Floating support friction pair impact dynamic load calculation method and system considering rough interface morphology characteristics

Abstract

The invention specifically discloses a floating support friction pair impact dynamic load calculation method and system considering rough interface morphology characteristics, and the method comprises the steps: obtaining the basic parameters of a floating support friction plate assembly to be calculated, representing the three-dimensional rough surface morphology, calculating the total contact rigidity of the whole rough interface, and calculating the impact dynamic load of the floating support friction pair. Calculating the rough surface contact rigidity of the gear teeth, calculating the bending, shearing and axial compression rigidity of the gear teeth, the matrix deformation and the matrix rigidity, calculating the comprehensive rigidity and the time variation rigidity of a single tooth pair, and deducing the relative displacement of the inner hub and the friction plate gear teeth under the load effect; calculating the number of random impact collision gear teeth of the floating support friction pair and the collision force; a bending-twisting random collision dynamic model of a floating support friction plate and an inner hub system is established, and the impact dynamic load of a floating support friction pair is obtained by adopting a Runge-Kutta method. By adopting the technical scheme, the impact dynamic load of the tooth part of the friction pair is obtained by constructing the rough interface morphology feature-collision force-rigidity coupled random collision dynamic model.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of variable speed mechanism, and relates to a floating support friction pair impact dynamic load calculation method and system considering rough interface topography characteristics. BACKGROUND

[0002] In the variable speed mechanism, when the clutch or brake is in the non-braking state, the friction plate is suspended on the inner hub and is in the floating support state. Due to the existence of the tooth side gap and the eccentric distance, only part of the teeth of the friction plate and the inner hub are in contact, and the mass of the friction plate is much smaller than that of the inner hub, so that the angular velocity difference between the two is generated in the non-stationary operation process. This difference can cause random collision phenomena such as positive collision, tooth separation, pursuit collision and reverse collision between the teeth, so that the number of collision teeth, the depth, the phase and the contact position present high uncertainty.

[0003] Existing research shows that the gear tooth collision dynamics behavior is affected by two key factors:

[0004] 1. Nonlinear excitation of rough interface topography: the distribution, truncation characteristics and dynamic load changes of the micro-convex body of the gear tooth contact surface can significantly change the contact stiffness, and then affect the transmission characteristics of the collision force;

[0005] 2. Dynamic excitation of multi-tooth pair random collision: the traditional single-tooth pair collision model of the gear pair cannot describe the time-varying contact behavior of the multi-tooth pair of the friction plate, and the randomness of the collision causes the boundary conditions of the system to change continuously, which aggravates the complexity of the dynamics analysis.

[0006] Existing research on the excitation characteristics of the rough interface of the gear tooth usually simplifies the three-dimensional rough surface of the gear tooth into a two-dimensional rough profile form superimposed by multiple cosine functions, and assumes the distribution characteristics of the micro-convex body by using an empirical power function. However, this assumption cannot accurately reflect the actual distribution characteristics of the micro-convex body of the real three-dimensional rough surface, resulting in insufficient characterization of the details of the rough interface excitation of the gear tooth. Moreover, the size of the contact load directly affects the size, position and number of the truncated micro-convex body on the rough interface, and then changes the rough interface excitation characteristics of the gear tooth. At the same time, the change of the rough interface excitation will in turn affect the dynamic characteristics of the system, indicating that there is a complex coupling effect among the rough interface topography characteristics, the dynamic load and the stiffness of the gear tooth.

[0007] The current research has not analyzed the influence of this coupling effect on the random collision dynamic characteristics of the floating support friction plate and the inner hub system. Therefore, it is necessary to develop a new method for reconstructing the three-dimensional rough surface on the basis of the traditional fractal function characterization method of the three-dimensional rough surface, combined with the influence of the waviness and surface roughness of the typical gear processing surface, and to develop a method for calculating the impact dynamic load of the friction pair tooth part by constructing a random collision dynamics model of the rough interface topography characteristics-collision force-stiffness coupling. SUMMARY

[0008] The purpose of the present invention is to provide a method and system for calculating the impact dynamic load of a floating support friction pair taking into account the rough interface morphology characteristics, so as to solve the uncertainty problem caused by random collisions between the friction plate floating support and the inner hub under non-steady operation.

[0009] To achieve the above objectives, the basic solution of the present invention is: a method for calculating the impact dynamic load of a floating support friction pair taking into account the rough interface morphology characteristics, comprising the following steps:

[0010] S1, obtaining basic parameters of the floating support friction plate assembly to be calculated;

[0011] S2, superimposes regular waviness and random surface roughness to characterize the three-dimensional rough surface morphology;

[0012] S3, calculate the scale, quantity and position distribution characteristics of the micro-asperities on the three-dimensional rough surface morphology;

[0013] S4, based on the parameters of the micro-asperities on the three-dimensional rough surface, calculate the critical deformation δ of each micro-asperity under load iec , contact load, contact stiffness and contact area of ​​a single asperity under different deformation modes;

[0014] Considering the distribution characteristics of the micro-asperities on the real three-dimensional rough interface, the total contact stiffness k of the entire rough interface is calculated. t ;

[0015] Considering the influence of the curvature of the contact position between the inner hub and the friction plate on the distribution density of the micro-asperities, the surface contact coefficient λ is introduced c ηξ , calculate the contact stiffness of the rough surface of the gear teeth;

[0016] S5, calculates the bending, shear and axial compression stiffness of the gear teeth based on the parameters of the inner hub and friction plate;

[0017] Based on the rigid-flexible coupling relationship and elastic ring theory, the matrix deformation and matrix stiffness k are calculated. f ;

[0018] S6, calculates the combined stiffness k of a single tooth pair based on the bending, shear and axial compression stiffness of the gear teeth and the matrix stiffness s and time-varying stiffness K s (t);

[0019] S7, obtaining the initial eccentricity of the friction plate and the actual radial tooth side clearance, and determining the relative offset between the friction plate and the inner hub gear teeth under a no-load state;

[0020] Based on the relative motion relationship between the gear teeth, the relative displacement of the inner hub and the friction plate teeth under load is derived;

[0021] By analyzing the deformation coordination relationship between the actual radial clearance of the gear tooth and the relative position, the actual collision tooth number, the collision tooth position, the collision depth, and the collision phase characteristics are determined;

[0022] S8, the number of randomly impacted and collided gear teeth of the floating support friction pair and the collision force are calculated;

[0023] S9, a bending-torsional random collision dynamics model of the floating support friction plate and the inner hub system is established, the Runge-Kutta method is used to obtain the impact dynamic load of the floating support friction pair, and the influence mechanism of parameters such as surface roughness, tooth side clearance, inner hub rotating speed fluctuation frequency and rotating speed fluctuation amplitude on random collision characteristics and vibration response is revealed, which is beneficial to hardware design and optimization, such as tooth side clearance and surface roughness design. Gap control: simulation shows that too small tooth side clearance increases the collision frequency, and too large tooth side clearance increases the collision force amplitude. Surface processing technology: roughness grade N5-N6 can inhibit high-frequency collision.

[0024] The working principle and beneficial effects of the basic scheme are that: the technical scheme combines the influences of the typical gear tooth processing surface waviness and surface roughness, develops a new method for three-dimensional reconstruction of rough surfaces, derives the calculation formula of the instantaneous collision tooth number, collision depth and collision phase of the floating support friction plate and the inner hub system under non-stable constraint conditions, proposes an analytical calculation method for gear random collision excitation, and solves the uncertainty problem caused by random collision under the non-stationary operation of the floating support friction plate and the inner hub.

[0025] By combining the coupling effect of gear rough interface excitation and random collision excitation, a system random collision dynamics model is established, the influence of different structures, working conditions and surface topography parameters on random collision dynamic characteristics is realized, and a more actual random collision mechanism analysis method of the floating support friction plate is developed.

[0026] Further, step S2 superimposes the regular waviness and the random surface roughness based on the basic parameters of the floating support friction plate assembly, and the method for characterizing the three-dimensional rough surface topography is:

[0027] S201, the gear tooth surface roughness topography function z3(x, y) is calculated and expressed as:

[0028]

[0029] Wherein, L is the sample length; G3 and D3 represent the fractal roughness and the fractal dimension respectively, 2 max3 is the maximum value of the frequency index range, n max3 = int[log(L / Ls ) / logγ], L s is the cut-off length, approximately six lattice distances; φ (m,n3) is a random phase in the range 0 and 2π; x and y are the position coordinates of the surface profile;

[0030] S202, selecting milling processing mode, calculating the sine wave roughness h(x) of the milling surface, expressed as:

[0031] h(x) = qR a sin(ω0x + θ) + b, 0≤x≤L

[0032] where R a is the surface roughness value; q is the contribution degree of the wave roughness to the surface roughness R a ; ω0is the wave roughness wavelength scaling factor; θ is the initial phase angle of the wave roughness; b is the wave roughness mean value;

[0033] S203, using sine wave roughness in the direction perpendicular to the cutting direction, and using straight line in the direction of the chip to develop, superimposing the regular wave roughness and the random surface roughness, the reconstructed three-dimensional rough surface is expressed as:

[0034] Z(x, y) = A·z3(x, y) + h(x, y)

[0035] where z3(x, y) is the surface roughness topography function; h(x, y) represents the wave roughness shape function; A is the surface roughness amplitude scaling factor;

[0036] S204, according to the measured three-dimensional rough surface, the roughness value R a is determined, and the optimization algorithm is used to iteratively optimize the parameters k, ω and θ, so that the Pearson correlation coefficient r of the wave roughness surface and the measured rough surface is greater than 0.7, and by adjusting the parameters G3, D3 and k, the relative error ε of the roughness value of the simulation and the measured surface is less than 5%, and finally the three-dimensional rough surface is obtained, which is fitted with the measured surface height, r is:

[0037]

[0038] where Z(x j ,y k ) and Z1(x j ,y k ) represent the profile height of the simulation and the measured rough surface at the coordinate point (x j ,y k ); and are the mean values ​​of the profile height of the rough surface obtained by simulation and measurement, respectively; J and K are the number of discrete points in the x and y directions, respectively; j and k represent the sequence numbers of the discrete points in the x and y directions.

[0039] Based on the basic parameters of the friction plate assembly, the three-dimensional rough surface morphology is characterized by superimposing regular waviness and random surface roughness.

