Design method and system of elliptical contact self-rolling elastohydrodynamic lubrication of non-gaussian rough surface in mixed lubrication state

Abstract

The application discloses a design method and system of an elliptical contact self-rotation elastohydrodynamic lubrication non-Gaussian rough surface under a mixed lubrication state, obtains initial density of lubricating oil and viscosity of the lubricating oil under an atmospheric pressure environment, sets nominal oil film thickness and fluid dynamic pressure of a rough contact surface, constructs an elliptical contact self-rotation elastohydrodynamic lubrication Reynolds equation based on a point contact elastohydrodynamic lubrication Reynolds equation; constructs an average flow Reynolds equation of an elliptical contact self-rotation elastohydrodynamic lubrication of a Gaussian rough surface, and further constructs an average flow Reynolds model of an elliptical contact self-rotation elastohydrodynamic lubrication of a non-Gaussian rough surface; thereby, the fluid dynamic pressure and oil film distribution under different rough surfaces are obtained; the contact pressure in a micro asperity contact area is calculated, and the micro asperity contact pressure under different rough surfaces is obtained. In the application, the fluid dynamic pressure, the micro asperity contact pressure and the oil film thickness distribution are determined, the non-Gaussian rough contact surface with better lubrication performance is designed, and the service life of key parts in an aero-engine and a machine tool is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of friction lubrication surface design, and particularly relates to a method and system for designing a non-Gaussian rough surface in an elliptical contact self-rotating elastohydrodynamic lubrication under a mixed lubrication state. BACKGROUND

[0002] During the operation of mechanical equipment, the problem of friction and wear at the assembly interface is often difficult to avoid, and excessive friction damage can cause serious damage to the mechanical equipment, leading to a significant decrease in equipment performance and a shortened service life. In addition, the elliptical contact area commonly found in actual mechanical equipment, especially during rotation and entrainment, brings more complexity to the study of friction and lubrication. The application of lubrication technology provides an effective way to solve this problem. Through reliable lubrication technology, a lubricating oil film can be formed between the friction surfaces, providing sufficient normal bearing capacity, reducing direct contact between the contacting surfaces, reducing wear, and thus improving the transmission efficiency and service life of the mechanical equipment. However, due to changes in working conditions and the influence of mechanical working surface roughness, many contact interfaces often exist in a mixed lubrication state. In this state, the thickness of the oil film cannot be maintained, and direct contact between the surfaces will be caused by the rough peaks, thus forming the so-called "mixed lubrication" phenomenon. Mixed lubrication state combines the characteristics of boundary lubrication and hydrodynamic lubrication, where the normal load is borne by hydrodynamic pressure and micro-asperity contact pressure, which easily leads to surface gluing, wear and other defects, seriously affecting the life and performance of the mechanical system. Under mixed lubrication conditions, the evaluation of lubrication performance usually uses the film thickness ratio, which is the ratio of the average oil film thickness to the surface comprehensive root mean square roughness. Different surface roughness characteristics have a significant impact on contact lubrication. When the micro-asperity contact pressure is too large, it may cause plastic deformation of the contact surface, thereby changing the physical properties of the material and significantly weakening the elastohydrodynamic lubrication performance. In addition, the texture direction, skewness and kurtosis of the surface roughness also have an important influence on the elastohydrodynamic lubrication performance. Therefore, studying the influence of rough surface characteristics on elastohydrodynamic lubrication performance has important academic significance and engineering application value.

[0003] Currently, most researches mainly focus on the influence of non-Gaussian roughness on the elastohydrodynamic lubrication performance of point contact, while the research on elliptical contact self-rotating elastohydrodynamic lubrication is relatively less. Due to the particularity of elliptical contact self-rotating lubrication, its research faces great challenges, especially in the convergence of numerical algorithms, which often shows poor convergence. At present, there is still a lack of more efficient and accurate rough surface design method for the non-Gaussian rough surface elliptical contact self-rotating elastohydrodynamic lubrication problem existing in key parts of aircraft engines and machine tools, in order to design non-Gaussian rough surfaces with different skewness and kurtosis surface characteristics, improve the lubrication performance of the contact area, reduce wear, and ensure the service life of important parts. SUMMARY

[0004] The present application aims at the problem that the prior art cannot effectively design a non-Gaussian surface to improve the self-rolling elastohydrodynamic lubrication performance of an elliptical contact under mixed lubrication, and provides a design method and system for a non-Gaussian rough surface of an elliptical contact self-rolling elastohydrodynamic lubrication under mixed lubrication, which can conveniently and quickly determine the influence of rough surface characteristics such as rough surface height standard deviation, rough surface texture direction, skewness and kurtosis on fluid dynamic pressure, micro-convex body contact pressure and oil film thickness distribution according to the elliptical contact self-rolling elastohydrodynamic lubrication problem under various working conditions, design a non-Gaussian rough contact surface with better lubrication performance, and improve the service life of key components in an aero-engine and a machine tool.

