A method for determining the lubrication state of a friction pair under fluid lubrication conditions

Abstract

This invention relates to a method for determining the lubrication state of a friction pair under fluid lubrication conditions, comprising the following steps: (1) extracting the surface morphology feature height value based on the Abbott-Firestone curve of the true morphology of the friction pair; (2) establishing a lubrication model of the friction pair based on the actual service conditions of the friction pair; (3) solving the lubrication model of the friction pair established in step (2) using numerical calculation methods to obtain the results including the lubricating oil film thickness. h (4) Compare the physical quantities included in the lubricating oil film thickness. h The relationship between the surface morphology feature height value and the lubrication state of the friction pair under fluid lubrication conditions is determined. This invention provides a simple, rapid, and easy-to-implement method that solves the problem of lacking quantitative criteria for judging the lubrication state of friction pairs. It lays the foundation for accurate quantitative analysis of the lubrication performance of friction pairs and is applicable to friction pairs with point, line, and surface contact.

Description

Technical Field

[0001] This invention relates to the field of fluid lubrication analysis of friction pairs, and more particularly to a method for determining the lubrication state of friction pairs under fluid lubrication conditions. Background Technology

[0002] Lubrication condition is an important reference indicator for evaluating the lubrication of friction pairs. According to Stribeck curves, actual engineering friction pairs exhibit various lubrication conditions, including full-film lubrication, elastohydrodynamic lubrication, thin-film lubrication, boundary lubrication, dry friction, and mixed lubrication conditions where multiple conditions coexist. The interfacial contact forms and friction mechanisms differ significantly depending on the lubrication condition: In full-film lubrication, the lubricating oil film is relatively thick, and the interface is characterized by fluid bearing and friction, closely related to the macroscopic geometry and dynamic service boundary of the friction pair; in elastohydrodynamic and thin-film lubrication, the lubricating oil film is relatively thin, and the interface is characterized by solid-liquid co-bearing and friction, closely related to mesoscopic morphology and micro-protrusion bearing characteristics; in boundary lubrication, the lubricating oil film is extremely thin, and the interface is primarily characterized by solid bearing and friction, closely related to the microstructure of the material and the intermolecular forces of the lubricating oil; in dry friction, there is essentially no lubricating oil film, and the interface is characterized by solid bearing and friction, related to the oil supply.

[0003] Currently, methods for determining the lubrication state of friction pairs mainly include qualitative methods and classical statistical methods. Qualitative methods primarily use physical quantities such as typical oil film thickness and typical friction coefficient. This method is relatively simple and convenient, suitable for preliminary assessment, but lacks quantitative criteria for classifying lubrication states, making it difficult to accurately determine the lubrication state of friction pairs. Classical statistical methods mainly use the film thickness ratio to determine the lubrication state. This method only uses the root mean square deviation of the profile as a morphological parameter to characterize the rough surface, and uses the ratio of this parameter to the oil film thickness to determine the lubrication state of the friction pair. Although this method uses quantitative means to determine the lubrication state of friction pairs, the surface morphology features are overly simplified, lacking the extraction of specific detailed surface morphology features.

[0004] In summary, there is currently no accurate and universally applicable method to quantitatively determine the lubrication status of friction pairs. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a simple, fast and easy-to-implement method for determining the lubrication state of friction pairs under fluid lubrication conditions.

[0006] To address the above problems, the present invention provides a method for determining the lubrication state of a friction pair under fluid lubrication conditions, comprising the following steps:

[0007] (1) Extract the surface morphology feature height value based on the Abbott-Firestone curve of the true morphology of the friction pair;

[0008] (2) Establish a lubrication model for the friction pair based on its actual service conditions;

[0009] (3) Solve the friction pair lubrication model established in step (2) using numerical calculation methods to obtain the results including the lubricating oil film thickness. h Physical quantities included;

[0010] (4) Compare the thickness of the lubricating oil film. h The relationship between the height value and the surface morphology features is used to determine the lubrication state of the friction pair under fluid lubrication conditions.

[0011] In step (1), the surface morphology feature height value is the peak height of the protrusion on the friction pair surface. Spk Core roughness depth Sk and the depth of the prominent valley Svk .

[0012] In step (2), the friction pair lubrication model consists of three sub-models: a lubricating oil fluid control model, a temperature control model, and a load balance model.

[0013] In step (3), the friction pair lubrication model is solved using the following method:

[0014] ① Determine the solution domain, divide the grid, discretize the partial differential equations, and give explicit or implicit expressions for the physical quantities to be solved;

[0015] ②Given the input parameters for the calculation;

[0016] ③ Calculate the elastic deformation vector / matrix;

[0017] ④ Solve the lubricating oil control equation and the elastic deformation calculation equation simultaneously;

[0018] ⑤ Solve the lubricating oil energy equation and the solid heat transfer equation simultaneously;

[0019] ⑥ Output the calculation results.

[0020] In step (4), the lubrication state refers to full film lubrication, elastohydrodynamic lubrication, thin film lubrication, boundary lubrication, dry friction, and mixed lubrication.

[0021] In step (4), the lubrication state of the friction pair under fluid lubrication conditions is determined as follows:

[0022] When min( h )> Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+Svk At time 2, the surface micro-protrusions are not in contact, and the friction pair is in a state of full film lubrication; among which Spk 1 represents the peak height of the protruding solid 1 surface in the friction pair; Sk 1 represents the core roughness depth of solid 1 in the friction pair; Svk 1 represents the depth of the valley value of solid 1 in the friction pair; Spk 2 represents the peak height of the solid 2 protruding from the surface of the friction pair; Sk 2 represents the core roughness depth of solid 2 in the friction pair; Svk 2 represents the depth of the valley value of solid 2 in the friction pair;

[0023] When min( h )= Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk At time 2, the micro-protrusion peaks at the contact interface begin to make contact, and the friction pair begins to transition from a full-film lubrication state to an elastohydrodynamic lubrication state.

[0024] when Sk 1+ Svk 1+ Sk 2+ Svk 2 <min( h )≤ Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk 2, and max( h )> Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk At time 2, the micro-protrusion peaks at the contact interface are in contact, and the friction pair is in a mixed lubrication state of full film lubrication and elastohydrodynamic lubrication;

[0025] when Sk 1+ Svk 1+ Sk 2+ Svk 2 <min( h )≤ Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk 2 and Sk 1+ Svk 1+ Sk 2+ Svk 2 <max(h )≤ Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk At time 2, all micro-protrusion peaks at the contact interface are in contact, and the friction pair is completely in an elastohydrodynamic lubrication state;

[0026] When min( h )= Sk 1+ Svk 1+ Sk 2+ Svk At time 2, the core areas of the micro-protrusions at the contact interface begin to make contact, and the friction pair begins to change from an elastohydrodynamic lubrication state to a thin film lubrication state.

[0027] when Svk 1+ Svk 2 <min( h )≤ Sk 1+ Svk 1+ Sk 2+ Svk 2 and max( h )> Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ [[ID= At time 2, the micro-protrusions at the contact interface can be in three states: no contact, peak area contact, and core area contact. The friction pair is in a mixed lubrication state of full film lubrication, elastohydrodynamic lubrication, and thin film lubrication.