[0040] Furthermore, step S3 is to calculate the size, quantity and position distribution characteristics of the micro-protrusions on the surface based on the three-dimensional rough surface morphology, as follows:

[0041] S301, define the spatial domain for generating the three-dimensional rough surface as Ω(x j ,y k ,Z(x j ,y k )), where Z1(x j ,y k ) represents the measured rough surface at the coordinate point (x j ,y k ), j = 1 ~ J, k = 1 ~ K, J and K are the discrete points in the x and y directions respectively, j and k represent the sequence numbers of the discrete points in the x and y directions;

[0042] Set the boundary value of the spatial domain Ω to 0 and redefine the system coordinates, namely Z'(x j ,y k )=Z(x j ,y k )-mean(Z(x j ,y k )), and update the spatial domain to Ω1(x j ,y k ,Z'(x j ,y k )), mean(Z(x j ,y k )) represents the average value of all heights of the entire surface;

[0043] S302, set the current node to the initial state Ω1, and regard the adjacent node η as the successor node of the current node. If the value of the adjacent node is smaller than the value of the current node, the state of the current node is retained; otherwise, the value of the adjacent node is replaced by the value of the current node;

[0044] Repeat this process until the values ​​of all subsequent nodes are smaller than the current node, that is, the node is a local maximum, and all local maxima are stored in the spatial domain Ω 2i (x (j,i) ,y (k,i) ,Z'(x (j,i) ,y (k,i)), i = 1 ~ N r , N r is the number of the asperities on the rough surface;

[0045] S303, the truncation height of the ith asperity is defined as δ i = Δ, Δ is the sample interval of the coordinate domain, when all the nodes near the node Ω 2i have a height greater than Z'(x (j,i) , y (k,i) )- δ i , the truncation radius R i of the ith asperity is represented as:

[0046]

[0047] where Δx and Δy are the sample intervals of the coordinate domain in x and y directions respectively; M ri is the number of elements in the truncated area of the ith asperity;

[0048] S304, it is assumed that the geometry of the ith asperity before deformation obeys a cosine function, which is represented as:

[0049]

[0050] where Z2(x si ) represents the position height of the point on the ith asperity with a radial distance of x si to the center point of the asperity, and the independent variable x si represents the radial distance of any point on the asperity to the center point of the asperity, and when the independent variable is 0, it is located at the center point, i.e. the maximum height; represents the height amplitude of the ith asperity, is the overall roughness of the ith asperity, and the index D i -1 represents the amplification of the dependence of the asperity height on the roughness; is the sensitivity of the height of the ith asperity to the base size, and the index 2-D i represents the change rate of the geometric properties of the ith asperity with the fractal dimension D i , when D i = 2, the asperity belongs to low fractal dimension, the surface is smooth, i.e. the asperity height is independent of the base size at this time; l i , G i and D i represent the base diameter, fractal roughness and fractal dimension of the ith asperity, respectively, and are:

[0051]

[0052] where n iand δ i are the frequency exponent and the cut-off height of the ith asperity, respectively; Z'(x (j,i) ,y (k, i ) ) is the height of the ith asperity; D3 represents the fractal dimension, γ is the scaling factor, l i and D i represent the base diameter and the fractal dimension of the ith asperity, respectively.

[0053] Based on the reconstructed three-dimensional rough surface topography, the distribution characteristics of the micro-asperity size, quantity and position of the surface are calculated, which is beneficial to subsequent use.

[0054] Further, in step S4, based on the parameters of the three-dimensional rough surface micro-asperity, the critical deformation δ iec of each micro-asperity under the action of load is calculated, and the contact load, contact stiffness and contact area of a single micro-asperity under different deformation modes are as follows: based on the K-E model, the critical deformation of the micro-asperity from the elastic stage to the elastic-plastic stage is calculated as:

[0055]

[0056] where H and E are the hardness and elastic modulus of the material, respectively; K v is the hardness coefficient related to the Poisson's ratio v; l i , G i and D i represent the base diameter, fractal roughness and fractal dimension of the ith asperity, respectively; represents the effective volume of the ith asperity under the fractal dimension D i , l i represents the base diameter, i.e. the lateral dimension of the ith asperity, the exponent D i represents the fractal dimension, which describes the complexity of the geometric shape of the ith asperity, is the overall roughness of the ith asperity, G i represents the fractal roughness of the ith asperity, and the exponent D i -1 represents the amplification of the dependence of the asperity height on the roughness;

[0057] With the increase of the applied load, the deformation δ i of the ith asperity may go through four stages of pure elasticity, first and second stage elastic-plasticity and complete plasticity, i.e.:

[0058]

[0059] In these four contact deformation stages, the contact load of the ith deformed asperity is represented as:

[0060]

[0061] where P ne , P nep1 , P nep2 , P np represent the contact load of the ith deformed asperity in the four contact deformation stages, respectively.

[0062] In the four contact deformation stages, the contact area a ne , a nep1 , a nep2 , a np of the ith deformed asperity is expressed as:

[0063]

[0064] In the four contact deformation stages, the contact stiffness k ne , k nep1 , k nep2 , k np of the ith deformed asperity is expressed as:

[0065]

[0066] Based on the parameters of the three-dimensional rough surface asperity, the critical deformation δ iec of each asperity under the load is calculated, and then the contact load, the contact stiffness and the contact area of a single asperity under different deformation modes can be calculated.

[0067] Further, considering the actual contact state of the asperity, the total contact stiffness k t and the contact load p t of the rough interface are calculated:

[0068]

[0069] where N t is the number of truncated asperities;

[0070] Based on the slicing method, considering the influence of the curvature of the contact position of the inner hub and the friction plate on the distribution density of the asperity, the surface contact coefficient λ c ηξ is introduced. h ηξ The contact stiffness k ce of the tooth rough surface is expressed as:

[0071]

[0072] where R ce ηξ and R cp ηξ are the radii of curvature at the contact position ξ; F′ηζ Load on the rough interface at the contact position; the symbol "+" represents the inner tooth contact, and the symbol "-" represents the outer tooth contact;

[0073] Since the inner hub and the friction plate tooth have the same curvature radius at the contact position, and the tooth gap is much smaller than the curvature radius, the contact position ξ can be approximated as the contact of two microelement rough interfaces with an area of Δw x Δu, and the surface contact coefficient λ c ηξ Approximately 1, the stiffness k h η Simplified as k t ηξ ; Δw and Δu are the sample lengths in the x direction and the y direction; the superscript ξ is the microelement position in the tooth profile direction; and the superscript η is the microelement position in the tooth width direction.

[0074] Based on the contact load, contact stiffness and contact area of a single microconvex body under different deformation modes, and further considering the distribution characteristics of the real three-dimensional rough interface microconvex body, the total contact stiffness k t of the entire rough interface is calculated. Finally, considering the influence of the curvature of the contact position of the inner hub and the friction plate on the microconvex body distribution density, the surface contact coefficient λ c ηξ The tooth rough surface contact stiffness k h is calculated.

[0075] Further, step S5 calculates the bending, shear and axial compression stiffness of the tooth based on the parameters of the inner hub and the friction plate, and calculates the substrate deformation and substrate stiffness k f based on the rigid-flexible coupling relationship and the elastic circular ring theory. The specific steps are as follows:

[0076] S501, the tooth of the inner hub and the friction plate is involute tooth profile. According to the principle of elastic potential energy, under the action of force F, the energy U tooth stored in the tooth due to bending, shear and compression deformation is represented as:

[0077] U tooth = U s + U a + U b

[0078] Wherein

[0079]

[0080]

[0081] Wherein, the parameters d of the inner hub and the friction plate represent the straight line distance from the meshing point to the tooth root, x represents the position coordinate along the tooth center line, h is the half tooth thickness at the meshing position, and α mis the pressure angle at the contact position; U b is the bending deformation of the tooth; U s is the shear deformation of the tooth; and U a is the axial compression deformation of the tooth; k b is the bending stiffness of the tooth; k s is the shear stiffness of the tooth; and k a is the axial compression stiffness of the tooth; G is the shear modulus of the material, G = E / 2(1 + μ); E and μ are the elastic modulus and Poisson's ratio, respectively; A x is the cross-sectional area at a distance x from the force application point; and I x is the cross-sectional moment of inertia, A x = 2h x W, W is the contact tooth width at the meshing position; h x is the half tooth thickness at the meshing position;

[0082] S502, the inner hub and the tooth of the friction plate are assumed to be rigid bodies, while the base body is considered to be flexible, and the base body deformation δ f is calculated based on the rigid-flexible coupling relationship and the elastic ring theory, and is expressed as:

[0083]

[0084] where τ = 1 represents the inner hub; τ = -1 represents the friction plate; the symbol u f represents the radial displacement of point p on the base body, r f is the tooth root circle radius, θ f is the load action range angle defined with point p as the starting point, h f represents the tooth root thickness, and p represents the intersection of the tooth root circle and the tooth center line; u r (θ = 0) and u t (θ = 0) are the radial and tangential displacements of point p, respectively, and are expressed as:

[0085]

[0086] χ = (ρ + 3μ) / (ρ + μ)

[0087] ρ = Eμ / ((1 + μ)(1 - 2μ))

[0088] where the parameters and are functions related to θ f and h f ; represents the Fourier cosine coefficients of the normal stress distribution shape function, represents the Fourier sine coefficients of the normal stress distribution shape function, represents the Fourier cosine coefficients of the tangential stress distribution shape function. are displacement influence coefficients composed of a set of elastic ring theory, wherein represents the comprehensive influence degree of the kth stress harmonic on the radial displacement of the elastic ring at θ = 0; represents the comprehensive influence degree of the kth stress harmonic on the tangential displacement and its derivative of the elastic ring at θ = 0; represents the comprehensive influence degree of the kth stress harmonic on the tangential displacement of the elastic ring at θ = 0;

[0089] S503, calculating the matrix stiffness k f .

[0090]

[0091] Based on the parameters of the inner hub and the friction plate, the bending, shear and axial compression stiffness of the gear teeth are calculated. The traditional empirical fitting method is abandoned, the gear teeth of the inner hub and the friction plate are assumed to be rigid bodies, and the matrix is regarded as flexible. The matrix deformation is calculated based on the rigid-flexible coupling relationship and the elastic ring theory, so as to calculate the matrix stiffness k f .