[0005] To achieve the above object, the technical scheme adopted by the present application is as follows:

[0006] A design method for a non-Gaussian rough surface of an elliptical contact self-rolling elastohydrodynamic lubrication under mixed lubrication, comprising the following steps:

[0007] S1, obtaining the initial density of lubricating oil and the viscosity of lubricating oil under atmospheric pressure environment, and setting the nominal oil film thickness and fluid dynamic pressure of the rough contact surface, and then constructing an elliptical contact self-rolling elastohydrodynamic lubrication Reynolds equation based on the point contact elastohydrodynamic lubrication Reynolds equation;

[0008] S2, constructing a Gaussian rough surface elliptical contact self-rolling elastohydrodynamic lubrication average flow Reynolds equation based on the elliptical contact self-rolling elastohydrodynamic lubrication Reynolds equation and the average flow model;

[0009] S3, constructing a non-Gaussian rough surface elliptical contact self-rolling elastohydrodynamic lubrication average flow Reynolds model based on the Gaussian rough surface elliptical contact self-rolling elastohydrodynamic lubrication average flow Reynolds equation; obtaining the fluid dynamic pressure and oil film distribution under different rough surfaces according to the non-Gaussian rough surface elliptical contact self-rolling elastohydrodynamic lubrication average flow Reynolds model; calculating the contact pressure in the micro-convex body contact area to obtain the micro-convex body contact pressure under different rough surfaces, and realizing the design of the non-Gaussian rough surface of the elliptical contact self-rolling elastohydrodynamic lubrication under mixed lubrication.

[0010] Further, in step S1, the elliptical contact self-rolling elastohydrodynamic lubrication Reynolds equation is:

[0011]

[0012] Wherein, p is the density, h is the nominal oil film thickness, ηη is the viscosity, p is the fluid dynamic pressure, u is the x-direction entrainment velocity, and v is the y-direction entrainment velocity of the elliptical self-rolling.

[0013] Further, in step S2, the Gaussian rough surface elliptical contact self-rolling elastohydrodynamic lubrication average flow Reynolds equation is:

[0014]

[0015] where p is the density, h is the nominal film thickness, η is the viscosity, p h is the hydrodynamic pressure, u is the entrainment velocity in the x direction, v is the entrainment velocity of the elliptical spin in the y direction, σ is the equivalent roughness standard deviation of the two rough surfaces, φ x , φ y are the pressure flow factors in the x and y directions, respectively, φ c is the contact factor on the Gaussian rough surface, φ s is the shear flow factor on the Gaussian rough surface.

[0016] Further, in step S3, the average flow Reynolds model of the non-Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication is:

[0017]

[0018] where p is the density, h is the nominal film thickness, η is the viscosity, p h is the hydrodynamic pressure, u is the entrainment velocity in the x direction, v is the entrainment velocity of the elliptical spin in the y direction, σ is the equivalent roughness standard deviation of the two rough surfaces, is the pressure flow factor in the x direction on the non-Gaussian rough surface, is the pressure flow factor in the y direction on the non-Gaussian rough surface, is the contact factor on the non-Gaussian rough surface, is the shear flow factor on the non-Gaussian rough surface.

[0019] Further, the calculation equation of the nominal film thickness h is:

[0020]

[0021] where h0 is the rigid center film thickness, R x is the equivalent curvature radius in the x direction, R y is the equivalent curvature radius in the y direction, and v(x, y) is the surface elastic deformation.

[0022] Further, the calculation equation of the surface elastic deformation v(x, y) is:

[0023]

[0024] where E' is the equivalent Young's modulus, and ξ and ζ are additional coordinates corresponding to x and y.

[0025] Further, the viscosity η is calculated by:

[0026]

[0027] Wherein, ηη0 is the viscosity of the lubricating oil in the atmospheric pressure environment, p is the oil film pressure, and z0 is the pressure viscosity index.

[0028] Further, the density p is calculated by the following formula:

[0029]

[0030] Wherein, p0 is the initial density of the lubricating oil, and p is the oil film pressure.

[0031] The swirl velocity u of the elliptical spin in the x direction and the swirl velocity v of the elliptical spin in the y direction are calculated by the following formula:

[0032]

[0033] Wherein, u1 is the velocity of the upper surface of the elliptical contact spin in the x direction, v1 is the velocity of the upper surface of the elliptical contact spin in the y direction, u2 is the velocity of the lower surface of the elliptical contact spin in the x direction, and v2 is the velocity of the lower surface of the elliptical contact spin in the y direction.

[0034] Further, the calculation formula of the microconvex body contact pressure p a is the KE contact model:

[0035]

[0036] Wherein, σ is the standard deviation of the equivalent roughness of the two rough surfaces, β is the surface roughness parameter, K represents the hardness coefficient, ω c is the critical value of the rough peak from elastic deformation to plastic deformation, h d is the hardness of the softer surface, d is the distance from the microconvex body intermediate surface to the equivalent smooth surface, and I is the KE model calculation parameter.

[0037] A design system of elliptical contact spin elastohydrodynamic lubrication of non-Gaussian rough surface in mixed lubrication state, comprising:

[0038] An elliptical contact spin elastohydrodynamic lubrication Reynolds equation construction module is configured to obtain the initial density of the lubricating oil and the viscosity of the lubricating oil in the atmospheric pressure environment, set the nominal oil film thickness and the fluid dynamic pressure of the rough contact surface, and then construct the elliptical contact spin elastohydrodynamic lubrication Reynolds equation based on the point contact elastohydrodynamic lubrication Reynolds equation;

[0039] A Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication average flow Reynolds equation construction module is configured to construct the Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication average flow Reynolds equation based on the elliptical contact spin elastohydrodynamic lubrication Reynolds equation and the average flow model;

[0040] The computing module is used for constructing a non-Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication average flow Reynolds model based on a Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication average flow Reynolds equation; the fluid dynamic pressure and the oil film distribution under different rough surfaces are obtained according to the non-Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication average flow Reynolds model; the contact pressure in the micro asperity contact area is calculated to obtain the micro asperity contact pressure under different rough surfaces, and the non-Gaussian rough surface design of the elliptical contact spin elastohydrodynamic lubrication under the mixed lubrication state is realized.

