A gear fatigue life simulation method based on ABAQUS secondary development

Abstract

A gear fatigue life simulation method based on ABAQUS secondary development includes: 1) constructing a three-dimensional geometric model of a spur gear planetary gear train, and obtaining a two-dimensional model of a spur gear planetary gear train by simplification; 2) pre-processing the two-dimensional model of the spur gear planetary gear train; 3) extracting the output variables of the two-dimensional model of the spur gear planetary gear train, and calculating the time-varying friction coefficient of the current gear node; 4) assigning the time-varying friction coefficient of the current gear node to the two-dimensional model of the spur gear planetary gear train, repeating step 3), and constructing a finite element model of a spur gear planetary gear train with a time-varying friction coefficient; 5) in the contact area, selecting a critical plane method based on the gear failure situation, and using the selected critical plane method to solve the fatigue life of each gear node in the finite element model of the spur gear planetary gear train with a time-varying friction coefficient. The present invention simplifies the three-dimensional model into a two-dimensional plane strain model, ensures the accuracy of the mesh, and greatly improves the calculation convergence and efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of gear transmission, and in particular to a gear fatigue life simulation method based on ABAQUS secondary development. Background Art

[0002] Gear transmission is the most widely used mechanical transmission method in modern equipment, with the advantages of high transmission efficiency, compact structure, high reliability and long life. Due to the high manufacturing and installation precision requirements of gears, there are many errors in manufacturing, installation, tooth shape, tooth pitch, etc., and the complexity of the operating environment and working conditions makes it easy for gears to have various contact fatigue failures during operation, such as severe wear, micropitting, pitting, plastic deformation, etc., which affect the working performance and service life of the transmission system. Therefore, how to accurately predict the fatigue life of gears has practical engineering significance.

[0003] Residual stress will be generated when the gear tooth surface and core are hardened. Due to the changes in material fatigue parameters and residual stress levels caused by the hardness gradient, accurate prediction of gear fatigue life is still one of the difficulties. There are many methods for calculating gear fatigue life, but the damage forms of different areas of the gear may be different. There will be large errors in calculating fatigue life based on a certain method. Therefore, it is necessary to find a simulation method that can quickly, accurately and effectively analyze the fatigue life of the tooth surface. Summary of the invention

[0004] The purpose of the present invention is to provide a gear fatigue life simulation method based on ABAQUS secondary development, comprising the following steps:

[0005] 1) Construct a three-dimensional geometric model of the spur gear planetary gear train, simplify the three-dimensional geometric model of the spur gear planetary gear train, obtain a two-dimensional model of the spur gear planetary gear train, and divide the contact area along the involute of the tooth surface.

[0006] 2) Pre-process the two-dimensional model of the spur gear planetary gear train.

[0007] 3) Extract the output variables of the two-dimensional model of the spur gear planetary gear train, and calculate the time-varying friction coefficient of the current gear node through the output variables.

[0008] 4) Assign the time-varying friction coefficient of the current gear node to the two-dimensional model of the spur gear planetary gear train, repeat step 3), and construct a finite element model of the spur gear planetary gear train with a time-varying friction coefficient.

[0009] 5) In the contact area, the critical plane method is selected based on the gear failure situation, and the selected critical plane method is used to solve the fatigue life of each gear node in the finite element model of the spur gear planetary gear train with time-varying friction coefficient.

[0010] Furthermore, the three-dimensional geometric model of the spur gear planetary gear train includes a three-dimensional geometric model of a sun gear, a three-dimensional geometric model of a planetary gear, and a three-dimensional geometric model of a ring gear.

[0011] The two-dimensional model of the spur gear planetary gear train is obtained by taking only the end faces of the gears of the three-dimensional geometric model of the spur gear planetary gear train as the two-dimensional plane model.

[0012] Furthermore, the pre-processing of the two-dimensional model of the spur gear planetary gear train includes meshing, defining material properties, assembly, setting analysis steps and output variables, setting loads and boundary conditions, setting contact properties and constraints, and selecting threads.

[0013] The tangential behavior in the contact properties is set to no friction coefficient.

[0014] Furthermore, the output variables of the two-dimensional model of the spur gear planetary gear train include field output variables and history output variables.

[0015] The field output variables include contact pressure variables, stress variables, strain variables, displacement variables, and force variables.

