A modeling method for a mixed lubrication model of a dynamic load sliding bearing coupled with thermal and viscoelastic effects

Abstract

The application relates to a modeling method of a mixed lubrication model of a dynamic load sliding bearing coupled with thermal and viscoelastic effects. The sliding bearing has obvious deformation time lag effects under time-varying load working conditions, is subjected to high pressure, shearing and friction, and obviously changes in temperature. The application is based on an average flow model, constructs a generalized average Reynolds equation considering surface topography effects and thermal effects, adopts a finite difference method to discretize the equation and uses a super relaxation iteration algorithm to obtain an oil film pressure distribution; according to the pressure distribution, the pressure gradient is calculated, the oil film velocity and the velocity gradient thereof are solved; an energy equation and a bushing heat conduction equation are constructed, boundary conditions are set to solve a temperature control equation, and the temperature distribution of the oil film and the bushing is obtained; the actual deformation at the current time is calculated by considering the deformation time lag effect of the bushing, the film thickness distribution is corrected, the lubricating oil viscosity distribution is updated, the pressure field and the temperature field are iteratively calculated, and finally, the lubrication performance parameters of the bearing are calculated.

Description

Technical Field

[0001] This invention belongs to the technical field of lubrication performance analysis of sliding bearings, specifically relating to a modeling method for a dynamic load sliding bearing hybrid lubrication model coupled with thermal and viscoelastic effects. Background Technology

[0002] Sliding bearings are important supporting components of mechanical equipment such as diesel engines, reciprocating compressors, and steam turbines. Their lubrication characteristics directly affect the operational stability and safety of the mechanical equipment.

[0003] For sliding bearings operating in high-speed, heavy-load environments, their eccentricity is large, local clearance is small, and the amplitude of surface roughness is on the same order of magnitude as the minimum oil film thickness, placing the bearing in a mixed lubrication state. Simultaneously, during bearing lubrication, factors such as viscous shear, compression, and rough surface friction cause the oil film temperature to rise and the lubricating oil viscosity to change, making the thermal effect on lubrication performance non-negligible. Existing hybrid elastohydrodynamic (MEHD) and hybrid thermoelastohydrodynamic (MTEHD) models generally assume that bearing deformation under load is instantaneous. However, research shows that bearing materials possess viscoelasticity; during dynamic loading, bearing deformation is divided into two parts: one part is completed instantaneously (transient deformation), and the other part requires a period of time to complete after loading (hysteresis deformation). Due to the hysteresis effect of bearing deformation, the elastic deformation of the bearing does not match the load change synchronously. The delayed deformation response cannot compensate for the oil film thickness in time, thereby increasing the hydrodynamic pressure effect, the probability of rough contact, and the opportunity for interfacial friction. Therefore, for dynamically loaded sliding bearings, the hybrid viscoelastic hydrodynamic lubrication (MVEHD) model and the hybrid thermo-viscoelastic hydrodynamic lubrication (MTVEHD) model, which consider the viscoelastic effect, are more in line with engineering practice.

[0004] To address the lack of theoretical basis for the physical field numerical analysis of the coupling of thermal and viscoelastic effects in dynamically loaded sliding bearings, this invention proposes a modeling method for a hybrid lubrication model of dynamically loaded sliding bearings with coupled thermal and viscoelastic effects. Summary of the Invention

[0005] The purpose of this invention is to propose a modeling method for a hybrid lubrication model of a dynamically loaded sliding bearing that couples thermal and viscoelastic effects, addressing the thermal effects of sliding bearings and the viscoelastic effects of deformation under load.

[0006] The objective of this invention is achieved through the following techniques:

[0007] First, based on the average flow model, a generalized average Reynolds equation considering surface morphology and thermal effects is constructed. The equation is discretized using the finite difference method, and the oil film pressure distribution is obtained using an over-relaxation iterative algorithm.

[0008] Secondly, the pressure gradient is calculated based on the oil film pressure distribution, and the oil film velocity and its velocity gradient are solved. The energy equation and the bearing heat conduction equation are constructed, boundary conditions are set, and the temperature control equation is calculated by difference until the bearing temperature and oil film temperature meet the convergence condition, thus obtaining the temperature distribution of the oil film and bearing.

[0009] Next, considering the time lag effect of bearing deformation, calculate the actual deformation at the current moment and correct the film thickness distribution; update the lubricating oil viscosity distribution, and iteratively calculate the pressure field and temperature field until the viscosity converges.

[0010] Finally, the bearing lubrication performance parameters at each moment are calculated.

[0011] A modeling method for a hybrid lubrication model of a dynamically loaded sliding bearing coupled with thermal and viscoelastic effects, characterized by the following steps:

[0012] The first step is to establish a thermal fluid mixed lubrication model for sliding bearings.