[0041] Compared with the prior art, the present application has beneficial effects at least including:

[0042] The design method of the present application provides an efficient calculation model for numerical analysis of the elliptical spin elastohydrodynamic lubrication problem existing in the mixed lubrication of the assembly interface in the mechanical equipment, and can effectively solve the problem of poor numerical solution convergence caused by the elliptical contact spin problem.

[0043] Further, the non-Gaussian rough surface flow factor and the contact factor correction equation are used to solve the non-Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication problem, the plastic deformation possibly generated by the contact surface is considered, the contact pressure in the micro asperity contact area is solved through the KE contact model, and the micro asperity contact behavior is more accurately described. The present application provides an efficient and accurate design method for the non-Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication problem under the mixed lubrication condition, can study the influence of the micro characteristics of the rough surface such as the root mean square roughness, the rough surface texture, the rough surface skewness and the kurtosis on the elliptical contact spin elastohydrodynamic lubrication performance, provides a theoretical basis for the design of the elliptical rough contact surface of the key parts in the aero-engine and the machine tool, improves the lubrication performance of the contact area, and improves the friction and wear service life of the parts. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 is a non-Gaussian rough surface elliptical contact elastohydrodynamic lubrication analysis flowchart;

[0045] Figure 2 is an elliptical contact schematic diagram;

[0046] Figure 3 is an elliptical contact rough surface equivalent transformation diagram;

[0047] Figure 4 is a non-Gaussian rough surface schematic diagram;

[0048] Figure 5is an elliptical contact self-rolling elastohydrodynamic lubrication characteristic distribution diagram, wherein (a) is a three-dimensional distribution diagram of hydrodynamic pressure, (b) is a three-dimensional distribution diagram of oil film thickness, (c) is a hydrodynamic pressure contour diagram, and (d) is an oil film thickness contour diagram;

[0049] Figure 6 is a schematic diagram of an elliptical contact self-rolling elastohydrodynamic lubrication non-Gaussian rough surface design system in a mixed lubrication state. DETAILED DESCRIPTION

[0050] For the purpose of the embodiment of the present application, the technical solutions and advantages, the technical solutions of the present application will be clearly and accurately described below in combination with the drawings of the embodiment of the present application. Based on the specific description of the embodiment of the present application, all other embodiments obtained by the person skilled in the art without creative labor belong to the scope of protection of the present application.

[0051] The present application provides a design method for an elliptical contact self-rolling elastohydrodynamic lubrication non-Gaussian rough surface in a mixed lubrication state, and the specific steps are as follows:

[0052] S1, obtaining the initial density of lubricating oil and the viscosity of lubricating oil under atmospheric pressure environment, and setting the nominal oil film thickness and hydrodynamic pressure of the rough contact surface, and then constructing an elliptical contact self-rolling elastohydrodynamic lubrication Reynolds equation based on the point contact elastohydrodynamic lubrication Reynolds equation;

[0053] S2, constructing a Gaussian rough surface elliptical contact self-rolling elastohydrodynamic lubrication average flow Reynolds equation based on the elliptical contact self-rolling elastohydrodynamic lubrication Reynolds equation and the average flow model in step S1;

[0054] S3, using a non-Gaussian rough surface flow factor and a contact factor correction equation, constructing a non-Gaussian rough surface elliptical contact self-rolling elastohydrodynamic lubrication average flow Reynolds model based on the Gaussian rough surface elliptical contact self-rolling elastohydrodynamic lubrication average flow Reynolds equation in step S2; obtaining the hydrodynamic pressure and oil film distribution under different rough surfaces (different rough textures, skewness and kurtosis) according to the non-Gaussian rough surface elliptical contact self-rolling elastohydrodynamic lubrication average flow Reynolds model; using the KE contact model to calculate the contact pressure in the micro-convex body contact area to obtain the micro-convex body contact pressure under different rough surfaces;

[0055] S4, judging the advantages and disadvantages of the elliptical contact self-rolling elastohydrodynamic lubrication performance under different rough contact surfaces according to the micro-convex body contact pressure, hydrodynamic pressure and oil film thickness distribution under different rough surfaces, selecting the rough contact surface with superior lubrication performance, and realizing the design of the non-Gaussian rough surface in the elliptical contact self-rolling elastohydrodynamic lubrication in the mixed lubrication state, and providing a theoretical basis for the design of the elliptical contact surface of the key parts in the aero-engine and machine tool.

[0056] In step S1, the Reynolds equation of point contact elastohydrodynamic lubrication is:

[0057]

[0058] Wherein, p is density, h is nominal oil film thickness, ηη is viscosity, p is fluid dynamic pressure, and u is the entrainment speed in the x direction.