[0092] Further, step S6 calculates the single-tooth comprehensive stiffness k s and the time-varying dynamic stiffness K s (t) based on the bending, shear and axial compression stiffness of the gear teeth and the matrix stiffness, and the steps are as follows:

[0093] S601, calculating the single-tooth comprehensive stiffness k s of the inner hub and the friction plate, which is expressed as:

[0094]

[0095] wherein, the subscripts e and p respectively represent the inner hub and the friction plate; η0 represents the number of microelements in the tooth width direction; q0 represents the number of microelements in the tooth profile direction; the comprehensive stiffness components k b , k s , k a and k f are constants related to the gear tooth profile, meshing position and material parameters, and the superscript ξ represents the microelement position in the tooth profile direction; the superscript η represents the microelement position in the tooth width direction; the contact stiffness k h ηξ [F ηξ '] has a strong nonlinear relationship with the meshing position impact force and the rough interface topography characteristics of the gear teeth;

[0096] S602, assuming that the number of teeth of the inner hub and the friction plate is N, the time-varying dynamic stiffness K s (t) is calculated, which is expressed as:

[0097]

[0098] Among them, k sn (t) represents the comprehensive stiffness of the nth gear tooth pair of the inner hub and the friction plate. If the inner hub and the nth gear tooth pair of the friction plate collide, k sn (t) is calculated by S601; if the inner hub and the nth gear tooth pair of the friction plate do not collide, then k sn (t) = 0; t is the instantaneous time, tooth pairs, tooth pairs.

[0099] Based on the bending, shear and axial compression stiffness of the gear teeth and the matrix stiffness calculated in step S5, the comprehensive stiffness k of the single tooth pair is obtained. s and time-varying stiffness K s (t), simple operation.

[0100] Furthermore, the specific steps of step S7 are as follows:

[0101] S701, assuming that the unilateral normal tooth side clearance between the inner hub and the friction plate follows a Gaussian random distribution, then the unilateral tooth side clearance C of the nth gear tooth pair is n Expressed as:

[0102] c n ~N(μ,σ 2 )

[0103] Wherein, μ is the average value of tooth side clearance; σ 2 is the discrete degree of tooth side clearance;

[0104] S702, under the action of gravity or radial force, the inner hub and the positive and negative tooth pairs of the friction plate will come into contact at certain specific positions. When the nth tooth pair comes into contact, the vertical displacement a generated by the positive and negative tooth pairs of the friction plate Fn , a Bn Expressed as:

[0105] a Fn =abs(c n / cos(α m +2π(n-1)N))

[0106] a Bn =abs(c n / cos(-α m +2π(n-1)N))

[0107] Where N is the number of teeth on the inner hub and friction plate; abs represents the absolute value function, α m is the pressure angle at the contact position;

[0108] The eccentricity e0 caused by the initial tooth side clearance is:

[0109]

[0110] S703, the friction plate under the action of eccentricity, the n tooth pair in the actual tooth side gap C Fn , C Bn , is:

[0111] c Fn =c n -e0sin(α m +2π(n-1) / N)

[0112] c Bn =c n +e0sin(-α m +2π(n-1) / N);

[0113] S704, according to the geometric relationship, the n tooth pair wheel in the driving side and the back side of the collision angle θ Fn and θ Bn , is:

[0114] θ Fn =2π(n-1) / N+ωt+θ0

[0115] θ Bn =2π(n-1) / N+ωt-θ0

[0116] Where, ω is the inner hub angular velocity; θ0 is the pitch circle position half tooth angle, that is, θ0=π / 2N; t is the instantaneous time;

[0117] S705, define the n tooth pair wheel in the driving side and the back side of the collision point tangent and x e axis positive direction angle respectively φ Fn and φ Bn , that is:

[0118]

[0119] Based on the deformation coordination relationship between the actual radial clearance of the tooth and the relative position, considering the bending and torsional vibration influence of the inner hub and the friction plate, the n tooth pair in the driving side and the back side of the collision deformation δ Fn and δ Bn , respectively, are:

[0120]

[0121] Where, x and y with subscript e or p are radial vibration displacement, subscript e and p represent the inner hub and the friction plate respectively; θ with subscript e or p is the torsional vibration angular displacement; r b is the base circle radius;

[0122] S706, according to the deformation of the inner hub and the n th collision tooth of the friction plate, the position of the collision tooth and its collision phase are determined, that is:

[0123]

[0124] Wherein, C Fn =1 and C Bn =1 represent that the inner hub and the n th tooth pair of the friction plate occur forward collision and reverse collision respectively; C Fn =0 and C Bn =0 mean that the inner hub and the n th tooth pair of the friction plate do not collide; Subscript Fn and Bn are used to determine the position of the tooth that occurs positive and reverse collision;

[0125] S707, by judging the position of the collision tooth and the collision phase, the total number of teeth N F , N B occurring forward and reverse collision between the inner hub and the friction plate at each moment is determined, that is:

[0126]

[0127] Firstly, the initial eccentricity of the friction plate and the actual radial tooth gap are calculated based on the geometric relationship, and then the relative offset of the friction plate and the inner hub tooth under no load condition is determined. Then, according to the relative motion relationship between the teeth, the relative displacement of the inner hub and the friction plate tooth under load is derived. Finally, by analyzing the deformation coordination relationship between the actual radial gap and the relative position of the tooth, the actual number of collision teeth, the position of the collision tooth, the collision depth and the collision phase (i.e. positive and reverse collision) are further determined.

[0128] Further, in step S8, the number of random impact collision teeth and the collision force of the floating support friction pair are calculated, and the specific steps are as follows:

[0129] S801, based on the principle of energy conservation, the energy loss ΔT before and after the tooth collision is calculated as:

[0130]

[0131] Wherein, m e and m p are the mass of the inner hub and the friction plate respectively; is the relative velocity of the tooth before collision; the rebound coefficient c r is the ratio of the relative velocity of the tooth collision separation to the relative velocity at the beginning of the collision, which is determined by the material properties of the collision tooth; the rebound coefficient c r usually takes a value between 0 and 1, when c r= 0, represents a completely inelastic collision, i.e. no restitution during the collision process, all kinetic energy is dissipated; when c r = 1, represents a completely elastic collision, i.e. the kinetic energy during the collision is completely preserved, no loss; the coefficient of restitution c r is expressed as:

[0132]

[0133] wherein the subscripts e and p represent the inner hub and the friction plate respectively;

[0134] S802, based on the Lankarani and Nikravesh model, the wheel tooth collision is calculated to obtain the damping force The energy dissipation ΔT in the form of work done is:

[0135]

[0136] wherein δ0 is the maximum deformation of the wheel tooth collision;

[0137] S803, according to the law of conservation of energy, the hysteresis damping coefficient μ0 is obtained, which is:

[0138]

[0139] wherein k s represents the comprehensive stiffness of the single wheel tooth of the inner hub and the friction plate;

[0140] S804, based on the hysteresis damping coefficient μ0, the single pair of wheel tooth nonlinear collision force calculation formula is obtained by substituting the Hertz contact theory, to obtain the normal collision force F n , i.e.:

[0141]

[0142] wherein k s δ m represents the elastic contact force part; δ is the normal relative deformation of the tooth part; m0 is the nonlinear index, m0 = 1.5; k sn is the comprehensive stiffness of the n th wheel tooth pair of the inner hub and the friction plate; μ0 is the hysteresis damping coefficient, which is related to the viscous damping coefficient, shear and volume deformation, etc.; δ Fn and δ Bn represent the collision deformation of the n th wheel tooth pair on the driving side and the back side;

[0143] S805, the components F nx , F ny of the n th wheel tooth forward and reverse collision force in x and y directions are expressed as:

[0144]

[0145] where t is the instantaneous time; ω is the inner hub angular velocity; θ0 is the pitch circle position half-tooth angle,

[0146] The total collision force and the total collision force component of the inner hub and all tooth pairs of the friction plate are expressed as:

[0147]

[0148] where the components of the nth pair of gear teeth forward and reverse collision forces in the x and y directions are expressed as F nx , F ny ; the normal collision force of the inner hub and the nth pair of gear teeth of the friction plate is expressed as F n , N represents the number of all tooth pairs of the inner hub and the friction plate.

[0149] The number of randomly impacted gear teeth and the collision force of the floating support friction pair are obtained, which is convenient to use.

[0150] Further, step S9 establishes a bending-torsional random collision dynamics model of the floating support friction plate and the inner hub system based on the lumped mass method, and obtains the impact dynamic load of the floating support friction pair by using the Runge-Kutta method. The specific method is as follows:

[0151] S901, the rotational speed of the inner hub is defined, and the bending-torsional dynamics equation of the inner hub and the bending-torsional dynamics equation of the friction plate are solved by the Runge-Kutta method, wherein the bending-torsional dynamics equation of the inner hub is:

[0152]

[0153] The bending-torsional dynamics equation of the friction plate is:

[0154]

[0155] wherein, and (j0=e,p) are the mass and moment of inertia of the inner hub and the friction plate, respectively; and (j0=e,p) are the support stiffness and support damping of the inner hub and the friction plate in the x and y directions, respectively; g is the acceleration of gravity; α is the angular acceleration of the inner hub; due to the influence of the tooth side gap, the floating support friction plate is suspended on the inner hub under the action of gravity or radial force, and its vibration is only affected by the collision force of the inner hub and the friction plate gear teeth, so the support stiffness and support damping of the friction plate are set to 0; r b is the base circle radius; F n is the normal collision force of the inner hub and the nth pair of gear teeth of the friction plate;

[0156] S902, the variable (i.e. the next time the hub and the friction plate parameters in the engagement point) is updated, and the next time the tooth rough interface excitation and random collision dynamic characteristics are iteratively solved.

[0157] Based on the lumped mass method, a bending-torsional random collision dynamics model of the floating support friction plate and the inner hub system is established, and the Runge-Kutta method is used to obtain the impact dynamic load of the floating support friction pair.

[0158] The application also provides a floating support friction pair impact dynamic load calculation system considering the rough interface topography characteristics, comprising a data acquisition module and a processing module, the data acquisition module is used to acquire the basic parameters of the floating support friction plate assembly to be calculated;

[0159] The input end of the processing module is connected with the output end of the data acquisition module, the processing module executes the method of the application, and the impact dynamic load of the floating support friction pair is obtained.