[0013] This invention combines the advantages of two lubrication models: the generalized Reynolds equation that takes into account viscosity variation along the film thickness and the average flow Reynolds equation that considers the effects of three-dimensional rough surfaces. It establishes a generalized average Reynolds equation that considers both thermal and surface morphology effects.

[0014]

[0015] Where p represents oil film pressure, x represents the circumferential coordinate, and y represents the axial coordinate. φ x and φ y φ represents the pressure-flow factor in the x and y directions, respectively. s This represents the shear flow factor, and U represents the journal tangential velocity. σ represents the standard deviation of the overall surface roughness of the bearing journal. j and σ b F0 represents the standard deviation of the surface roughness of the journal and bearing, respectively; t represents time; F0 is the average viscosity function; F1 is the displacement viscosity function; F2 is the displacement viscosity function. 20 It is the nominal displacement quadratic viscosity function.

[0016] F 20 The expressions for F1 and F0 are:

[0017]

[0018] Where z represents the radial coordinate of the oil film, h T The average oil film thickness is represented by h, the nominal oil film thickness is represented by η, and the lubricating oil viscosity is represented by F. 00 F is the nominal average viscosity function. 10 This is the nominal displacement viscosity function.

[0019] Flow factor φ x φ y and φ s Calculated using the following formula:

[0020] φ x =1+0.225Λ -1.5 (3)

[0021] φ y =1-1.18e -0.42Λ (4)

[0022]

[0023] Where e is the natural constant, and Λ=h / σ is the film thickness judgment index, which represents the ratio of film thickness to roughness.

[0024] The finite difference method is used to discretize equation (1), and the oil film pressure is solved by the over-relaxation iterative algorithm. The calculation process requires convergence judgment of the oil film pressure. The convergence criterion is as follows:

[0025]

[0026] Where M and N are the number of circumferential and axial mesh nodes, respectively; i and j are the circumferential and axial mesh node numbers, respectively; m is the time step; and n is the number of iterations in the oil film pressure solution process. and Let ζ represent the oil film pressure obtained at node (i, j) in the nth and (n-1)th iterations at the m-th time step, respectively. p This represents the convergence tolerance of the oil film pressure; a recommended value for the convergence tolerance is 1×10⁻⁶. -5 ~1×10 -7 .

[0027] The second step is to calculate the oil film velocity and velocity gradient.

[0028] During bearing operation, the journal is in an eccentric position, forming a converging wedge shape between the journal and the bearing bush. The oil film flow generates hydrodynamic pressure, providing the oil film support force. The oil film flow velocity is affected by the pressure gradient, journal speed, and viscosity distribution. The expression for the oil film velocity is:

[0029]

[0030] Where u, v, and w represent the circumferential velocity, axial velocity, and radial velocity of the oil film, respectively.

[0031] The radial velocity gradients of the oil film's circumferential velocity u and axial velocity v are respectively expressed as:

[0032]

[0033] The third step is to solve the temperature control equation.

[0034] (1) Energy equation:

[0035]

[0036] Among them, T f Indicates oil film temperature, ρ f c represents the density of lubricating oil. f K represents the specific heat of lubricating oil. f Φ represents the oil film thermal conductivity coefficient, and Φ represents the dissipated work.

[0037] The dissipated work Φ consists of two parts: viscous dissipated work and frictional heat from the contact of the micro-scrapers, expressed as:

[0038]

[0039] Where η represents viscosity, μ c p represents the boundary friction coefficient. c The value represents the contact pressure at the rough peak, and h represents the oil film thickness.

[0040] (2) Heat conduction equation of bearing:

[0041]

[0042] Among them, T b Indicates bearing temperature, kJ b ρ represents the thermal conductivity coefficient of the bearing bush. b c represents the density of the bearing. b The specific heat of the bearing is represented by θ, where θ is the circumferential angular coordinate and r is the radial coordinate of the bearing.

[0043] (3) Boundary condition settings

[0044] 1) Setting boundary conditions at the oil inlet:

[0045]

[0046] Among them, T bush-inlet T represents the oil film temperature at the oil inlet. mix Q is the mixing temperature. rc Q s These are the circulating hot oil flow rate and the make-up cold oil flow rate, respectively, T rc T s These are the circulating hot oil temperature and the replenishing cold oil temperature, respectively.

[0047] 2) Setting the boundary conditions at the interface between the oil film and the journal:

[0048]

[0049] Among them, T oil-journal T represents the oil film temperature at the interface between the oil film and the journal. j q is the journal surface temperature. j This indicates the heat flux along the journal in the circumferential direction.

[0050] 3) Setting the boundary conditions at the interface between the oil film and the bearing bush:

[0051]

[0052] Among them, T oil-bush The value represents the temperature at the junction of the oil film and the bearing bush, C represents the bearing clearance, and R represents the bearing inner radius.

[0053] 4) Setting boundary conditions between the outer surface of the bearing bush and the environment:

[0054]

[0055] Among them, T bush-out h is the surface temperature of the bearing bush. b T is the convective heat transfer coefficient of the bearing bush. a Indicates ambient temperature.