[0028] when ​ 1+ ​ 2≤min( h )≤ ​ 1+ ​ 1+ ​ 2+ ​ 2 and ​ 1+ ​ 1+ ​ 2+ ​ 2 <max( h )≤ ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ At time 2, the micro-protrusions at the contact interface can be either in the peak region or in the core region, and the friction pair is in a mixed lubrication state of elastohydrodynamic lubrication and thin film lubrication.

[0029] when ​ 1+ ​ 2 <min(h )≤ ​ 1+ ​ 1+ ​ 2+ ​ 2 and ​ 1+ ​ 2 <max( h )≤ ​ 1+ ​ 1+ ​ 2+ ​ At time 2, all micro-protrusion core areas of the contact interface are in contact, and the friction pair is completely in a thin film lubrication state;

[0030] When min( h )= ​ 1+ ​ At time 2, the valley areas of the surface micro-protrusions begin to contact, and the friction pair begins to transition from a thin film lubrication state to a boundary lubrication state.

[0031] When 0 <min( h )≤ ​ 1+ ​ 2 and max( h )> ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ At time 2, the micro-protrusions at the contact interface can be in four states: no contact, peak area contact, core area contact, and valley area contact. The friction pair is in a mixed lubrication state of full film lubrication, elastohydrodynamic lubrication, thin film lubrication, and boundary lubrication.

[0032] When 0 <min( h )≤ ​ 1+ ​ 2 and ​ 1+ ​ 1+ ​ 2+ ​ 2 <max( h )≤ ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ At time 2, the micro-protrusions at the contact interface exhibit three types of contact: peak region contact, core region contact, and valley region contact. The friction pair is in a mixed lubrication state of elastohydrodynamic lubrication, thin film lubrication, and boundary lubrication.

[0033] When 0 <min( h )≤ ​ 1+ ​ 2 and ​ 1+ ​ 2 <max(h )≤ ​ 1+ ​ 1+ ​ 2+ ​ At time 2, the micro-protrusions at the contact interface can have two types of contact: core area contact and valley area contact. The friction pair is in a mixed lubrication state of both thin film lubrication and boundary lubrication.

[0034] When 0 <min( h )≤ ​ 1+ ​ 2 and 0 <max( h )≤ ​ 1+ ​ At time 2, all micro-protrusions on the contact interface are in valley contact, and the friction pair is completely in boundary lubrication state;

[0035] When min( h When )=0, the base surfaces of the micro-protrusions at the contact interface begin to contact, and the friction pair begins to transition from boundary lubrication to dry friction.

[0036] When min( h ) = 0 and max( h )> ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ At time 2, the micro-protrusions at the contact interface can be in five states: no contact, peak area contact, core area contact, valley area contact, and base surface contact. The friction pair is in a mixed lubrication state of five types: full film lubrication, elastohydrodynamic lubrication, thin film lubrication, boundary lubrication, and dry friction.

[0037] When min( h )=0 and ​ 1+ ​ 1+ ​ 2+ ​ 2 <max( h )≤ ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ At time 2, the micro-protrusions at the contact interface can be in four states: peak area contact, core area contact, valley area contact, and base surface contact. The friction pair is in a mixed lubrication state of elastohydrodynamic lubrication, thin film lubrication, boundary lubrication, and dry friction.

[0038] When min( h )=0 and ​ 1+ ​ 2 <max( h )≤ ​ 1+​ 1+ ​ 2+ ​ At time 2, the micro-protrusions at the contact interface can be in three states: core area contact, valley area contact, and base surface contact. The friction pair is in a mixed lubrication state of film lubrication, boundary lubrication, and dry friction.

[0039] When min( h )=0 and 0 <max( h )≤ ​ 1+ ​ At time 2, the micro-protrusions at the contact interface can be either in the valley area or on the base surface, and the friction pair is in a mixed lubrication state of boundary lubrication and dry friction.

[0040] When min( h ) = 0 and max( h When )=0, the two base surfaces of the contact interface are in complete contact, and the friction pair is in a completely dry friction state.

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] 1. This invention obtains the Abbott-Firestone curves of the true morphology of the friction pair surface through experimental methods, and defines the characteristic height value of the true morphology of the surface according to the ISO 25178 standard. ​ , ​ , ​ That is, the height values ​​of the peak, core and valley regions of the corresponding micro-protrusions. The contact lubrication problem of numerous irregular micro-protrusions in the contact area is transformed into the contact lubrication problem of two micro-protrusions, which makes it easier to compare the relationship between the thickness of the lubricating oil film and the position of the friction pair surface, and thus makes it easier to determine the lubrication state of the friction pair.

[0043] 2. This invention breaks through the traditional method of qualitatively classifying lubrication states, and is based on the characteristic height value of the actual morphology. ​ , ​ , ​ The relationship between the friction film thickness and the lubrication state of the friction pair is used to quantitatively classify the lubrication state of the friction pair, which solves the problem of lacking a quantitative basis for judging the lubrication state of the friction pair and lays the foundation for accurate quantitative analysis of the lubrication performance of the friction pair.

[0044] 3. The method of the present invention is simple, fast and easy to implement, and is applicable to friction pairs with point, line and surface contact forms. Attached Figure Description

[0045] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0046] ​The Abbott-Firestone curve (right figure) and characteristic height value of the true surface morphology of solid 1 in the friction pair of this invention are shown. ​ 1. ​ 1. ​ 1 (Left image).

[0047] ​ The Abbott-Firestone curve (right figure) and characteristic height value of the solid 2 surface in the friction pair of this invention are shown. ​ 2. ​ 2. ​ 2 (Left image).

[0048] ​ This is a flowchart of the calculation process for step (3) of the present invention.

[0049] ​ This is the initial value of the lubricating oil film pressure of the line contact friction pair of the present invention.

[0050] ​ This is a diagram showing the thickness distribution of the lubricating oil film in the line contact friction pair of the present invention.

[0051] ​ This is the result of determining the lubrication state of the line contact friction pair of the present invention. Detailed Implementation

[0052] A method for determining the lubrication state of a friction pair under fluid lubrication conditions includes the following steps:

[0053] (1) Extract the surface morphology feature height value based on the Abbott-Firestone curve of the true morphology of the friction pair.

[0054] The Abbott-Firestone curve is obtained experimentally using a morphology inspection device to capture the profile support ratio of the true morphology of the friction pair. The morphology inspection device can be one of the following: interferometer, white light interferometer, profilometer / probe profiler, atomic force microscope, or scanning electron microscope. A white light interferometer is preferred.

[0055] Among them, the surface morphology feature height value is calculated and extracted according to the definition in ISO 25178 standard, which is the peak height of the protrusion on the friction pair surface. ​ Core roughness depth ​ and the depth of the prominent valley ​ This corresponds to the peak region height, core region height, and valley region height values ​​of the micro-protrusions on the surface of the friction pair.

