Two-scale numerical value calculation method for performance of sliding bearing with impact of roughness taken into consideration

Abstract

Disclosed in the present invention are a two-scale numerical value calculation method for the performance of a sliding bearing with the impact of roughness taken into consideration. The method solves the problem of the calculation accuracy and speed regarding the impact of roughness on lubrication performance of sliding bearings, and overcomes the problem of calculation being inaccurate and unsuitable in conventional methods without taking roughness into consideration. In the present invention, cavitation in sliding bearings is taken into consideration, and a fluid dynamic behavior model is established on the basis of roughness. In order to solve the problem of fluid dynamics in a macroscopic domain, a two-scale normalization method is provided, such that microscale effects are coupled into a macroscopic scale by means of finite difference partial derivatives, and then a response of a fluid dynamic behavior in a microscale domain to roughness is calculated by using the normalization method; and a linearization method is provided to calculate finite difference partial derivatives. The present invention provides a two-scale normalization-based numerical value calculation method for the bearing capacity and friction coefficient of a sliding bearing, thereby providing a more accurate and more universally applicable method for numerical value calculation of the performance of sliding bearings with the impact of roughness taken into consideration.

Description

A two-scale numerical calculation method for sliding bearing performance considering the influence of roughness Technical Field

[0001] The present invention belongs to the technical field of mechanical engineering, and specifically designs a two-scale sliding bearing performance numerical calculation method considering the influence of roughness. Background Art

[0002] Hydrodynamic sliding bearings are widely used in various mechanical equipment (such as pressurized water-cooled reactors, turbines, spacecraft, and marine vessels) to support the rotation of rotating parts. They have the advantages of smooth, reliable, and quiet operation. Under liquid lubrication conditions, the sliding surfaces are separated by lubricating oil without direct contact, which can greatly reduce friction loss and surface wear. At the same time, the oil film also has a certain vibration absorption capacity. To improve the efficiency of mechanical systems, currently designed parts are often required to operate under harsh conditions. Therefore, the roughness of the lubricated surface has a significant impact on the lubrication performance of the mechanical system.

[0003] There are currently two main methods for dealing with the effects of surface roughness. One is to use a completely deterministic solution method, which requires a large number of grid points to capture changes in surface roughness, and therefore requires a very high computational cost. Especially when the roughness wavelength is very small, the time required for calculation using this method is unacceptable. To overcome the shortcomings of this method, another method is to use averaging technology, using flow factors to describe the effects of roughness and incorporating them into the classical Reynolds equation. Although this method can save a lot of computing time, when dealing with the effects of roughness, the averaging method will ignore the effect of individual roughness on the lubrication performance of the fluid.

[0004] Current numerical calculation methods only consider pressure boundary conditions when solving equations, without analyzing mass conservation boundary conditions. Therefore, the accuracy of the calculation results will be affected.

[0005] Summary of the Invention

[0006] The present invention addresses the shortcomings of existing technologies by providing a two-scale numerical calculation method for sliding bearing performance that considers the influence of roughness. This method integrates microscale surface structure information with macroscopic information through normalization and linearization techniques, enabling accurate calculation of sliding bearing lubrication performance parameters that account for the influence of roughness.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] A two-scale numerical calculation method for sliding bearing performance considering the influence of roughness includes the following steps:

[0009] 1) According to the given surface roughness, rotation speed, oil film thickness, and considering the influence of cavitation effect, the six variables in the macro domain are given. The dimensionless flow function and in, represents the dimensionless density ratio, represents the ratio gradient in the X direction, represents the ratio gradient in the Y direction, H represents the oil film thickness, X represents the position in the X direction, Indicates the position in the Y direction;

[0010] 2) Take the dimensionless flow function in two directions respectively and For 6 variables Partial derivatives, and according to the principle of conservation of mass, the fluid lubrication control equation is established, thereby establishing the fluid lubrication control equation about partial derivatives;

[0011] 3) On the circumferential boundary, based on the periodic boundary conditions, boundary constraints on the conservation of fluid pressure and flow are established;

[0012] 4) Introducing the parameter ∈ to represent the dimensionless microscale wavelength and defining the microscale domain with respect to the grid points, thereby achieving macro-microscale separation;

[0013] 5) Define the fluid w in the microscale domain as incompressible and isovusible, list the governing equations of fluid dynamics, and define dimensionless quasi-periodic boundary constraints and corner constraints in the microscale domain.