[0160] The system is based on the traditional three-dimensional rough surface fractal function representation method, combines the influence of the waviness and surface roughness in the typical tooth processing surface, constructs a rough interface topography characteristics-collision force-stiffness coupled random collision dynamics model, and obtains the impact dynamic load of the friction pair tooth part. BRIEF DESCRIPTION OF DRAWINGS

[0161] Figure 1 It is the flowchart of the floating support friction pair impact dynamic load calculation method considering the rough interface topography characteristics of the application;

[0162] Figure 2 It is the structure diagram of the tooth rough contact interface of the floating support friction pair impact dynamic load calculation method considering the rough interface topography characteristics of the application;

[0163] Figure 3 It is the structure diagram of the inner hub and friction plate tooth non-uniform cantilever beam model of the floating support friction pair impact dynamic load calculation method considering the rough interface topography characteristics of the application;

[0164] Figure 4 It is the structure diagram of the inner hub and friction plate tooth base body deformation geometric parameters of the floating support friction pair impact dynamic load calculation method considering the rough interface topography characteristics of the application;

[0165] Figure 5 It is the structure diagram of the tooth collision position geometric relationship of the floating support friction pair impact dynamic load calculation method considering the rough interface topography characteristics of the application;

[0166] Figure 6 It is the structure diagram of the random collision dynamics model of the floating support friction pair impact dynamic load calculation method considering the rough interface topography characteristics of the application. DETAILED DESCRIPTION

[0167] Embodiments of the present application are described below in detail with reference to the accompanying drawings, wherein the same or similar components or components having the same or similar functions are denoted by the same or similar reference numerals throughout. The embodiments described below by reference to the accompanying drawings are exemplary and are intended only for explanation of the present application, and are not to be construed as limiting the present application.

[0168] In the description of the present application, it should be understood that the terms "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and therefore cannot be construed as indicating or implying that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be construed as limiting the present application.

[0169] In the description of the present application, unless otherwise specified and limited, it should be noted that the terms "mounting", "connection", "connection" should be understood broadly, for example, it can be a mechanical connection or an electrical connection, it can be a communication between two elements, it can be directly connected, or indirectly connected through an intermediate medium, and those skilled in the art can understand the specific meaning of the above terms according to the specific circumstances.

[0170] The application discloses a floating support friction pair impact dynamic load calculation method considering rough interface topography characteristics, as shown in the figure, comprising the following steps: Figure 1

[0171] S1, obtaining the basic parameters of the floating support friction plate assembly to be calculated, including structural parameters, material parameters and working condition parameters, the friction plate assembly including a friction plate and an inner hub, specifically including the number of teeth, modulus, tooth width, tooth thickness, base circle radius, gear length, pressure angle of the division circle, elastic modulus, Poisson's ratio, mass of the friction plate and the inner hub, moment of inertia, tooth side clearance, rotational speed and rotational speed fluctuation frequency and amplitude of the inner hub, tooth surface fractal roughness, fractal dimension, frequency index, waviness and surface roughness; initial contact phase, contact tooth width;

[0172] S2, superimposing regular waviness and random surface roughness to represent three-dimensional rough surface topography;

[0173] S3, calculating the size, number and position distribution characteristics of the microconvex bodies on the surface of the three-dimensional rough surface topography;

[0174] S4, based on the parameters of the three-dimensional rough surface microconvex bodies, calculating the critical deformation δ of each microconvex body under the action of the load iec ​The contact load, contact stiffness and contact area of a single asperity under different deformation modes;

[0175] The total contact stiffness k of the entire rough interface is calculated by considering the distribution characteristics of the three-dimensional rough interface asperities t ;

[0176] The surface contact coefficient λ is introduced by considering the influence of the curvature of the contact position of the inner hub and the friction plate on the asperity distribution density c ηξ The tooth rough surface contact stiffness is calculated;

[0177] S5, based on the parameters of the inner hub and the friction plate, the bending, shear and axial compression stiffness of the tooth are calculated;

[0178] Based on the rigid-flexible coupling relationship and the elastic circular ring theory, the substrate deformation and the substrate stiffness k are calculated f ;

[0179] S6, based on the bending, shear and axial compression stiffness of the tooth and the substrate stiffness, the single-tooth pair comprehensive stiffness k s and the time-varying dynamic stiffness K s (t) are calculated;

[0180] S7, the initial eccentricity and the actual radial tooth gap of the friction plate are obtained, and the relative offset of the friction plate and the inner hub tooth under no-load state is determined;

[0181] According to the relative motion relationship between the teeth, the relative displacement of the inner hub and the friction plate teeth under load is derived;

[0182] By analyzing the deformation coordination relationship between the actual radial gap and the relative position of the teeth, the actual collision tooth number, the collision tooth position, the collision depth and the collision phase characteristics are determined;

[0183] S8, the random impact collision tooth number and the collision force of the floating support friction pair are calculated;

[0184] S9, a bending-torsional random collision dynamic model of the floating support friction plate and the inner hub system is established, the Runge-Kutta method is used to obtain the impact dynamic load of the floating support friction pair, and the influences of the surface roughness, the tooth side gap, the inner hub rotation speed fluctuation frequency and the rotation speed fluctuation amplitude and other parameters on the random collision characteristics and the vibration response are revealed, which can be used for hardware design and optimization, for example, when the impact dynamic load exceeds the threshold value, the size of the tooth side gap and the size of the surface roughness can be adjusted to make the impact dynamic load return to the threshold value range. In a more preferred mode, the tooth side gap is too small to increase the collision frequency, and the tooth side gap is too large to increase the collision force amplitude, and the collision frequency and the collision force amplitude can meet the requirements by adjusting the tooth side gap, in addition, it is found through calculation that the roughness grade N5-N6 can inhibit high-frequency collision, and the roughness grade can be adjusted by adjusting the surface processing process to fall within the N5-N6 grade.

[0185] The present application combines the influences of the waviness and the surface roughness in the typical tooth processing surface, develops a new method for three-dimensional reconstruction of the rough surface, and deduces the calculation formula of the non-deterministic characteristics of the instantaneous collision tooth number, the collision depth and the collision phase of the floating support friction plate and the inner hub system under the non-stable constraint condition, and proposes an analytical calculation method for the random collision excitation of the tooth, which solves the uncertainty problem caused by the random collision of the floating support friction plate and the inner hub under the non-stationary operation.

[0186] By combining the coupling effect of the rough interface excitation and the random collision excitation of the tooth, a random collision dynamic model of the system is established, the influences of different structures, working conditions and surface topography and other parameters on the random collision dynamic characteristics are realized, and a more practical random collision mechanism analysis method of the floating support friction plate is developed.

[0187] In a preferred scheme of the present application, the step S2 superimposes the regular waviness and the random surface roughness based on the basic parameters of the floating support friction plate assembly, and the method for characterizing the three-dimensional rough surface topography is:

[0188] S201, the tooth surface roughness topography function z3(x, y) is calculated and is expressed as:

[0189]

[0190] Wherein, L is the sample length; G3 and D3 respectively represent the fractal roughness and the fractal dimension, 2 max3 is the maximum value of the frequency index range, n max3 =int[log(L / L s ) / logγ], L s is the truncation length, which is about six lattice distances, and is usually 1.5; φ (m,n3)for random phase in the range of 0 and 2π; x and y are the position coordinates of the surface profile respectively;

[0191] S202, selecting milling processing mode, calculating the sinusoidal waviness h(x) of the milling processed surface, expressed as:

[0192] h(x) = qR a sin(ω0x+θ) + b, 0≤x≤L

[0193] wherein, R a is the surface roughness value; q is the contribution degree of the waviness to the surface roughness R a ; ω0is the waviness wavelength scaling factor; θ is the initial phase angle of the waviness; b is the mean value of the waviness;

[0194] S203, using sinusoidal waviness in the direction perpendicular to the cutting direction, and using straight line in the direction of the chip to develop, superimposing the regular waviness and the random surface roughness, the reconstructed three-dimensional rough surface is expressed as:

[0195] Z(x, y) = A·z3(x, y) + h(x, y)

[0196] wherein, z3(x, y) is the surface roughness topography function; h(x, y) represents the waviness shape function; A is the surface roughness amplitude scaling factor;

[0197] S204, determining the roughness value R a according to the measured three-dimensional rough surface, using optimization algorithm to iteratively optimize the parameters k, ω and θ, so that the Pearson correlation coefficient r of the waviness surface and the measured rough surface is greater than 0.7, by adjusting the parameters G3, D3 and k, the relative error ε of the roughness value of the simulation and the measured surface is less than 5%, and finally the three-dimensional rough surface is obtained which is fitted with the measured surface height, r is:

[0198]

[0199] wherein, Z(x j ,y k ) and Z1(x j ,y k ) represent the profile height of the simulation and the measured rough surface at the coordinate point (x j ,y k ) respectively; and are the profile height mean values of the simulation and the measured rough surface respectively; J and K are the discrete point numbers in x and y directions respectively, j and k represent the discrete point number sequence in x and y directions respectively.