[0056] The area below the valley region of the micro-protrusions on the surface of the friction pair is the base surface of the friction pair.

[0057] (2) Based on the actual service conditions of the friction pair, a lubrication model for the friction pair is established. This lubrication model consists of three sub-models: a fluid control model for the lubricating oil, a temperature control model, and a load balance model. Among them:

[0058] ① The fluid control model of lubricating oil includes the lubricating oil control equation and its boundary conditions, the lubricating oil viscosity-temperature-pressure characteristic equation, the lubricating oil density-temperature-pressure characteristic equation, and the lubricating oil film thickness equation.

[0059] The lubricating oil control equation is one of the following: the Reynolds equation, the average Reynolds equation, or the generalized Reynolds equation. The Reynolds equation is preferred, and its expression is:

[0060] (1)

[0061] in, x , y These are position coordinates, in meters (m). h The thickness of the lubricating oil film is expressed in meters (m). ​ This refers to the dynamic viscosity of the lubricating oil, expressed in Pa·s. ​ This refers to the density of the lubricating oil, expressed in kg / m³. 3 ; p This refers to the lubricating oil film pressure, expressed in Pa. u , v For friction pair in x and y The relative velocity in the direction of motion, expressed in m / s; t The time unit is seconds (s).

[0062] The boundary conditions for the lubricating oil governing equation are the forced boundary conditions and natural boundary conditions of the lubricating oil film pressure, and their expressions are as follows:

[0063] (2)

[0064] (3)

[0065] in, s For the lubrication solution region ​ The boundary; n For the boundary s normal direction; p s For the lubrication solution region ​ boundary s The oil film pressure on the surface.

[0066] The viscosity-temperature-pressure characteristic equation for lubricating oil can be derived from models such as the Barus-Reynolds model and the Roelands model. The Roelands model is preferred, and its expression is as follows:

[0067] (4)

[0068] in, ​ 0 represents the reference viscosity of the lubricating oil, in Pa·s; T 0 represents the reference temperature, in Kelvin (K). T This refers to the actual temperature of the lubricating oil, expressed in Kelvin (K). p 0 represents the viscosity-pressure coefficient of the lubricating oil, in Pa. -1 ; s 0 represents the viscosity-pressure index of lubricating oil, which is dimensionless; z 0 represents the viscosity-temperature index of lubricating oil, which is dimensionless.

[0069] The density-temperature-pressure characteristic equation of lubricating oil is based on the Dowson-Higginson model, etc. The expression for the Dowson-Higginson model is...

[0070] (5)

[0071] in, ​ 0 represents the reference density of the lubricating oil, in kg / m³. 3 ; C 1. C 2 represents the lubricating oil pressure coefficient, in Pa. -1 ; C 3 represents the temperature coefficient of lubricating oil, in Kelvin (K). -1 .

[0072] The lubricating oil film thickness equation is determined by the minimum oil film thickness, the normal approximation distance of the friction pair, and the elastic deformation of the friction pair, and its expression is:

[0073] h = h 0+ h s + v e (6)

[0074] in, h 0 represents the minimum oil film thickness, determined by solving the lubricating oil control equation, and its unit is meters (m). h s The normal approximation distance of the friction pair is determined by the functional expression of the friction pair's external profile, and its unit is meters (m). v e This represents the elastic deformation of the friction pair, expressed in meters (m).

[0075] The elastic deformation of a friction pair is determined by the Flamant formula or the Boussinesq integral. The Flamant formula is used for calculating the elastic deformation of one-dimensional contact friction pairs, i.e., line contact friction pairs. The Boussinesq integral is used for calculating the elastic deformation of two-dimensional contact friction pairs, i.e., point contact friction pairs. Their expressions are respectively:

[0076] (7)

[0077] (8)

[0078] in, c These are undetermined constants, with units of meters (m). ​ , ς for x , y Additional coordinates; E' Let be the combined elastic modulus of the friction pair, and its expression is:

[0079] (9)

[0080] in, v 1 represents the Poisson's ratio for a solid, which is dimensionless; v 2 represents the Poisson's ratio for solids, which is dimensionless. E 1 represents the elastic modulus of a solid, in Pa. E 2 represents the elastic modulus of the solid, in Pa.

[0081] ②The temperature control model includes the lubricating oil energy equation and its boundary conditions, and the solid heat transfer equation and its boundary conditions.

[0082] The lubricating oil energy equation includes terms for heat convection, heat conduction, thermal expansion, and heat dissipation, and its expression is as follows:

[0083] (10)

[0084] in, K It is the heat transfer coefficient of lubricating oil, with units of W / (m·K); C p This refers to the specific heat capacity of lubricating oil, expressed in J / (kg·K). x , y , z The coordinates are the location; u , v , w for x , y , z Velocity in three directions, in m / s.

[0085] The equation for heat conduction in solids is the Fourier equation, and its expression is:

[0086] (11)

[0087] in, C pi solid i Specific heat capacity, expressed in J / (kg·K); K i solid i Heat transfer coefficient, measured in W / (m·K).

[0088] The boundary conditions for the lubricating oil energy equation and the solid heat transfer equation include the lubricating oil / solid temperature forced boundary condition, the lubricating oil / solid temperature natural boundary condition, and the solid-lubricating oil heat transfer boundary condition, with the following expressions:

[0089] (12)

[0090] (13)

[0091] (14)

[0092] in, T s Let s be the temperature at the boundary, in Kelvin.

[0093] ③ The load balance model includes the force balance equations for external load, lubricating oil film bearing capacity, interface micro-protrusion bearing capacity, and inertial force, and its expression is:

[0094] (15)

[0095] in, F i These represent different types of external loads on the friction pair, expressed in Newtons (N). p asp The pressure borne by the micro-protrusion is expressed in Pa. m j solid j The equivalent mass, in kg; a j solid j The acceleration of the moving parts, expressed in m / s². 2 .

[0096] External loads include one or more of the following: transmission loads, thermal expansion loads, gas loads, and solid tension loads.

[0097] Inertial force is .

[0098] The bearing capacity of the interface micro-protrusion is obtained by numerical integration of the bearing pressure of the micro-protrusion.

[0099] The pressure borne by the micro-protrusion is calculated using statistical models of rough surface contact and contact deformation theory. Statistical models of rough surface contact include the Greenwood-Tripp model, the Greenwood-Williams model, and the Lee-Ren rough surface contact fitting formula. The contact deformation theory includes Hertz contact theory and Chang contact theory. Chang contact theory is preferred, and its expression is:

[0100] (16a)

[0101] (16b)

[0102] (16c)

[0103] (16d)

[0104] in, p asp The pressure borne by the micro-protrusion is expressed in Pa. P c The yield strength of the material; the unit is Pa. ​ This represents the deformation of the micro-convex body, expressed in meters (m). ​ c This represents the critical deformation of the micro-convexity, expressed in meters (m). K a The coefficient of hardness for solids is dimensionless. H Hardness of solids, measured in Pa; R denoted as the equivalent radius of the micro-convexity, in meters (m).