[0014] 6) Using step 5) to calculate the fluid parameters in the micro-scale domain, a normalization method is proposed to calculate the normalized flow rate, friction force and other parameters, and transfer them to the macro-domain;

[0015] 7) Using the normalized flow obtained in step 6), a linear solution method for the partial differential term is proposed. This method assumes that there is a disturbance variable to calculate the partial derivative; according to the flow function in step 1) and The partial derivatives of the flow are solved by linearization method, where the flow at each point is obtained by normalization method at micro scale;

[0016] 8) A finite difference partial derivative method is proposed to solve the fluid dynamics equations in the macroscopic domain and calculate key performance parameters such as fluid pressure and friction.

[0017] Prioritize, in step 1), when considering the surface roughness, the expression of the governing equation of the fluid dynamics of the lubricating oil between the contacting surfaces is different from that of the smooth surface. Combining the combined effects of cavitation effect and surface roughness, the flow rate in the X and Y directions can be expressed as a function of six variables, namely The variable Θ is the density ratio, which is used to describe the ratio of the oil film area to the lubrication area, thus ensuring the conservation of the oil mass during the calculation process. and represent the gradients of the variable Θ in the X and Y directions respectively; H represents the oil film thickness.

[0018] After dimensionless transformation, the flow rates in the X and Y directions are expressed as:

[0019] Preferably, in step 2), respectively and For variable Θ, The partial derivative of

[0020] According to the principle of conservation of fluid mass, the following equation is obtained:

[0021] Combining formulas (5)(6)(7), we can get

[0022] Preferably, after the finite difference method is used to obtain the value of the variable Θ in formula (8), the macroscopic performance parameters can be calculated by the following formula:

[0023] Where, represents the shear stress in the x-direction, represents the shear stress in the y direction, Θ * Indicates the density ratio.

[0024] Preferably, in step 3), in order to accurately solve formula (8), it is necessary to specify the boundary conditions within the macroscopic calculation domain. The boundary conditions for the fluid pressure need to meet the following conditions:

[0025] On the boundary Π1 in the Y direction Fluid pressure on boundary Π2 Equal to atmospheric pressure That is, π2

[0026] Boundary in the X direction On, P and It's about Periodically changing;

[0027] Since formula (8) is an equation about the variable Θ, the above equation about The boundary conditions need to be converted into variables Θ. Since the fluid pressure at both ends of the sliding bearing is constant,

[0028] in, and Respectively expressed in and The density ratio at the location, and is the pressure at both ends of the sliding bearing, B is the width of the sliding bearing, and L represents the axial length of the sliding bearing; represents the bulk modulus; Indicates external pressure;

[0029] In the circumferential direction, periodic boundary conditions are adopted, that is,

[0030] in, and Respectively expressed in and The density ratio at the location.

[0031] Preferably, in step 3), in order to accurately solve formula (8), it is necessary to specify the boundary conditions in the macroscopic calculation domain.

[0032] Regarding the boundary conditions for mass conservation, the mass conservation equation needs to be satisfied, namely in, represents the flow vector of the unit lubrication surface, n represents the unit vector perpendicular to the periodic boundary, and the directions of the perpendicular vectors of the two boundaries are opposite, that is, After arranging and simplifying, we get the following formula: Based on the above boundary conditions (9)-(11), (14), the density ratio Θ value of each point in the computational domain is obtained by solving formula (8) using the two-scale normalization method. Subsequently, the normalized fluid pressure in the computational domain can be calculated using the following formula: Among them, the normalized G * Depends on the formula Here, * represents a normalized value obtained by a normalization method.

[0033] Preferably, in step 4), it is assumed that the surface roughness within the dimensionless microscale period is determined by the wavelength ∈, which can be regarded as the scale ratio to define the scale separation problem. To satisfy the two-scale separation theory, its value should be one order of magnitude or smaller than that of the lubrication domain. The oil film thickness in the microscale domain It can be expressed as follows:

[0034] in, and Representing microscale domains The size of the internal microstructure, represents the dimensionless amplitude of surface roughness;

[0035] To meet the requirements of the two-scale model, six parameters are The size of the micro-scale domain is very small relative to the macro-lubricated surface, so that periodic boundary conditions can be used, so that and

[0036] The microscale geometry is defined in the computational domain Ω micro The computational domain changes periodically in the x and y directions. Due to the shape changes of the microstructure in this microscale problem, this patent will consider the cavitation phenomenon in the microscale. Assuming that the fluid in the microscale domain is incompressible and has constant viscosity, the fluid dynamics governing equation can be expressed as, Where θ is the density ratio and the switching function g is defined by,

[0037] Formula (18) can be solved by the finite difference method to obtain the dimensionless full flow value in the microscale calculation domain, that is,

[0038] here, and represent the flow rates in the y and x directions within the microscale domain, respectively.