[0200] In a preferred scheme of the present application, the step S3 is based on the three-dimensional rough surface morphology, and the step of calculating the size, number and position distribution characteristics of the micro-convexities on the surface is:

[0201] S301, defining the spatial domain of generating a three-dimensional rough surface as Ω(x j ,y k ,Z(x j ,y k )) where Z1(x j ,y k ) represents the profile height of the measured rough surface at the coordinate point (x j ,y k ), j = 1 ~ J, k = 1 ~ K, J and K are the number of discrete points in the x and y directions respectively, and j, k represent the serial number of the discrete points in the x and y directions;

[0202] The boundary value of the spatial domain Ω is set to 0, the system coordinate is redefined, i.e. Z'(x j ,y k ) = Z(x j ,y k )-mean(Z(x j ,y k )), and the spatial domain is updated as Ω1(x j ,y k ,Z'(x j ,y k )), and mean(Z(x j ,y k )) represents the average value of all heights of the entire surface;

[0203] S302, setting the current node as the initial state Ω1, and regarding the adjacent node η as the successor node of the current node, if the value of the adjacent node is less than that of the current node, the state of the current node is retained; otherwise, the value of the adjacent node is replaced by that of the current node;

[0204] This process is repeated until the value of all successor nodes is less than that of the current node, i.e. the node is a local maximum value, and all local maximum values are stored in the spatial domain Ω 2i (x (j,i) ,y (k,i) ,Z'(x (j,i) ,y (k,i) )), i = 1 ~ N r , N r is the number of micro-convexities of the rough surface;

[0205] S303, in order to avoid interference between adjacent micro-convexities, the truncation height of the i-th micro-convexity is defined as δ i = Δ, Δ is the sample interval value of the coordinate domain, when the node Ω 2iThe height of all nodes in the vicinity is greater than Z'(x (j,i) ,y (k,i) )-δ i , the truncation radius R i of the ith microconvexity is expressed as:

[0206]

[0207] where Δx and Δy are the sample intervals of the coordinate domain in the x and y directions, respectively; M ri is the number of elements in the truncated area of the ith microconvexity;

[0208] In S304, it is assumed that the geometric shape of the ith microconvexity before deformation conforms to a cosine function, which is expressed as:

[0209]

[0210] where Z2(x si ) represents the position height of a point on the ith microconvexity with a radial distance of x si from the center point of the microconvexity, and the independent variable x si represents the radial distance of any point on the microconvexity from the center point of the microconvexity, and when the independent variable is 0, it is located at the center point, i.e., the maximum height; represents the height amplitude of the ith microconvexity, is the overall roughness of the ith microconvexity, and the index D i -1 represents the amplification of the dependence of the microconvexity height on the roughness; is the sensitivity of the height of the ith microconvexity to the base size, and the index 2-D i represents the rate of change of the geometric properties of the ith microconvexity with the fractal dimension D i , and when D i = 2, the microconvexity belongs to a low fractal dimension, the surface is smooth, i.e., the microconvexity height at this time is independent of the base size; l i , G i , and D i represent the base diameter, fractal roughness, and fractal dimension of the ith microconvexity, respectively, and are expressed as:

[0211]

[0212] where n i and δ i are the frequency index and the truncation height of the ith microconvexity, respectively; Z'(x (j,i) ,y (k, i ) ) is the height of the ith microconvexity; D3 represents the fractal dimension, γ is the scaling factor, l i , and D irespectively represent the base diameter and fractal dimension of the i-th micro asperity.

[0213] Through the improved hill climbing algorithm, the distribution characteristics of the scale, quantity and position of the micro asperities of the real three-dimensional rough surface can be obtained, and the limitations of the traditional empirical power function assumption are avoided.

[0214] In a preferred scheme of the present application, in step S4, the critical deformation δ iec of each micro asperity under the load is calculated based on the parameters of the three-dimensional rough surface micro asperity

[0215]

[0216] wherein H and E respectively represent the hardness and elastic modulus of the material; K v is the hardness coefficient related to the Poisson's ratio v, which can be approximately expressed as K v = 0.454 + 0.41 v; l i , G i and D i respectively represent the base diameter, fractal roughness and fractal dimension of the i-th micro asperity; represents the effective volume of the i-th micro asperity under the fractal dimension D i , l i represents the base diameter, i.e., the lateral dimension of the i-th micro asperity, the index D i represents the fractal dimension, which describes the complexity of the geometric shape of the i-th micro asperity, is the overall roughness of the i-th micro asperity, G i represents the fractal roughness of the i-th micro asperity, the index D i -1 represents the amplification of the dependence of the micro asperity height on the roughness;

[0217] With the increase of the applied load, the deformation δ i of the i-th micro asperity may undergo four stages of pure elasticity, first and second stage elastoplasticity and complete plasticity, i.e.,

[0218]

[0219] In the four contact deformation stages, the contact load of the i-th deformed micro asperity is represented as:

[0220]

[0221] wherein P ne , P nep1 , P nep2, P np They represent the contact loads of the i-th deformed asperity in the four contact deformation stages respectively;

[0222] In these four contact deformation stages, the contact area a of the i-th deformed micro-convex body is ne , a nep1 , a nep2 , a np Expressed as:

[0223]

[0224] In these four contact deformation stages, the contact stiffness k of the i-th deformed asperity is ne , k nep1 , k nep2 , k np Expressed as:

[0225]

[0226] In a preferred embodiment of the present invention, the actual contact state of the asperities is considered and the total contact stiffness k of the rough interface is calculated. t and contact load p t :

[0227]

[0228] Among them, N t is the number of truncated asperities;

[0229] Based on the slicing method, the surface contact coefficient λ is introduced to consider the influence of the curvature of the contact position between the inner hub and the friction plate on the distribution density of the micro-asperities. c ηξ , contact stiffness k of the rough surface of the gear teeth h ηξ Expressed as:

[0230]

[0231] Among them, R ce ηξ and R cp ηξ are the curvature radius at the contact position ξ; F′ ηζ is the load on the rough interface at the contact position; the symbol “+” indicates internal gear tooth contact, and the symbol “-” indicates external gear tooth contact;

[0232] Since the curvature radius of the inner hub and the friction plate teeth at the contact position is the same, and the tooth side clearance is much smaller than the curvature radius, the contact position ξ can be approximately regarded as two micro-element rough interface contacts with an area of ​​Δw×Δu (e.g. Figure 2 As shown), the surface contact coefficient λ cηξ Approximately 1, the stiffness k of the tooth contact position h η Simplified as k t ηξ ; Δw and Δu are the sample lengths in the x direction and the y direction; the superscript ξ is the microelement position in the tooth profile direction; and the superscript η is the microelement position in the tooth width direction.

[0233] In a preferred scheme of the present application, the step S5 calculates the bending, shear and axial compression stiffness of the tooth based on the parameters of the inner hub and the friction plate, and calculates the substrate deformation and the substrate stiffness k based on the rigid-flexible coupling relationship and the elastic circular ring theory f The specific steps are as follows:

[0234] S501, the tooth of the inner hub and the friction plate is involute tooth profile, and the deformation calculation of the tooth is similar to the calculation method of the external meshing gear and the internal meshing gear, and the non-uniform cantilever beam model of the tooth of the inner hub and the friction plate is as shown in Figure 3 According to the elastic potential energy principle, under the action of the force F, the energy U stored in the tooth due to bending, shear and compression deformation is expressed as: tooth

[0235] U tooth = U s + U a + U b

[0236] Wherein

[0237]

[0238] Wherein, the parameter d of the inner hub and the friction plate represents the straight line distance from the meshing point to the tooth root, x represents the position coordinate along the tooth center line, h represents the half tooth thickness at the meshing position, and α m is the pressure angle at the contact position; U b , U s and U a are the bending deformation, shear deformation and axial compression deformation of the tooth respectively; k b , k s and k a are the bending stiffness, shear stiffness and axial compression stiffness of the tooth respectively; G is the shear modulus of the material, G = E / 2(1+μ); E and μ are the elastic modulus and Poisson's ratio respectively; the parameters A x and I x are the cross-sectional area and the cross-sectional moment of inertia at the force action point x, A x = 2h x W, W is the contact tooth width at the meshing position; h x is the half tooth thickness at the meshing point;

[0239] ​S502, the gear teeth of the inner hub and friction plate are assumed to be rigid bodies, while the matrix is ​​considered to be flexible, and the matrix deformation δ is calculated based on the rigid-flexible coupling relationship and elastic ring theory. f , expressed as:

[0240]

[0241] Among them, τ = 1 represents the inner hub; τ = -1 represents the friction plate; (such as Figure 4 Symbol u f represents the radial displacement of point p on the substrate, r f Root circle radius, θ f The load range angle defined by point p, h f represents the tooth root thickness, p represents the intersection of the tooth center line and the tooth root circle; u r (θ=0) and u t (θ=0) are the radial and tangential displacements of point p, respectively, expressed as:

[0242]

[0243] χ=(ρ+3μ) / (ρ+μ)

[0244] ρ=Eμ / ((1+μ)(1-2μ))

[0245] Among them, the parameters and is related to θ f and h f Related functions; Fourier cosine coefficients representing the shape function of the normal stress distribution, Fourier sine coefficients representing the shape function of the normal stress distribution, Fourier cosine coefficients representing the shape function of the tangential stress distribution. The displacement influence coefficients are composed of the elastic ring theoretical coefficients, where Characterizes the comprehensive influence of the kth-order stress harmonic on the radial displacement of the elastic ring at θ = 0; Characterize the comprehensive influence of the k-th order stress harmonic on the tangential displacement and its derivative of the elastic ring at θ = 0; Characterizes the comprehensive influence of the kth-order stress harmonic on the tangential displacement of the elastic ring at θ = 0;

[0246] S503, calculate the matrix stiffness k f have to:

[0247]

[0248] In a preferred scheme of the present application, step S6 calculates the single-tooth pair comprehensive stiffness k based on the bending, shearing and axial compression stiffness of the gear tooth and the matrix stiffness s and the time-varying dynamic stiffness K s (t), and the steps are as follows:

[0249] S601, calculate the single-tooth pair comprehensive stiffness k of the inner hub and the friction plate s , which is expressed as:

[0250]

[0251] wherein the subscripts e and p respectively represent the inner hub and the friction plate; η0 represents the number of microelements in the tooth width direction; q0 represents the number of microelements in the tooth profile direction; the comprehensive stiffness components k b , k s , k a and k f are constants related to the tooth profile, meshing position and material parameters of the gear tooth, and the superscript ξ represents the microelement position in the tooth profile direction; the superscript η represents the microelement position in the tooth width direction; the contact stiffness k h ηξ [F ηξ '] has a strong nonlinear relationship with the meshing position impact force and the rough interface topography characteristics of the gear tooth;

[0252] S602, set the number of teeth of the inner hub and the friction plate as N, and calculate the time-varying dynamic stiffness K s (t), which is expressed as:

[0253]

[0254] wherein k sn (t) represents the comprehensive stiffness of the n-th gear tooth pair of the inner hub and the friction plate, k sn (t) is obtained by calculation in S601 if the n-th gear tooth pair of the inner hub and the friction plate collides; if the n-th gear tooth pair of the inner hub and the friction plate does not collide, k sn (t) = 0; t is the instantaneous time; and n represents the gear tooth pair.

[0255] In a preferred scheme of the present application, the specific steps of step S7 are as follows:

[0256] S701, assuming that the single-side normal tooth side clearance of the inner hub and the friction plate obeys a Gaussian random distribution, the single-side tooth side clearance C n of the n-th gear tooth pair is expressed as:

[0257] c n ~ N(μ, σ 2 )

[0258] wherein μ represents the average value of the tooth side clearance; σ 2 represents the dispersion degree of the tooth side clearance.

