension and fractal scale coefficient of the optimization target are determined.

[0018] The second object of the application can be achieved by adopting the following technical scheme:

[0019] A friction system stability analysis device comprises the following steps:

[0020] A first construction module is configured to construct a fractal contact model of contact stiffness and contact damping based on the joint surface and according to the fractal theory;

[0021] A second construction module is configured to construct a linear system state equation according to a five-degree-of-freedom friction pair dynamics model;

[0022] A solving and analyzing module is configured to solve eigenvalues according to the fractal contact model and the linear system state equation, and analyze stability and modal coupling of the friction system.

[0023] A determining module is configured to determine fractal dimension and fractal scale coefficient of the optimization target according to the dynamic response result of the friction system.

[0024] The third object of the present application can be achieved by adopting the following technical solution:

[0025] An electronic device comprises a processor and a memory for storing a program executable by the processor, and the processor implements the friction system stability analysis method when executing the program stored in the memory.

[0026] The fourth object of the present application can be achieved by adopting the following technical solution:

[0027] A storage medium stores a program, and the program is executed by a processor to implement the friction system stability analysis method.

[0028] The present application has the following beneficial effects relative to the prior art:

[0029] The present application explicitly introduces fractal parameters (fractal dimension D and scale coefficient G) into contact modeling to improve the accuracy of describing real contact behavior. A five-degree-of-freedom dynamic model is constructed, and micro-contact stiffness and damping are coupled therein. The effects of friction block mass, thickness, and torsional stiffness on modal and stability are systematically studied. Based on linearization analysis and eigenvalue solving, the Hopf bifurcation point, modal coupling interval, and squeal risk area can be accurately located. This method is suitable for structural optimization of friction pairs such as high-speed train braking systems, automobile brakes, and precision machinery, and can improve stability, suppress squeal noise, and prolong service life. BRIEF DESCRIPTION OF DRAWINGS

[0030] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments or prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0031] Figure 1 A flowchart of a friction system stability analysis method according to an embodiment of the present application.

[0032] Figure 2 An equivalent schematic diagram of a micro-protrusion according to an embodiment of the present application.

[0033] Figure 3A schematic diagram of a five-degree-of-freedom friction pair model according to an embodiment of the present application.

[0034] Figure 4 A schematic diagram of the influence of the change of the fractal dimension D on the real part (a) and frequency (b) of the complex eigenvalue of the disc-block friction pair, and the influence of the change of the fractal scale coefficient G and fractal dimension D on the real part (c) and frequency (d) of the complex eigenvalue of the system according to an embodiment of the present application.

[0035] Figure 5 A structural diagram of a friction system stability analysis device according to an embodiment of the present application. DETAILED DESCRIPTION

[0036] In order to make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0037] Figure 1 A flowchart of a friction system stability analysis method according to an embodiment of the present application. As shown in the figure, the friction system stability analysis method comprises: Figure 1

[0038] S1: constructing a contact stiffness and contact damping model of a joint surface based on fractal theory.

[0039] S11: assuming that the rough surface is composed of a group of micro-convex bodies, and establishing a single micro-convex body contact model according to the Hertz theory and the Greenwood-Williamson improved model:

[0040] According to the equivalent plane structure in (2), the right triangle can be obtained by the Pythagorean theorem: Figure 2

[0041] R 2 = r' 2 θ(R-ζ) 2 (1)

[0042] Since the value of R is much larger than ζ, it is assumed that R >> ζ / 2, so according to formula (1), it is obtained that

[0043]

[0044] The cross-sectional area of the equivalent micro-convex body and the rigid plane contact is

[0045] A=πr' 2 ≈2πRζ (3)​​

[0046] S12: Based on the Yan and Komvopoulos fractal model, the equivalent contact radius, deformation and contact area of the micro asperity are calculated by using the fractal dimension D and the fractal scale coefficient G, respectively:

[0047] According to the improved W-M function of Yan and Komvopoulos, a simplified micro asperity contact base wave profile function z0(x) about r' can be obtained as

[0048]

[0049] wherein,

[0050]

[0051] L is the sampling length of the measuring instrument; D is the fractal dimension, 2<D<3 for a three-dimensional surface, and 1<D<2 for a two-dimensional profile curve; G is the fractal scale coefficient of the surface topography; γ (γ>1) is the parameter of frequency density, which is 1.5 when normally distributed; x, Φ 1,n0 are surface parameters.