[0039] Preferably, in step 5), the fluid boundary conditions of the microscale domain need to be determined. Due to the characteristics of the microscale domain, quasi-periodic boundary conditions are determined. At the same time, flow balance needs to be satisfied in both directions. Quasi-periodic boundary conditions require that there is a pressure offset on the corresponding boundary and the corresponding pressure gradients are equal, thus obtaining the following equation: and The above equations do not include the corner points in the microscale computational domain, which will satisfy different constraints. Here, due to the relationship between fluid pressure and density ratio The relationship between fluid pressures is described by the density ratio, and The definition is as follows,

[0040] To satisfy the quasi-periodic boundary conditions in both directions, the density ratio of the four corner points in the computational domain satisfies the following equation, Corresponding to the The corner points, and Corresponding to the The corner point. At the same time, in order to satisfy the mass conservation, the gradients of the four corner points in the calculation domain satisfy

[0041] Corner points corresponding to positions and Corresponding to the The corner point.

[0042] Preferably, in step 6), the density ratio value in the microscale domain is calculated using a normalization method, and the formula is:

[0043] This formula reflects the influence of surface roughness in the lubrication model. is the density ratio calculated in the microscopic domain;

[0044] The oil film height is The flow rate per unit length is calculated as follows:

[0045] Shear stress formula in microscale domain:

[0046] Preferably, in step 7), the normalized function value is obtained at the microscale, and its corresponding partial derivative at the macroscale is obtained by the following formula: Here, δ is the Dirichlet function, which is equal to 1 when i=j and 0 when i≠j. Assume that there is a small disturbance variable Δx in the function f, which is sufficient to calculate the linear gradient of the function. The value of this disturbance variable depends on the parameter γ, and its value γ>2, which means that the design variable x j The value range is within 1%.

[0047] The choice of disturbance variable depends on the following calculation formula:

[0048] log 10 (Δx j ) <log 10 (max(x j )-min(x j))-γ(43) and γ≥2 to meet two requirements. First, the value of the disturbance variable must be small enough to ensure that the flow gradient at any location can be captured; second, the solution must be independent of the value of the disturbance function. Therefore, the linearization method proposed in this invention can be used to calculate the partial derivatives of the flow with respect to the four parameters.

[0049] Dimensionless flow at macro position (i, j) and It is obtained by normalization method at microscale and is a function of six parameters, namely

[0050] Similarly, the density ratio and shear stress can be calculated in the same way and expressed as,

[0051] Preferably, in step 8), equation (8) can be discretized using the finite difference method, which contains N and M grid points in the axial and circumferential directions respectively. The discretized form of the improved partial differential equation (8) is, Among them, as the number of iterations t increases, will approach infinitely Right now

[0052] Here, the partial derivatives of the flow function in the axial and axial directions are 6 parameters The function of

[0053] The above expression is calculated using the linearization method. When the microscale effect is considered, the value of the parameter density ratio Θ in the computational domain can be obtained by solving equation (44) based on the two-scale method.

[0054] Combined with boundary conditions (9)-(11), (13), the unknown parameters Θ are updated at each grid point in the computational domain using a relaxation iterative algorithm. and G to solve equation (44). Use equation (15) to obtain the fluid pressure After that, the performance parameters of the sliding bearing can be calculated, that is, the bearing capacity formula of the sliding bearing is:

[0055] The shear stress formulas for the circumferential and axial upper and lower surfaces obtained by the two-scale method are:

[0056] The friction formula of the sliding bearing is obtained as follows: The friction coefficient is calculated by the ratio of dimensionless friction force to load-bearing force.

