Determination Method for Film Thickness of Point-Contact Hybrid Elastohydrodynamic Lubrication

Abstract

The present invention provides a method for determining the lubricating oil film thickness in point - contact elastohydrodynamic lubrication, including: measuring the three - dimensional profile heights of the first object and the second object forming the point contact, calculating the initial oil film thickness h0 based on the profile heights, and setting the initial pressure distribution p0(x, y) of the oil film according to the externally applied load F; deriving the lubricating oil film thickness equation based on h0 and p0(x, y), then introducing the Reynolds equation characterizing the relationship between the oil film thickness and pressure, and non - dimensionalizing and discretizing the film thickness equation and the Reynolds equation; calculating the oil film thickness h and pressure p at each node of the contact interface according to step 2, thereby calculating the true contact area of the solid part; calculating the solid contact force F s and the total contact force F of the mixed lubrication interface n ; determining whether the calculated load F n and the externally applied load F satisfy the convergence condition. If not, update until the load converges, and finally obtain the oil film thickness distribution of the point - contact mixed lubrication interface. The oil film thickness calculated by the present invention has high accuracy.

Description

Technical Field

[0001] The invention belongs to the technical field of oil film thickness calculation, and particularly relates to a method for determining the oil film thickness of point contact mixed elastohydrodynamic lubrication. Background Art

[0002] The surfaces of parts obtained by machining have micron-scale roughness, and the rough surface topography has self-similar characteristics at different scales. When two rough surfaces come into contact, the asperities on the rough surfaces will squeeze each other, resulting in the actual contact area being much smaller than the nominal contact area. For precision mechanical instruments, such as precision rolling bearings, high-precision friction pairs are often in a mixed lubrication state. Especially under working conditions such as low speed, heavy load, and low-viscosity lubrication, there is simultaneous fluid lubrication and asperity contact at the contact interface, and the externally applied load is borne by both the lubricating oil and the asperities. In modern precision instruments, the lubrication state directly determines the quality of the working performance and the length of the service life of mechanical parts. Accurately obtaining the oil film thickness distribution at different positions under the point contact mixed lubrication state is of great significance for analyzing and improving the lubrication state of parts and increasing the service life of parts.

[0003] At present, in terms of experimental testing, the qualitative methods for measuring oil film thickness include the resistance method, the discharge voltage method, etc.; the quantitative methods include the capacitance method, the resistance-capacitance oscillation method, the optical interference method, the X-ray method, the magnetoresistance method, the strain gauge method, and the ultrasonic method, etc. Although the test accuracy of some experimental methods can reach the nanometer level, the measurement accuracy is greatly affected by factors such as temperature, sensor accuracy, and background noise environment, and the operation is cumbersome. Especially for mechanical parts with low speed, heavy load, and low-viscosity lubricating oil, the current experimental means are difficult to obtain the quantitative law of the change of oil film thickness with the microscopic topography under the mixed elastohydrodynamic lubrication state, which restricts the effective improvement of the lubrication performance of precision instruments. In terms of theoretical research, according to the microscopic elastohydrodynamic lubrication theory, the oil film thickness distribution is calculated. This type of method assumes that the surface is completely smooth and does not consider the microscopic rough topography of parts. In recent years, with the development of computer technology, a variety of numerical calculation methods for lubricating oil film thickness considering surface roughness have been proposed. However, the existing theoretical calculation methods are mainly based on statistical topography parameters such as Ra and Rq values. The statistical parameters are affected by the resolution of topography instruments and cannot truly reflect the self-similar fractal characteristics of rough topography at different scales, resulting in low accuracy of the calculated oil film thickness. Summary of the Invention

[0004] The purpose of the invention is to provide a method for determining the oil film thickness of point contact mixed elastohydrodynamic lubrication for the deficiencies of the existing technology. The invention fully considers the self-similar fractal characteristics of rough topography at different scales, and the calculated oil film thickness has higher accuracy.