[0259] S702, under the action of gravity or radial force, the positive tooth pair and the reverse tooth pair of the inner hub and the friction plate will contact at certain positions, when the nth tooth pair contacts, the positive tooth pair (drive side) and the reverse tooth pair (back side) of the friction plate will produce vertical displacement a Fn , a Bn is expressed as:

[0260] a Fn = abs(c n / cos(α m +2π(n-1)N))

[0261] a Bn = abs(c n / cos(-α m +2π(n-1)N))

[0262] Wherein, N is the number of teeth of the inner hub and the friction plate; abs represents the absolute value function, α m is the pressure angle of the contact position;

[0263] The eccentricity e0 caused by the initial tooth side clearance is:

[0264]

[0265] S703, under the action of the eccentricity, the actual tooth side clearance C Fn , C Bn of the nth tooth pair in the positive direction and the reverse direction of the friction plate is:

[0266] c Fn = c n -e0sin(α m +2π(n-1) / N)

[0267] c Bn = c n +e0sin(-α m +2π(n-1) / N);

[0268] S704, due to the existence of the tooth side clearance and the eccentricity, the inner hub and the friction plate tooth will collide and deform during the non-steady operation. The positive collision deformation is defined as the deformation of the tooth pair along the driving side action line direction, and the reverse collision deformation is the deformation along the back side action line direction. Figure 5 The geometric relationship of the tooth pair when colliding in the positive direction and the reverse direction is shown, and points A and B represent the intersection of the driving side and the back side involute tooth profile and the pitch circle respectively. According to the geometric relationship, the collision angles θ Fn and θ Bn of the nth tooth pair in the driving side and the back side are:

[0269] θ Fn =2π(n-1) / N+ωt+θ0

[0270] θ Bn =2π(n-1) / N+ωt-θ0

[0271] Where ω is the inner hub angular velocity; θ0 is the half tooth angle at the pitch circle position, i.e. θ0 = π / 2N; t is the instantaneous time;

[0272] S705, define the tangent line of the collision point of the n-th gear tooth pair on the driving side and the back side tooth profile and x e The angles in the positive direction of the axis are φ Fn and φ Bn ,Right now:

[0273]

[0274] Based on the deformation coordination relationship between the actual radial clearance of the gear teeth and the relative position, and considering the bending and torsional vibration of the inner hub and the friction plate, the collision deformation δ of the nth gear tooth pair on the driving side (positive) and the back side (reverse) is Fn and δ Bn Respectively expressed as:

[0275]

[0276] Where x and y with subscript e or p are radial vibration displacements, subscript e and p represent the inner hub and friction plate, respectively; θ with subscript e or p is torsional vibration angular displacement; r b is the base circle radius;

[0277] S706, based on the deformation of the inner hub and the nth collision tooth of the friction plate, determine the position of the collision tooth and its collision phase, namely:

[0278]

[0279] Among them, C Fn =1 and C Bn =1 indicates that the nth gear tooth pair of the inner hub and the friction plate has a positive collision and a negative collision respectively; C Fn =0 and C Bn =0 means that there is no collision between the nth gear tooth pair of the inner hub and the friction plate; the subscripts Fn and Bn are used to determine the positions where the gear teeth collide head-on and head-back;

[0280] S707, by judging the collision tooth position and collision phase, determine the total number of teeth N that collide with the inner hub and the friction plate in the forward and reverse directions at each moment F , N B ,Right now:

[0281]

[0282] In a preferred embodiment of the present invention, in step S8, the number of random impact and collision teeth of the floating support friction pair and the collision force are calculated, and the specific steps are as follows:

[0283] S801, based on the principle of energy conservation, calculate the energy loss ΔT before and after the gear tooth collision:

[0284]

[0285] Among them, m e and m p are the masses of the inner hub and friction plate respectively; is the relative speed of the gear teeth before collision; rebound coefficient c r Refers to the relative speed when the gear teeth collide and separate Relative velocity to the start of the collision The ratio is mainly determined by the material properties of the collision gear teeth; the rebound coefficient c r The value range is usually between 0 and 1. r = 0, it indicates a completely inelastic collision, that is, there is no elastic recovery during the collision, and all kinetic energy is dissipated; when c r =1, indicating a completely elastic collision, that is, the kinetic energy during the collision is completely retained without loss; the rebound coefficient c r Expressed as:

[0286]

[0287] Wherein, subscripts e and p represent the inner hub and friction plate, respectively;

[0288] S802, calculation of gear tooth collision and damping forces based on Lankarani and Nikravesh model The energy dissipation ΔT in the form of work is:

[0289]

[0290] Among them, δ0 is the maximum deformation of gear tooth collision;

[0291] S803, according to the energy conservation theorem, the hysteresis damping coefficient μ0 is obtained as:

[0292]

[0293] Among them, k s Indicates the combined stiffness of the inner hub and a single tooth of the friction plate;

[0294] S804, based on the hysteresis damping coefficient μ0, substitute the Hertz contact theory and the nonlinear collision force calculation formula of a single pair of gear teeth to obtain the normal collision force F between the inner hub and the nth pair of gear teeth of the friction plate. n ,Right now:

[0295]

[0296] Among them, k s δ m represents the elastic contact force; δ is the relative normal deformation of the tooth; m0 is the nonlinear index, m0 = 1.5; k sn is the combined stiffness of the nth gear tooth pair between the inner hub and the friction plate; μ0 is the hysteresis damping coefficient, whose value is related to the viscous damping coefficient, shear and volume deformation, etc.; δ Fn and δ Bn Represents the collision deformation of the nth pair of teeth on the driving side and the back side;

[0297] S805, components F of the positive and negative collision forces of the nth pair of teeth in the x and y directions nx , F ny Expressed as:

[0298]

[0299] Where, t is the instantaneous time; ω is the angular velocity of the inner hub; θ0 is the half tooth angle at the pitch circle position,

[0300] Total collision force F between the inner hub and all tooth pairs of the friction plate total and the total collision force component F x , F y Expressed as:

[0301]

[0302] Among them, the components of the positive and negative collision forces of the nth pair of teeth in the x and y directions are represented by F nx , F ny The normal collision force between the inner hub and the nth pair of teeth of the friction plate is expressed as F n , N represents the number of all tooth pairs between the inner hub and the friction plate.

[0303] In a preferred embodiment of the present invention, step S9 is based on the lumped mass method to establish a bending-torsion random collision dynamics model of the floating support friction plate and the inner hub system (such as Figure 6 As shown in Figure 2, the Runge-Kutta method is used to obtain the impact dynamic load of the floating support friction pair. The specific method is as follows:

[0304] S901, based on the inner hub defines the speed (the application adopts the sine function waveform to simulate the nonlinear speed fluctuation of the inner hub, and the actual speed waveform or other waveform functions can also be used to describe the speed of the inner hub), the bending-torsional dynamic equation of the inner hub and the bending-torsional dynamic equation of the friction plate are solved by Runge-Kutta method respectively, wherein the bending-torsional dynamic equation of the inner hub is:

[0305]

[0306] The bending-torsional dynamic equation of the friction plate is:

[0307]

[0308] Wherein, And (j0=e,p) are the mass and moment of inertia of the inner hub and the friction plate respectively; And (j0=e,p) are the support stiffness and support damping of the inner hub and the friction plate in x and y directions respectively; g is the acceleration of gravity; alpha is the angular acceleration of the inner hub; due to the influence of the backlash, the floating support friction plate is suspended on the inner hub under the action of gravity or radial force, and its vibration is only affected by the inner hub and the friction plate gear impact force, so the support stiffness and support damping of the friction plate are set to 0; r b is the base circle radius; F n is the normal impact force of the inner hub and the friction plate of the nth pair of gear teeth;

[0309] S902, update the next time meshing point inner hub and friction plate parameters (variables), and iteratively solve the next time gear rough interface excitation and random collision dynamic characteristics.

[0310] The application also provides a floating support friction pair impact dynamic load calculation system considering the rough interface topography characteristics, which comprises a data acquisition module and a processing module.

[0311] The input end of the processing module is connected with the output end of the data acquisition module, the processing module executes the method described in the application, and the floating support friction pair impact dynamic load is obtained.

[0312] In the description of the specification, reference to "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" means that a particular feature, structure, material, or characteristic being described is included in at least one embodiment or example of the application. The appearances of the above expressions in various places in the specification are not necessarily referring to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

[0313] Although embodiments of the present application have been shown and described, it would be appreciated by those skilled in the art that changes, modifications, alternatives and variations to these embodiments could be made without departing from the principles and spirit of the application, the scope of which is defined in the claims and their equivalents.

Claims

1. A method for calculating impact dynamic load of a floating support friction pair considering rough interface topography characteristics, characterized in that, The method comprises the following steps: S1, obtaining basic parameters of a floating support friction plate assembly to be calculated; S2, superimposing regular corrugation and random surface roughness to represent three-dimensional rough surface topography; S3, calculating the size, number and position distribution characteristics of the micro-convex bodies on the surface of the three-dimensional rough surface topography; S4, based on the parameters of the three-dimensional rough surface micro asperities, calculate the critical deformation δ of each micro asperity under the load iec , the contact load, contact stiffness and contact area of a single micro asperity under different deformation modes; Considering the distribution characteristics of the real three-dimensional rough interface asperities, the total contact stiffness k of the whole rough interface is calculated t ; Considering the influence of the curvature of the contact position between the inner hub and the friction plate on the distribution density of the micro convex body, the surface contact coefficient λ is introduced c ηξ The tooth rough surface contact stiffness is calculated S5, calculating the bending, shearing and axial compression stiffness of the gear teeth based on the parameters of the inner hub and the friction plate; Based on the rigid-flexible coupling relationship and the elastic circular ring theory, the substrate deformation and the substrate stiffness k f ; S6, based on the bending, shearing and axial compression stiffness of the gear tooth and the matrix stiffness, calculate the single-tooth pair comprehensive stiffness k s and time-varying dynamic stiffness K s (t); S7, obtaining the initial eccentricity of the friction plate and the actual radial tooth gap, and determining the relative offset of the friction plate and the inner hub gear teeth in the no-load state; According to the relative motion relationship between the gear teeth, the relative displacement of the inner hub and the friction plate gear teeth under the action of the load is derived; By analyzing the deformation coordination relationship between the actual radial gap and the relative position of the gear teeth, the actual number of collision teeth, the position of the collision teeth, the collision depth and the collision phase characteristics are determined; S8, calculating the number of randomly impacted and collided gear teeth of the floating support friction pair and the collision force; S9, establishing a bending-torsion random collision dynamics model of the floating support friction plate and the inner hub system, and obtaining the impact dynamic load of the floating support friction pair by using the Runge-Kutta method.