[0057] Worth getting, that is

[0058] The present invention has at least the following beneficial technical effects:

[0059] 1) The present invention provides a two-scale numerical calculation method for sliding bearing performance considering the influence of roughness, which makes up for the shortcomings of the current technology in considering the influence of roughness using deterministic solutions and homogenization methods. The technology of the present invention integrates the influence of microscale roughness into the macro domain, can consider the influence of a single roughness on the performance of the sliding bearing, and is more accurate in calculating the lubrication performance of the sliding bearing.

[0060] 2) The technology of the present invention fully considers the influence of cavitation effect on the calculation of lubrication performance of two-scale sliding bearings, and proposes a finite difference coupling framework by taking the density ratio describing the cavitation phenomenon as the solution object.

[0061] 3) The technology of the present invention establishes a perturbation parameter constraint equation and proposes a linearized gradient calculation method to realize the calculation of partial derivative coefficients in the macroscopic equation, thereby coupling the density ratio in the microscale domain to the macroscopic domain.

[0062] 4) In addition to considering pressure boundary conditions, the present invention fully considers the principle of fluid mass conservation within the macroscopic domain, establishing boundary condition constraint equations at the entry and exit boundaries. Simultaneously, within the microscale domain, in addition to the aforementioned boundary constraints, pressure and mass conservation boundary conditions at corner points are also considered. As a result, the present invention establishes more accurate boundary constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] FIG1 is a flow chart of a two-scale numerical calculation method for sliding bearing performance considering the influence of roughness according to the present invention;

[0064] Figure 2 is a schematic diagram of the fluid dynamics physical model of a sliding bearing;

[0065] Figure 3 is a schematic diagram of the boundary condition model of the sliding bearing macro domain;

[0066] Figure 4 is a schematic diagram of a three-dimensional physical model of a sliding bearing in a micro-scale domain;

[0067] FIG5 is a schematic diagram of the flow chart of the micro-scale domain fluid dynamics solution;

[0068] Figure 6 is a dimensionless fluid pressure diagram based on two-scale normalization;

[0069] FIG7 is a schematic diagram showing the comparison of fluid pressure based on the two-scale normalization method and the deterministic solution;

[0070] FIG8 is a graph showing the change of relative bearing capacity with roughness amplitude;

[0071] FIG9 is a graph showing the change of relative friction coefficient with roughness amplitude. DETAILED DESCRIPTION

[0072] The following further illustrates and explains a two-scale sliding bearing performance numerical calculation method considering the influence of roughness of the present invention in conjunction with the accompanying drawings and embodiments.

[0073] As shown in FIG1 , a two-scale numerical calculation method for sliding bearing performance considering the influence of roughness includes the following steps:

[0074] 1) Assuming that the sliding bearing is smooth, the classical Reynolds equation is used to estimate the fluid pressure and pressure gradient;

[0075] 2) Estimate the disturbance variable value Δx of fluid pressure, pressure gradient and oil film thickness. This value is small enough to calculate the linear gradient of the function. The disturbance variable value depends on the parameter γ, and its value γ>2 means that the design variable x j The choice of disturbance variable depends on the following calculation formula:

[0076] log 10 (Δx j ) <log 10 (max(x j )-min(x j ))-γ(1) and γ≥2 in order to meet the following two requirements. First, the value of the disturbance variable must be small enough to ensure that the flow gradient at any location can be captured; second, the solution must be independent of the value of the disturbance function.

[0077] 3) When considering surface roughness, the expression of the governing equations of lubricating oil fluid dynamics between contacting surfaces is different from that of smooth surfaces. Combining the combined effects of cavitation effect and surface roughness, the flow rate in the X and Y directions can be expressed as a function of six variables, namely

[0078] The variable Θ is the density ratio, which describes the ratio of the oil film area to the lubricated area, thus ensuring the conservation of oil mass during the calculation process. and denote the gradient of the variable Θ in the X and Y directions respectively.

