A quantitative evaluation method for gear scuffing failure based on surface topography

Abstract

The present invention belongs to the technical field of gear anti-seizing design, and discloses a method for quantitatively evaluating gear seizing failure based on surface morphology, comprising the following steps: establishing a microscopic thermal elastohydrodynamic lubrication model of a tooth surface under non-Newtonian fluid conditions according to the elastohydrodynamic lubrication theory, and solving the temperature distribution characteristics of the gear; calculating the critical temperature of tooth surface seizing, and determining the gear seizing area; changing multiple influencing parameters of the microscopic thermal elastohydrodynamic lubrication model of each tooth surface, and performing simulation to obtain the gear seizing area under different influencing parameters; using a multiple linear regression method to fit a multiple linear regression equation between the tooth surface seizing area and each influencing parameter; and using experimental data to screen or adjust the obtained multiple linear regression equation until a multiple linear regression equation that meets the fitting conditions is obtained as a quantitative evaluation model for gear seizing failure. The present invention can improve the evaluation accuracy of gear seizing failure.

Description

Technical Field

[0001] The invention relates to a quantitative evaluation method for gear scuffing failure, and belongs to the technical field of gear anti-scuffing design. Background Art

[0002] Gears are key components in power transmission in high-end equipment such as aircraft engines and high-speed rail. Their health is directly related to the safety and reliability of the system. Tooth surface scuffing failure, a typical type of gear damage, can occur with a short period of overload and rapidly spread, causing vibration, noise, and a rapid increase in surface temperature, leading to gear loss of function. Therefore, it is necessary to assess gear scuffing failure in equipment to improve operational reliability.

[0003] Existing methods for assessing tooth surface scuffing failure primarily rely on flash temperature and integral temperature methods. While these methods can determine the temperatures at different gear meshing locations, they rely primarily on empirical formulas and fail to comprehensively consider the influence of multiple factors, making it difficult to accurately assess the scuffing failure process. Furthermore, because the gear scuffing failure process is dependent on multiple factors, including lubricant properties, gear material, and operating conditions, it is currently impossible to accurately determine the instantaneous surface temperature at the time of scuffing failure, making it difficult to intuitively and quantitatively assess tooth surface scuffing. Summary of the Invention

[0004] In order to solve the technical problem that the evaluation methods in the existing technology cannot accurately and quantitatively evaluate gear bonding failure, the present invention proposes a quantitative evaluation method for gear bonding failure based on surface morphology. By comprehensively considering the influence of factors such as thermal effects, non-Newtonian fluid properties and tooth surface roughness, the accuracy of gear bonding failure evaluation is improved.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is: a quantitative assessment method for gear scuffing failure based on surface morphology, comprising the following steps:

[0006] Step 1: Based on the elastohydrodynamic lubrication theory, a microscopic thermal elastohydrodynamic lubrication model of the tooth surface under non-Newtonian fluid conditions is established to solve the temperature distribution characteristics of the gear;

[0007] Step 2: Calculate the critical temperature of tooth surface bonding and determine the gear bonding area based on the gear temperature distribution characteristics and the critical temperature of tooth surface bonding;

[0008] Step 3: Change multiple influencing parameters of the microscopic thermal elastic hydrodynamic lubrication model of each tooth surface and perform simulation to obtain the gear scuffing area under different influencing parameters;

[0009] Step 4: Use the multiple linear regression method to fit the multiple linear regression equation between the tooth surface bonding area and various influencing parameters, and calculate the regression coefficient of each influencing factor based on the least squares method;

[0010] Step 5: Use the experimental data to perform significance test and goodness of fit test on the obtained multiple linear regression equation; if the equation does not meet the significance test and goodness of fit test, screen the influencing parameters or adjust the regression coefficients, repeat the significance test and goodness of fit test until both test criteria are met at the same time, and then use the obtained multiple linear regression equation as the quantitative assessment model for gear scuffing failure to conduct gear scuffing failure assessment.

[0011] In step 1, the established microscopic thermal elastohydrodynamic lubrication model for the tooth surface under non-Newtonian fluid conditions includes the Reynolds equation, the film thickness equation, the viscosity-pressure-viscosity-temperature equation, the density-pressure-density-temperature equation, the load balance equation, and the energy equation.