[0005] To solve the above technical problems, the invention adopts the following technical solutions:

[0006] A method for determining the lubricant film thickness of point - contact mixed elastohydrodynamic lubrication, comprising the following steps:

[0007] S1: Measure the three - dimensional profile heights of the first object and the second object forming a point contact. Among them, the first object is an object with a curved surface. Based on the obtained three - dimensional profile heights, establish the profile height function of the rough surface, then calculate the initial lubricant film thickness h0 according to the profile height function, and set the initial pressure distribution p0(x, y) of the lubricant film according to the external load F;

[0008] S2: Calculate the viscosity η and density ρ of the lubricant under the initial pressure, and deduce the lubricant film thickness equation according to the initial lubricant film thickness h0 and the initial pressure distribution p0(x, y). Then, introduce the Reynolds equation characterizing the relationship between the lubricant film thickness and pressure according to the calculated lubricant viscosity η, density ρ and the lubricant film thickness equation. Nondimensionalize the film thickness equation and the Reynolds equation, and discretize the nondimensionalized equations by the finite - difference method;

[0009] S3: Calculate the lubricant film thickness h of each node at the contact interface according to the film thickness equation in step 2, and calculate the pressure p of each node at the contact interface according to the discretized nondimensionalized equation in step 2, to obtain the mixed elastohydrodynamic lubricant film thickness distribution h(x, y) and pressure distribution p(x, y), and calculate the proportion λ of the solid - contact nodes in the total number of nodes according to the pressure distribution p(x, y), so as to obtain the true contact area of the solid part;

[0010] S4: Calculate the maximum contact area a of a single rough peak according to the true contact area obtained in step 3 L and then combine the maximum contact area a L to calculate the solid contact force F s According to the solid contact force and the liquid contact force, obtain the total contact force F of the mixed - lubrication interface n ;

[0011] S5: Determine whether the calculated load F n and the external load F satisfy the convergence condition. If not, correct the initial lubricant film thickness h0 and the lubricant film pressure distribution p0(x, y) according to the calculated load F n and perform iterative calculations until the load converges, and finally obtain the lubricant film thickness distribution h(x, y) of the point - contact mixed - lubrication interface.

[0012] Furthermore, step 1 specifically includes:

[0013] The three-dimensional profile heights of the first object and the second object are obtained by using a measuring instrument, the autocorrelation function of the contact interface is established, the Fourier transform is performed on the autocorrelation function to obtain the power spectrum of the true surface profile, the double logarithmic coordinates of the power spectrum function and the spatial frequency are established, and the slope and intercept of the fitting line are obtained by fitting the power and spatial frequency scatter points, so as to calculate the fractal dimension D and the fractal roughness G of the rough surface

[0014]

[0015] where k is the slope of the fitting line and b is the intercept of the fitting line;

[0016] Based on the fractal theory, the profile height function of the rough surface is established:

[0017]

[0018] where L represents the sample length; γ represents the scale parameter; M represents the number of superimposed peaks on the generated surface, n represents the frequency factor, and n max = int[log(L / L s ) / logγ]; L s represents the truncation length; φ m,n represents the random phase, and x and y represent the horizontal and vertical coordinates of the surface respectively;

[0019] Considering the self-similar fractal characteristics of the rough surface at different scales, the initial thickness h0 of the point-contact mixed elastohydrodynamic lubricating oil film is:

[0020]

[0021] where A n represents the nominal contact area of the interface, that is, the geometric area without considering the microscopic rough topography; z s (x, y) represents the upper surface profile height function, and z f (x, y) represents the lower surface profile height function.

[0022] Furthermore, in step 1, under the action of the external load F, the set initial oil film pressure distribution p0(x, y) is:

[0023]

[0024] where R represents the radius of the first object, E represents the equivalent elastic modulus, υ s and E s respectively represent the Poisson's ratio and elastic modulus of the sphere, and υ f and E f respectively represent the Poisson's ratio and elastic modulus of the flat plate.