[0079] After dimensionless transformation, the flow rates in the X and Y directions are expressed as:

[0080] Take separately and For variable Θ, The partial derivative of

[0081] According to the principle of conservation of mass, we get the following equation:

[0082] Combining formulas (5)(6)(7), we can get

[0083] (9) To accurately solve formula (9), it is necessary to specify the boundary conditions within the macroscopic calculation domain. The boundary conditions for fluid pressure need to meet the following conditions:

[0084] On the boundary Π1 in the Y direction On the boundary Π2

[0085] Boundary in the X direction superior, and It's about Periodically changing;

[0086] Since formula (9) is an equation about the variable Θ, the above equation about fluid pressure The boundary conditions need to be converted into variables Θ. Since the fluid pressure at both ends of the sliding bearing is constant,

[0087] in, and is the pressure at both ends of the sliding bearing, B is the width of the sliding bearing, and L represents the axial length of the sliding bearing;

[0088] In the circumferential direction, periodic boundary conditions are adopted, that is,

[0089] In order to accurately solve formula (9), it is necessary to specify the boundary conditions within the macroscopic calculation domain. Regarding the boundary conditions for mass conservation, the mass conservation equation needs to be satisfied, that is,

[0090] Where n represents a unit vector perpendicular to the periodic boundary. In this patent, the directions of the perpendicular vectors of the two boundaries are opposite, i.e.

[0091] Formula (13) is simplified to get the following formula:

[0092] Equation (9) can be discretized using the finite difference method, which contains N and M grid points in the axial and circumferential directions respectively. The discretized form of the improved partial differential equation (9) is, Among them, as the number of iterations t increases, will approach infinitely Right now

[0093] Here, the partial derivatives of the flow function in the axial and axial directions are 6 parameters The function of

[0094] The above expression is calculated using the linearization method. When the microscale effect is considered, the density ratio Θ in the computational domain can be obtained by solving equation (16) based on the two-scale method.

[0095] Combine boundary conditions (10)-(12), (15), and use the relaxation iterative algorithm to update the unknown parameters Θ at each grid point in the computational domain. and G to solve equation (44). Use equation (15) to obtain the fluid pressure After that, the performance parameters of the sliding bearing can be calculated.

[0096] Based on the above boundary conditions, the density ratio Θ value of each point in the computational domain is obtained by solving formula (16) using the two-scale normalization method. Subsequently, the normalized fluid pressure in the computational domain can be calculated using the following formula:

[0097] Among them, the normalized G * Depends on the formula

[0098] Here, * represents a normalized value obtained by a normalization method.

[0099] 4) After calculating the fluid density ratio and other parameters, check whether the convergence condition is met. If so, proceed to step 5). If not, proceed to step (6).

[0100] 5) Calculate the performance parameters of the sliding bearing. The bearing capacity formula of the sliding bearing is:

[0101] The shear stress formulas for the circumferential and axial upper and lower surfaces obtained by the two-scale method are:

[0102] Then the friction formula of the sliding bearing is obtained as follows:

[0103] The friction coefficient is obtained by calculating the ratio of dimensionless friction force and bearing capacity, that is,

[0104] 6) Calculate the normalized parameters of the microscale domain for each grid point in the macroscale domain, namely flow, shear stress, and pressure. The calculation process is shown in Figure 5.

[0105] In the first step, the density ratio, gradient, oil film thickness, position and other parameters of each grid point in the macro domain are input;

[0106] In the second step, positive / negative disturbance variables are added to the design variables and their values ​​are calculated;

[0107] In the third step, we assume that the surface roughness within the dimensionless microscale period is determined by the wavelength ∈. ∈ can be regarded as the scale ratio, which is used to define the scale separation problem. To satisfy the two-scale separation theory, its value should be one order of magnitude smaller than the lubrication domain or smaller. The oil film thickness in the microscale domain is expressed as follows:

[0108] in, and Representing microscale domains

[0109] The size of the internal microstructure, Representation table

[0110] Dimensionless amplitude of surface roughness;

[0111] To meet the requirements of the two-scale model, six parameters are The size of the micro-scale domain is very small relative to the macro-lubricated surface, so that periodic boundary conditions can be used, so that and

[0112] The microscale geometry is defined in the computational domain Ω micro The computational domain changes periodically in the x and y directions. Due to the shape changes of the microstructure in this microscale problem, this patent will consider the cavitation phenomenon in the microscale. Assuming that the fluid in the microscale domain is incompressible and has constant viscosity, the fluid dynamics governing equation can be expressed as,

[0113] Where θ is the density ratio and the switching function g is defined by,

[0114] Formula (25) can be solved by the finite difference method to obtain the dimensionless flow value in the microscale calculation domain, that is,

[0115] here, and represent the flow rates in the y and x directions within the microscale domain, respectively.