[0012] In step 1, the calculation method of the gear temperature distribution characteristics is:

[0013] Step 1.1: Determine the Reynolds equation, film thickness equation, viscosity-pressure-viscosity-temperature equation, density-pressure-density-temperature equation, load balance equation, and energy equation;

[0014] Step 1.2: After non-dimensionalizing the above equation, input the pressure and the initial value of the minimum oil film thickness h min and the lubricating oil ambient temperature T0, the multigrid method is used to divide the calculation area into multiple layers of grids with different densities, and the equations to be solved are discretized on each layer of grid. Then, the iterative solution is performed on each layer of grid, and the approximate solution and deviation of the algebraic equations are transferred layer by layer. Finally, the oil film pressure and thickness distribution with the required accuracy is obtained on the densest grid.

[0015] Step 1.3: Taking the oil film pressure and film thickness as known conditions, solve the energy equation of the lubricating film column by column to obtain the temperature distribution on the tooth surface.

[0016] In step 1.1, the Reynolds equation is:

[0017]

[0018] Where, Indicates equivalent parameters, p is the oil film pressure, h is the oil film thickness, v u is the entrainment speed, x is the coordinate variable along the tooth profile direction, ρ * Indicates the equivalent density of lubricating oil;

[0019] The film thickness equation is:

[0020]

[0021] Where h(x) represents the oil film thickness distribution, h0 is the rigid body displacement, R z is the equivalent curvature radius, δ(x) is the elastic deformation, Sa (x) and S b (x) are the roughness functions of gear teeth a and b respectively;

[0022] The viscosity-pressure-viscosity-temperature equation is:

[0023]

[0024] Where η is the viscosity of the lubricating oil, η0 represents the initial viscosity, g is the viscosity-pressure-temperature coefficient, T is the oil film temperature, and T0 is the lubricating oil ambient temperature;

[0025] The density-pressure-temperature equation is:

[0026]

[0027] Where ρ is the density of lubricating oil, ρ0 is the initial density of lubricating oil;

[0028] The load balance equation is:

[0029]

[0030] Where W is the normal load on the tooth surface, and p(x) represents the oil film pressure distribution in the contact area;

[0031] The energy equation is:

[0032]

[0033] Where ρ is the density of the lubricating oil, c is the specific heat capacity of the fluid, k is the thermal conductivity of the fluid, u is the flow velocity in the x direction, ω is the flow velocity in the z direction, and η * is the equivalent viscosity of lubricating oil.

[0034] In step 1.2, the input lubricating oil ambient temperature is the gear body temperature field, and the gear body field temperature is obtained by solving the gear body temperature field using the finite element method. The specific method is:

[0035] Input gear basic parameters and lubricant performance parameters;

[0036] Determine gear thermal analysis boundary adjustments and convection heat transfer coefficients on each surface, and calculate gear friction heat and friction heat flux density;

[0037] The temperature field of the gear body is solved based on the finite element method.

[0038] In step 1.2, the minimum oil film thickness initial value h is entered min The calculation formula is:

[0039]

[0040] Where E' is the comprehensive elastic modulus, W / L is the unit load, α is the viscosity-pressure coefficient, η0 is the initial viscosity of the lubricating oil, and v u represents the suction speed, and R represents the comprehensive curvature radius.

[0041] In step 2, the specific method for determining the gear bonding area according to the gear temperature distribution characteristics and the critical bonding temperature of the tooth surface is:

[0042] According to the gear temperature distribution characteristics, the area of ​​the region with a temperature greater than the gear scuffing critical temperature is calculated and its ratio w to the working tooth surface area is calculated to see whether it is less than 20%. If so, the area is used as the gear scuffing area.

[0043] In step 2, the calculation formula for the critical temperature Ts of tooth surface bonding is:

[0044] T S =80+(0.85+1.4X W )·X L ·(S FZG ) 2 ;

[0045] Among them, X W represents the organizational coefficient, X L Indicates the lubricating oil coefficient, S FZG Indicates the load level at which bonding of the tooth surfaces occurs during the test.