[0025] Furthermore, based on the initial oil film thickness h0 and initial pressure p0 obtained in step 1, the theoretical expression for the lubricating oil film thickness considering the microscopic rough fractal characteristics is derived as follows:

[0026]

[0027] where x and y represent the coordinate variables in the velocity direction and perpendicular to the velocity direction, R represents the radius of the first object, E represents the equivalent elastic modulus, z s (x, y) represents the upper surface profile height function, z f (x, y) represents the lower surface profile height function, ξ and ζ respectively represent arbitrary points on the x-axis and y-axis, and p(ξ, ζ) represents the pressure at the coordinate (ξ, ζ).

[0028] Furthermore, in step 2, according to the calculated lubricating oil viscosity η and density ρ and the oil film thickness equation, the Reynolds equation characterizing the relationship between the oil film thickness and pressure is introduced, and the film thickness equation and the Reynolds equation are made dimensionless:

[0029]

[0030] where represents the dimensionless density, represents the dimensionless viscosity, H represents the dimensionless oil film thickness, E′ represents the equivalent elastic modulus, represents the cube of the equivalent curvature radius, a and b are both coefficients; U represents the dimensionless velocity; P represents the dimensionless pressure; p H represents the maximum Hertz contact force; W represents the dimensionless load parameter, and X and Y respectively correspond to the dimensionless x and y;

[0031] The boundary conditions for the dimensionless equation are taken as:

[0032] P(X0, Y) = 0

[0033]

[0034] P / Y＝±1 = 0

[0035] where X0 is the starting coordinate value of the calculation region, and X e is the ending coordinate value of the calculation region.

[0036] Furthermore, calculate the proportion λ of the solid contact nodes to the total number of nodes according to the pressure distribution p(x, y):

[0037]

[0038] where N totalDenotes the total number of nodes at the contact interface, N s Denotes the number of solid contact nodes;

[0039] If the nominal geometric area of the contact interface is A n , the contact area of asperities on the point-contact mixed elastohydrodynamic lubrication contact interface is λA n .

[0040] Furthermore, in step 4, combining the true contact area of the solid part obtained in step 3, the maximum contact area among all the asperities that come into contact is calculated as:

[0041]

[0042] In the formula, D is the fractal dimension of the rough surface, A n is the nominal geometric area of the contact interface;

[0043] The load in mixed elastohydrodynamic lubrication is borne jointly by the solid and the liquid. The solid contact load F s is:

[0044]

[0045] In the formula, a represents the contact area of a single asperity, l min and l max respectively represent the minimum length scale and the maximum length scale, E represents the equivalent elastic modulus, and f(a) represents the elastic contact force of a single asperity:

[0046]

[0047] n(l) and n(a) respectively represent the distribution functions of the length scale and the contact area:

[0048]

[0049] The solid contact load and the liquid contact load are added together to obtain the total contact load F of the mixed lubrication interface n .

[0050] Furthermore, step 5 specifically includes:

[0051] Given the convergence accuracy ε, determine whether the calculated load F n and the externally applied load F satisfy |F n -F| / F < ε. If not convergent, then update the initial oil film thickness h0 and the oil film pressure distribution p0(x,y) according to F n , and iteratively calculate the oil film thickness distribution h(x,y) until the load converges, to obtain the point-contact mixed elastohydrodynamic lubrication oil film thickness distribution corresponding to the externally applied load F and the sliding velocity u.

[0052] Further, when updating the initial oil film thickness h0 according to F n set the minimum oil film thickness H according to the initial working conditions min to calculate the initial oil film variable value ΔH0 = (0.01 - 0.005)H min ; if F n > F, then update h0 = h0 - ΔH0; if F n < F, then update h0 = h0 + ΔH0; after multiple iterations, increase the convergence speed by changing ΔH0 to ΔH0 / 2.