[0116] To solve equation (25), it is necessary to determine the fluid boundary conditions of the microscale domain. Due to the characteristics of the microscale domain, quasi-periodic boundary conditions are determined. At the same time, flow balance needs to be satisfied in both directions. Quasi-periodic boundary conditions require that there is a pressure offset on the corresponding boundary and the corresponding pressure gradients are equal, thus obtaining the following equation, and

[0117] The above equations do not include the corner points in the microscale computational domain, which will satisfy different constraints. Here, due to the relationship between fluid pressure and density ratio The relationship between fluid pressures is described by the density ratio, where and The definition is as follows,

[0118] In order to satisfy the quasi-periodic boundary conditions in two directions, the density ratio of the four corner points in the computational domain satisfies the following equation: Corresponding to the The corner points, and Corresponding to the The corner point.

[0119] Combining the above formulas (35)-(38), we can get At the same time, in order to satisfy the mass conservation, the gradients of the four corner points in the calculation domain satisfy

[0120] Corner points corresponding to positions and

[0121] Corresponding to the The corner point.

[0122] The fourth step is to calculate the density ratio value in the microscale domain using the normalization method, and the formula is:

[0123] This formula reflects the influence of surface roughness in the lubrication model. It is calculated in the microscopic domain

[0124] The density ratio of the oil film is The flow rate per unit length is calculated as follows:

[0125] Shear stress formula in microscale domain:

[0126] The fifth step is to calculate the partial derivatives of the flow rate with respect to parameters such as density ratio and its gradient, oil film thickness, etc. The corresponding partial derivatives at the macro scale are obtained by the following formula:

[0127] Here, δ is the Dirichlet function, which is equal to 1 when i=j and 0 when i≠j. j Determined by formula (1) in step (2).

[0128] Example

[0129] In order to demonstrate the advantages of the present invention, a sliding bearing is selected, and its basic parameters are shown in Table 1.

[0130] Table 1 Mechanical and physical parameters of sliding bearings

[0131] The width, radius, rotation speed, eccentricity, clearance, lubricating oil viscosity and other parameters of the bearing are used as input to specify the amplitude and size of the roughness. Figure 6 shows a dimensionless three-dimensional diagram of the fluid pressure based on the two-scale normalization method. Taking the deterministic solution as a reference, the sliding bearing fluid pressure solved based on the two-scale normalization method is compared with it, and the fluid pressure at the symmetry plane is shown in Figure 7. It can be seen from the figure that the two-scale normalization method can be very close to the deterministic solution method. Therefore, the method proposed in the present invention can accurately predict the pressure of the fluid, overcome the problem of large memory usage of the deterministic solution method, and adapt to a wider range of roughness scales. Because the present invention couples the influence of a single texture to the macroscopic domain, it can more accurately predict the influence of surface microstructure on lubrication performance compared to current research methods. The relative bearing capacity and relative friction coefficient curves calculated based on the two-scale normalization method proposed in the present invention are shown in Figures 8 and 9, respectively.

Claims

1. A two-scale numerical calculation method for sliding bearing performance considering the influence of roughness, characterized in that: The following steps are involved: 1) According to the given surface roughness, rotation speed, oil film thickness and cavitation effect, six variables in the macro domain are given: The dimensionless flow function and in, represents the dimensionless density ratio, represents the ratio gradient in the X direction, Represents the ratio gradient in the Y direction, Indicates the oil film thickness, Indicates the position in the X direction, Indicates the position in the Y direction; 2) Take the dimensionless flow function in two directions respectively and For 6 variables The partial derivative of flow rate is obtained, and the fluid lubrication control equation about the partial derivative of flow rate is established according to the principle of mass conservation. 3) On the circumferential boundary, based on the periodic boundary conditions, boundary constraints on the conservation principles of fluid pressure and flow are established; 4) Introducing the parameter ∈ to represent the wavelength of the dimensionless microscale domain and defining the size of the microscale domain with respect to the grid points, thus achieving macro-microscale separation; 5) Assuming that the fluid in the micro-scale domain is incompressible and of equal viscosity, the fluid dynamics governing equations are listed, and dimensionless quasi-periodic boundary constraints and corner constraints in the micro-scale domain are defined; 6) Using step 5) to calculate the fluid parameters in the micro-scale domain, a normalization method is proposed to calculate the normalized flow rate and friction force parameters, and then transferred to the macro-domain; 7) Using the normalized flow obtained in step 6), a linear solution method for partial differential terms is proposed. This method assumes that there is a disturbance variable to calculate the partial derivative; according to the flow function in step 1) and The partial derivatives of the flow are solved by linearization method, where the flow at each point is obtained by normalization method at micro scale; 8) A finite difference partial derivative method is proposed to solve the fluid dynamics control equations in the macroscopic domain and calculate the key performance parameters of fluid pressure and friction.