[0016] The process output variables include resultant force variables, resultant moment variables, and central force displacement variables.

[0017] The step of extracting the output variables of the two-dimensional model of the spur gear planetary gear train and calculating the time-varying friction coefficient of the current gear node through the output variables comprises:

[0018] 3.1) Extract the central force displacement variable and the resultant force variable and calculate the maximum Hertzian contact stress as follows:

[0019]

[0020]

[0021] Where, CFN1 and CFN2 are the resultant force variables of the external and internal meshing intermediate gears in the xy direction, respectively. XN1 and XN2 are the central force displacement variables of the external and internal meshing intermediate gears in the xy direction, respectively. E is the elastic modulus. h is the maximum Hertzian contact stress. F(t) and R(t) are the intermediate functions of the resultant force variable and the central force displacement variable, respectively.

[0022] 3.2) Calculate the time-varying friction coefficient of the current gear node as follows:

[0023]

[0024] f(ξ,P h ,μ0,S)=b1+b4|ξ|P h log10 (μ0)+b5exp(-|ξ|P h log 10 (μ0))+b9exp(S) (4)

[0025] Where P h is the maximum Hertzian contact stress. μ0 is the dynamic viscosity of the lubricant. S is the root mean square of the gear surface roughness. R is the comprehensive curvature radius at the meshing point. b1~b9 are all empirical coefficients. u(t) is the time-varying friction coefficient. f(ξ,P h ,μ0,S) is the intermediate function.

[0026] The entrainment velocity u at the meshing point is as follows:

[0027]

[0028] Where u1 and u2 represent the relative speeds of the driving wheel and the driven wheel respectively.

[0029] The sliding-rolling ratio ξ of the gear contact surface is given by:

[0030]

[0031] Furthermore, when the gear failure condition is tooth surface contact fatigue failure, the selected critical plane methods include BM, FS, and Morrow.

[0032] When the gear failure condition is tooth root bending fatigue failure, the selected critical plane method includes SWT.

[0033] Further, the steps of selecting the critical plane method based on the gear failure condition include:

[0034] 5.1) Construct the mapping relationship between gear failure conditions and the critical plane method.

[0035] 5.1.1) Simulate the current gear failure situation and use the BM, FS, Morrow, and SWT methods to solve the fatigue life of each gear node in the finite element model of the spur gear planetary gear train with time-varying friction coefficient, and compare the solution results with the actual life.

[0036] 5.1.2) The critical plane method with the smallest error between the solution result and the true life and the current gear failure condition are used as a set of mappings.

[0037] 5.1.3) Repeat step 5.1.2) to construct the mapping relationship between different gear failure conditions and the critical plane method.

[0038] 5.2) In the mapping relationship between gear failure conditions and critical plane methods, find the critical plane method corresponding to the current gear failure condition.

[0039] Furthermore, the calculation formula for the fatigue life of each node of the gear in the finite element model of the spur gear planetary gear train with a time-varying friction coefficient is solved by the Morrow critical plane method as follows:

[0040]

[0041] Where Δε is the normal strain amplitude on the critical plane. n,m is the mean stress. f ′ is the fatigue strength coefficient. ε f ′ is the fatigue ductility coefficient. σ res is the residual stress. b is the fatigue strength index. c is the fatigue ductility index. E is the elastic modulus, N f is the fatigue life.

[0042] Furthermore, the BM critical plane method is used to solve the calculation formula of the fatigue life of each node of the gear in the finite element model of the spur gear planetary gear train with time-varying friction coefficient as follows:

[0043]

[0044] In the formula, Δγ max is the maximum shear strain amplitude, S, A, and B are all material constants. Δε is the normal strain amplitude on the critical plane. σ n,m is the mean stress. f ′ is the fatigue strength coefficient. ε f ′ is the fatigue ductility coefficient. σ res is the residual stress. b is the fatigue strength index. c is the fatigue ductility index. E is the elastic modulus, N f is the fatigue life.

[0045] Furthermore, the FS critical plane method is used to solve the calculation formula of the fatigue life of each node of the gear in the finite element model of the spur gear planetary gear train with time-varying friction coefficient as follows:

[0046]

[0047] In the formula, σ max is the maximum normal stress on the critical plane, k is the material constant, σ Y is the yield stress, v e 、v p are the elastic and plastic Poisson’s ratios of the material, respectively. max is the maximum shear strain amplitude, σ f ′ is the fatigue strength coefficient. ε f ′ is the fatigue ductility coefficient. σ res is the residual stress. b is the fatigue strength index. c is the fatigue ductility index. E is the elastic modulus, N f is the fatigue life.