[0059] Based on the Reynolds equation of point contact elastohydrodynamic lubrication, the Reynolds equation of elliptical contact self-rotation elastohydrodynamic lubrication can be written as:

[0060]

[0061] Based on the elliptical contact self-rotation elastohydrodynamic lubrication Reynolds equation and the average flow model (average flow model, see literature: An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication, Journal of lubrication Technology, JANUARY 1978, VOL 100, p12-17) described in step S1, the Gaussian rough surface elliptical contact self-rotation elastohydrodynamic lubrication Reynolds equation is constructed, which specifically includes:

[0062] Further, in step S2, the average flow Reynolds equation of Gaussian rough surface elliptical contact self-rotation elastohydrodynamic lubrication can be written as:

[0063]

[0064] Wherein, h is the nominal oil film thickness, p h is the fluid dynamic pressure, h T is the local oil film thickness, φ x , φ y are the pressure flow factors in the x and y directions respectively and φ y (h, γ) = φ x (h, 1 / γ), φ s is the shear flow factor on the Gaussian rough surface, γ is the corrugation length factor, which can represent the texture direction of the rough surface, and σ is the equivalent roughness standard deviation of the two rough surfaces and σ1 is the standard deviation of the height distribution of the microconvex body of the upper rough surface, σ2 is the standard deviation of the height distribution of the microconvex body of the lower rough surface, u is the entrainment speed of the ellipse self-rotation in the x direction, and v is the entrainment speed of the ellipse self-rotation in the y direction.

[0065] Wherein, the calculation formula of the local oil film thickness h T is:

[0066]

[0067] where δ is the integrated roughness.

[0068] Further, the Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication average flow Reynolds equation in step S2 can be written as which can be defined as a representation containing the contact factor, and the calculation formula is:

[0069]

[0070] where φ can be defined as the contact factor.

[0071] Therefore, the calculation formula of the Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication average flow Reynolds equation in step S2 can be written as:

[0072]

[0073] where φ s is the shear flow factor on the Gaussian rough surface, and φ c is the contact factor on the Gaussian rough surface.

[0074] The calculation formula of the contact factor φ c in the Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication average flow Reynolds equation in step S2 is:

[0075]

[0076] where λ is the ratio of the local oil film thickness h T to the standard deviation σ of the equivalent roughness of the two surfaces.

[0077] Further, the non-Gaussian rough surface height probability density distribution function in step S3 based on the Gaussian rough surface height probability density distribution function can be represented as a combination of a polynomial and a Gaussian rough surface height probability density function, and the calculation formula of the final non-Gaussian rough surface height probability density distribution function χ(z) is:

[0078]

[0079] where S k is the skewness of the non-Gaussian rough surface, K u is the kurtosis of the non-Gaussian rough surface, and z is the rough peak height.

[0080] Based on the Gaussian rough surface flow factor, a non-Gaussian rough surface flow factor correction equation is constructed, and the pressure flow factor on the non-Gaussian rough surface in the x direction is The calculation formula of the shear flow factor of the non-Gaussian rough surface is:

[0081]

[0082] Wherein, the pressure flow factor calculation parameter N g = -10λ -3 S k + 15λ -4 (K u - 3), S k is the skewness of the non-Gaussian rough surface, K u is the kurtosis of the non-Gaussian rough surface.

[0083] The calculation formula of the shear flow factor of the non-Gaussian rough surface is:

[0084]

[0085] Wherein, φ s is the shear flow factor of the Gaussian rough surface.

[0086] The calculation formula of the non-Gaussian rough surface contact factor in step S3 is:

[0087]

[0088] Wherein, s represents the ratio of the rough peak height to the standard deviation of the equivalent roughness, which can be expressed as z / σ.

[0089] The specific expression formula of the non-Gaussian rough surface contact factor is:

[0090]

[0091] Wherein, the first coefficient A1 = 4λ 2 - 4, the second coefficient A2 = λ 3 - λ, the third coefficient A3 = 4m1+m1m3-3m1m2i+K u m1m3i+K u m1m2i, the fourth coefficient The fifth coefficient m2 = erfi(λi / 2), the sixth coefficient

[0092] Further, the expression of the non-Gaussian rough surface elliptical contact self-rolling lubrication average flow Reynolds model in S3 is:

[0093]

[0094] ​​where u is the swirl velocity of the elliptical spin in the x direction, v is the swirl velocity of the elliptical spin in the y direction, is the pressure flow factor on the x direction non-Gaussian rough surface, is the pressure flow factor on the y direction non-Gaussian rough surface.

[0095] In order to obtain the oil film thickness distribution characteristics, the oil film thickness in the contact area needs to be calculated, and the calculation equation of the nominal oil film thickness h is:

[0096]

[0097] where h0 is the rigid center film thickness, R x is the equivalent curvature radius in the x direction, R y is the equivalent curvature radius in the y direction, and v(x, y) is the surface elastic deformation.

[0098] The calculation equation of the surface elastic deformation v(x, y) in the calculation equation of the nominal oil film thickness h is:

[0099]

[0100] where E' is the equivalent Young's modulus, and ξ and ζ are additional coordinates corresponding to x and y.

[0101] The relationship between the oil film pressure and the viscosity η in step S3 is the formula:

[0102]

[0103] where η0 is the viscosity of the lubricating oil under atmospheric pressure, p is the oil film pressure, and z0 is the pressure viscosity index, which is 0.68.

[0104] The formula for the change of the density p with the oil film pressure is:

[0105]

[0106] Further, p0 is the initial density of the lubricating oil.

[0107] The swirl velocity of the ellipsoid in the average flow Reynolds equation of the elliptical contact spin elastohydrodynamic lubrication is:

[0108]

[0109] where u1=ωy is the velocity of the upper surface of the elliptical contact spin in the x direction, v1=-ωx is the velocity of the upper surface of the elliptical contact spin in the y direction, u2=0 is the velocity of the lower surface of the elliptical contact spin in the x direction, v2=0 is the velocity of the lower surface of the elliptical contact spin in the y direction. u is the swirl velocity of the elliptical spin in the x direction, and v is the swirl velocity of the elliptical spin in the y direction.