[0046] In step 4, the multivariate linear regression equation between the tooth surface bonding area and various influencing parameters is:

[0047] Y=Xβ+ε;

[0048] Among them, Y is the tooth surface bonding area vector under different states, X is the vector of each influencing factor, ε is the random error vector, and β is the regression coefficient vector of the independent variable;

[0049] In step 5, a significance test is performed by a t-test, and the constructed t-statistic of the t-test is:

[0050]

[0051] Among them, T test represents the t statistic, is the regression coefficient Standard error of the estimate, β j represents the influence coefficient of the jth influencing factor;

[0052] In step 5, R 2 The goodness of fit test is carried out by testing the R 2 The test conditions are:

[0053] |R2 -1|<RU;

[0054] Where RU is the set fitting error, R 2 Represents the fitting parameter, the fitting parameter R 2 The calculation formula is:

[0055]

[0056] RSS is the residual sum of squares, and TSS is the total sum of squares;

[0057] In step 5, the influencing parameters or the adjustment regression coefficients are screened by the stepwise selection method based on the Akaike information criterion; the Akaike information criterion evaluates the quality of the candidate models by calculating the AIC value of each candidate model, and selects the model with the smallest AIC value as the optimal model. The AIC value calculation formula is:

[0058] AIC=-2lnL m +2n;

[0059] Among them, AIC represents the unbiased estimate of KL divergence, L m represents the maximum likelihood function of the model, and n represents the number of model parameters.

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] The present invention proposes a quantitative assessment method for gear bonding failure based on surface morphology. Combining the elastohydrodynamic lubrication theory and the existing gear bonding failure assessment method, simulation data is obtained by comprehensively considering the influence of factors such as thermal effects, non-Newtonian fluid properties and tooth surface roughness. A multivariate linear regression method is used to obtain a regression equation for the tooth surface bonding area and multiple influencing factors. The equation is then tested and adjusted using experimental data, and finally an assessment equation that can quantitatively determine the tooth surface bonding area is obtained. This provides a quantitative assessment method for gear bonding failure and improves the accuracy of the assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 A schematic flow chart of a method for quantitatively evaluating gear abrasion failure based on surface morphology provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are part of the embodiments of the present invention, not all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0064] like Figure 1 As shown, an embodiment of the present invention provides a method for quantitatively evaluating gear abrasion failure based on surface morphology, comprising the following steps:

[0065] Step 1: Based on the elastohydrodynamic lubrication theory, a microscopic thermal elastohydrodynamic lubrication model of the tooth surface under non-Newtonian fluid conditions is established to solve the temperature distribution characteristics of the gear.

[0066] In step 1, the established microscopic thermal elastohydrodynamic lubrication model for the tooth surface under non-Newtonian fluid conditions includes the Reynolds equation, the film thickness equation, the viscosity-pressure-viscosity-temperature equation, the density-pressure-density-temperature equation, the load balance equation, and the energy equation.

[0067] The Reynolds equation is:

[0068]

[0069] Where h is the oil film thickness, p is the oil film pressure, x is the coordinate variable along the tooth profile direction, and v is u is the entrainment velocity, ρ * Indicates the equivalent density of lubricating oil; Represents the equivalent parameter, where the expressions of various related parameters are:

[0070]

[0071] ρ * =[ρ e 'η e (ν b -ν a )+ρ e ν a ] / ν u ; (3)

[0072]

[0073]

[0074] Where ρ is the density of lubricating oil, η is the viscosity of lubricating oil, z is the coordinate variable along the film thickness direction, ρ * and η * They represent the equivalent density and viscosity of the lubricating oil, which are parameters introduced by the non-Newtonian effect of the fluid. a and vb Denote the rotational speeds of gear teeth a and b, respectively, ρ e and η e They represent the density equivalent and viscosity equivalent of lubricating oil respectively.

[0075] Specifically, since the surface roughness changes with time during the gear meshing process, the time-varying term of the surface roughness function is added to the film thickness equation. The film thickness equation considering the surface roughness is:

[0076]

[0077] Where h(x) represents the oil film thickness distribution, h0 is the rigid body displacement, R z is the equivalent curvature radius, δ(x) is the elastic deformation, S a (x) and S b (x) are the roughness functions of gear teeth a and b respectively.

[0078] Specifically, the expression of the roughness function is:

[0079]

[0080] Among them, A a and A b Represent the amplitude of the roughness function, l a and l b represent the wavelength of the roughness function along the x direction.

[0081] Specifically, for high-speed and heavy-loaded gears, the physical and chemical properties of the lubricant will change, and the viscosity-pressure-viscosity-temperature equation is:

[0082]

[0083] Where η is the viscosity of the lubricating oil, η0 represents the initial viscosity of the lubricating oil, g is the viscosity-pressure-temperature coefficient, T is the oil film temperature, and T0 is the ambient temperature of the lubricating oil.