[0056] 5) Setting boundary conditions between the bearing end face and the environment:

[0057]

[0058] Among them, T bush-end This refers to the temperature of the bearing end face.

[0059] The calculation process of the temperature control equation requires convergence judgment of oil film temperature and bearing temperature. The convergence criteria are as follows:

[0060]

[0061] Among them, M, N, G f G b These represent the number of grid nodes in the circumferential direction, the axial direction, the oil film thickness direction, and the bearing thickness direction, respectively. i, j, and k correspond to the grid node numbers in the circumferential, axial, and radial directions, respectively. and Let represent the oil film temperatures obtained by node (i, j, k) in the nth and (n-1)th iterations at the mth time step, respectively. and Let ζ represent the bearing temperatures obtained at node (i, j, k) in the nth and (n-1)th iterations at the m-th time step, respectively. T This represents the temperature convergence tolerance; a recommended convergence tolerance value is 1 × 10⁻⁶. -5 ~1×10 -7 .

[0062] The fourth step is to correct the oil film thickness.

[0063] Sliding bearings subjected to time-varying loads exhibit significant viscoelastic properties. During loading, the bearing bush simultaneously experiences transient deformation that remains constant over time, as well as time-delayed deformation that develops over time. The time-delayed deformation of the bearing bush is not synchronized with the load change; that is, the deformation always lags behind the load change. The viscoelastic deformation mechanism of the bearing bush can be characterized by the following equation:

[0064]

[0065] Where, △δ lag (x,y,△t)| m δ represents the bearing deformation per unit time delay at the m-th time step. lag (x,y,t-△t) represents the cumulative time-delay deformation of the bearing at the previous simulation moment. δ(x,y,t) represents the fully time-delayed deformation of the bearing under oil film pressure p at the previous simulation moment, and δ(x,y,t) represents the actual deformation of the bearing at the current simulation moment. t (x,y,t) represents the transient elastic deformation of the bearing at this simulation moment, τ represents the viscoelastic relaxation time of the bearing material, q represents the total number of simulation time steps, and Δt represents the time step.

[0066] The elastic deformation of the bearing is calculated using the compliance matrix method.

[0067]

[0068] δ F (x i ,y j ) is at the node (x) on the bearing surface i ,y j The radial deformation of ). G E (x i ,y j ,x r ,y s ) is the compliance matrix, which physically represents the compliance applied to node (x). r ,y s Force F0(x) per unit size at point ) r ,y s ) makes node (x i ,y j The radial deformation generated by p(x) r ,y s ) is the action on node (x) r ,y s The oil film pressure at (). This represents the area of ​​the bearing mesh unit.

[0069] For heavy-duty bearings, the elastic deformation of the bearing bush has a significant impact on the oil film thickness. Therefore, it is necessary to correct the oil film thickness based on the actual deformation, and then use a multinomial probability density function that approximates a Gaussian distribution to calculate the average oil film thickness. The calculation method is as follows:

[0070]

[0071]

[0072] Among them, h and h T These represent the nominal oil film thickness and the average oil film thickness, respectively; C is the bearing clearance; and e is the bearing average oil film thickness. cc Where θ is the eccentricity and θ is the circumferential angular coordinate. The offset angle is Λ = h / σ, which is the film thickness judgment index, representing the ratio of film thickness to roughness. g is the film thickness judgment ratio, g = Λ / 3.

[0073] Fifth step: Update the viscosity of the lubricating oil.

[0074] Viscosity is an important bearing lubrication parameter. Under high temperature and pressure, lubricating oil exhibits significant viscosity-pressure and viscosity-temperature effects. Based on the oil film pressure and temperature distributions obtained in the first and third steps, the Roelands formula is used to update and calculate the lubricating oil viscosity.

[0075]

[0076] Where, η a To be at ambient temperature T a The viscosity of the oil film is given by p, where p is the oil film pressure.

[0077] The calculation of lubricating oil viscosity should meet the following convergence conditions:

[0078]

[0079] in, and Let ζ represent the oil film viscosity obtained at node (i, j, k) in the nth and (n-1)th iterations at the m-th time step, respectively. η This represents the convergence tolerance of the oil film viscosity; a recommended value for the convergence tolerance is 1×10⁻⁶. -5 ~1×10 -6 .

[0080] Step 6: Calculate the mixed lubrication parameters.

[0081] Under mixed lubrication conditions, the bearing's supporting reaction force consists of two parts: one is the oil film force composed of oil film pressure, and the other is the rough contact force. The bearing reaction force can be solved by integrating the pressure.

[0082]

[0083] in, and These are the components of the oil film force in the x and z directions, respectively. and These are the components of the rough contact force in the x and z directions, respectively, and F is the supporting reaction force. x With F z These are the components of the supporting reaction force in the x and z directions, respectively.