[0053] Compared with the prior art, the beneficial effects of the present invention are as follows: The method proposed by the present invention takes into account the influence of external load, surface rough topography, and interface sliding speed on the three-dimensional distribution law of oil film thickness, and also considers the self-similar fractal characteristics of the surface rough topography of the sphere and the flat plate, so that the accuracy of the calculated oil film thickness is relatively high; in addition, the fractal parameter has the advantage of scale independence and is not affected by the resolution of the topography instrument, solving the limitations of existing experimental measurement methods and theoretical calculations;

[0054] Based on the point contact mixed elastohydrodynamic lubrication oil film thickness calculation method proposed by the present invention, the three-dimensional distribution characteristics of the oil film thickness under given working conditions such as load and rotational speed can be predicted, and it can also provide basic parameter support for improving the service life of precision mechanical components such as rolling bearings. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a schematic flow chart of the method for determining the point contact mixed elastohydrodynamic lubrication oil film thickness according to the embodiment of the present invention;

[0056] Figure 2 is a schematic diagram of the point contact mixed elastohydrodynamic lubrication three-dimensional model provided by the embodiment of the present invention, where (a) is a schematic diagram of the macroscopic contact interface and (b) is a schematic diagram of the microscopic rough contact interface;

[0057] Figure 3 is a schematic diagram of the rough fractal characteristics of the engineering surface at different scales provided by the embodiment of the present invention;

[0058] Figure 4 is a three-dimensional calculation result diagram of the point contact mixed elastohydrodynamic lubrication oil film thickness provided by the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0059] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0060] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0061] The present invention will be further described below in conjunction with specific embodiments, but it is not intended to limit the present invention.

[0062] The present invention provides a method for determining the lubricating oil film thickness of point contact mixed elastohydrodynamic lubrication. The flowchart of the specific method is as Figure 1 shown and includes the following steps:

[0063] S1: Measure the three-dimensional profile heights of the first object and the second object forming the point contact, establish a profile height function of the rough surface according to the obtained three-dimensional profile heights, then calculate the initial oil film thickness h0 according to the profile height function, and set the initial pressure distribution p0(x, y) of the oil film according to the externally applied load F;

[0064] In this embodiment, the elastic contact of a steel ball - flat plate is taken as an example for illustration. Refer to Figures 2 to 4 . As Figure 2 shown, on the macroscopic scale, the steel ball and the flat plate constitute a point contact mixed lubrication interface. On the microscopic scale, the surfaces of the sphere and the plane have roughness, resulting in different oil film thicknesses at different positions. An optical profiler or other topography measurement instrument is used to obtain the three-dimensional profile heights of the sphere and the flat plate, establish the autocorrelation function of the contact interface, perform Fourier transform on the autocorrelation function to obtain the power spectrum of the real surface profile, establish the double logarithmic coordinates of the power spectrum function and the spatial frequency, fit the scatter points of the power and the spatial frequency to obtain the slope and intercept of the fitted straight line, and calculate the fractal dimension D and fractal roughness G of the rough surface according to the fitting results of the slope and intercept:

[0065]

[0066] where k is the slope of the fitted straight line and b is the intercept of the fitted straight line;

[0067] Based on the fractal theory, establish a profile height function of the rough surface:

[0068]

[0069] where L represents the sample length; γ represents the scale parameter, and for common engineering surfaces, generally γ = 1.5; M represents the number of superimposed peaks of the generated surface, n represents the frequency factor, n max = int[log(L / L s ) / logγ]; L s represents the truncation length; φ m,n represents the random phase, and x, y represent the horizontal and vertical coordinates of the surface.