[0084] Specifically, the density-pressure-temperature equation is:

[0085]

[0086] Where ρ is the density of the lubricating oil, ρ0 is the initial density of the lubricating oil, and T0 is the ambient temperature of the lubricating oil.

[0087] Specifically, the load balance equation is:

[0088]

[0089] Where W is the normal load on the tooth surface, and p(x) represents the oil film pressure distribution in the contact area.

[0090] Specifically, the energy equation is:

[0091]

[0092] Where ρ is the density of the lubricating oil, c is the specific heat capacity of the fluid, k is the thermal conductivity of the fluid, u is the flow velocity in the x direction, ω is the flow velocity in the z direction, and η * is the equivalent viscosity of lubricating oil.

[0093] Considering the non-Newtonian fluid properties of the gear lubricant, in this embodiment, the Ree-Erying rheological model is adopted, and its rheological properties can be expressed by the following constitutive equation:

[0094]

[0095] Where τ0 is the characteristic shear stress of non-Newtonian fluid, τ a is the shear stress acting on the surface a of the gear tooth.

[0096] In step 1, the calculation method of the gear temperature distribution characteristics is:

[0097] Step 1.1: Determine the Reynolds equation, film thickness equation, viscosity-pressure-viscosity-temperature equation, density-pressure-density-temperature equation, load balance equation, and energy equation.

[0098] Step 1.2: After non-dimensionalizing the above equation, input the pressure and the initial value of the minimum oil film thickness h min and the lubricating oil ambient temperature T0, the multi-grid method is used to divide the calculation area into multiple layers of grids with different densities, and the equations to be solved are discretized on each layer of grids, and then iteratively solved on each layer of grids. The approximate solutions and deviations of the algebraic equations are transferred layer by layer, and finally the oil film pressure and thickness distribution with the required accuracy are obtained on the densest grid.

[0099] Step 1.3: Taking the oil film pressure and film thickness as known conditions, solve the energy equation of the lubricating film column by column to obtain the temperature distribution on the tooth surface.

[0100] Specifically, if Figure 1 As shown, in step 1.2, the input lubricating oil ambient temperature is the gear body temperature field, and the gear body field temperature is obtained by solving the gear body temperature field using the finite element method. The specific method is: input the basic parameters of the gear and the lubricating oil performance parameters; determine the gear thermal analysis boundary adjustment and the convection heat transfer coefficient of each surface, and calculate the gear friction heat and friction heat flux density; solve the gear body temperature field based on the finite element method.

[0101] In this embodiment, in order to iteratively solve the film thickness, it is necessary to give the minimum film thickness initial value. In step 1.2, the minimum oil film thickness initial value h is input. min The calculation formula is:

[0102]

[0103] Where E' is the comprehensive elastic modulus, W / L is the unit load, α is the viscosity-pressure coefficient, η0 is the initial viscosity of the lubricating oil, and v u represents the suction speed, and R represents the comprehensive curvature radius.

[0104] Step 2: Calculate the critical temperature of tooth surface bonding and determine the gear bonding area based on the gear temperature distribution characteristics and the critical temperature of tooth surface bonding.

[0105] In step 2, the specific method for determining the gear bonding area based on the gear temperature distribution characteristics and the critical bonding temperature of the tooth surface is as follows: based on the gear temperature distribution characteristics, the area of ​​the region with a temperature greater than the critical bonding temperature of the gear is calculated, and the ratio w of the area of ​​the region to the working tooth surface area is calculated to determine whether it is less than 20%. If so, the area is used as the gear bonding area.

[0106] That is, in this embodiment, the actual gear bonding area is obtained by using the quantitative evaluation criteria of the gear bonding failure during simulation. The quantitative evaluation criteria of the gear bonding failure is:

[0107]

[0108] Where, T represents the gear temperature, T s It represents the critical temperature of tooth surface bonding, and w represents the ratio of the area where the temperature is greater than the critical temperature of gear bonding to the area of ​​the working tooth surface.