[0105] The bearing capacity of the lubricating oil film is obtained by numerical integration of the lubricating oil film pressure.

[0106] (3) Solve the friction pair lubrication model established in step (2) using numerical calculation methods to obtain the results including the lubricating oil film thickness. h The physical quantity included. The specific process is as follows:

[0107] ① Determine the solution domain, divide the grid, discretize the partial differential equations, and give explicit or implicit expressions for the physical quantities to be solved.

[0108] The solution domain is the spatial range for calculating the lubricating oil model of the friction pair. This spatial domain is determined by several times the Hertz contact half-width or the nominal contact range. For point and line contact friction pairs, several times the Hertz contact half-width is used to determine the solution domain; for surface contact friction pairs, the nominal contact range is used.

[0109] Meshing the solution domain involves dividing the solution domain into several nodes and elements. x Directional division n One node; y Directional division m If there are n nodes, then the spatial step size is 1.

[0110] (17)

[0111] (18)

[0112] Where, Δ x Δ y To determine the discrete spatial step size within the solution region, in meters; L x , L y To calculate the spatial distance of the region, the unit is meters.

[0113] Discrete partial differential equations include the lubricating oil control equation, the lubricating oil energy equation, and the solid heat transfer equation.

[0114] Methods for providing explicit or implicit expressions for physical quantities include the finite difference method, the finite element method, and the boundary element method. The finite difference method is preferred.

[0115] The physical quantities to be solved are lubricating oil film pressure, lubricating oil film temperature, and solid temperature.

[0116] Taking the discrete Reynolds equation as an example, the numerical calculation process is illustrated. The Reynolds equation can be rewritten as follows:

[0117] (19)

[0118] in, A , B , C , D , E Pressure without lubricating oil film p The mathematical expression for is obtained by applying the central difference quotient instead of the partial derivative to each node using the finite difference method, thus obtaining the expression for the node ( i , j The relationship between the lubricating oil film pressure and adjacent nodes is expressed as follows: p The explicit expression is,

[0119] (20a)

[0120] (20b)

[0121] (20c)

[0122] (20d)

[0123] (20e)

[0124] (20f)

[0125] (20g)

[0126] in, C N , C S , C E , C W , G The coefficients for each node with respect to the lubricating oil film pressure are dimensionless.

[0127] The process of rewriting the lubricating oil energy equation and the solid heat transfer equation into discrete expressions for temperature is the same as rewriting the discrete expression for lubricating oil film pressure, and will not be repeated here.

[0128] ② Given the calculation input parameters. The calculation input parameters mainly include the deterministic calculation parameters of the friction pair; the initial and boundary values ​​of the lubricating oil film pressure; the initial and boundary values ​​of the lubricating oil film temperature; and the initial value of the minimum oil film thickness.

[0129] The deterministic calculation parameters for friction pairs include geometric parameters such as the length, width, and height of the friction pair, the contact surface profile, and the solution region; material properties such as the density, specific heat capacity, elastic modulus, and Poisson's ratio of the friction pair material; kinematic parameters such as the speed and acceleration of the friction pair; external load parameters such as the transmission load, thermal expansion load, gas load, and solid tension of the friction pair; and property parameters of the lubricating oil under normal temperature and pressure conditions, such as the reference viscosity, viscosity coefficient, viscosity-pressure coefficient, viscosity-temperature index, density-temperature coefficient, and density-pressure coefficient.

[0130] The initial value of the lubricating oil film pressure is the assumed lubricating oil film pressure value at each node within the lubrication solution domain before calculation. The initial value of the lubricating oil film pressure can be set to 0 Pa, standard atmospheric pressure, the boundary value of the lubricating oil film pressure, Hertz contact pressure, etc. For surface contact friction pairs, standard atmospheric pressure is preferred; for point and line contact friction pairs, Hertz contact pressure is preferred, and this Hertz contact pressure value is calculated by Hertz contact elasticity theory.

[0131] For line contact friction pairs, the Hertz contact pressure value is...

[0132] (21a)

[0133] (21b)

[0134] (21c)

[0135] in, p H This is the Hertz contact pressure value; the unit is Pa. P hl This represents the maximum contact pressure in the form of line contact, expressed in Pa. a l The contact half-width is in meters (m); L is the width of the line contact in the non-movement direction, also in meters. R x The equivalent radius of line contact is expressed in meters (m).

[0136] For point contact friction pairs, the Hertz contact pressure value is:

[0137] (22a)

[0138] (22b)

[0139] (22c)

[0140] (22d)

[0141] (22e)

[0142] in, P hp This represents the maximum contact pressure in point contact configuration, expressed in Pa. a p , b p These are the minor and major axes of the contact area, in meters (m). R The equivalent radius of point contact is expressed in meters. k Ellipticity, dimensionless. I 2 represents the elliptic integral of the second kind.

[0143] The boundary value of the lubricating oil film pressure is the pressure value of the lubricating oil film in contact with the external environment at the boundary of the lubrication solution domain of the friction pair.

[0144] The initial value of the lubricating oil film temperature is the assumed lubricating oil film temperature value at each node in the lubrication solution domain before calculation. The initial value of the lubricating oil film temperature can be set to 300 K, or a boundary value of the lubricating oil film temperature, etc. The boundary value of the lubricating oil film temperature is preferred.

[0145] The boundary value of the lubricating oil film temperature is the temperature at which the lubricating oil film contacts the external environment at the boundary of the lubrication solution domain of the friction pair.

[0146] The initial value of the minimum oil film thickness is the minimum oil film thickness within the lubrication solution domain given before calculation, which can be given through empirical assumptions or empirical formulas for the minimum oil film thickness. The empirical formulas for the minimum oil film thickness are the Dowson-Higginson line contact film thickness formula and the Hamrock-Dowson point contact film thickness formula, whose expressions are as follows:

[0147] (23a)

[0148] (23b)

[0149] in, H 0 represents the dimensionless minimum oil film thickness; G * represents material parameters, which are dimensionless; U * represents the velocity parameter, which is dimensionless; W * represents the load parameter, which is dimensionless.

[0150] ③ Calculate the elastic deformation vector / matrix. Calculating the elastic deformation vector / matrix includes calculating the discrete elastic deformation equation and then calculating the elastic deformation vector / matrix.

[0151] The equation for calculating discrete elastic deformation is a rewriting of the Flamant formula or Boussinesq integral as a product of the elastic deformation vector / matrix and the load distribution.

[0152] For a line contact friction pair, its expression is:

[0153] (twenty four)

[0154] in, I ( i , k () is the elastic deformation vector, which physically represents the force acting on the nodes. x i Unit pressure at the node x k The amount of deformation caused.

[0155] For a point contact friction pair, its expression is:

[0156] (25)

[0157] in, The elastic deformation matrix, its physical meaning is the force acting on the nodes ( x i , yj The unit pressure at the node ( x k , y l The amount of deformation caused by ).

[0158] The elastic deformation coefficient / matrix can be calculated using methods such as direct superposition, multiple integration, finite element method, and discrete convolution fast Fourier transform. Direct superposition and discrete convolution fast Fourier transform are preferred methods.