[0052] The deformation ζ of the micro asperity under load is defined by the difference between the wave peak and the wave trough of the base wave profile function, so that when formula (4) is brought in, we have

[0053]

[0054] When formula (5) is brought into formula (2), the equal curvature radius can be expressed as

[0055]

[0056] When a' is the cross-sectional area of the micro asperity, a' = 2πr' 2 , then the size distribution function n(a') of the micro contact area can be expressed as

[0057]

[0058] In the formula, a l is the maximum micro asperity cross-sectional area,

[0059]

[0060] wherein E is the equivalent elastic modulus,

[0061]

[0062] E1, E2 are the elastic moduli of the two contact materials, υ1, υ2 are their Poisson's ratios, F n is the overall normal force, n max = ln(L / Ls ) / lnγ, deformation has γ nmax = L / L s , L s is the detectable wavelength depending on the measurement resolution.

[0063] a c is the critical deformation of the micro-asperity, which can be expressed as

[0064]

[0065] ε is used to represent the reduction of the average micro-asperity height, which reflects the interaction of the micro-asperities, so according to the literature

[0066]

[0067] where f a is the force applied on a single micro-asperity, A a is the nominal contact area.

[0068] Then, due to the interaction of the micro-asperities and the deformation of the micro-asperities under load, we can get

[0069]

[0070] When the micro-asperities are in the elastic deformation stage, i.e. a l > a c , the critical elastic deformation area a e of a single micro-asperity and the corresponding load f e are

[0071] a e = πRδ (11)

[0072]

[0073] Then, substituting equation (12) into equation (10), and replacing f a with f e , we can get

[0074]

[0075] Since a' = 2πr' 2 , and substituting equation (5) into equation (13), we can get

[0076]

[0077] Then, the elastic deformation area of the contact surface and the load it bears are

[0078]

[0079] When the micro asperity is in the plastic deformation stage, i.e. a l ≤a c , the critical elastic deformation area a p of the single micro asperity and the corresponding load f p are

[0080] a p = 2πRδ (17)

[0081] f p = Ha p (18)

[0082] Here H is the hardness of the softer material between the two contact materials.

[0083] Substituting equation (18) into equation (10) can obtain

[0084]

[0085] Then the plastic deformation area of the contact surface and the load are

[0086]

[0087] The contact area on the joint surface and the overall load are

[0088] A na = A p +A e (22)

[0089] F na = F p +F e (23)

[0090] The dimensionless form of equations (15), (16), (19), (20), (21), (22) is

[0091]

[0092] S13: Derive the normal elastic stiffness Kn and the normal damping Cn of the joint surface;

[0093] The normal contact stiffness of the single micro asperity in the elastic deformation state is

[0094]

[0095] The normal contact stiffness of the joint surface is

[0096]

[0097] The elastic potential energy stored by the single micro asperity is

[0098]

[0099] The elastic potential energy of the whole interface is

[0100]

[0101] The energy dissipated by the asperities in the plastic deformation state is

[0102] w np = vHRδ 2 = 2 5-D G D-2 (ln γ) 0.5 π (D-3) / 2 Ha' (5-D) / 2 (29)

[0103] The energy dissipated by the interface due to plastic deformation is

[0104]

[0105] The damping loss factor is a parameter to measure the energy dissipation ability of the material, which is defined as the ratio of the loss modulus to the storage modulus of the material. So the expression of the normal damping dissipation factor η n is

[0106]

[0107] C c is the critical damping coefficient of the system and

[0108]

[0109] M b is the mass of the rough surface, so the normal contact damping C n of the interface is

[0110]

[0111] The dimensionless form of K n and C n is

[0112]

[0113] S14: Derive the normal elastic stiffness K t and the normal damping C t of the interface.