[0109] The area at which tooth scuffing occurs is determined based on the tooth surface temperature distribution characteristics described in step 1 and the national standard GB / Z 6413.2-2003, "Calculation Method for Scuffing Load Capacity of Cylindrical, Bevel, and Hypoid Gears." Scuffing occurs when the tooth surface temperature exceeds the critical temperature for tooth scuffing. The area at which tooth scuffing fails is determined based on the standard JB / T5664-2007, "Failure Criteria for Heavy-Duty Gears." When the ratio w of the tooth surface scuffing area to the working tooth surface area is ≥ 20%, the gear pair is considered to have failed.

[0110] In step 2, the critical temperature of tooth surface bonding is T s The calculation formula is:

[0111]

[0112] Among them, X W represents the organizational coefficient, X L Indicates the lubricating oil coefficient, S FZG Indicates the load level at which bonding of the tooth surfaces occurs during the test.

[0113] Step 3: Change multiple influencing parameters of the microscopic thermal elastic hydrodynamic lubrication model of each tooth surface and perform simulation to obtain the gear bonding area under different influencing parameters.

[0114] Step 4: Use the multiple linear regression method to fit the multiple linear regression equation between the tooth surface bonding area and various influencing parameters, and calculate the regression coefficient of the influencing factors based on the least squares method.

[0115] In step 4, the multivariate linear regression equation between the tooth surface bonding area and various influencing parameters is:

[0116] y i =β0+β1x i1 +β2x i2 +…+β p x ip +ε i ,i=1,…,n; (21)

[0117] Its matrix expression is:

[0118] Y=Xβ+ε; (22)

[0119] Where Y is the tooth surface bonding area vector under different states, X is the vector of various influencing factors, such as speed, load, non-Newtonian fluid type, and tooth surface roughness, and ε is the random error vector, satisfying E(ε) = 0, var(ε) = σ 2 I, β are regression coefficient vectors; the least squares estimate of the unknown parameter β is:

[0120]

[0121] It has been statistically proven It is an unbiased estimate of β. Therefore, the estimation function of the multiple linear regression equation without bias term is:

[0122]

[0123] Among them, X1...X p Indicates various influencing factors; Represents the regression coefficient of each influencing factor.

[0124] Step 5: Use the experimental data to test the obtained multiple linear regression equation. First, use the t test to test the significance of the multiple linear regression equation, and then use the R 2The multivariate linear regression equation is tested for goodness of fit; if the equation does not meet the significance test and goodness of fit test, the influencing parameters are screened or the regression coefficients are adjusted, and the significance test and goodness of fit test are repeated until the two test criteria are met. The obtained multivariate linear regression equation is then used as a quantitative assessment model for gear scuffing failure to conduct gear scuffing failure assessment.

[0125] Specifically, in step 5, the reliability of the estimate can be determined by performing a significance test on the regression coefficient of the equation through a t-test. In this embodiment, the t-statistic constructed by the t-test is:

[0126]

[0127] Where, T test represents the t statistic, is the regression coefficient The standard error of the estimate, for the influencing factor X j Separately design the null hypothesis H0: β j =0 and the alternative hypothesis is H1: β j ≠ 0. If |T test If | is greater than the critical value, then the alternative hypothesis is accepted. Otherwise, the original hypothesis is accepted, indicating that the influencing factor X j The relationship with the bonding area Y is so small that it can be ignored and should be eliminated.

[0128] Specifically, in step 5, by R 2 The goodness of fit test is carried out by testing the R 2 The test conditions are:

[0129] |R 2 -1|<RU; (26)

[0130] Where RU is the set fitting error, R 2 Represents the fitting parameter, the fitting parameter R 2 The calculation formula is:

[0131]

[0132] RSS is the residual sum of squares, and TSS is the total sum of squares. The expressions are:

[0133]

[0134]

[0135] Fitting parameter R 2 The closer the value of is to 1, the better the fitting effect of the regression equation is. On the contrary, R 2 The closer it is to 0, the worse the fitting effect.

[0136] Furthermore, in step 5, the influencing parameters or the adjusted regression coefficients are screened by the stepwise selection method based on the Akaike information criterion, and the obtained multiple linear regression equation is repeatedly tested for significance and goodness of fit using the experimental data until the optimal regression equation is obtained as the evaluation model; the expression of the Akaike information criterion is:

[0137] AIC=-2lnL m +2n; (30)

[0138] Among them, AIC represents the unbiased estimate of KL divergence, L m represents the maximum likelihood function of the model, and n represents the number of model parameters. The Akaike Information Criterion first evaluates the quality of the model by calculating the AIC value of each candidate model in turn using the test data. The model with the smallest AIC value is then selected as the model with the best combination of model fit and model complexity.