[0070] Considering the self-similar fractal characteristics of the rough surface at different scales, the initial thickness h0 of the point-contact mixed elastohydrodynamic lubricating oil film is set as:

[0071]

[0072] In the formula, A n represents the nominal contact area of the interface, that is, the geometric area without considering the microscopic rough topography; z s (x, y) represents the upper surface profile height function, and z f (x, y) represents the lower surface profile height function;

[0073] Under the action of the external load F, according to the Hertz elastic contact theory of the sphere, the initial pressure distribution p0(x, y) of the oil film is set as:

[0074]

[0075] In the formula, R represents the radius of the sphere, and E represents the equivalent elastic modulus. υ s and E s respectively represent the Poisson's ratio and elastic modulus of the sphere, and υ f and E f respectively represent the Poisson's ratio and elastic modulus of the flat plate.

[0076] Step 2: Calculate the lubricating oil viscosity η and density ρ under the initial pressure, and derive the lubricating oil film thickness equation based on the initial oil film thickness h0 and the initial pressure distribution p0(x, y). Introduce the Reynolds equation characterizing the relationship between the oil film thickness and pressure according to the calculated lubricating oil viscosity η and density ρ and the oil film thickness equation. Nondimensionalize the film thickness equation and the Reynolds equation, and discretize the nondimensionalized equations by the finite difference method;

[0077] In this step, without considering the influence of temperature, calculate the lubricating oil viscosity η and density ρ under the initial pressure according to the viscosity-pressure and density-pressure equations:

[0078]

[0079] In the formula, p is the oil film pressure;

[0080] According to the initial oil film thickness h0 and the initial pressure p0, derive the theoretical expression of the lubricating oil film thickness considering the microscopic rough fractal characteristics:

[0081]

[0082] In the formula, x and y represent the coordinate variables in the velocity direction and perpendicular to the velocity direction, ξ and ζ respectively represent any points on the x-axis and y-axis, and p(ξ, ζ) represents the pressure at the coordinate (ξ, ζ);

[0083] According to the calculated lubricating oil viscosity η and density ρ, and the oil film thickness equation, the Reynolds equation characterizing the relationship between the oil film thickness and pressure is introduced, and the film thickness equation and the Reynolds equation are made dimensionless:

[0084]

[0085] In the formula, represents the dimensionless density, represents the dimensionless viscosity, where is obtained from the lubricating oil viscosity η and density ρ obtained in the previous steps; H represents the dimensionless oil film thickness, E′ represents the equivalent elastic modulus, represents the cube of the equivalent curvature radius, a and b are both coefficients; U represents the dimensionless velocity; P represents the dimensionless pressure; p H represents the maximum Hertz contact force; W represents the dimensionless load parameter, and X and Y respectively correspond to the dimensionless x and y.

[0086] The boundary conditions for the dimensionless equation are taken as:

[0087] P(X0,Y) = 0

[0088]

[0089] P / Y＝±1 = 0

[0090] In the formula, X0 is the starting coordinate value of the calculation region, and X e is the ending coordinate value of the calculation region;

[0091] Based on the finite difference method, the above dimensionless equation is discretized, and the polynomial interpolation function is used to approximate the real pressure distribution on the grid cells, thereby establishing the influence coefficient matrix. According to the superposition principle of the linear system, the elastic deformation can be expressed as a linear combination of the nodal pressures:

[0092]

[0093]

[0094] In the formula, i, j, k, and l are the specific coordinates of a certain point.

[0095] Step 3: Calculate the oil film thickness \(h\) of each node on the contact interface according to the film thickness equation in Step 2, and calculate the pressure \(p\) of each node according to the dimensionless equation after discretization in Step 2, so as to obtain the mixed elastohydrodynamic lubrication oil film thickness distribution \(h(x,y)\) and pressure distribution \(p(x,y)\). Calculate the proportion \(\lambda\) of the solid contact nodes in the total number of nodes according to the pressure distribution \(p(x,y)\), so as to obtain the true contact area of the solid part;

[0096] Calculate the oil film thickness \(h\) of each node on the contact interface according to the film thickness equation in Step 2, and calculate the pressure \(p\) of each node according to the discretized dimensionless equation, so as to obtain the mixed elastohydrodynamic lubrication oil film thickness distribution \(h(x,y)\) and pressure distribution \(p(x,y)\), and calculate the proportion \(\lambda\) of the solid contact nodes in the total number of nodes:

[0097]

[0098] where \(N\) total represents the total number of nodes on the contact interface, and \(N\) s represents the number of solid contact nodes.