[0114] The expressions of the tangential displacement and the tangential load of the asperities are given:

[0115]

[0116] where μ is the friction coefficient, T is the tangential load on the asperity, G' is the equivalent shear modulus,

[0117]

[0118] According to equation (33), we have

[0119]

[0120] When the asperity is deformed plastically under the normal load, the local region of the asperity will experience flow and deformation, which leads to the change of the shape of the asperity and the change of the surface properties. When the tangential force is generated, the microstructure inside the asperity will start to flow due to the plastic deformation, so that it loses the ability to resist the shear force. Therefore, the asperity in the plastic deformation state is not considered, and only the asperity in the elastic deformation state is considered. The tangential stiffness of the asperity in the elastic deformation state is

[0121]

[0122] The tangential contact stiffness of the interface is

[0123]

[0124] The elastic potential energy stored by a single asperity is

[0125]

[0126] The elastic potential energy of the interface is

[0127]

[0128] The energy dissipated by the asperity in the final stage due to plastic deformation is

[0129]

[0130] Let The energy dissipated by the interface due to plastic deformation is

[0131]

[0132] Considering the influence of the friction factor on the tangential contact damping fractal estimation model of the interface and the influence of the interface topography on the modal coupling unstable system, in the embodiment, Λ = 1, T e / F e = 0.05.

[0133] The tangential damping dissipation factor is

[0134]

[0135] The tangential contact damping of the mating surface is

[0136]

[0137] Then C t K t The dimensionless form is

[0138]

[0139] S2: Construct a five-degree-of-freedom friction pair dynamic model, and establish and linearize the system state equations;

[0140] S21: The friction system is simplified into a five-degree-of-freedom model, including the horizontal and vertical displacements x1 and y1 of the friction block.

[0141] The horizontal and vertical displacements of the friction disc are x2 and y2, and the torsional angle of the friction block is θ.

[0142] S22: In the model, consider the tilting spring stiffness k1, k2 and damping c1, c2 of the friction block and base, the basic spring stiffness k3, k4 and damping c3, ​​c4 of the friction disk, and the torsional stiffness k r and torsional damping c r ; and contact stiffness K n ,K t and contact damping C n C t .

[0143] S23: Constructing the system dynamics equations

[0144] according to Figure 3 Consider a five-degree-of-freedom frictional vibration system. Let the density of the friction block be ρ, the tilt angle be θ0, and the length, width, and height be a, b, and h, respectively. Then, what is the mass of the block?

[0145] m b =ρabh (45)

[0146] Then the moment of inertia I of the friction block is

[0147]

[0148] In this five-degree-of-freedom friction model, x1 and y1 represent the horizontal and vertical displacements of the friction block, x2 and y2 represent the horizontal and vertical displacements of the friction disk, and the torsional angle of the friction block is θ. Then, the normal contact force F of the friction between the disk and the block is... CN and tangential contact force F CT for

[0149]

[0150] Due to the twist of the block, the friction force F f appears at the edge of the block, Figure 3 where l is the eccentric moment of the friction force, the motion equation of the five-DOF system can be expressed as

[0151]

[0152] where

[0153]

[0154] In the stiffness matrix

[0155] K 11 = k1sin 2 (θ0+θ) + k2cos 2 (θ0+θ),

[0156] K 12 = k2sin(θ0+θ)cos(θ0+θ) - k1sin(θ0+θ)cos(θ0+θ),

[0157] K 13 = k1cos 2 (θ0+θ) + k2sin 2 (θ0+θ).