[0084] The rough contact pressure is calculated as follows:

[0085]

[0086] Where λ is the distribution density of the rough peaks, χ is the radius of the rough peaks, σ is the standard deviation of the overall roughness of the bearing journal surface, E is the equivalent elastic modulus of the contact material, and F 2.5 (Λ) is the mathematical expectation function related to the film thickness assessment index Λ, and its calculation is as follows:

[0087]

[0088] The frictional power consumption of the bearing is calculated by the following formula:

[0089]

[0090] Where, φ f For shear flow factor, φ fs φ is the shear stress factor. fp This represents the frictional pressure flow factor.

[0091] φ f φ fs and φ fp The following formula is used for calculation:

[0092]

[0093]

[0094]

[0095] Lubricating oil leakage flow rate Q at the front and rear faces of the bearing F and Q L Calculated using the following formula:

[0096]

[0097] Total outflow rate Q leak :

[0098] Q leak =QF +Q L (32)

[0099] Among them, v F v is the axial velocity of the oil film on the front face of the bearing. L This represents the axial velocity of the oil film on the rear end face of the bearing. Attached Figure Description

[0100] Figure 1 Flowchart for solving the hybrid lubrication model of dynamically loaded sliding bearings coupled with thermal and viscoelastic effects

[0101] Figure 2 Three-dimensional diagrams of bearing pressure distribution at time zero (left) and temperature distribution at the interface between oil film and bearing bush (right).

[0102] Figure 3 Pressure distribution and peak oil film pressure curves at the bearing mid-section at various times

[0103] Figure 4 Peak oil film temperature curve

[0104] Figure 5 Maximum deformation curve of bearing

[0105] Figure 6 Oil film force curve

[0106] Figure 7 Rough contact pressure curve

[0107] Figure 8 Triboelectric power consumption curve

[0108] Figure 9 End face leakage curve Detailed Implementation

[0109] To better understand the technical solution of the present invention, the specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0110] For bearing dynamic load conditions, this invention incorporates eccentric motion with an eccentricity velocity of ε′=15sin(2mπ / q). The eccentricity varies according to the formula ε=ε-ε′△t, and the initial eccentricity is set to ε0=1-3σ / C. The relationship between eccentricity and eccentricity is ε=e cc / C. Set the total number of time points q = 80; set the time step to Δt = 1 × 10. -5 s.

[0111] like Figure 1 The flowchart shown illustrates the solution process for a thermo-fluid hybrid lubrication model of a dynamically loaded sliding bearing considering viscoelastic effects. A modeling method for a dynamically loaded sliding bearing hybrid lubrication model coupling thermal and viscoelastic effects is characterized by the following steps:

[0112] The first step is to establish a thermal fluid mixed lubrication model for sliding bearings.

[0113] This invention combines the advantages of two lubrication models: the generalized Reynolds equation that takes into account viscosity variation along the film thickness and the average flow Reynolds equation that considers the effects of three-dimensional rough surfaces. It establishes a generalized average Reynolds equation that considers both thermal and surface morphology effects.

[0114]

[0115] Where p represents oil film pressure, x represents the circumferential coordinate, and y represents the axial coordinate. φ x and φ y φ represents the pressure-flow factor in the x and y directions, respectively. s This represents the shear flow factor, and U represents the journal tangential velocity. σ represents the standard deviation of the overall surface roughness of the bearing journal. j and σ b F0 represents the standard deviation of the surface roughness of the journal and bearing, respectively; t represents time; F0 is the average viscosity function; F1 is the displacement viscosity function; F2 is the displacement viscosity function. 20 It is the nominal displacement quadratic viscosity function.

[0116] F 20 The expressions for F1 and F0 are:

[0117]

[0118] Where z represents the radial coordinate of the oil film, h T The average oil film thickness is represented by h, the nominal oil film thickness is represented by η, and the lubricating oil viscosity is represented by F. 00 F is the nominal average viscosity function. 10 This is the nominal displacement viscosity function.

[0119] Flow factor φ x φ y and φ s Calculated using the following formula:

[0120] φ x =1+0.225Λ -1.5 (3)

[0121] φ y =1-1.18e -0.42Λ (4)

[0122]

[0123] Where e is the natural constant, and Λ=h / σ is the film thickness judgment index, which represents the ratio of film thickness to roughness.

[0124] The finite difference method is used to discretize equation (1), and the oil film pressure is solved by the over-relaxation iterative algorithm. The calculation process requires convergence judgment of the oil film pressure. The convergence criterion is as follows:

[0125]

[0126] Where M and N are the number of circumferential and axial mesh nodes, respectively; i and j are the circumferential and axial mesh node numbers, respectively; m is the time step; and n is the number of iterations in the oil film pressure solution process. and Let ζ represent the oil film pressure obtained at node (i, j) in the nth and (n-1)th iterations at the m-th time step, respectively. p This represents the convergence tolerance of the oil film pressure; a recommended value for the convergence tolerance is 1×10⁻⁶. -5 ~1×10 -7 The three-dimensional distribution of oil film pressure at the initial moment is as follows: Figure 2 As shown on the left, the pressure distribution and peak oil film pressure curves of the bearing's intermediate cross-section at various times are as follows: Figure 3 As shown.