[0099] If the nominal geometric area of the interface is \(A\) n , then the contact area of asperities on the point-contact mixed elastohydrodynamic lubrication contact interface is \(\lambda A\) n .

[0100] Step 4: Based on the true contact area calculated in Step 3, calculate the maximum contact area \(a\) of a single rough peak according to the fractal theory L , and calculate the solid contact force \(F\) s according to the obtained maximum contact area. Combine the solid contact force and the liquid contact force to obtain the total contact force \(F\) of the mixed lubrication interface n ;

[0101] As Figure 3 shown, the rough surface has self-similar fractal characteristics at different scales. According to the fractal theory, combined with the solid contact area \(\lambda A\) n , calculate the maximum contact area among all the contacting asperities:

[0102]

[0103] The load of the mixed elastohydrodynamic lubrication is borne by both the solid and the liquid. The solid contact load \(F\) s

[0104]

[0105] where \(a\) represents the contact area of a single asperity, \(l\) min and \(l\) maxrespectively represent the minimum length scale and the maximum length scale, E represents the equivalent elastic modulus, and f(a) represents the elastic contact force of a single asperity:

[0106]

[0107] n(l) and n(a) respectively represent the distribution functions of the length scale and the contact area:

[0108]

[0109] The solid contact load and the liquid contact load are added together, where the liquid contact load is obtained by integrating the liquid pressure to obtain the total contact load F of the mixed lubrication interface n .

[0110] S5: Determine the calculated load F n and whether the external load F satisfies the convergence condition. If not, then according to the calculated load F n correct the initial oil film thickness h0 and the oil film pressure distribution p0(x, y), and perform iterative calculations until the load converges, finally obtaining the oil film thickness distribution h(x, y) of the point contact mixed lubrication interface;

[0111] Given the convergence accuracy ε, determine whether the calculated load F n and the external load F satisfy |F n -F| / F < ε. If not convergent, then according to F n update the initial oil film thickness h0 and the oil film pressure distribution p0(x, y):

[0112] Set the minimum oil film thickness H according to the initial working conditions min = aG *α U *β W *γ , where a is a constant, α, β, γ are the exponents of the empirical formula, G * is the material parameter, U * is the non-dimensionalized velocity, G * = αE, W * is the load parameter.

[0113] Calculate the initial oil film variable value ΔH0 = (0.01 - 0.005)H min ; if F n > F, then update h0 = h0 - ΔH0; if F n < F, then update h0 = h0 + ΔH0.

[0114] After multiple iterations, the convergence speed can be increased by changing ΔH0 to ΔH0 / 2.

[0115] Repeat steps 2, 3, and 4 to iteratively calculate the oil film thickness distribution h(x, y) until the load converges, and obtain the point-contact mixed elastohydrodynamic lubrication oil film thickness distribution h(x, y) corresponding to the applied load F and sliding velocity u. The calculation results are as Figure 4 shown. It can be seen from Figure 4 that due to the influence of surface micro-roughness, the point-contact mixed elastohydrodynamic lubrication oil film thickness varies with the spatial position. The above calculation results illustrate the accuracy and superiority of the algorithm proposed by the present invention.