2. A two-scale sliding bearing performance numerical calculation method considering the influence of roughness according to claim 1, It is characterized in that In step 1), when considering the surface roughness, the expression of the fluid dynamics control equation between the contacting surfaces is different from that of the smooth surface. Combining the combined influence of cavitation effect and surface roughness, the flow in the X and Y directions is expressed as a function of 6 variables, namely The variable Θ is the density ratio, which is used to describe the ratio of the oil film area to the lubrication area, thereby ensuring the conservation of the mass of the oil during the calculation process. and represent the gradients of the variable Θ in the X and Y directions, respectively, and H represents the oil film thickness; After dimensionless conversion, the flow in the X and Y directions and Respectively expressed as:

3. A two-scale sliding bearing performance numerical calculation method considering the influence of roughness according to claim 1, It is characterized in that In step 2), take and For variables The partial derivative of According to the principle of fluid mass conservation, the following equation is obtained: Combining formula (5), (6), (7), we can get 4. A two-scale sliding bearing performance numerical calculation method considering the influence of roughness according to claim 3, It is characterized in that The finite difference method is used to obtain the variables in formula (8) After the values ​​are obtained, the performance parameters at the macro scale can be calculated by the following formula: In the formula, represents the shear stress in the x direction, represents the shear stress in the y direction, Θ * Represents the dimensionless density ratio.

5. A two-scale sliding bearing performance numerical calculation method considering the influence of roughness according to claim 3, It is characterized in that In step 3), in order to accurately solve formula (8), it is necessary to specify the boundary conditions in the macroscopic calculation domain. The boundary conditions for fluid pressure need to meet the following conditions: The boundary Π in the Y direction 1 superior At the border 2 Upper fluid pressure Equal to atmospheric pressure Right now The boundary in the X direction superior, and About Periodically changing; Since formula (8) is an equation about the variable Θ, the above equation about The boundary conditions need to be converted into variables Θ. Since the fluid pressure at both ends of the sliding bearing is constant, in, and Respectively expressed in and The density ratio at the location, and is the pressure at both ends of the sliding bearing, B is the width of the sliding bearing, and L represents the axial length of the sliding bearing; represents the bulk modulus; Indicates external pressure; In the circumferential direction, periodic boundary conditions are adopted, that is, in, and Respectively expressed in and The density ratio at the location.

6. A two-scale sliding bearing performance numerical calculation method considering the influence of roughness according to claim 3, It is characterized in that In step 3), in order to accurately solve formula (8), it is necessary to specify the boundary conditions in the macroscopic calculation domain. Regarding the boundary conditions for mass conservation, the mass conservation equation needs to be satisfied, that is, in, represents the flow vector of the unit lubrication surface, n represents the unit vector perpendicular to the periodic boundary, and the directions of the perpendicular vectors of the two boundaries are opposite, that is, After arranging and simplifying, we get the following formula: Based on the above boundary conditions, the density ratio θ of each point in the calculation domain is obtained by solving formula (8) through the two-scale normalization method. Then, the normalized fluid pressure in the calculation domain is It can be calculated by the following formula: Among them, the normalized G * Depends on the formula Here, * represents a normalized value obtained by a normalization method.

7. A two-scale sliding bearing performance numerical calculation method considering the influence of roughness according to claim 1, It is characterized in that In step 4), it is assumed that the surface roughness within the dimensionless microscale period is determined by the wavelength ∈, which can be regarded as the scale ratio to define the scale separation problem. To satisfy the two-scale separation theory, its value should be one order of magnitude or smaller than the lubrication domain. The oil film thickness in the microscale domain is It can be expressed as follows: in, and Represents microscale domain The size of the internal microstructure, Represents the dimensionless amplitude of surface roughness; To meet the requirements of the two-scale model, six parameters are The size of the determined microscale domain is very small relative to the macroscopic lubrication surface, so that periodic boundary conditions can be used, so that and in, Respectively expressed in and density ratio at a location; The microscale geometry is defined in the computational domain Ω micro The computational domain changes periodically in the x and y directions. Due to the shape change of the microstructure in the microscale problem, this patent will consider the cavitation phenomenon in the microscale. Assuming that the fluid in the microscale domain is incompressible and has equal viscosity, the fluid dynamics control equation can be expressed as, Where θ is the density ratio and the switching function g is defined by, Formula (18) can be solved by the finite difference method to obtain the dimensionless flow value in the microscale calculation domain, that is, here, and represent the flow rates in the y and x directions within the microscale domain, respectively.