[0159] ④ Solve the lubricating oil control equation and the elastic deformation calculation equation simultaneously. The specific process is to calculate the elastic deformation, calculate the lubricating oil viscosity and density, calculate the lubricating oil film thickness, calculate the lubricating oil film pressure, calculate the bearing capacity of the micro-protrusion, determine whether the load is balanced, and determine whether the elastic deformation has converged.

[0160] The amount of elastic deformation is calculated using the Flamant formula or the Boussinesq integral.

[0161] The viscosity of the lubricating oil was calculated using either the Barus-Reynolds model or the Roelands model. The Roelands model is preferred.

[0162] The density of the lubricating oil was calculated using the Dowson-Higginson model.

[0163] The thickness of the lubricating oil film is determined by three factors: the minimum oil film thickness, the functional expression of the friction pair profile, and the elastic deformation of the friction pair.

[0164] The lubricating oil film pressure is obtained by solving the discrete lubricating oil control equation using a numerical calculation method, and the convergent lubricating oil film pressure is obtained.

[0165] The numerical calculation method is one of the following: low-relaxation iteration method, ultra-relaxation iteration method, direct iteration method, Newton-Raphson full-system iteration method, multigrid method, or quasi-system numerical solution method. For surface contact friction pairs, the ultra-relaxation iteration method is preferred; for point and line contact friction pairs, the quasi-system numerical solution method is preferred.

[0166] The convergent lubricating oil film pressure is determined using a relative error judgment method, which involves determining the relationship between the relative error value of the lubricating oil film and the iterative error limit value of the lubricating oil film pressure.

[0167] (26)

[0168] in, For nodes ( i , j ) in the n -1 step lubricating oil film pressure, in Pa; node(i , j ) in the n The lubricating oil film pressure of the step, in Pa. ​ p This is the limit value for the iterative error of the lubricating oil film pressure, which is dimensionless.

[0169] If the relative error value of the lubricating oil film is greater than the iterative error limit value of the lubricating oil film pressure, the lubricating oil film pressure is updated and substituted into the discrete lubricating oil control equation to continue calculating the lubricating oil film pressure; if the relative error value of the lubricating oil film is less than the iterative error limit value of the lubricating oil film pressure, the converged lubricating oil film pressure is obtained, and the load balance is determined. In other words: if the relative error value of the lubricating oil film pressure between the two steps is greater than the iterative error limit value of the lubricating oil film pressure, the lubricating oil film pressure continues to be calculated; if the relative error value between the two steps is less than the iterative error limit value of the lubricating oil film pressure, the load balance is determined.

[0170] The relative error determination method is used to determine whether the load is balanced.

[0171] (27)

[0172] in, ​ load This is the load iteration error limit value, which is dimensionless.

[0173] If the relative load error value is greater than the load iteration error limit value, the minimum oil film thickness is adjusted and the lubricating oil film pressure is recalculated; if the relative load error value is less than the load iteration error limit value, the minimum oil film thickness that has converged is obtained, and the elastic deformation is judged to determine whether it has converged.

[0174] The method for adjusting the minimum oil film thickness is as follows:

[0175] (28)

[0176] in, h 0,old The minimum oil film thickness before the update, in meters; h 0,app The minimum oil film thickness to be adjusted, in meters (m). h 0,new λ1 represents the updated minimum oil film thickness in meters (m); λ1 is an adjustment parameter, dimensionless.

[0177] The method for determining whether the elastic deformation has converged is the same as the method for determining whether the minimum oil film thickness has converged, and the detailed process and mathematical expression will not be repeated here. If the relative error value of the elastic deformation is greater than the iteration error limit value of the elastic deformation, the obtained converged lubricating oil film pressure is substituted into the elastic deformation calculation equation to recalculate the elastic deformation and lubricating oil film thickness; if the relative error value of the elastic deformation is less than the iteration error limit value of the elastic deformation, then the converged elastic deformation is obtained.

[0178] ⑤ Solve the lubricating oil energy equation and the solid heat transfer equation simultaneously. The specific process is as follows: iteratively calculate the lubricating oil film temperature and the solid temperature, and determine whether the lubricating oil film temperature and the solid temperature converge.

[0179] The lubricating oil film temperature is obtained by solving the discretized lubricating oil film energy equation using a numerical calculation method. This process is consistent with the calculation process of solving the discretized lubricating oil control equation.

[0180] The solid temperature is obtained by solving the discrete solid heat transfer equation using numerical calculation methods. This process is consistent with the calculation process of solving the discrete lubricating oil control equation.

[0181] To determine whether the lubricating oil film temperature and solid temperature have converged, the relative error determination method is used, which relates the relative error values ​​of the lubricating oil film temperature and solid temperature to the iteration error limits of the lubricating oil film temperature and solid temperature. If the relative error value of the lubricating oil film temperature and solid temperature is greater than the iteration error limit of the lubricating oil film temperature and solid temperature, step four is repeated; if the relative error value of the lubricating oil film temperature and solid temperature is less than the iteration error limit of the lubricating oil film temperature and solid temperature, step four is repeated.

[0182] ⑥ Output the calculation results. The main output calculation results include the lubricating oil film thickness. h Physical quantities.

[0183] (4) Compare the thickness of the lubricating oil film. h The relationship between the height value and the surface morphology features is used to determine the lubrication state of the friction pair under fluid lubrication conditions.

[0184] Lubrication condition refers to full film lubrication, elastohydrodynamic lubrication, thin film lubrication, boundary lubrication, dry friction, and mixed lubrication, and is determined as follows:

[0185] When min( h )> ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ At time 2, the surface micro-protrusions are not in contact, and the friction pair is in a state of full film lubrication; among which ​ 1 represents the peak height of the protruding solid 1 surface in the friction pair;​ 1 represents the core roughness depth of solid 1 in the friction pair; ​ 1 represents the depth of the valley value of solid 1 in the friction pair; ​ 2 represents the peak height of the solid 2 protruding from the surface of the friction pair; ​ 2 represents the core roughness depth of solid 2 in the friction pair; ​ 2 represents the depth of the valley value of solid 2 in the friction pair;

[0186] When min( h )= ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ At time 2, the micro-protrusion peaks at the contact interface begin to make contact, and the friction pair begins to transition from a full-film lubrication state to an elastohydrodynamic lubrication state.

[0187] when ​ 1+ ​ 1+ ​ 2+ ​ 2 <min( h )≤ ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ 2, and max( h )> ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ At time 2, the micro-protrusion peaks at the contact interface are in contact, and the friction pair is in a mixed lubrication state of full film lubrication and elastohydrodynamic lubrication;

[0188] when ​ 1+ ​ 1+ ​ 2+ ​ 2 <min( h )≤ ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ 2 and ​ 1+ ​ 1+ ​ 2+ ​ 2 <max( h )≤ ​ 1+ ​ 1+ ​ 1+ ​ 2+​ 2+ ​ At time 2, all micro-protrusion peaks at the contact interface are in contact, and the friction pair is completely in an elastohydrodynamic lubrication state;

[0189] When min( h )= ​ 1+ ​ 1+ ​ 2+ ​ At time 2, the core areas of the micro-protrusions at the contact interface begin to make contact, and the friction pair begins to change from an elastohydrodynamic lubrication state to a thin film lubrication state.