[0048] Furthermore, the SWT critical plane method is used to solve the calculation formula of the fatigue life of each gear node in the finite element model of the spur gear planetary gear train with time-varying friction coefficient as shown below:

[0049]

[0050] In the formula, σ max is the maximum normal stress on the critical plane, σ res is the residual stress. Δε is the normal strain amplitude on the critical plane. σ f ′ is the fatigue strength coefficient. ε f ′ is the fatigue ductility coefficient. b is the fatigue strength index. c is the fatigue ductility index. E is the elastic modulus, N f is the fatigue life.

[0051] The technical effect of the present invention is unquestionable. The present invention simplifies the three-dimensional spur gear planetary gear train into a two-dimensional plane strain model, which ensures the accuracy of the grid while greatly improving the calculation convergence and efficiency.

[0052] The present invention takes into account factors such as tooth surface roughness, stress state, and lubrication characteristics to obtain a time-varying friction coefficient, which is more consistent with the actual situation when the tooth surfaces are in contact and ensures accurate stress / strain components.

[0053] The present invention adopts four critical plane methods to analyze the fatigue life of the tooth surface. Different fatigue life results can be obtained corresponding to failure conditions of different types and positions. The results are more in line with actual engineering and can provide guidance for the optimal design of gear structure and fatigue life reliability and durability. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is the overall flow chart of the simulation method of the present invention;

[0055] Figure 2 This is the assembly diagram of the spur gear planetary gear train;

[0056] Figure 3 is the time-varying friction coefficient of external / internal meshing; Figure 3 (a) is a schematic diagram of the time-varying friction coefficient of external meshing; Figure 3 (b) is a schematic diagram of the time-varying friction coefficient of internal meshing;

[0057] Figure 4 Schematic diagram of stress / strain rotation transformation;

[0058] Figure 5 is the hardness and residual stress distribution diagram of the sun gear;

[0059] Figure 6 This is the result diagram of fatigue life analysis of the sun gear; Figure 6 (a) is the result diagram of fatigue life analysis using Brown-Miller critical plane method; Figure 6 (b) is the result diagram of fatigue life analysis using the Fatemi-Socie critical plane method. DETAILED DESCRIPTION

[0060] The present invention is further described below in conjunction with the embodiments, but it should not be understood that the above subject matter of the present invention is limited to the following embodiments. Without departing from the above technical ideas of the present invention, various substitutions and changes are made according to the common technical knowledge and customary means in the art, which should all be included in the protection scope of the present invention.

[0061] Embodiment 1:

[0062] See also Figures 1 to 6 , a gear fatigue life simulation method based on ABAQUS secondary development, including the following steps:

[0063] 1) Construct a three-dimensional geometric model of the spur gear planetary gear train, simplify the three-dimensional geometric model of the spur gear planetary gear train, obtain a two-dimensional model of the spur gear planetary gear train, and divide the contact area along the involute of the tooth surface.

[0064] 2) Pre-process the two-dimensional model of the spur gear planetary gear train.

[0065] 3) Extract the output variables of the two-dimensional model of the spur gear planetary gear train, and calculate the time-varying friction coefficient of the current gear node through the output variables.

[0066] 4) Assign the time-varying friction coefficient of the current gear node to the two-dimensional model of the spur gear planetary gear train, repeat step 3), and construct a finite element model of the spur gear planetary gear train with a time-varying friction coefficient.

[0067] 5) In the contact area, the critical plane method is selected based on the gear failure situation, and the selected critical plane method is used to solve the fatigue life of each gear node in the finite element model of the spur gear planetary gear train with time-varying friction coefficient.

[0068] Embodiment 2:

[0069] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content is shown in Example 1, further, the spur gear planetary gear train three-dimensional geometric model includes a sun gear three-dimensional geometric model, a planetary gear three-dimensional geometric model, and a ring gear three-dimensional geometric model.

[0070] The two-dimensional model of the spur gear planetary gear train is obtained by taking only the end faces of the gears of the three-dimensional geometric model of the spur gear planetary gear train as the two-dimensional plane model.