[0127] The second step is to calculate the oil film velocity and velocity gradient.

[0128] During bearing operation, the journal is in an eccentric position, forming a converging wedge shape between the journal and the bearing bush. The oil film flow generates hydrodynamic pressure, providing the oil film support force. The oil film flow velocity is affected by the pressure gradient, journal speed, and viscosity distribution. The expression for the oil film velocity is:

[0129]

[0130] Where u, v, and w represent the circumferential velocity, axial velocity, and radial velocity of the oil film, respectively.

[0131] The radial velocity gradients of the oil film's circumferential velocity u and axial velocity v are respectively expressed as:

[0132]

[0133] The third step is to solve the temperature control equation.

[0134] (1) Energy equation:

[0135]

[0136] Among them, T f Indicates oil film temperature, ρ f c represents the density of lubricating oil. f K represents the specific heat of lubricating oil. f Φ represents the oil film thermal conductivity coefficient, and Φ represents the dissipated work.

[0137] The dissipated work Φ consists of two parts: viscous dissipated work and frictional heat from the contact of the micro-scrapers, expressed as:

[0138]

[0139] Where η represents viscosity, μ c p represents the boundary friction coefficient. c The value represents the contact pressure at the rough peak, and h represents the oil film thickness.

[0140] (2) Heat conduction equation of bearing:

[0141]

[0142] Among them, T b Indicates bearing temperature, kJ b ρ represents the thermal conductivity coefficient of the bearing bush. b c represents the density of the bearing. b The specific heat of the bearing is represented by θ, where θ is the circumferential angular coordinate and r is the radial coordinate of the bearing.

[0143] (3) Boundary condition settings

[0144] 1) Setting boundary conditions at the oil inlet:

[0145]

[0146] Among them, T bush-inlet T represents the oil film temperature at the oil inlet. mix Q is the mixing temperature. rc Q s These are the circulating hot oil flow rate and the make-up cold oil flow rate, respectively, T rc T s These are the circulating hot oil temperature and the replenishing cold oil temperature, respectively.

[0147] 2) Setting the boundary conditions at the interface between the oil film and the journal:

[0148]

[0149] Among them, T oil-journal T represents the oil film temperature at the interface between the oil film and the journal. j q is the journal surface temperature. j This indicates the heat flux along the journal in the circumferential direction.

[0150] 3) Setting the boundary conditions at the interface between the oil film and the bearing bush:

[0151]

[0152] Among them, T oil-bushThe value represents the temperature at the junction of the oil film and the bearing bush, C represents the bearing clearance, and R represents the bearing inner radius.

[0153] 4) Setting boundary conditions between the outer surface of the bearing bush and the environment:

[0154]

[0155] Among them, T bush-out h is the surface temperature of the bearing bush. b T is the convective heat transfer coefficient of the bearing bush. a Indicates ambient temperature.

[0156] 5) Setting boundary conditions between the bearing end face and the environment:

[0157]

[0158] Among them, T bush-end This refers to the temperature of the bearing end face.

[0159] The calculation process of the temperature control equation requires convergence judgment of oil film temperature and bearing temperature. The convergence criteria are as follows:

[0160]

[0161] Among them, M, N, G f G b These represent the number of grid nodes in the circumferential direction, the axial direction, the oil film thickness direction, and the bearing thickness direction, respectively. i, j, and k correspond to the grid node numbers in the circumferential, axial, and radial directions, respectively. and Let represent the oil film temperatures obtained by node (i, j, k) in the nth and (n-1)th iterations at the mth time step, respectively. and Let ζ represent the bearing temperatures obtained at node (i, j, k) in the nth and (n-1)th iterations at the m-th time step, respectively. T This represents the temperature convergence tolerance; a recommended convergence tolerance value is 1 × 10⁻⁶. -5 ~1×10 -7 .

[0162] The three-dimensional distribution of oil film temperature at the initial moment is as follows: Figure 2 As shown on the right, the peak oil film temperature curves at various times are as follows: Figure 4 As shown.

[0163] The fourth step is to correct the oil film thickness.

[0164] Sliding bearings subjected to time-varying loads exhibit significant viscoelastic properties. During loading, the bearing bush simultaneously experiences transient deformation that remains constant over time, as well as time-delayed deformation that develops over time. The time-delayed deformation of the bearing bush is not synchronized with the load change; that is, the deformation always lags behind the load change. The viscoelastic deformation mechanism of the bearing bush can be characterized by the following equation:

[0165]

[0166] Where, △δ lag (x,y,△t)| m δ represents the bearing deformation per unit time delay at the m-th time step. lag (x,y,t-△t) represents the cumulative time-delay deformation of the bearing at the previous simulation moment. δ(x,y,t) represents the fully time-delayed deformation of the bearing under oil film pressure p at the previous simulation moment, and δ(x,y,t) represents the actual deformation of the bearing at the current simulation moment. t (x,y,t) represents the transient elastic deformation of the bearing at this simulation moment, τ represents the viscoelastic relaxation time of the bearing material, q represents the total number of simulation time steps, and Δt represents the time step.