8. A two-scale sliding bearing performance numerical calculation method considering the influence of roughness according to claim 1, It is characterized in that In step 5), the fluid boundary conditions of the microscale domain need to be determined. The characteristics of the microscale domain determine the quasi-periodic boundary conditions. At the same time, the flow balance needs to be satisfied in both directions. The quasi-periodic boundary conditions require that there is a pressure offset on the corresponding boundary and the corresponding pressure gradients are equal, thus obtaining the following equation: and The above equations do not include the corner points in the microscale computational domain, which will satisfy different constraints. Here, due to the relationship between fluid pressure and density ratio The relationship between fluid pressures is described by the density ratio, where and The definition is as follows, in, and Represents the fluid pressure variation in the x and y directions within the microscale domain. To satisfy the quasi-periodic boundary conditions in both directions, the density ratio of the four corner points in the computational domain satisfies the following equation, Corresponding to the The corner points, and Corresponding to the The corner point of Combining formulas (28), (29), (30), and (31), we can obtain: At the same time, in order to satisfy the principle of mass conservation, the gradients of the four corner points in the calculation domain satisfy The corner point corresponding to the position and Corresponding to the The corner point.

9. A two-scale sliding bearing performance numerical calculation method considering the influence of roughness according to claim 1, It is characterized in that In step 6), the density ratio in the microscale domain is calculated using the normalization method, and the formula is: Formula (38) reflects the influence of surface roughness in the lubrication model, where is the density ratio calculated in the microscopic domain; The oil film height is The flow rate calculation formula per unit length is: Shear stress formula in microscale domain:

10. A two-scale sliding bearing performance numerical calculation method considering the influence of roughness according to claim 7, It is characterized in that In step 7), the normalized function value is obtained at the microscale, and its corresponding partial derivative at the macroscale is obtained by the following formula: Here, δ is the Dirichlet function, which is equal to 1 when i=j and 0 when i≠j. It is assumed that there is a small disturbance variable Δx in the function f, which is sufficient to calculate the linear gradient of the function. The value of the disturbance variable depends on the parameter γ, and the value γ>2 means that when the design variable x j 1% change within the range of values; The choice of disturbance variable depends on the following calculation formula: log 10 (Δx j ) <log 10 (max(x j )-min(x j ))-c (43) And γ≥2 in order to meet two requirements: first, the value of the disturbance variable must be small enough to ensure that the flow gradient at any position can be captured; second, the solution must be independent of the value of the disturbance function; Therefore, the linearization method proposed in this study can be used to calculate the partial derivatives of flow with respect to the four parameters; Dimensionless flow at macro position (i,j) and It is obtained by normalization method in the microscale domain and is a function of six parameters, namely Similarly, the density ratio and shear stress can be calculated in the same way and expressed as, In step 8), equation (8) can be discretized using the finite difference method, where The upper and lower parts contain N and M grid points respectively. The discretized form of the improved partial differential equation (8) is: (44) As the number of iterations t increases, will approach infinitely Right now Here, the partial derivatives of the flow function in the axial and radial directions are 6 parameters The function of Among them, the above expression is calculated using the linearization method; when considering the influence of the microscale, the value of the parameter density ratio Θ in the calculation domain can be obtained by solving equation (44) based on the two-scale method; Combined with boundary conditions (9)-(11), (13), the unknown parameters Θ are updated at each grid point in the computational domain using a relaxation iterative algorithm. and G to solve equation (44); use equation (15) to obtain the fluid pressure After that, the performance parameters of the sliding bearing can be calculated, that is, the bearing capacity formula of the sliding bearing is: The shear stress formulas of the circumferential and axial upper and lower surfaces obtained by the two-scale method are: The friction formula of the sliding bearing is obtained as follows: The friction coefficient is obtained by calculating the ratio of dimensionless friction force and bearing capacity, that is,

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