[0110] Optionally, in step S3, the micro-protrusion contact pressure p a The calculation formula, i.e., the KE contact model, is:

[0111]

[0112] Where β is the surface roughness parameter, K is the hardness coefficient, and ω c h is the critical value for the roughness peak to transition from elastic deformation to plastic deformation. d The hardness of the softer surface is given by d, and d is the distance from the intermediate surface of the micro-protrusion to the equivalent smooth surface.

[0113] Key parameters in the KE contact model include: hardness coefficient K and the critical value ω for the roughness peak to transition from elastic deformation to plastic deformation. c The calculation formula is:

[0114]

[0115] Where v is the Poisson's ratio of the material of the softer contact surface, and r as Let be the radius of curvature of the micro-convex body.

[0116] Furthermore, the load balance equation is used to determine whether the obtained fluid dynamic pressure distribution is correct. The calculation formula for the load balance equation is as follows:

[0117] w=∫∫(p h (x, y) + p a (x, y))dxdy

[0118] Where w is the external load, p h p is the fluid dynamic pressure. a This refers to the contact pressure of the micro-convex body.

[0119] The hydrodynamic pressure and oil film distribution under different surface roughness (different roughness textures, skewness, and kurtosis) in step S3 are obtained through the following process: See Figure 1 First, initial parameters such as external load and Young's modulus are set, and the elastohydrodynamic lubrication boundary conditions are determined. Second, the surface elastic deformation, oil film thickness distribution, lubricating viscosity, and density are calculated. Then, the Reynolds equation for spin-averaged flow in elliptical contact on a non-Gaussian rough surface and the KE contact model are solved to obtain the pressure distribution, including hydrodynamic pressure and micro-protrusion contact pressure. Next, the newly obtained pressure distribution is used to solve for elastic deformation, oil film thickness, and lubricating oil viscosity and density. Finally, it is determined whether the pressure converges. If it does not converge, the pressure is corrected and iterative calculation continues. If it converges, it is further determined whether the load is balanced. If the load is unbalanced, the central oil film thickness is corrected and iterative calculation continues. If the load is balanced, the pressure distribution and oil film thickness distribution are output.

[0120] Example 1

[0121] For the non-Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication problem, the working condition environment is first determined, and the basic parameters such as the equivalent Young's modulus E' = 0.0366 GPa, the lubricating oil viscosity η0= 0.05 Pa·s, the root mean square roughness σ = 2 um, the skewness S k = -0.5, and the kurtosis K u = 3 are determined. Secondly, the equivalent curvature radius R x = 475.7 mm and R y = 957.9 mm of the elliptical contact and the elliptical spin angular velocity ω = 400 rad / s are determined, and the elliptical contact spin problem is converted into a problem of a plane rotating around the contact center at an angular velocity ω, as shown in Figure 2 The formula for calculating the entrainment velocity of the elliptical contact spin is:

[0122]

[0123] The processing of the elliptical contact spin mixed lubrication problem can be analogous to the typical rough surface point contact lubrication problem, and by equivalent conversion of the two rough surfaces into a single rough surface, a mixed lubrication numerical model for the smooth ellipsoid self-spinning on the rough plane is obtained, as shown in Figure 3 The formula for the standard deviation σ of the equivalent roughness of the rough surface, i.e., the root mean square roughness, is:

[0124]

[0125] where σ1is the standard deviation of the height distribution of the microconvexities of the upper rough surface, and σ2is the standard deviation of the height distribution of the microconvexities of the lower rough surface.

[0126] The basic parameters are brought into the non-Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication average flow Reynolds model, as follows:

[0127]

[0128] where p h is the fluid pressure; h is the nominal oil film thickness; ηη is the viscosity of the lubricating oil; ρ is the density of the lubricating oil, h T is the local oil film thickness, and f are the pressure flow factors in the x and y directions, respectively, and f is the shear flow factor. u and v represent the entrainment velocities in the x and y directions, respectively, and u = u1 / 2, v = v1 / 2, and σ is the root mean square roughness.

[0129] In the non-Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication average flow Reynolds model, the formula for calculating the nominal oil film thickness of the elliptical contact can be written as:

[0130]

[0131] where h0 is the initial central oil film thickness, R x and R y are the equivalent radii of curvature in the x and y directions, respectively, and v(x, y) is the surface elastic deformation caused by pressure.

[0132] where the surface elastic deformation v(x, y) is calculated by the formula:

[0133]

[0134] where E' is the equivalent Young's modulus, and ξ and ζ are additional coordinates corresponding to the x and y directions, respectively.

[0135] The relationship between the oil film pressure and the viscosity is given by the formula:

[0136]

[0137] where ηη0 is the viscosity of the lubricating oil under atmospheric pressure, and z0 is the pressure viscosity index, which is taken as 0.68.

[0138] The formula for the change in the density with the oil film pressure p is:

[0139]

[0140] where ρ0 is the density of the lubricating oil under atmospheric pressure.

[0141] The formula for calculating the pressure flow factor on the non-Gaussian rough surface in the x direction is:

[0142]

[0143] where the pressure flow factor calculation parameter N g = -10λ -3 S k + 15λ -4 (K u - 3), S k is the skewness of the non-Gaussian rough surface, K u is the kurtosis of the non-Gaussian rough surface, and φ x is the pressure flow factor on the Gaussian rough surface.