[0167] The elastic deformation of the bearing is calculated using the compliance matrix method.

[0168]

[0169] δ F (x i ,y j ) is at the node (x) on the bearing surface i ,y j The radial deformation of ). G E (x i ,y j ,x r ,y s ) is the compliance matrix, which physically represents the compliance applied to node (x). r ,y s Force F0(x) per unit size at point ) r ,y s ) makes node (x i ,y j The radial deformation generated by p(x) r ,y s ) is the action on node (x) r ,y s The oil film pressure at (). This represents the area of ​​the bearing mesh element. The maximum deformation of the bearing at various times is shown below. Figure 5 As shown.

[0170] For heavy-duty bearings, the elastic deformation of the bearing bush has a significant impact on the oil film thickness. Therefore, it is necessary to correct the oil film thickness based on the actual deformation, and then use a multinomial probability density function that approximates a Gaussian distribution to calculate the average oil film thickness. The calculation method is as follows:

[0171]

[0172]

[0173] Among them, h and h T These represent the nominal oil film thickness and the average oil film thickness, respectively; C is the bearing clearance; and e is the bearing average oil film thickness. cc Where θ is the eccentricity and θ is the circumferential angular coordinate. The offset angle is Λ = h / σ, which is the film thickness judgment index, representing the ratio of film thickness to roughness. g is the film thickness judgment ratio, g = Λ / 3.

[0174] Fifth step: Update the viscosity of the lubricating oil.

[0175] Viscosity is an important bearing lubrication parameter. Under high temperature and pressure, lubricating oil exhibits significant viscosity-pressure and viscosity-temperature effects. Based on the oil film pressure and temperature distributions obtained in the first and third steps, the Roelands formula is used to update and calculate the lubricating oil viscosity.

[0176]

[0177] Where, η a To be at ambient temperature T a The viscosity of the oil film is given by p, where p is the oil film pressure.

[0178] The calculation of lubricating oil viscosity should meet the following convergence conditions:

[0179]

[0180] in, and Let ζ represent the oil film viscosity obtained at node (i, j, k) in the nth and (n-1)th iterations at the m-th time step, respectively. η This represents the convergence tolerance of the oil film viscosity; a recommended value for the convergence tolerance is 1×10⁻⁶. -5 ~1×10 -6 .

[0181] Step 6: Calculate the mixed lubrication parameters.

[0182] Under mixed lubrication conditions, the bearing's supporting reaction force consists of two parts: one is the oil film force composed of oil film pressure, and the other is the rough contact force. The bearing reaction force can be solved by integrating the pressure.

[0183]

[0184] in, and These are the components of the oil film force in the x and z directions, respectively. and These are the components of the rough contact force in the x and z directions, respectively, and F is the supporting reaction force. x With F z These represent the components of the supporting reaction force in the x and z directions, respectively. The oil film force curve is shown below. Figure 6 As shown.

[0185] The rough contact pressure is calculated as follows:

[0186]

[0187] Where λ is the distribution density of the rough peaks, χ is the radius of the rough peaks, σ is the standard deviation of the overall roughness of the bearing journal surface, E is the equivalent elastic modulus of the contact material, and F 2.5 (Λ) is the mathematical expectation function related to the film thickness assessment index Λ, and its calculation is as follows:

[0188]

[0189] Rough contact pressure curve as shown Figure 7 As shown.

[0190] The frictional power consumption of the bearing is calculated by the following formula:

[0191]

[0192] Where, φ f For shear flow factor, φ fs φ is the shear stress factor. fp This represents the frictional pressure flow factor. Figure 8 This is a graph showing the triboelectric power consumption.

[0193] φ f φ fs and φ fp The following formula is used for calculation:

[0194]

[0195]

[0196]

[0197] Lubricating oil leakage flow rate Q at the front and rear faces of the bearing F and Q L Calculated using the following formula:

[0198]

[0199] Total outflow rate Q leak :

[0200] Q leak =Q F +Q L (32)

[0201] Among them, v F v is the axial velocity of the oil film on the front face of the bearing. L This represents the axial velocity of the oil film on the rear end face of the bearing. Figure 9 This is a graph showing the leakage rate at the end face.