[0190] when ​ 1+ ​ 2 <min( h )≤ ​ 1+ ​ 1+ ​ 2+ ​ 2 and max( h )> ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ At time 2, the micro-protrusions at the contact interface can be in three states: no contact, peak area contact, and core area contact. The friction pair is in a mixed lubrication state of full film lubrication, elastohydrodynamic lubrication, and thin film lubrication.

[0191] when ​ 1+ ​ 2≤min( h )≤ ​ 1+ ​ 1+ ​ 2+ ​ 2 and ​ 1+ ​ 1+ ​ 2+ ​ 2 <max( h )≤ ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ At time 2, the micro-protrusions at the contact interface can be either in the peak region or in the core region, and the friction pair is in a mixed lubrication state of elastohydrodynamic lubrication and thin film lubrication.

[0192] when ​ 1+ ​ 2 <min( h )≤ ​ 1+ ​ 1+ ​ 2+ ​ 2 and​ 1+ ​ 2 <max( h )≤ ​ 1+ ​ 1+ ​ 2+ ​ At time 2, all micro-protrusion core areas of the contact interface are in contact, and the friction pair is completely in a thin film lubrication state;

[0193] When min( h )= ​ 1+ ​ At time 2, the valley areas of the surface micro-protrusions begin to contact, and the friction pair begins to transition from a thin film lubrication state to a boundary lubrication state.

[0194] When 0 <min( h )≤ ​ 1+ ​ 2 and max( h )> ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ At time 2, the micro-protrusions at the contact interface can be in four states: no contact, peak area contact, core area contact, and valley area contact. The friction pair is in a mixed lubrication state of full film lubrication, elastohydrodynamic lubrication, thin film lubrication, and boundary lubrication.

[0195] When 0 <min( h )≤ ​ 1+ ​ 2 and ​ 1+ ​ 1+ ​ 2+ ​ 2 <max( h )≤ ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ At time 2, the micro-protrusions at the contact interface exhibit three types of contact: peak region contact, core region contact, and valley region contact. The friction pair is in a mixed lubrication state of elastohydrodynamic lubrication, thin film lubrication, and boundary lubrication.

[0196] When 0 <min( h )≤ ​ 1+ ​ 2 and ​ 1+ ​ 2 <max( h )≤ ​ 1+ ​ 1+ ​ 2+ ​At time 2, the micro-protrusions at the contact interface can have two types of contact: core area contact and valley area contact. The friction pair is in a mixed lubrication state of both thin film lubrication and boundary lubrication.

[0197] When 0 <min( h )≤ ​ 1+ ​ 2 and 0 <max( h )≤ ​ 1+ ​ At time 2, all micro-protrusions on the contact interface are in valley contact, and the friction pair is completely in boundary lubrication state;

[0198] When min( h When )=0, the base surfaces of the micro-protrusions at the contact interface begin to contact, and the friction pair begins to transition from boundary lubrication to dry friction.

[0199] When min( h ) = 0 and max( h )> ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ At time 2, the micro-protrusions at the contact interface can be in five states: no contact, peak area contact, core area contact, valley area contact, and base surface contact. The friction pair is in a mixed lubrication state of five types: full film lubrication, elastohydrodynamic lubrication, thin film lubrication, boundary lubrication, and dry friction.

[0200] When min( h )=0 and ​ 1+ ​ 1+ ​ 2+ ​ 2 <max( h )≤ ​ 1+ ​ 1+ ​ 1+ ​ 2+ ​ 2+ ​ At time 2, the micro-protrusions at the contact interface can be in four states: peak area contact, core area contact, valley area contact, and base surface contact. The friction pair is in a mixed lubrication state of elastohydrodynamic lubrication, thin film lubrication, boundary lubrication, and dry friction.

[0201] When min( h )=0 and ​ 1+ ​ 2 <max( h )≤ ​ 1+ ​ 1+ ​ 2+ ​At time 2, the micro-protrusions at the contact interface can be in three states: core area contact, valley area contact, and base surface contact. The friction pair is in a mixed lubrication state of film lubrication, boundary lubrication, and dry friction.

[0202] When min( h )=0 and 0 <max( h )≤ ​ 1+ ​ At time 2, the micro-protrusions at the contact interface can be either in the valley area or on the base surface, and the friction pair is in a mixed lubrication state of boundary lubrication and dry friction.

[0203] When min( h ) = 0 and max( h When )=0, the two base surfaces of the contact interface are in complete contact, and the friction pair is in a completely dry friction state.

[0204] The embodiment takes a line contact friction pair as an example, and describes a method for determining the lubrication state of a friction pair under fluid lubrication conditions, including the following steps:

[0205] (1) Extract the surface morphology feature height value based on the Abbott-Firestone curve of the true morphology of the friction pair.

[0206] The three-dimensional morphology of the two solid surfaces of the line contact friction pair was obtained using a white light interferometer. The three-dimensional morphology of the two solid surfaces was then directly converted into Abbott-Firestone curves, as shown below. ​ , ​ As shown.

[0207] Extract the surface topography feature height value according to the definition in ISO 25178 standard. ​ , ​ It can be seen that: for the peak height of solid 1 on the surface ​ 1. Core roughness depth ​ 1 and prominent valley depth ​ The peak heights of solid 1 are 0.891 μm, 3.835 μm, and 1.857 μm, respectively; for solid 2, the peak height is prominent. ​ 2. Core roughness depth ​ 2 and prominent valley depth ​ The micrometers of the two samples are 1.182 μm, 5.587 μm, and 1.927 μm, respectively.

[0208] (2) Establish a lubrication model for the friction pair based on its actual service conditions.

[0209] For line contact friction pairs, the lubricating oil control equation adopts the one-dimensional steady-state Reynolds equation, whose expression is:

[0210] (29)

[0211] The lubricating oil film pressure boundary condition is a combination of forced and natural boundary conditions, and its expression is as follows:

[0212] (30)

[0213] (31)

[0214] The viscosity-temperature-pressure characteristic equation for lubricating oil is as follows:

[0215] (32)

[0216] The density-temperature-pressure characteristic equation for lubricating oil is:

[0217] (33)

[0218] The equation for the thickness of the lubricating oil film in a line contact friction pair is:

[0219] (34a)

[0220] (34b)

[0221] The lubricating oil energy equation for line contact friction pairs is:

[0222] (35)

[0223] The solid heat transfer equation for a line contact friction pair is:

[0224] (36)

[0225] The boundary conditions for the lubricating oil energy equation and the solid heat transfer equation are as follows:

[0226] (37a)

[0227] (37b)

[0228] (38a)

[0229] (38b)

[0230] The load balance equation is,

[0231] (39)

[0232] The calculation of the contact pressure of the micro-protrusion is as follows:

[0233] (40a)

[0234] (40b)

[0235] (40c)

[0236] (40d)

[0237] (3) Solve the friction pair lubrication model established in step (2) using numerical calculation methods to obtain the lubricating oil film thickness. h Equal physical quantities, the calculation process is as follows ​ As shown.