[0158] When the system is in equilibrium state, its equilibrium equation is

[0159]

[0160] where

[0161]

[0162] The stiffness matrix

[0163]

[0164] S24: Perform perturbation analysis, introduce perturbation variables Linearize the contact force and stiffness matrix;

[0165] Let the disturbance suffered by the system when it is at the equilibrium point be Then the displacement matrix can be expressed as

[0166]

[0167] Substitute equations (49) and (51) into equation (48) to get

[0168] ​

[0169] According to Taylor expansion and ignoring high order terms, F CN and F CT Linearization process has

[0170]

[0171] In addition, K 11 , K 12 , K 13 Linearization process has

[0172]

[0173] Where

[0174]

[0175] Joint formula (55), (56), (57), formula (52) in Can be expressed as

[0176]

[0177] S25: derive the system Jacobian matrix Get the state space equation Joint formula (53), (54), (58), formula (52) in Can be expressed as

[0178]

[0179] Formula (52) is expressed as

[0180]

[0181] Where

[0182]

[0183] Rewrite formula (49) as the following state equation

[0184]

[0185] Then J is the Jacobian matrix of the system, Z is the coordinate transformation vector, so

[0186]

[0187] S3: fractal contact model is introduced into the five degree of freedom friction pair dynamics model, the eigenvalue is solved, and the system stability and modal coupling are analyzed;

[0188] S31: determine the initial value of each parameter in the friction system, as shown in table 1 and table 2.

[0189] Table 1

[0190]

[0191] Table 2

[0192]

[0193] S32: Determine the value range of the fractal dimension and the fractal scale coefficient G with the fractal dimension D and the fractal scale coefficient G as control parameters.

[0194] S33: Solve the system eigenvalue to determine the system stability under different fractal parameters.

[0195] By solving the eigenvalue λ of the Jacobian matrix J, the stability characteristics of the system can be determined:

[0196] If all Re(λ)≤0, the system is stable;

[0197] If there is Re(λ)>0, the system is unstable, and may induce Hopf bifurcation or friction squeal;

[0198] If there is a complex conjugate eigenvalue crossing the imaginary axis, the system may have modal coupling phenomenon.

[0199] S4: According to the analysis of the dynamic response results of the friction system, the fractal dimension D and the fractal scale coefficient G of the required optimization target can be determined, and the prediction of the stability of the friction system, the modal coupling and the squeal risk area can be realized.

[0200] Figure 4 The influence of the change of the fractal scale coefficient G and the fractal dimension D on the real part and frequency of the complex eigenvalue of the system is shown. From Figure 4 (a) it can be found that when G is a constant, with the increase of D, the system real part experiences a process from closure to bifurcation to closure. In the bifurcation region, the unstable region of the system increases with the increase of D; with the increase of G, the starting point and the closure point of the Hopf bifurcation of the system move to a larger D value, but the overall unstable region of the system expands. Correspondingly Figure 4 (b) the system has modal coupling phenomenon, the unstable state region of the system has modal coupling, and with the increase of G, the modal coupling point of the system moves to a larger D value. Figure 4 (c-d) it can also be found that with the increase of D, the system experiences a process from stable to unstable to stable, and the unstable interval is in the range of 1.2<D<1.6, and with the increase of G, the Hopf bifurcation point of the system moves to a larger D value, and the unstable region of the system expands.

[0201] Those skilled in the art can understand that all or part of the steps in the method of the above embodiment can be instructed by a program to relevant hardware, and the corresponding program can be stored in a computer readable storage medium.

[0202] It should be noted that although the method operations of the above embodiments are described in a particular order in the accompanying drawings, this does not require or imply that the operations must be performed in that particular order, or that all of the illustrated operations must be performed to achieve desirable results. Instead, the steps can be changed in execution order. Additionally or alternatively, some steps can be omitted, a plurality of steps can be combined into one step, and / or one step can be divided into a plurality of steps.

[0203] As shown in Figure 5 The embodiment provides a friction system stability analysis device, which comprises:

[0204] A first construction module 501 is configured to construct a fractal contact model of contact stiffness and contact damping based on a joint surface according to fractal theory.

[0205] A second construction module 502 is configured to construct a linear system state equation according to a five-degree-of-freedom friction pair dynamics model.

[0206] A solving analysis module 503 is configured to solve eigenvalues according to the fractal contact model and the linear system state equation, and analyze stability and modal coupling of a friction system.

[0207] A determination module 504 is configured to determine fractal dimension and fractal scale coefficient of an optimization target according to a dynamic response result of the friction system.