[0139] In summary, the present invention provides a quantitative evaluation method for gear bonding failure based on surface morphology. According to the elastohydrodynamic lubrication theory, a microscopic thermal elastohydrodynamic lubrication model of the tooth surface under non-Newtonian fluid conditions is established, and the gear temperature distribution is calculated using the multi-grid method. Then, the gear bonding area under various influencing parameters is obtained by combining the tooth surface bonding critical temperature simulation, and the multivariate linear regression method is used to fit the multivariate linear regression equation between the tooth surface bonding area and various influencing parameters. Finally, the regression equation is subjected to regression analysis through experimental data. The final regression equation can be used as an evaluation model to predict the quantitative relationship between the tooth surface bonding area and influencing factors such as speed, load, non-Newtonian fluid type and tooth surface roughness, accurately evaluate the gear bonding area, and improve the accuracy of gear bonding evaluation.

[0140] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A quantitative evaluation method for gear scuffing failure based on surface morphology, characterized in that: The following steps are involved: Step 1: Based on the elastohydrodynamic lubrication theory, a microscopic thermal elastohydrodynamic lubrication model of the tooth surface under non-Newtonian fluid conditions is established to solve the temperature distribution characteristics of the gear; Step 2: Calculate the critical temperature of tooth surface bonding and determine the gear bonding area based on the gear temperature distribution characteristics and the critical temperature of tooth surface bonding; Step 3: Change multiple influencing parameters of the microscopic thermal elastic hydrodynamic lubrication model of each tooth surface and perform simulation to obtain the gear scuffing area under different influencing parameters; Step 4: Use the multiple linear regression method to fit the multiple linear regression equation between the tooth surface bonding area and various influencing parameters, and calculate the regression coefficient of each influencing factor based on the least squares method; Step 5: Use the experimental data to perform significance test and goodness of fit test on the obtained multiple linear regression equation; if the equation does not meet the significance test and goodness of fit test, screen the influencing parameters or adjust the regression coefficients, repeat the significance test and goodness of fit test until both test criteria are met at the same time, and then use the obtained multiple linear regression equation as the quantitative assessment model for gear scuffing failure to conduct gear scuffing failure assessment.

2. A method for quantitatively evaluating gear scuffing failure based on surface topography according to claim 1, characterized in that: In step 1, the established microscopic thermal elastohydrodynamic lubrication model for the tooth surface under non-Newtonian fluid conditions includes the Reynolds equation, the film thickness equation, the viscosity-pressure-viscosity-temperature equation, the density-pressure-density-temperature equation, the load balance equation, and the energy equation.

3. A method for quantitatively evaluating gear scuffing failure based on surface topography according to claim 1, characterized in that: In step 1, the calculation method of the gear temperature distribution characteristics is: Step 1.1: Determine the Reynolds equation, film thickness equation, viscosity-pressure-viscosity-temperature equation, density-pressure-density-temperature equation, load balance equation, and energy equation; Step 1.2: After non-dimensionalizing the above equation, input the pressure and the initial value of the minimum oil film thickness h min and the lubricating oil ambient temperature T0, the multigrid method is used to divide the calculation area into multiple layers of grids with different densities, and the equations to be solved are discretized on each layer of grid. Then, the iterative solution is performed on each layer of grid, and the approximate solution and deviation of the algebraic equations are transferred layer by layer. Finally, the oil film pressure and thickness distribution with the required accuracy is obtained on the densest grid. Step 1.3: Taking the oil film pressure and film thickness as known conditions, solve the energy equation of the lubricating film column by column to obtain the temperature distribution of the tooth surface.