[0144] The formula for calculating the shear flow factor on the non-Gaussian rough surface is:

[0145]

[0146] where φ s ​​S is the shear flow factor on Gaussian rough surface k K is the skewness of non-Gaussian rough surface u λ is the kurtosis of non-Gaussian rough surface, γ is the ratio of local oil film thickness to the standard deviation of equivalent roughness of two surfaces, and γ is the corrugation length factor.

[0147] Figure 4 is a schematic diagram of a non-Gaussian rough surface, and the calculation formula of the probability density distribution function χ(z) of the rough peak height of the non-Gaussian rough surface is:

[0148]

[0149] Non-Gaussian rough surface contact factor The modified calculation formula is:

[0150]

[0151] Wherein, s represents the ratio of rough peak height to the standard deviation of equivalent roughness of two surfaces, which can be expressed as z / σ.

[0152] The final non-Gaussian rough surface contact factor obtained is The specific calculation formula is:

[0153]

[0154] Wherein, the first coefficient A1=4λ 2 -4, the second coefficient A2=λ 3 -λ, the third coefficient A3=4m1+m1m3-3m1m2i+K u m1m3i+K u m1m2i, the fourth coefficient The fifth coefficient m2=erfi(λi / 2), the sixth coefficient

[0155] Further, the calculation formula of the microconvex contact pressure p a in the KE contact model is:

[0156]

[0157] Wherein, β is the surface roughness parameter, K is the hardness coefficient, ω c is the critical value of rough peak from elastic deformation to plastic deformation, and h d is the hardness of the softer surface.

[0158] The calculation formula of the important parameters in the KE contact model is:

[0159]

[0160] Where v is the Poisson's ratio of the material of the softer contact surface, and r as Let be the radius of curvature of the micro-convex body.

[0161] Furthermore, we analyze whether the obtained fluid pressure distribution satisfies the load balance condition. The calculation formula for the load balance equation is as follows:

[0162] w=∫∫(p h (x, y) + p a (x, y))dxdy

[0163] To facilitate numerical calculations, the mean Reynolds equations for elliptical contact spin elastohydrolubrication are treated dimensionlessly: X = x / a, Y = y / a, H = hR. x / a 2 P h =p h / P H , U X =u / u0, V Y =v / u0, W=w / E′R x 2 ,

[0164] Where X and Y are dimensionless coordinate variables; It is a dimensionless density; H is dimensionless viscosity; H is dimensionless film thickness; P h denoted as dimensionless pressure; W as dimensionless load; a as the half-width of the elliptical contact area in the x-direction; R as the contact radius. x Let P be the equivalent radius of curvature in the x-direction. H This represents the maximum Hertzian contact pressure.

[0165] The dimensionless form of the Reynolds equation for average flow is as follows:

[0166]

[0167] in,

[0168] The dimensionless result of the KE contact model is:

[0169]

[0170] in, The height of the dimensionless micro-convex body. Let be the distance from the intermediate surface of the dimensionless micro-convex body to the equivalent smooth surface. This represents the critical value for the dimensionless roughness peak to transition from elastic deformation to plastic deformation. Parameters for the dimensionless KE contact model. The standard deviation of the dimensionless roughness of the rough surface.

[0171] The present application adopts finite difference method to discretize the equation, and uses first-order backward difference method, which has good effect, is suitable for most working conditions, and on the solution domain, the grid is divided along the X and Y directions according to equal step length DX. Considering that the convergence of the numerical solution process of the elliptical contact spin elastohydrodynamic lubrication is poor, and is easily affected by the boundary, load, angular velocity and the like, the pressure in the low pressure area is solved by using the Gauss-Seidel iteration method, and the pressure in the high pressure area is solved by using the Jacobi bipolar iteration method, so that the local high pressure is avoided to cause the non-convergence of the solution.

[0172] The value range of X and Y directions is-5 to 5, the grid density is 128*128, and the typical hydrodynamic pressure and oil film thickness distribution of the elliptical contact spin elastohydrodynamic lubrication are as shown in (a), (b), (c) and (d) of FIG. Figure 5

[0173] The design method of the non-Gaussian rough surface of the elliptical contact spin elastohydrodynamic lubrication under the mixed lubrication state can efficiently and accurately study the basic characteristics of the elliptical spin elastohydrodynamic lubrication, consider the influence of various complex working conditions such as different Gaussian rough surfaces, rough surface textures, skewness and kurtosis on the elliptical contact spin elastohydrodynamic lubrication, and provide a simple, convenient and high-efficiency new method for studying this kind of problem, and provide a theoretical method for better designing the elliptical contact rough surface in key parts.

[0174] Referring to Figure 6 A design system of non-Gaussian rough surface of elliptical contact spin elastohydrodynamic lubrication under mixed lubrication state, comprising:

[0175] An elliptical contact spin elastohydrodynamic lubrication Reynolds equation construction module is used to obtain the initial density of lubricating oil and the viscosity of lubricating oil under atmospheric pressure environment, set the nominal oil film thickness and fluid dynamic pressure of the rough contact surface, and then construct the elliptical contact spin elastohydrodynamic lubrication Reynolds equation based on the point contact elastohydrodynamic lubrication Reynolds equation;

[0176] A Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication average flow Reynolds equation construction module is used to construct the Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication average flow Reynolds equation based on the elliptical contact spin elastohydrodynamic lubrication Reynolds equation and the average flow model;

[0177] ​The computing module is used for constructing the non-Gaussian rough surface elliptical contact self-rotating elastohydrodynamic lubrication average flow Reynolds model based on the Gaussian rough surface elliptical contact self-rotating elastohydrodynamic lubrication average flow Reynolds equation; the fluid dynamic pressure and the oil film distribution under different rough surfaces are obtained according to the non-Gaussian rough surface elliptical contact self-rotating elastohydrodynamic lubrication average flow Reynolds model; the contact pressure in the micro asperity contact area is calculated to obtain the micro asperity contact pressure under different rough surfaces, and the non-Gaussian rough surface design of the elliptical contact self-rotating elastohydrodynamic lubrication under the mixed lubrication state is realized.