Claims

1. A modeling method for a hybrid lubrication model of dynamically loaded sliding bearings coupled with thermal and viscoelastic effects, characterized in that... Includes the following steps: The first step is to establish a thermal fluid mixed lubrication model for sliding bearings; Combining the advantages of both the generalized Reynolds equation, which takes into account viscosity variations along the film thickness, and the average flow Reynolds equation, which considers the effects of three-dimensional rough surfaces, a generalized average Reynolds equation considering both thermal and surface morphology effects is established: Where p represents oil film pressure, x represents the circumferential coordinate, and y represents the axial coordinate; φ x and φ y φ represents the pressure-flow factor in the x and y directions, respectively. s This represents the shear flow factor, and U represents the journal tangential velocity. σ represents the standard deviation of the overall surface roughness of the bearing journal. j and σ b F0 represents the standard deviation of the surface roughness of the journal and bearing, respectively; t represents time; F0 is the average viscosity function; F1 is the displacement viscosity function; F2 is the displacement viscosity function. 20 The nominal displacement is a quadratic viscosity function; F 20 The expressions for F1 and F0 are: Where z represents the radial coordinate of the oil film, h T The average oil film thickness is represented by h, the nominal oil film thickness is represented by η, and the lubricating oil viscosity is represented by F. 00 F is the nominal average viscosity function. 10 The nominal displacement viscosity function; Flow factor φ x φ y and φ s Calculated using the following formula: f x =1+0.225Λ -1.5 (3) f y =1-1.18e -0.42Λ (4) Where e is the natural constant, and Λ=h / σ is the film thickness judgment index, which represents the ratio of film thickness to roughness; The finite difference method is used to discretize equation (1), and the oil film pressure is solved by the over-relaxation iterative algorithm. The calculation process requires convergence judgment of the oil film pressure. The convergence criterion is as follows: Where M and N are the number of circumferential and axial mesh nodes, respectively; i and j are the circumferential and axial mesh node numbers, respectively; m is the time step; and n is the number of iterations in the oil film pressure solution process. and ζ represents the oil film pressure obtained by node (i, j) in the nth and (n-1)th iterations at the mth time step, respectively; p This represents the convergence tolerance of the oil film pressure; a recommended value for the convergence tolerance is 1×10⁻⁶. -5 ~1×10 -7 ; The second step is to calculate the oil film velocity and velocity gradient. During bearing operation, the journal is in an eccentric position, forming a converging wedge shape between the journal and the bearing bush. Oil film flow generates hydrodynamic pressure, providing the oil film support force. The oil film flow velocity is affected by the pressure gradient, journal speed, and viscosity distribution. The expression for the oil film velocity is: Where u, v, and w represent the circumferential velocity, axial velocity, and radial velocity of the oil film, respectively; The radial velocity gradients of the oil film's circumferential velocity u and axial velocity v are respectively expressed as: The third step is to solve the temperature control equation; (1) Energy equation: Among them, T f Indicates oil film temperature, ρ f c represents the density of lubricating oil. f K represents the specific heat of lubricating oil. f The coefficient of thermal conductivity of the oil film is represented by Φ, where Φ is the work dissipated. The dissipated work Φ consists of two parts: viscous dissipated work and frictional heat from the contact of the micro-scrapers, expressed as: Where η represents viscosity, μ c p represents the boundary friction coefficient. c This represents the contact pressure at the rough peak, where h is the oil film thickness. (2) Heat conduction equation of bearing: Among them, T b Indicates bearing temperature, kJ b ρ represents the thermal conductivity coefficient of the bearing bush. b c represents the density of the bearing. b The bearing specific heat is represented by θ, where θ is the circumferential angular coordinate and r is the radial coordinate of the bearing. (3) Boundary condition settings 1) Setting boundary conditions at the oil inlet: Among them, T bush-inlet T represents the oil film temperature at the oil inlet. mix Q is the mixing temperature. rc Q s These are the circulating hot oil flow rate and the make-up cold oil flow rate, respectively, T rc T s These are the circulating hot oil temperature and the replenishing cold oil temperature, respectively. 2) Setting the boundary conditions at the interface between the oil film and the journal: Among them, T oil-journal T represents the oil film temperature at the interface between the oil film and the journal. j q is the journal surface temperature. j This indicates the heat flux along the journal in the circumferential direction; 3) Setting the boundary conditions at the interface between the oil film and the bearing bush: Among them, T oil-bush The temperature at the junction of the oil film and the bearing bush is indicated by C, where C represents the bearing clearance and R represents the bearing inner radius. 