[0238] ① Divide the solution domain into a grid, discretize the partial differential equations, and provide explicit or implicit expressions for the physical quantities to be solved.

[0239] Define the solution domain ( x The spatial step size (in mm) is...

[0240] (41)

[0241] Using the central difference method to discretize formula (29), the discretized explicit expression for the lubricating oil film pressure is:

[0242] (42a)

[0243] (42b)

[0244] (42c)

[0245] (42d)

[0246] (42e)

[0247] (42f)

[0248] (42g)

[0249] The discretization methods for the lubricating oil energy equation and the solid heat transfer equation of the line contact friction pair are consistent with the methods described above.

[0250] ②Given the input parameters for the calculation.

[0251] The calculation parameters for the deterministic nature of the friction pair are shown in Table 1 below.

[0252] Table 1 Calculation parameters for the deterministic nature of friction pairs

[0253]

[0254] The initial value of the lubricating oil film pressure is the Hertz contact pressure value for line contact, such as... ​ As shown. The boundary value of the lubricating oil film pressure is 0 Pa; the boundary value and initial value of the lubricating oil film temperature are 300 K; the boundary value and initial value of the temperature of the solids in the friction pair are 300 K.

[0255] The initial value for the minimum oil film thickness is,

[0256] (43)

[0257] ③ Calculate the elastic deformation vector / matrix.

[0258] The elastic deformation vector is calculated using the direct superposition method.

[0259] ④ Solve the lubricating oil control equation and the elastic deformation calculation equation simultaneously.

[0260] The process of simultaneously solving the lubricating oil control equation and the elastic deformation calculation equation includes, in sequence, calculating the elastic deformation; calculating the lubricating oil viscosity and density; calculating the lubricating oil film thickness; calculating the lubricating oil film pressure; calculating the bearing capacity of the micro-protrusion and determining whether the load is balanced; and determining whether the elastic deformation has converged.

[0261] The viscosity, density, film thickness, and elastic deformation of the lubricating oil are obtained by formulas (32), (33), (34a), and (34b), respectively.

[0262] The lubricating oil film pressure is obtained by multigrid method from (42a) and determined by the following formula.

[0263] (44)

[0264] If the relative error between the two steps of the lubricating oil film pressure calculation is greater than the limit value of the lubricating oil film pressure iteration error, the relaxation iteration method is used to continue calculating the lubricating oil film pressure; if the relative error between the two steps of the lubricating oil film pressure calculation is less than the limit value of the lubricating oil film pressure iteration error, it is determined whether the load is balanced.

[0265] The following formula is used to determine whether the load is balanced.

[0266] (45)

[0267] If the relative load error value is greater than the load iteration error limit value, the minimum oil film thickness is adjusted and the lubricating oil film pressure is recalculated; if the relative load error value is less than the load iteration error limit value, it is determined whether the elastic deformation has converged. The method for adjusting the minimum oil film thickness is as follows:

[0268] (46)

[0269] The method for determining whether the elastic deformation has converged is the same as the method for determining whether the minimum oil film thickness has converged. If the relative error value of the elastic deformation is greater than the iteration error limit value of the elastic deformation, the converged lubricating oil film pressure is substituted into the elastic deformation calculation equation to recalculate the elastic deformation and the lubricating oil film thickness; if the relative error value of the elastic deformation is less than the iteration error limit value of the elastic deformation, then step ⑤ is performed.

[0270] ⑤ Solve the lubricating oil energy equation and the solid heat transfer equation simultaneously.

[0271] The process of simultaneously solving for the lubricating oil film temperature and the solid temperature includes iterating over the lubricating oil film temperature and the solid temperature, and determining whether the lubricating oil film temperature and the solid temperature converge.

[0272] The process of iterating the lubricating oil film temperature and solid temperature is consistent with the process of iterating the lubricating oil film pressure.

[0273] The method for determining whether the lubricating oil film temperature and solid temperature have converged is the same as the method for determining whether the minimum oil film thickness has converged. If the relative error value of the lubricating oil film temperature and solid temperature is greater than the iteration error limit value of the lubricating oil film temperature and solid temperature, then repeat step 4; if the relative error value of the lubricating oil film temperature and solid temperature is less than the iteration error limit value of the lubricating oil film temperature and solid temperature, then proceed to step 6.

[0274] ⑥ Output the calculation results.

[0275] The calculated value of the obtained lubricating oil film thickness is as follows: ​ As shown.

[0276] (4) Compare the thickness of the lubricating oil film. h With surface morphology feature height value ( ​ , ​ , ​ The relationship between the two is used to determine the lubrication state of the friction pair under fluid lubrication conditions.

[0277] Based on the above calculations, we can conclude that max( h ) = 9.6497 μm, min( h ) = 0.0725 μm,

[0278] when hour, ​ 1+​ 1+ ​ 2+ ​ 2≥ h > ​ 1+ ​ 2. At this time, the friction pair is in a thin film lubrication state.

[0279] when hour, ​ 1+ ​ 2≥ h >0, at this time the friction pair is in the boundary lubrication state.

[0280] In summary, in this embodiment, the line contact friction pair is in a mixed lubrication state of both thin-film lubrication and boundary lubrication, such as... ​ As shown.

[0281] It should be understood that the embodiments discussed herein are merely illustrative, and various modifications and variations can be made by those skilled in the art, which will be included within the spirit and scope of this application and the appended claims.

Claims

1. A method for determining the lubrication state of a friction pair under fluid lubrication conditions, comprising the following steps: (1) Extract the surface morphology feature height value based on the Abbott-Firestone curve of the true morphology of the friction pair; The surface morphology feature height value is the peak height of the protrusion on the friction pair surface. Spk Core roughness depth Sk and the depth of the prominent valley Svk ;in Spk 1 represents the peak height of the protruding solid 1 surface in the friction pair; Sk 1 represents the core roughness depth of solid 1 in the friction pair; Svk 1 represents the depth of the valley value of solid 1 in the friction pair; Spk 2 represents the peak height of the solid 2 protruding from the surface of the friction pair; Sk 2 represents the core roughness depth of the solid 2 in the friction pair; Svk 2 represents the depth of the valley value of solid 2 in the friction pair; (2) Based on the actual service conditions of the friction pair, a lubrication model for the friction pair is established. The lubrication model for the friction pair consists of three sub-models: a fluid control model for lubricating oil, a temperature control model, and a load balance model. The fluid control model for lubricating oil includes the lubricating oil control equation and its boundary conditions, the lubricating oil viscosity-temperature-pressure characteristic equation, the lubricating oil density-temperature-pressure characteristic equation, and the lubricating oil film thickness equation. The temperature control model includes the lubricating oil energy equation and its boundary conditions, and the solid heat transfer equation and its boundary conditions. The load balance model includes the force balance equations for external load, lubricating oil film bearing capacity, interface micro-protrusion bearing capacity, and inertial force; (3) Solve the friction pair lubrication model established in step (2) using numerical calculation methods to obtain the results including the lubricating oil film thickness. h Physical quantities included; (4) Compare the minimum value of the lubricating oil film thickness (min) h ), maximum value max( h ) and the two solid surfaces of the friction pair Spk 1. Sk 1. Svk 1. Spk 2. Sk 2. Svk The quantitative relationship of the combined values ​​is used to determine the lubrication state of the friction pair under fluid lubrication conditions; the lubrication state refers to full film lubrication, elastohydrodynamic lubrication, thin film lubrication, boundary lubrication, dry friction, and mixed lubrication.