[0178] The above is the description of the implementation method of the present application, but it cannot be understood as the limitation of the claims. The present application is not limited to the above embodiments, and the specific structure allows changes. Any changes made within the protection scope of the independent claims of the present application are within the protection scope of the present application.

[0179] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in the description herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

Claims

1. A method for designing a non-Gaussian rough surface with elliptical contact spin elastohydrodynamic lubrication under mixed lubrication conditions, characterized in that, Includes the following steps: S1. Obtain the initial density and viscosity of the lubricating oil under atmospheric pressure, and set the nominal oil film thickness and hydrodynamic pressure of the rough contact surface. Then, construct the Reynolds equation for elliptical contact spin elastohydrodynamic lubrication based on the Reynolds equation for point contact elastohydrodynamic lubrication. S2. Based on the Reynolds equation and average flow model for elliptical contact spin elastohydrolubrication, construct the average flow Reynolds equation for Gaussian rough surface elliptical contact spin elastohydrolubrication. S3. Using the non-Gaussian rough surface flow factor and contact factor correction equation, and based on the Reynolds equation for the average flow rate of spin elastohydrodynamic lubrication in elliptical contact on a Gaussian rough surface, a Reynolds model for the average flow rate of spin elastohydrodynamic lubrication in elliptical contact on a non-Gaussian rough surface is constructed. Based on the Reynolds model for the average flow rate of spin elastohydrodynamic lubrication in elliptical contact on a non-Gaussian rough surface, the hydrodynamic pressure and oil film distribution under different rough surfaces are obtained. The contact pressure in the contact area of ​​the micro-protrusion is calculated using the KE contact model to obtain the micro-protrusion contact pressure under different rough surfaces. S4. Based on the micro-protrusion contact pressure, hydrodynamic pressure and oil film thickness distribution under different rough surfaces, judge the superiority or inferiority of elliptical contact spin elastohydrodynamic lubrication performance under different rough contact surfaces, select a rough contact surface with superior lubrication performance, and realize the design of elliptical contact spin elastohydrodynamic lubrication non-Gaussian rough surface under mixed lubrication conditions. The hydrodynamic pressure and oil film distribution under different rough surfaces in step S3 are obtained through the following process: First, set the initial parameters, including external load and Young's modulus, and determine the elastohydrodynamic lubrication boundary conditions; second, calculate the surface elastic deformation, oil film thickness distribution, lubrication viscosity and density. Then, the Reynolds equation for spin-averaged flow in elliptical contact on a non-Gaussian rough surface and the KE contact model are solved to obtain the pressure distribution, including hydrodynamic pressure and micro-protrusion contact pressure. Next, the newly obtained pressure distribution is used to solve for elastic deformation, oil film thickness, and lubricating oil viscosity and density. Finally, it is determined whether the pressure converges. If it does not converge, the pressure is corrected and iterative calculation continues. If it converges, it is further determined whether the load is balanced. If the load is unbalanced, the central oil film thickness is corrected and iterative calculation continues. If the load is balanced, the pressure distribution and oil film thickness distribution are output.

2. The method for designing a non-Gaussian rough surface for elliptical contact spin elastohydrodynamic lubrication under mixed lubrication conditions according to claim 1, characterized in that, In step S1, the Reynolds equation for elliptical contact spin elastohydrodynamic lubrication is: Where ρ is density, h is nominal oil film thickness, η is viscosity, p is hydrodynamic pressure, u is entrainment velocity in the x-direction, and v is entrainment velocity of the elliptical spin in the y-direction.

3. The method for designing a non-Gaussian rough surface for elliptical contact spin elastohydrodynamic lubrication under mixed lubrication conditions according to claim 1, characterized in that, In step S2, the Reynolds equation for the average flow rate of the Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication is: Where ρ is density, h is nominal oil film thickness, η is viscosity, and p h Let ρ be the fluid dynamic pressure, u be the entrainment velocity in the x-direction, v be the entrainment velocity of the elliptical spin in the y-direction, σ be the standard deviation of the equivalent roughness of the two rough surfaces, and φ be the fluid dynamic pressure. x φ y The pressure-flow factors in the x and y directions are φ, respectively. c φ is the contact factor on a Gaussian rough surface. s is the shear flow factor on a Gaussian rough surface.

4. The method for designing a non-Gaussian rough surface for elliptical contact spin elastohydrodynamic lubrication under mixed lubrication conditions according to claim 1, characterized in that, In step S3, the Reynolds model for the average flow rate of spin elastohydrodynamic lubrication in elliptical contact on a non-Gaussian rough surface is: Where ρ is density, h is nominal oil film thickness, η is viscosity, and p h Let be the fluid dynamic pressure, u be the entrainment velocity in the x-direction, v be the entrainment velocity of the elliptical spin in the y-direction, and σ be the standard deviation of the equivalent roughness of the two rough surfaces. Let be the pressure-flow factor on a non-Gaussian rough surface in the x-direction. Let be the pressure-flow factor on a non-Gaussian rough surface in the y-direction. For non-Gaussian rough surface contact factor, is the shear flow factor on a non-Gaussian rough surface.