4) Setting boundary conditions between the outer surface of the bearing bush and the environment: Among them, T bush-out h is the surface temperature of the bearing bush. b T is the convective heat transfer coefficient of the bearing bush. a Indicates ambient temperature; 5) Setting boundary conditions between the bearing end face and the environment: Among them, T bush-end This refers to the temperature of the bearing end face. The calculation process of the temperature control equation requires convergence judgment of oil film temperature and bearing temperature. The convergence criteria are as follows: Among them, M, N, G f G b These represent the number of grid nodes in the circumferential direction, the axial direction, the oil film thickness direction, and the bearing thickness direction, respectively. i, j, and k correspond to the grid node numbers in the circumferential, axial, and radial directions, respectively. and Let represent the oil film temperatures obtained by node (i, j, k) in the nth and (n-1)th iterations at the mth time step, respectively. and ζ represents the bearing temperature obtained by node (i, j, k) in the nth and (n-1)th iterations at the mth time step, respectively; T This represents the temperature convergence tolerance; a recommended convergence tolerance value is 1 × 10⁻⁶. -5 ~1×10 -7 ; Step 4: Oil film thickness correction; Sliding bearings subjected to time-varying loads exhibit significant viscoelastic properties; during the loading process, the bearing bush simultaneously exhibits transient deformation that does not change with time and time-delayed deformation that develops over time; the time-delayed deformation of the bearing bush is not synchronized with the load change, i.e., the deformation always lags behind the load change; the viscoelastic deformation mechanism of the bearing bush is characterized by the following equation: Where, △δ lag (x,y,△t)| m δ represents the bearing deformation per unit time delay at the m-th time step. lag (x,y,t-△t) represents the cumulative time-delay deformation of the bearing at the previous simulation moment. δ(x,y,t) represents the fully time-delayed deformation of the bearing under oil film pressure p at the previous simulation moment, and δ(x,y,t) represents the actual deformation of the bearing at the current simulation moment. t (x,y,t) represents the transient elastic deformation of the bearing at this simulation moment, τ represents the viscoelastic relaxation time of the bearing material, q represents the total number of simulation time steps, and Δt represents the time step size. The elastic deformation of the bearing is calculated using the compliance matrix method; δ F (x i ,y j ) is at the node (x) on the bearing surface i ,y j Radial deformation of G; E (x i ,y j ,x r ,y s ) is the compliance matrix, which physically represents the compliance applied to node (x). r ,y s Force F0(x) per unit size at point ) r ,y s ) makes node (x i ,y j The radial deformation generated by p(x); r ,y s ) is the action on node (x) r ,y s Oil film pressure at ( ); The area of ​​the bearing mesh unit; For heavy-duty bearings, the elastic deformation of the bearing bush has a significant impact on the oil film thickness. Therefore, it is necessary to correct the oil film thickness based on the actual deformation, and then use a multinomial probability density function that approximates a Gaussian distribution to calculate the average oil film thickness. The calculation method is as follows: Among them, h and h T These represent the nominal oil film thickness and the average oil film thickness, respectively; C is the bearing clearance; and e is the bearing average oil film thickness. cc Where θ is the eccentricity and θ is the circumferential angular coordinate. The offset angle is Λ = h / σ, which is the film thickness judgment index, representing the ratio of film thickness to roughness. g is the film thickness judgment ratio, g = Λ / 3. Fifth step, update the viscosity of the lubricating oil; Viscosity is an important bearing lubrication parameter. Under high temperature and pressure, lubricating oil exhibits significant viscosity-pressure and viscosity-temperature effects. Based on the oil film pressure and temperature distributions obtained in the first and third steps, the Roelands formula is used to update and calculate the lubricating oil viscosity. Where, η a To be at ambient temperature T a The oil film viscosity is given by p, where p is the oil film pressure. The calculation of lubricating oil viscosity should meet the following convergence conditions: in, and ζ represents the oil film viscosity obtained at node (i, j, k) in the nth and (n-1)th iterations at the mth time step, respectively; η This represents the convergence tolerance of the oil film viscosity; a recommended value for the convergence tolerance is 1×10⁻⁶. -5 ~1×10 -6 ; Step 6: Calculate the mixed lubrication parameters; Under mixed lubrication conditions, the bearing's supporting reaction force consists of two parts: one is the oil film force composed of oil film pressure, and the other is the rough contact force. The bearing reaction force can be solved by integrating the pressure. in, and These are the components of the oil film force in the x and z directions, respectively. and These are the components of the rough contact force in the x and z directions, respectively, and F is the support reaction force. x With F z These are the components of the supporting reaction force in the x and z directions, respectively; The rough contact pressure is calculated as follows: Where λ is the distribution density of the rough peaks, χ is the radius of the rough peaks, σ is the standard deviation of the overall roughness of the bearing journal surface, E is the equivalent elastic modulus of the contact material, and F 2.5 (Λ) is the mathematical expectation function related to the film thickness assessment index Λ, and its calculation is as follows: The frictional power consumption of the bearing is calculated by the following formula: Where, φ f For shear flow factor, φ fs φ is the shear stress factor. fp Frictional pressure flow factor; φ f φ fs and φ fp The following formula is used for calculation: Lubricating oil leakage flow rate Q at the front and rear faces of the bearing F and Q L Calculated using the following formula: Total outflow Q leak : Q leak =Q F +Q L (32) Among them, v F v is the axial velocity of the oil film on the front face of the bearing. L This represents the axial velocity of the oil film on the rear end face of the bearing.

Images