[0116] The above are only the preferred embodiments of the present invention, and thus do not limit the implementation manners and protection scope of the present invention. For those skilled in the art, it should be realized that all the equivalent replacements and obvious changes made by using the content of the specification of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for determining the thickness of a point-contact mixed elastohydrodynamic lubricating oil film, characterized in that The steps are as follows: S1: Measure the three-dimensional profile heights of the first object and the second object that form a point contact. Here, the first object is an object with a curved surface. Based on the obtained three-dimensional profile heights, establish the profile height function of the rough surface, then calculate the initial oil film thickness h0 according to the profile height function, and set the initial pressure distribution p0(x, y) of the oil film according to the externally applied load F; S2: Calculate the lubricating oil viscosity η and density ρ under the initial pressure, and derive the lubricating oil film thickness equation based on the initial oil film thickness h0 and the initial pressure distribution p0(x, y). Then, introduce the Reynolds equation that characterizes the relationship between the oil film thickness and the pressure according to the calculated lubricating oil viscosity η, density ρ, and the oil film thickness equation. Nondimensionalize the film thickness equation and the Reynolds equation, and discretize the nondimensionalized equations by the finite difference method; S3: Calculate the oil film thickness h of each node at the contact interface according to the film thickness equation in step S2, and calculate the pressure p of each node at the contact interface according to the nondimensionalized equation discretized in step S2, to obtain the mixed elastohydrodynamic lubricating oil film thickness distribution h(x, y) and the pressure distribution p(x, y), and calculate the proportion λ of the solid contact nodes to the total number of nodes according to the pressure distribution p(x, y), so as to obtain the true contact area of the solid part; S4: Calculate the maximum contact area a of a single asperity based on the true contact area obtained in step S3 L , and then combine the maximum contact area a L to calculate the solid contact force F s . Obtain the total contact force F of the mixed lubrication interface based on the solid contact force and the liquid contact force n ; S5: Determine the calculated load F n and the externally applied load F satisfy the convergence condition. If not, according to the calculated load F n correct the initial oil film thickness h0 and the oil film pressure distribution p0(x, y), and perform iterative calculations until the load converges. Finally, obtain the oil film thickness distribution h(x, y) of the point contact mixed lubrication interface; Among them, step S1 specifically includes: Use a measuring instrument to obtain the three-dimensional profile heights of the first object and the second object, establish the autocorrelation function of the contact interface, perform Fourier transform on the autocorrelation function to obtain the power spectrum of the true surface profile, establish the double logarithmic coordinates of the power spectrum function and the spatial frequency, and fit the power and spatial frequency scatter points to obtain the slope and intercept of the fitted straight line, thereby calculating the fractal dimension D and the fractal roughness G of the rough surface In the formula, k is the slope of the fitted straight line, and b is the intercept of the fitted straight line; Based on the fractal theory, establish the profile height function of the rough surface: Wherein, L represents the sample length; γ represents the scale parameter; M represents the number of superimposed peaks of the generated surface, n represents the frequency factor, and n max = int[log(L / L s ) / logγ]; L s represents the truncation length; φ m,n represents the random phase, and x and y respectively represent the horizontal and vertical coordinates of the surface; Considering the self-similar fractal characteristics of the rough surface at different scales, the initial thickness h0 of the point contact mixed elastohydrodynamic lubricating oil film is: Where, A n represents the nominal contact area of the interface, i.e., the geometric area without considering the microscopic rough morphology; z s (x, y) represents the upper surface profile height function, and z f (x, y) represents the lower surface profile height function.

2. The method for determining the thickness of the point contact hybrid elastohydrodynamic lubricating oil film according to claim 1, characterized in that In step S1, under the action of the externally applied load F, the set initial pressure distribution p0(x, y) of the oil film is: Wherein, R represents the radius of the first object, and E represents the equivalent elastic modulus. υ s 、E s respectively correspond to represent the Poisson's ratio and elastic modulus of the sphere, and υ f 、E f respectively correspond to represent the Poisson's ratio and elastic modulus of the flat plate.