5. The method for designing a non-Gaussian rough surface for elliptical contact spin elastohydrodynamic lubrication under mixed lubrication conditions according to claim 4, characterized in that, The equation for calculating the nominal oil film thickness h is: Where h0 is the thickness of the rigid body's central membrane, R x R is the equivalent radius of curvature in the x-direction. y Let y be the equivalent radius of curvature in the y direction, and v(x,y) be the elastic deformation of the surface.

6. The method for designing a non-Gaussian rough surface for elliptical contact spin elastohydrodynamic lubrication under mixed lubrication conditions according to claim 5, characterized in that, The equation for calculating the surface elastic deformation v(x,y) is: Where E′ is the equivalent Young's modulus, and ξ and ζ are the additional coordinates corresponding to x and y.

7. The method for designing a non-Gaussian rough surface for elliptical contact spin elastohydrodynamic lubrication under mixed lubrication conditions according to claim 5, characterized in that, Viscosity η is calculated using the following formula: Where η0 is the viscosity of the lubricating oil under atmospheric pressure, p is the oil film pressure, and z0 is the pressure viscosity index.

8. The method for designing a non-Gaussian rough surface for elliptical contact spin elastohydrodynamic lubrication under mixed lubrication conditions according to claim 5, characterized in that, Density ρ is calculated using the following formula: Where ρ0 is the initial density of the lubricating oil, and p is the oil film pressure; The entrainment velocity u of the elliptical spin in the x-direction and the entrainment velocity v of the elliptical spin in the y-direction are calculated by the following formulas: Where u1 is the velocity of the elliptical spin in the x-direction, v1 is the velocity of the elliptical spin in the y-direction, u2 is the velocity of the lower surface of the elliptical contact spin in the x-direction, and v2 is the velocity of the lower surface of the elliptical contact spin in the y-direction.

9. The method for designing a non-Gaussian rough surface for elliptical contact spin elastohydrodynamic lubrication under mixed lubrication conditions according to claim 5, characterized in that, Micro-convexity contact pressure p a The calculation formula, i.e., the KE contact model, is: Where σ is the standard deviation of the equivalent roughness of the two rough surfaces, β is the surface roughness parameter, K represents the hardness coefficient, and ω c h is the critical value for the roughness peak to transition from elastic deformation to plastic deformation. d d represents the hardness of the softer surface, d is the distance from the intermediate surface of the micro-protrusion to the equivalent smooth surface, and I is the calculation parameter of the KE model.

10. A design system for an elliptical contact spin elastohydrodynamic lubrication non-Gaussian rough surface under mixed lubrication conditions, characterized in that, include: The module for constructing the Reynolds equation for elliptical contact spin elastohydrodynamic lubrication is used to obtain the initial density and viscosity of the lubricating oil under atmospheric pressure, and to set the nominal oil film thickness and hydrodynamic pressure of the rough contact surface. Then, the Reynolds equation for elliptical contact spin elastohydrodynamic lubrication is constructed based on the Reynolds equation for point contact elastohydrodynamic lubrication. A module for constructing the Reynolds equation for the average flow rate of spin elastohydrolubrication in elliptical contact on Gaussian rough surfaces is used to construct the Reynolds equation for the average flow rate of spin elastohydrolubrication in Gaussian rough surfaces based on the Reynolds equation for spin elastohydrolubrication in elliptical contact and the average flow rate model. The calculation module uses the non-Gaussian rough surface flow factor and contact factor correction equation to construct the average flow Reynolds model for non-Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication based on the average flow Reynolds equation for Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication. Based on the average flow Reynolds model for non-Gaussian rough surface elliptical contact spin elastohydrodynamic lubrication, the hydrodynamic pressure and oil film distribution under different surface roughness are obtained. The KE contact model is used to calculate the contact pressure within the micro-protrusion contact area, obtaining the micro-protrusion contact pressure under different surface roughness. Based on the micro-protrusion contact pressure, hydrodynamic pressure and oil film thickness distribution under different rough surfaces, the superiority or inferiority of elliptical contact spin elastohydrodynamic lubrication performance under different rough contact surfaces is judged. A rough contact surface with superior lubrication performance is selected to realize the design of non-Gaussian rough surface for elliptical contact spin elastohydrodynamic lubrication under mixed lubrication conditions. The hydrodynamic pressure and oil film distribution under different rough surfaces are obtained through the following process: First, set the initial parameters, including external load and Young's modulus, and determine the elastohydrodynamic lubrication boundary conditions; second, calculate the surface elastic deformation, oil film thickness distribution, lubrication viscosity and density. Then, the Reynolds equation for spin-averaged flow in elliptical contact on a non-Gaussian rough surface and the KE contact model are solved to obtain the pressure distribution, including hydrodynamic pressure and micro-protrusion contact pressure. Next, the newly obtained pressure distribution is used to solve for elastic deformation, oil film thickness, and lubricating oil viscosity and density. Finally, it is determined whether the pressure converges. If it does not converge, the pressure is corrected and iterative calculation continues. If it converges, it is further determined whether the load is balanced. If the load is unbalanced, the central oil film thickness is corrected and iterative calculation continues. If the load is balanced, the pressure distribution and oil film thickness distribution are output.

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