4. A method for quantitatively evaluating gear scuffing failure based on surface topography according to claim 3, characterized in that: In step 1.1, the Reynolds equation is: Where, Indicates equivalent parameters, p is the oil film pressure, h is the oil film thickness, v u is the entrainment speed, x is the coordinate variable along the tooth profile direction, ρ * Indicates the equivalent density of lubricating oil; The film thickness equation is: Where h(x) represents the oil film thickness distribution, h0 is the rigid body displacement, R z is the equivalent curvature radius, δ(x) is the elastic deformation, S a (x) and S b (x) are the roughness functions of gear teeth a and b respectively; The viscosity-pressure-viscosity-temperature equation is: Where η is the viscosity of the lubricating oil, η0 represents the initial viscosity, g is the viscosity-pressure-temperature coefficient, T is the oil film temperature, and T0 is the lubricating oil ambient temperature; The density-pressure-temperature equation is: Where ρ is the density of lubricating oil, ρ0 is the initial density of lubricating oil; The load balance equation is: Where W is the normal load on the tooth surface, and p(x) represents the oil film pressure distribution in the contact area; The energy equation is: Where ρ is the density of the lubricating oil, c is the specific heat capacity of the fluid, k is the thermal conductivity of the fluid, u is the flow velocity in the x direction, ω is the flow velocity in the z direction, and η * is the equivalent viscosity of lubricating oil.

5. A method for quantitatively evaluating gear scuffing failure based on surface topography according to claim 3, characterized in that: In step 1.2, the input lubricating oil ambient temperature is the gear body temperature field, and the gear body field temperature is obtained by solving the gear body temperature field using the finite element method. The specific method is: Input gear basic parameters and lubricant performance parameters; Determine gear thermal analysis boundary adjustments and convection heat transfer coefficients on each surface, and calculate gear friction heat and friction heat flux density; The temperature field of the gear body is solved based on the finite element method.

6. A method for quantitatively evaluating gear scuffing failure based on surface topography according to claim 3, characterized in that: In step 1.2, the minimum oil film thickness initial value h is entered min The calculation formula is: Where E' is the comprehensive elastic modulus, W / L is the unit load, α is the viscosity-pressure coefficient, η0 is the initial viscosity of the lubricating oil, and v u represents the suction speed, and R represents the comprehensive curvature radius.

7. A method for quantitatively evaluating gear scuffing failure based on surface morphology according to claim 1, characterized in that: In step 2, the specific method for determining the gear bonding area according to the gear temperature distribution characteristics and the critical bonding temperature of the tooth surface is: According to the gear temperature distribution characteristics, the area of ​​the region with a temperature greater than the gear scuffing critical temperature is calculated and its ratio w to the working tooth surface area is calculated to see whether it is less than 20%. If so, the area is used as the gear scuffing area.

8. A method for quantitatively evaluating gear scuffing failure based on surface topography according to claim 7, characterized in that: In step 2, the critical temperature of tooth surface bonding is T s The calculation formula is: T S =80+(0.85+1.4X W )·X L ·(S FZG ) 2 ; Among them, X W represents the organizational coefficient, X L Indicates the lubricating oil coefficient, S FZG Indicates the load level at which bonding of the tooth surfaces occurs during the test.

9. A method for quantitatively evaluating gear scuffing failure based on surface morphology according to claim 1, characterized in that: In step 4, the multivariate linear regression equation between the tooth surface bonding area and various influencing parameters is: Y=Xβ+ε; Among them, Y is the tooth surface bonding area vector under different states, X is the vector of each influencing factor, ε is the random error vector, and β is the independent variable regression coefficient vector.

10. A method for quantitatively evaluating gear scuffing failure based on surface morphology according to claim 1, characterized in that: In step 5, a significance test is performed by a t-test, and the constructed t-statistic of the t-test is: Among them, T test represents the t statistic, is the regression coefficient Standard error of the estimate, β j represents the influence coefficient of the jth influencing factor; In step 5, R 2 The R 2 The test conditions are: |R 2 -1|<RU; Where RU is the set fitting error, R 2 Represents the fitting parameter, the fitting parameter R 2 The calculation formula is: RSS is the residual sum of squares, and TSS is the total sum of squares; In step 5, the influencing parameters or the adjustment regression coefficients are screened by the stepwise selection method based on the Akaike information criterion; the Akaike information criterion evaluates the quality of the candidate models by calculating the AIC value of each candidate model, and selects the model with the smallest AIC value as the optimal model. The AIC value calculation formula is: <h2 style=";text-align:left;direction:ltr">AIC=-2lnL<h2 style=";text-align:left;direction:ltr"> m <h2 style=";text-align:left;direction:ltr"> +2n; Among them, AIC represents the unbiased estimate of KL divergence, L m represents the maximum likelihood function of the model, and n represents the number of model parameters.

Images