[0208] The embodiment provides an electronic device, which comprises a processor, a memory, an input device, a display device and a network interface connected through a system bus. The processor is configured to provide computing and control capabilities. The memory comprises a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operating system and the computer program in the non-volatile storage medium. The computer program is executed by the processor to implement the friction system stability analysis method of the above embodiment.

[0209] The embodiment provides a storage medium, which is a computer readable storage medium and stores a computer program. The computer program is executed by the processor to implement the friction system stability analysis method of the above embodiment.

[0210] It should be noted that the computer readable storage medium in the embodiments of the present application can be a computer readable signal medium or a computer readable storage medium or any combination of the two. The computer readable storage medium may, for example, but is not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or apparatus, or any combination of the above. More specific examples of the computer readable storage medium can include, but are not limited to, an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0211] In the embodiments of the present application, the computer readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus or device. In the embodiments of the present application, the computer readable signal medium can include a data signal carried in a baseband or as a part of a carrier wave, which carries computer readable programs. Such a propagated data signal can take many forms, including but not limited to an electromagnetic signal, an optical signal or any suitable combination of the above. The computer readable signal medium can also be any computer readable medium other than the computer readable storage medium that can send, propagate or transmit programs for use by or in connection with an instruction execution system, apparatus or device. The computer programs contained in the computer readable storage medium can be transmitted by any suitable medium, including but not limited to a wire, a cable, a RF (radio frequency) or the like, or any suitable combination of the above.

[0212] The computer readable storage medium described above can be written in one or more programming languages or a combination of the above for executing the computer programs of the embodiments of the present application, including object oriented programming languages such as Java, Python, C++, and conventional procedural programming languages such as C language or similar programming languages. The program can be executed entirely on a user computer, partially on a user computer, as a separate software package, partially on a user computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer can be connected to the user computer through any kind of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (for example, through the Internet by using an Internet service provider).

[0213] The above merely describes preferred embodiments of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can make equivalent substitutions or changes within the scope disclosed by the present application, according to the technical solution and inventive concept of the present application, and such substitutions or changes shall also fall within the protection scope of the present application.

Claims

1. A method of friction system stability analysis, characterized by, The method comprises the following steps: a fractal contact model of contact stiffness and contact damping is constructed based on a contact surface according to fractal theory; a linear system state equation is constructed according to a five-degree-of-freedom friction pair dynamics model; eigenvalues are solved according to the fractal contact model and the linear system state equation, and stability and modal coupling of the friction system are analyzed; fractal dimension and fractal scale coefficient of an optimization target are determined according to a dynamic response result of the friction system.

2. The friction system stability analysis method of claim 1, wherein, The fractal contact model of contact stiffness and contact damping is constructed based on the contact surface according to fractal theory, and the method comprises the following steps: a single micro-asperity contact model is established; a normal contact stiffness of the contact surface is calculated according to a maximum micro-asperity cross-sectional area, a critical deformation variable of the micro-asperity, fractal dimension and an equivalent elastic modulus, as shown in the following formula: wherein a l is the maximum asperity cross-sectional area, a c is the critical deformation of the asperity, D is the fractal dimension, and E is the equivalent elastic modulus; a normal contact damping of the contact surface is calculated according to a mass of the rough surface, the normal contact stiffness and a normal damping dissipation factor, as shown in the following formula: where M b is the mass of the rough surface, K n is the normal contact stiffness, η n is the normal damping dissipation factor; a tangential contact stiffness of the contact surface is calculated according to the maximum micro-asperity cross-sectional area, the critical deformation variable of the micro-asperity, the fractal dimension, an equivalent shear modulus and a friction coefficient, as shown in the following formula: wherein a l is the maximum asperity cross-sectional area, a c is the critical deformation of the asperity, D is the fractal dimension, G' is the equivalent shear modulus, μ is the friction factor, T e / F e = a preset value; a tangential contact damping of the contact surface is calculated according to the mass of the rough surface, the tangential contact stiffness and a tangential damping dissipation factor, as shown in the following formula: where M b is the mass of the rough surface, K t is the tangential contact stiffness, η t is the tangential damping dissipation factor.