2. The method for determining the lubrication state of a friction pair under fluid lubrication conditions as described in claim 1, characterized in that: In step (3), the friction pair lubrication model is solved using the following method: ① Determine the solution domain, divide the grid, discretize the partial differential equations, and give explicit or implicit expressions for the physical quantities to be solved; ②Given the input parameters for the calculation; ③ Calculate the elastic deformation vector / matrix; ④ Solve the lubricating oil control equation and the elastic deformation calculation equation simultaneously; ⑤ Solve the lubricating oil energy equation and the solid heat transfer equation simultaneously; ⑥ Output the calculation results.

3. The method for determining the lubrication state of a friction pair under fluid lubrication conditions as described in claim 1, characterized in that: In step (4), the lubrication state of the friction pair under fluid lubrication conditions is determined as follows: When min( h )> Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk At time 2, the surface micro-protrusions are not in contact, and the friction pair is in a state of full film lubrication. When min( h )= Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk At time 2, the micro-protrusion peaks at the contact interface begin to make contact, and the friction pair begins to transition from a full-film lubrication state to an elastohydrodynamic lubrication state. when Sk 1+ Svk 1+ Sk 2+ Svk 2 <min( h )≤ Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk 2, and max( h )> Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk At time 2, the micro-protrusion peaks at the contact interface are in contact, and the friction pair is in a mixed lubrication state of full film lubrication and elastohydrodynamic lubrication; when Sk 1+ Svk 1+ Sk 2+ Svk 2 <min( h )≤ Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk 2 and Sk 1+ Svk 1+ Sk 2+ Svk 2 <max( h )≤ Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk At time 2, all micro-protrusion peaks at the contact interface are in contact, and the friction pair is completely in an elastohydrodynamic lubrication state; When min( h )= Sk 1+ Svk 1+ Sk 2+ Svk At time 2, the core areas of the micro-protrusions at the contact interface begin to make contact, and the friction pair begins to change from an elastohydrodynamic lubrication state to a thin film lubrication state. when Svk 1+ Svk 2 <min( h )≤ Sk 1+ Svk 1+ Sk 2+ Svk 2 and max( h )> Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk At time 2, the micro-protrusions at the contact interface can be in three states: no contact, peak area contact, and core area contact. The friction pair is in a mixed lubrication state of full film lubrication, elastohydrodynamic lubrication, and thin film lubrication. when Svk 1+ Svk 2≤min( h )≤ Sk 1+ Svk 1+ Sk 2+ Svk 2 and Sk 1+ Svk 1+ Sk 2+ Svk 2 <max( h )≤ Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk At time 2, the micro-protrusions at the contact interface can be either in the peak region or in the core region, and the friction pair is in a mixed lubrication state of elastohydrodynamic lubrication and thin film lubrication. when Svk 1+ Svk 2 <min( h )≤ Sk 1+ Svk 1+ Sk 2+ Svk 2 and Svk 1+ Svk 2 <max( h )≤ Sk 1+ Svk 1+ Sk 2+ Svk At time 2, all micro-protrusion core areas of the contact interface are in contact, and the friction pair is completely in a thin film lubrication state; When min( h )= Svk 1+ Svk At time 2, the valley areas of the surface micro-protrusions begin to contact, and the friction pair begins to transition from a thin film lubrication state to a boundary lubrication state. When 0 <min( h )≤ Svk 1+ Svk 2 and max( h )> Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk At time 2, the micro-protrusions at the contact interface can be in four states: no contact, peak area contact, core area contact, and valley area contact. The friction pair is in a mixed lubrication state of full film lubrication, elastohydrodynamic lubrication, thin film lubrication, and boundary lubrication. When 0 <min( h )≤ Svk 1+ Svk 2 and Sk 1+ Svk 1+ Sk 2+ Svk 2 <max( h )≤ Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk At time 2, the micro-protrusions at the contact interface exhibit three types of contact: peak region contact, core region contact, and valley region contact. The friction pair is in a mixed lubrication state of elastohydrodynamic lubrication, thin film lubrication, and boundary lubrication. When 0 <min( h )≤ Svk 1+ Svk 2 and Svk 1+ Svk 2 <max( h )≤ Sk 1+ Svk 1+ Sk 2+ Svk At time 2, the micro-protrusions at the contact interface can have two types of contact: core area contact and valley area contact. The friction pair is in a mixed lubrication state of both thin film lubrication and boundary lubrication. When 0 <min( h )≤ Svk 1+ Svk 2 and 0 <max( h )≤ Svk 1+ Svk At time 2, all micro-protrusions on the contact interface are in valley contact, and the friction pair is completely in boundary lubrication state; When min( h When )=0, the base surfaces of the micro-protrusions at the contact interface begin to contact, and the friction pair begins to transition from boundary lubrication to dry friction. When min( h ) = 0 and max( h )> Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk At time 2, the micro-protrusions at the contact interface can be in five states: no contact, peak area contact, core area contact, valley area contact, and base surface contact. The friction pair is in a mixed lubrication state of five types: full film lubrication, elastohydrodynamic lubrication, thin film lubrication, boundary lubrication, and dry friction. When min( h )=0 and Sk 1+ Svk 1+ Sk 2+ Svk 2 <max( h )≤ Spk 1+ Sk 1+ Svk 1+ Spk 2+ Sk 2+ Svk At time 2, the micro-protrusions at the contact interface can be in four states: peak area contact, core area contact, valley area contact, and base surface contact. The friction pair is in a mixed lubrication state of elastohydrodynamic lubrication, thin film lubrication, boundary lubrication, and dry friction. When min( h )=0 and Svk 1+ Svk 2 <max( h )≤ Sk 1+ Svk 1+ Sk 2+ Svk At time 2, the micro-protrusions at the contact interface can be in three states: core area contact, valley area contact, and base surface contact. The friction pair is in a mixed lubrication state of film lubrication, boundary lubrication, and dry friction. When min( h )=0 and 0 <max( h )≤ Svk 1+ Svk At time 2, the micro-protrusions at the contact interface can be either in the valley area or on the base surface, and the friction pair is in a mixed lubrication state of boundary lubrication and dry friction. When min( h ) = 0 and max( h When )=0, the two base surfaces of the contact interface are in complete contact, and the friction pair is in a completely dry friction state.

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