3. The method for determining the thickness of the point contact mixed elastohydrodynamic lubricating oil film according to claim 1, characterized in that According to the initial oil film thickness h0 and the initial pressure p0 obtained in step S1, derive the theoretical expression of the lubricating oil film thickness considering the microscopic rough fractal characteristics as: Wherein, x and y represent the coordinate variables in the velocity direction and perpendicular to the velocity direction, R represents the radius of the first object, E represents the equivalent elastic modulus, and z s (x, y) represents the upper surface profile height function, and z f (x, y) represents the lower surface profile height function, ξ and ζ respectively represent arbitrary points on the x-axis and y-axis, and p(ξ, ζ) represents the pressure at the coordinate (ξ, ζ).

4. The method for determining the thickness of the point-contact mixed elastohydrodynamic lubricating oil film according to claim 3, wherein In step S2, according to the calculated lubricating oil viscosity η, density ρ, and the oil film thickness equation, introduce the Reynolds equation that characterizes the relationship between the oil film thickness and the pressure, and nondimensionalize the film thickness equation and the Reynolds equation: In the formula, represents the dimensionless density, represents the dimensionless viscosity, H represents the dimensionless oil film thickness, and E′ represents the equivalent elastic modulus, represents the cube of the equivalent curvature radius, and a and b are both coefficients; U represents the dimensionless velocity; P represents the dimensionless pressure; p H represents the maximum Hertz contact force; W represents the dimensionless load parameter, and X and Y respectively correspond to the dimensionless x and y; Take the boundary conditions for the nondimensionalized equation as: P(X0,Y) = 0 P / Y＝±1 ＝0 where X0 is the starting coordinate value of the calculation region, and X e is the ending coordinate value of the calculation region.

5. The method for determining the thickness of the point-contact mixed elastohydrodynamic lubricating oil film according to claim 1, characterized in that, Calculate the proportion λ of the solid contact nodes to the total number of nodes according to the pressure distribution p(x, y): Where N total represents the total number of nodes of the contact interface, and N s represents the number of solid contact nodes; If the nominal geometric area of the contact interface is A n , the contact area of asperities on the point-contact mixed EHL contact interface is λA n .

6. The method for determining the thickness of the point-contact mixed elastohydrodynamic lubricating oil film according to claim 1, wherein In step S4, combining the true contact area of the solid part obtained in step S3, calculate the maximum contact area among all the contacting asperities as: where D is the fractal dimension of the rough surface, and A n is the nominal geometric area of the contact interface; In mixed elastohydrodynamic lubrication, the load is borne jointly by solids and liquids, and the solid contact load F s is as follows: where a represents the contact area of a single asperity, l min and l max represent the minimum length scale and the maximum length scale respectively, E represents the equivalent elastic modulus, and f(a) represents the elastic contact force of a single asperity: n(l) and n(a) respectively represent the distribution functions of the length scale and the contact area: The solid contact load and the liquid contact load are added together to obtain the total contact load F of the mixed lubrication interface n .

7. The method for determining the thickness of the point-contact hybrid elastohydrodynamic lubricating oil film according to claim 1, characterized in that, Step S5 specifically includes: Given the convergence accuracy ε, determine the calculated load F n and whether it satisfies |F n - F| / F < ε with the external load F. If it does not converge, then according to F n update the initial oil film thickness h0 and the oil film pressure distribution p0(x, y), and iteratively calculate the oil film thickness distribution h(x, y) until the load converges, so as to obtain the point-contact mixed elastohydrodynamic lubrication oil film thickness distribution corresponding to the external load F and the sliding velocity u.

8. The method for determining the film thickness of point-contact hybrid elastohydrodynamic lubrication according to claim 7, characterized in that When updating the initial oil film thickness h0 according to F n , set the minimum oil film thickness H according to the initial working condition min , and calculate the initial oil film variable value ΔH0 = (0.01 - 0.005)H min ; if F n > F, then update h0 = h0 - ΔH0; if F n < F, then update h0 = h0 + ΔH0; after multiple iterations, improve the convergence speed by changing ΔH0 to ΔH0 / 2.

Images