2. The method for calculating impact dynamic load of a floating support friction pair considering rough interface topography features according to claim 1, characterized in that, In step S2, the method for superimposing regular corrugation and random surface roughness to represent three-dimensional rough surface topography based on the basic parameters of the floating support friction plate assembly is as follows: S201, calculating the surface roughness topography function z3(x, y) and representing it as: where L is the sample length; G3 and D3 represent the fractal roughness and fractal dimension, respectively, 2 < D3 < 3; γ is a scaling factor; M is the number of generated ridge lines, m is the ridge line number; n3 is a frequency exponent; n max3 = max(n3), n max3 = int[log(L / L s ) / log γ], L s is a cut-off length, approximately six lattice distances; φ (m,n3) is a random phase in the range 0 and 2π; x and y are the position coordinates of the surface profile; S202, selecting a milling processing mode and calculating the sinusoidal corrugation h(x) of the milling processed surface and representing it as: h(x) = qR a sin(ω0x + θ) + b, 0 ≤ x ≤ L wherein R a is the surface roughness value; q is the waviness contribution to the surface roughness R a ; ω0is the waviness wavelength scaling factor; θ is the initial phase angle of the waviness; and b is the waviness mean value. S203, superimposing regular corrugation and random surface roughness by using sinusoidal corrugation in the direction perpendicular to the cutting direction and using a straight line in the cutting direction for development, and reconstructing the three-dimensional rough surface represented as: Z(x, y) = A·z3(x, y) + h(x, y) Wherein, z3(x, y) is the surface roughness topography function; h(x, y) represents the corrugation shape function; A is the surface roughness amplitude scaling coefficient; S204, determining the roughness value R according to the measured three-dimensional rough surface a The k, ω and θ parameters are iteratively optimized by using an optimization algorithm, so that the Pearson correlation coefficient r of the corrugated surface and the measured rough surface is greater than 0.7, the relative error ε of the roughness values of the simulation and the measured surface is less than 5% by adjusting the G3, D3 and k parameters, and finally the three-dimensional rough surface is obtained which is fitted with the measured surface height, and r is: where Z(x j ,y k ) and Z1(x j ,y k ) represent the profile height of the simulated and measured rough surface at coordinate point (x j ,y k ), respectively; and are the profile height mean values of the simulated and measured rough surface, respectively; J and K are the discrete point numbers in x and y directions, respectively, and j, k represent the discrete point number sequence in x and y directions, respectively.

3. The method for calculating impact dynamic load of a floating support friction pair considering rough interface topography features according to claim 1, characterized in that, In step S3, the steps for calculating the size, number and position distribution characteristics of the micro-convex bodies on the surface of the three-dimensional rough surface topography are as follows: S301, define the spatial domain of generating three-dimensional rough surface as Ω(x j ,y k ,Z(x j ,y k )) where Z1(x j ,y k ) represents the profile height of the measured rough surface at coordinate point (x j ,y k ), j = 1 ~ J, k = 1 ~ K, J and K are the discrete point numbers in x and y directions respectively, j, k represent the discrete point number sequence in x and y directions; The boundary values of the spatial domain Ω are set to 0, the system coordinates are redefined, i.e. Z'(x j ,y k ) = Z(x j ,y k )-mean(Z(x j ,y k )) and the spatial domain is updated to Ω1(x j ,y k ,Z'(x j ,y k )), mean(Z(x j ,y k )) representing the average of all heights over the entire surface; S302, setting the current node as an initial state Ω1 and regarding the adjacent node η as a successor node of the current node, if the value of the adjacent node is less than the value of the current node, the state of the current node is retained; otherwise, the value of the adjacent node is replaced with the value of the current node; This process is repeated until all the values of the successor nodes are smaller than the current node, i.e. the node is a local maximum, and all the local maxima are stored in the spatial domain Ω 2i (x (j,i) ,y (k,i) ,Z'(x (j,i) ,y (k,i) )), i = 1 ~ N r , N r is the number of micro-protuberances of the rough surface; S303, define the truncation height of the i-th microconvexity as δ i = Δ, Δ is the coordinate domain sample interval value, when the node Ω 2i nearby all nodes are greater than Z'(x (j,i) ,y (k,i) )- δ i , the truncation radius R i of the i-th microconvexity is represented as: where Δx and Δy are the sample intervals of the coordinate domain in x and y directions, respectively; M ri N is the number of elements in the truncated region of the ith microconvexity. S304, assuming that the geometric shape of the i-th micro-convex body before deformation conforms to a cosine function form, and representing it as: where Z2(x si ) represents the position height of the point on the ith microconvexity with the radial distance x si to the center point of the microconvexity, the independent variable x si represents the radial distance of any point on the microconvexity to the center point of the microconvexity, and when the independent variable is 0, it is located at the center point, i.e. the maximum height; represents the height amplitude of the ith microconvexity, is the overall roughness of the ith microconvexity, and the index D i -1 represents the amplification of the dependence of the microconvexity height on the roughness; is the sensitivity of the height of the ith microconvexity to the base size, and the index 2-D i represents the rate of change of the geometric properties of the ith microconvexity with the fractal dimension D i , and when D i = 2, the microconvexity belongs to a low fractal dimension, the surface is smooth, i.e. the microconvexity height at this time is independent of the base size; l i , G i and D i respectively represent the base diameter, fractal roughness and fractal dimension of the ith microconvexity, and are: where n i and δ i are the frequency exponent and the cutoff height of the ith asperity, respectively; Z'(x (j,i) ,y (k, i ) ) is the height of the ith asperity; D3is the fractal dimension, γ is the scaling factor, l i and D i are the base diameter and the fractal dimension of the ith asperity, respectively.

4. The method for calculating impact dynamic load of a floating support friction pair considering rough interface topography features according to claim 1, characterized in that, In step S4, the critical deformation δ of each micro asperity under the load is calculated based on the parameters of the three-dimensional rough surface micro asperity iec The steps of the contact load, the contact stiffness and the contact area of a single micro asperity under different deformation modes are as follows: based on the K-E model, the critical deformation δ of the micro asperity from the elastic stage to the elastic-plastic stage is calculated, which is: where H and E are the hardness and elastic modulus of the material, respectively; K v is the hardness coefficient related to the Poisson's ratio v; l i , G i and D i represent the base diameter, fractal roughness and fractal dimension of the ithasperity, respectively; represents the effective volume of the ithasperity in the fractal dimension D i , l i represents the base diameter, i.e. the lateral dimension of the ithasperity, the exponent D i represents the fractal dimension, describing the complexity of the geometry of the ithasperity, is the overall roughness of the ithasperity, G i represents the fractal roughness of the ithasperity, the exponent D i -1represents the amplification of the dependence of the asperity height on the roughness; As the applied load increases, the deformation δi of the ith asperity i Four stages of deformation can occur, namely pure elastic, first and second stage elastic-plastic and fully plastic, namely: In the four contact deformation stages, the contact load of the i-th deformed micro-convex body is represented as: where P ne , P nep1 , P nep2 , P np represent the contact load of the ith asperity in the four contact deformation stages, respectively. In the four contact deformation stages, the contact area a ne , a nep1 , a nep2 , a np is expressed as: In the four contact deformation stages, the contact stiffness k ie , k iep1 , k iep2 , k ip is expressed as:

5. The method for calculating impact dynamic load of a floating support friction pair considering rough interface topography features according to claim 4, characterized in that, Considering the actual contact state of asperities, the total contact stiffness k of rough interface is calculated t and the contact load p t : where N t is the number of truncated asperities; Based on the slice method, the influence of the curvature of the contact position between the inner hub and the friction plate on the distribution density of the micro convex body is considered, and the surface contact coefficient λ is introduced c ηξ The tooth rough surface contact stiffness k h ηξ is expressed as: where R ce ηξ and R cp ηξ are the radii of curvature at the contact location ξ; F' ηζ is the load on the rough interface at the contact location; the symbol "+" indicates the inner tooth contact, and the symbol "-" indicates the outer tooth contact; Since the curvature radius of the inner hub and the friction plate gear tooth at the contact position is the same, and the tooth side gap is much smaller than the curvature radius, the contact position ξ can be approximated as the contact of two micro rough interface with an area of Δw x Δu, and the surface contact coefficient λ c ηξ The stiffness k of the gear tooth contact position is approximately 1 h η Simplified as k t ηξ ; Δw and Δu are the sample lengths in the x direction and the y direction; the superscript ξ is the micro element position in the tooth profile direction; and the superscript η is the micro element position in the tooth width direction.

6. The method for calculating impact dynamic load of floating support friction pair considering rough interface topography characteristics according to claim 1, characterized in that, Step S5 calculates the bending, shearing and axial compression stiffness of the gear teeth based on the inner hub and friction plate parameters, and calculates the base deformation and base stiffness k based on the rigid-flex coupling relationship and elastic ring theory f The specific steps are as follows: S501, the inner hub and the friction plate are involute tooth profiles, according to the principle of elastic potential energy, under the action of force F, the energy U stored in the tooth due to bending, shearing and compression deformation tooth is represented as: U tooth = U s + U a + U b Wherein wherein the parameters d of the inner hub and the friction plate represent the linear distance from the meshing point to the root, x represents the position coordinate along the tooth center line, h is the half tooth thickness at the meshing position, a m is the contact angle at the meshing position; U b , U s and U a are the bending deformation, shear deformation and axial compression deformation of the gear tooth respectively; k b , k s and k a are the bending stiffness, shear stiffness and axial compression stiffness of the gear tooth respectively; G is the material shear modulus, G = E / 2(1 + μ); E and μ are the elastic modulus and Poisson's ratio respectively; the parameters A x and I x are the cross-sectional area and the cross-sectional moment of inertia at the position x of the force action point respectively, A x = 2h x W, W is the contact tooth width at the meshing position; h x is the half tooth thickness at the meshing point; S502, the inner hub and the friction plate wheel teeth are assumed to be rigid bodies, while the base body is considered flexible, and the base body deformation δ is calculated based on the rigid-flexible coupling relationship and the elastic circular ring theory f is expressed as: where τ = 1 indicates the inner hub; τ = -1 indicates the friction plate; the symbol u f denotes the radial displacement of the point p on the base, r f the dedendum radius, θ f the angle of the load action range defined with the point p as origin, h f denotes the dedendum thickness, p indicates the intersection of the tooth center line with the dedendum circle; u r (θ = 0) and u t (θ = 0) are the radial and tangential displacements of the point p, respectively, and are expressed as: Wherein χ = (ρ + 3μ) / (ρ + μ) ρ = Eμ / ((1 + μ) (1 - 2μ)) wherein the parameters and are functions related to θ f and h f ; denote the Fourier cosine coefficients of the normal stress distribution shape function, denote the Fourier sine coefficients of the normal stress distribution shape function, denote the Fourier cosine coefficients of the tangential stress distribution shape function; are displacement influence coefficients composed of the elastic ring theory system, wherein denotes the comprehensive influence degree of the kth order stress harmonic on the radial displacement of the elastic ring at θ = 0; denotes the comprehensive influence degree of the kth order stress harmonic on the tangential displacement and its derivative of the elastic ring at θ = 0; denotes the comprehensive influence degree of the kth order stress harmonic on the tangential displacement of the elastic ring at θ = 0; S503, calculate the matrix stiffness k f Obtained:

7. The method for calculating impact dynamic load of floating support friction pair considering rough interface topography characteristics according to claim 1, characterized in that, Step S6 calculates the single-tooth pair overall stiffness k based on the bending, shearing and axial compression stiffness of the tooth and the base stiffness s and time-varying dynamic stiffness K s (t), the steps being: S601, calculate the integrated stiffness k of the inner hub and the single tooth of the friction plate s is expressed as: wherein the subscripts e and p represent the inner hub and the friction plate, respectively; η0represents the number of infinitesimal elements in the tooth width direction; q0is the number of infinitesimal elements in the tooth profile direction; the comprehensive stiffness component k b , k s , k a and k f are constants related to the parameters of the tooth profile, the meshing position and the material, etc., the superscript ξ is the position of the infinitesimal element in the tooth profile direction; the superscript η is the position of the infinitesimal element in the tooth width direction; the contact stiffness k h ηξ [F ηξ '] has a strong nonlinear relationship with the meshing position impact force and the rough interface topography characteristics of the gear teeth. S602, assuming that the number of teeth of the inner hub and the friction plate is N, the time-varying dynamic stiffness K is calculated s (t), is expressed as: wherein k sn (t) represents the combined stiffness of the inner hub and the n th tooth pair of the friction plate, k sn (t) is calculated by S601; if the n th tooth pair of the inner hub and the friction plate does not collide, then k sn (t) = 0; t is the instantaneous time.

8. The method for calculating impact dynamic load of floating support friction pair considering rough interface topography characteristics according to claim 1, characterized in that, The specific steps of step S7 are as follows: S701, assuming that the single-sided normal tooth side gap between the inner hub and the friction plate is subject to Gaussian random distribution, the single-sided tooth side gap C of the nth gear tooth pair is n is represented as: c n ~N(μ,σ 2 ) where μ is the average value of the side clearance; σ 2 is the degree of dispersion of the side clearance; S702, under the action of gravity or radial force, the positive tooth pair and the reverse tooth pair of the inner hub and the friction plate will contact at certain positions, when the nth tooth pair contacts, the vertical displacement a generated by the positive tooth pair and the reverse tooth pair of the friction plate Fn , a Bn is expressed as: a Fn = abs(c n / cos(α m +2π(n-1)N)) a Bn = abs(c n / cos(-α m +2π(n-1) / N)) where N is the number of teeth of the inner hub and the friction plate; abs represents the absolute value function, a m is the contact position pressure angle; The eccentricity e0 caused by the initial tooth gap is: S703, under the action of eccentricity, the nth gear tooth pair has actual tooth side clearance C in forward and reverse directions Fn , C Bn , is: c Fn = c n - e0sin(a m + 2π(n - 1) / N) c Bn = c n + e0sin(-α m + 2π(n - 1) / N); S704, according to the geometric relationship, the collision angle θ of the nth tooth pair at the driving side and the back side Fn and θ Bn is: θ Fn = 2π(n - 1) / N + ωt + θ0 θ Bn = 2π(n - 1) / N + ωt - θ0 Wherein, ω is the angular velocity of the inner hub; θ0 is the position half-tooth angle of the pitch circle, i.e. θ0 = π / 2N; t is the instantaneous time; S705, defining the tangent of the collision point on the drive side and the back side tooth profile of the nth gear tooth pair and x e The included angle of the shaft positive direction is φ Fn And φ Bn That is: Based on the deformation coordination relationship between the actual radial clearance of the gear teeth and the relative position, considering the bending and torsional vibration effects of the inner hub and the friction plate, the collision deformation δ Fn and δ Bn of the nth gear tooth pair on the driving side and the back side are respectively represented as: where x and y with subscript e or p are the radial vibration displacements, and subscript e and p denote the inner hub and the friction plate, respectively; θ with subscript e or p is the torsional vibration angular displacement; r b is the base circle radius; S706, determining the position of the collision tooth and the collision phase according to the deformation amount of the n-th collision tooth of the inner hub and the friction plate, i.e. where C Fn = 1 and C Bn = 1 represent the positive and negative impact of the inner hub with the nth tooth pair of the friction plate, respectively; C Fn = 0 and C Bn = 0 mean that the inner hub does not impact the nth tooth pair of the friction plate; the subscripts Fnand Bnare used to determine the position of the tooth impact. S707, by judging the collision tooth position and the collision phase, determine the total tooth number N of the inner hub and the friction plate that occurs positive and negative collision at each time F , N B , that is:

9. The method for calculating impact dynamic load of a floating support friction pair considering rough interface topography features according to claim 1, characterized in that, In step S8, the number of randomly impacted and collided gear teeth of the floating support friction pair and the collision force are calculated, and the specific steps are as follows: S801, based on the principle of energy conservation, the energy loss ΔT before and after the gear tooth collision is calculated as: Among them, m e and m p are the masses of the inner hub and friction plate respectively; is the relative speed of the gear teeth before collision; rebound coefficient c r Refers to the relative speed when the gear teeth collide and separate Relative velocity to the start of the collision The ratio is determined by the material properties of the collision gear teeth; the rebound coefficient c r The value range is usually between 0 and 1. r = 0, it indicates a completely inelastic collision, that is, there is no elastic recovery during the collision, and all kinetic energy is dissipated; when c r =1, indicating a completely elastic collision, that is, the kinetic energy during the collision is completely retained without loss; the rebound coefficient c r Expressed as: Wherein, the subscript e and p represent the inner hub and the friction plate respectively; S802, calculate the gear tooth impact to dampen force based on Lankarani and Nikravesh model The energy dissipation ΔT of the form work is: Wherein, δ0 is the maximum deformation of the gear tooth collision; S803, according to the energy conservation theorem, the hysteresis damping coefficient μ0 is obtained as: wherein k s represents the combined stiffness of the inner hub and the individual tooth of the friction plate; S804, based on the hysteresis damping coefficient μ0, substitute into the Hertz contact theory, the nonlinear collision force calculation formula of single pair of gear teeth, obtain the normal collision force F of the n pair of gear teeth between the inner hub and the friction plate n ; Based on the Hertz contact theory, the nonlinear collision force of a single pair of gear teeth is represented as: The normal collision force F of the inner hub with the nth pair of teeth of the friction plate n may be expressed as: wherein k s δ m represents the elastic contact force part; δ is the normal relative deformation of the tooth part; m0 is a non-linear index, m0 = 1.5; k sn is the comprehensive stiffness of the n-th tooth pair of the inner hub and the friction plate; μ0 is a hysteresis damping coefficient, the value of which is related to the viscous damping coefficient, shear and volume deformation, etc.; δ Fn and δ Bn represent the collision deformation of the n-th tooth pair on the driving side and the back side. S805, the forward and reverse impact force components of the nth pair of teeth in the x and y directions F nx , F ny is expressed as: Wherein, t is the instantaneous time; ω is the angular velocity of the inner hub; θ0 is the position of the pitch circle half-tooth angle, The total collision force F of the inner hub with all tooth pairs of the friction plate total and the total collision force component F x , F y is expressed as: where the components of the normal and reverse collision forces of the nth pair of teeth in the x and y directions are denoted by F nx , F ny ; the normal collision force of the inner hub with the nth pair of teeth of the friction plate is denoted by F n , and N denotes the number of all pairs of teeth of the inner hub and the friction plate.

10. The method for calculating impact dynamic load of a floating support friction pair considering rough interface topography features according to claim 1, characterized in that, Step S9 is based on the lumped mass method, and a bending-torsional random collision dynamics model of the floating support friction plate and the inner hub system is established. The Runge-Kutta method is used to obtain the impact dynamic load of the floating support friction pair. The specific method is as follows: S901, based on the definition of the inner hub rotation speed, the bending-torsional dynamic equation of the inner hub and the bending-torsional dynamic equation of the friction plate are solved by the Runge-Kutta method, wherein the bending-torsional dynamic equation of the inner hub is: The bending-torsional dynamic equation of the friction plate is: wherein, and (j0 = e, p) are the mass and moment of inertia of the inner hub and the friction plate, respectively; and (j0 = e, p) are the support stiffness and support damping of the inner hub and the friction plate in x and y directions, respectively; g is the gravity acceleration; a is the angular acceleration of the inner hub; due to the influence of the backlash, the floating support friction plate is suspended on the inner hub under the action of gravity or radial force, and its vibration is only affected by the impact force of the inner hub and the friction plate gear teeth, so the support stiffness and support damping of the friction plate are set to 0; r b is the base circle radius; f n is the normal impact force of the nth pair of gear teeth of the inner hub and the friction plate; S902, update the inner hub and friction plate parameters of the next time meshing point, and iteratively solve the gear rough interface excitation and random collision dynamic characteristics at the next time.

11. A system for calculating impact dynamic load of a floating support friction pair considering rough interface topography features, characterized by, It comprises a data acquisition module and a processing module, the data acquisition module is used to acquire the basic parameters of the floating support friction plate assembly to be calculated; The input end of the processing module is connected with the output end of the data acquisition module, the processing module executes the method of any one of claims 1-10, and the impact dynamic load of the floating support friction pair is obtained.

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