3. The friction system stability analysis method of claim 1, wherein, The linear system state equation is constructed according to the five-degree-of-freedom friction pair dynamics model, and the method comprises the following steps: the friction system is simplified into a five-degree-of-freedom model, and the five-degree-of-freedom model comprises horizontal displacement and vertical displacement x1, y1 of the friction block, horizontal displacement and vertical displacement x2, y2 of the friction disc and a torsion angle θ of the friction block; In the five degree of freedom model, the tilt spring stiffness k1, k2 and damping c1, c2 of the friction block and the base, the base spring stiffness k3, k4 and damping c3, c4 of the friction disc, and the torsional stiffness k r And torsional damping c r ; And the contact stiffness K n ,K t And the contact damping C n ,C t , and then the system dynamics equation is established, and the disturbance analysis is carried out, the disturbance variable is introduced, the contact force and stiffness matrix are linearized, the system Jacobian matrix is derived, and the state space equation is obtained.

4. The friction system stability analysis method of claim 3, wherein, the system dynamics equation is constructed, as shown in the following formula: in the stiffness matrix: K 11 = k1sin 2 (θ0+θ) + k2cos 2 (θ0+θ); K 12 = k2sin(θ0+ θ)cos(θ0+ θ) - klsin(θ0+ θ)cos(θ0+ θ); K 13 = k1cos 2 (θ0+θ) + k2sin 2 (θ0+θ); m b m represents the mass of the friction block, a, b, h are the length, width and height of the friction block, θ0 is the inclination angle, l is the eccentric moment of the friction force, I represents the moment of inertia of the friction block, m d m represents the mass of the friction block, a, b, h are the length, width and height of the friction block, θ0 is the inclination angle, l is the eccentric moment of the friction force, I represents the moment of inertia of the friction block, m CN m represents the mass of the friction block, a, b, h are the length, width and height of the friction block, θ0 is the inclination angle, l is the eccentric moment of the friction force, I represents the moment of inertia of the friction block, m CT μ is the friction factor, F n is the overall normal force.

5. The friction system stability analysis method of claim 4, wherein, The normal contact force F of the disc block friction CN And the tangential contact force F CT As follows: The perturbation variable is 6. The friction system stability analysis method of claim 3, wherein, The eigenvalues are solved according to the fractal contact model and the linear system state equation, and the stability and modal coupling of the friction system are analyzed, and the method comprises the following steps: initial values of parameters in the friction system are determined; fractal dimension and fractal scale coefficient are taken as control parameters, and a value range of the fractal dimension and the fractal scale coefficient is determined; the stability and modal coupling of the system are determined by solving eigenvalues of a Jacobian matrix.

7. The friction system stability analysis method of claim 6, wherein, The stability and modal coupling of the system are determined by solving eigenvalues of the Jacobian matrix, and the method comprises the following steps: if all eigenvalues are less than or equal to a threshold value, the system is stable; if there is an eigenvalue greater than the threshold value, the system is unstable; if there is a complex conjugate eigenvalue crossing the imaginary axis, the system has a modal coupling phenomenon.

8. A friction system stability analysis device characterized by comprising: The method comprises the following steps: a first construction module is configured to construct a fractal contact model of contact stiffness and contact damping based on a contact surface according to fractal theory; a second construction module is configured to construct a linear system state equation according to a five-degree-of-freedom friction pair dynamics model; a solving and analyzing module is configured to solve eigenvalues according to the fractal contact model and the linear system state equation, and analyze stability and modal coupling of a friction system; a determining module is configured to determine fractal dimension and fractal scale coefficient of an optimization target according to a dynamic response result of the friction system.

9. A computer-readable storage medium, characterized in that, The computer readable storage medium comprises a stored program, wherein the program controls a processor of the device to execute the friction system stability analysis method in any one of claims 1 to 7 when the program is running.

10. An electronic device, comprising: The device comprises the following components: one or more processors; a storage device for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors are caused to perform the friction system stability analysis method according to any one of claims 1 to 7.

Images