[0071] Embodiment 3:

[0072] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of Examples 1 to 2. Furthermore, the pre-processing of the two-dimensional model of the spur gear planetary gear train includes meshing, defining material properties, assembly, setting analysis steps and output variables, setting loads and boundary conditions, setting contact properties and constraints, and selecting threads.

[0073] The tangential behavior in the contact properties is set to no friction coefficient.

[0074] Embodiment 4:

[0075] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of Examples 1 to 3. Furthermore, the output variables of the two-dimensional model of the spur gear planetary gear train include field output variables and history output variables.

[0076] The field output variables include contact pressure variables, stress variables, strain variables, displacement variables, and force variables.

[0077] The process output variables include resultant force variables, resultant moment variables, and central force displacement variables.

[0078] The step of extracting the output variables of the two-dimensional model of the spur gear planetary gear train and calculating the time-varying friction coefficient of the current gear node through the output variables comprises:

[0079] 3.1) Extract the central force displacement variable and the resultant force variable and calculate the maximum Hertzian contact stress as follows:

[0080]

[0081]

[0082] Where, CFN1 and CFN2 are the resultant force variables of the external and internal meshing intermediate gears in the xy direction, respectively. XN1 and XN2 are the central force displacement variables of the external and internal meshing intermediate gears in the xy direction, respectively. E is the elastic modulus. h is the maximum Hertzian contact stress. F(t) and R(t) are the intermediate functions of the resultant force variable and the central force displacement variable, respectively.

[0083] 3.2) Calculate the time-varying friction coefficient of the current gear node as follows:

[0084]

[0085] f(ξ,P h ,μ0,S)=b1+b4|ξ|P h log 10 (μ0)+b5exp(-|ξ|Ph log 10 (μ0))+b9exp(S) (4)

[0086] Where P h is the maximum Hertzian contact stress. μ0 is the dynamic viscosity of the lubricant. S is the root mean square of the gear surface roughness. R is the comprehensive curvature radius at the meshing point. b1~b9 are all empirical coefficients. u(t) is the time-varying friction coefficient. f(ξ,P h ,μ0,S) is the intermediate function.

[0087] The entrainment velocity u at the meshing point is as follows:

[0088]

[0089] Where u1 and u2 represent the relative speeds of the driving wheel and the driven wheel respectively.

[0090] The sliding-rolling ratio ξ of the gear contact surface is given by:

[0091]

[0092] Embodiment 5:

[0093] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of Examples 1 to 4. Further, when the gear failure condition is tooth surface contact fatigue failure, the selected critical plane methods include BM, FS, and Morrow.

[0094] When the gear failure condition is tooth root bending fatigue failure, the selected critical plane method includes SWT.

[0095] Embodiment 6:

[0096] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of embodiments 1 to 5, and further, the step of selecting a critical plane method based on the gear failure condition comprises:

[0097] 5.1) Construct the mapping relationship between gear failure conditions and the critical plane method.

[0098] 5.1.1) Simulate the current gear failure situation and use the BM, FS, Morrow, and SWT methods to solve the fatigue life of each gear node in the finite element model of the spur gear planetary gear train with time-varying friction coefficient, and compare the solution results with the actual life.

[0099] 5.1.2) The critical plane method with the smallest error between the solution result and the true life and the current gear failure condition are used as a set of mappings.

[0100] 5.1.3) Repeat step 5.1.2) to construct the mapping relationship between different gear failure conditions and the critical plane method.

[0101] 5.2) In the mapping relationship between gear failure conditions and critical plane methods, find the critical plane method corresponding to the current gear failure condition.

[0102] Embodiment 7:

[0103] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of Embodiments 1 to 6. Further, the calculation formula for the fatigue life of each node of the gear in the finite element model of a spur gear planetary gear train with a time-varying friction coefficient is solved by using the Morrow critical plane method as follows:

[0104]

[0105] Where Δε is the normal strain amplitude on the critical plane. n,m is the mean stress. f ′ is the fatigue strength coefficient. ε f ′ is the fatigue ductility coefficient. σ res is the residual stress. b is the fatigue strength index. c is the fatigue ductility index. E is the elastic modulus, N f is the fatigue life.

[0106] Embodiment 8:

[0107] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of Embodiments 1 to 7. Further, the calculation formula for the fatigue life of each node of the gear in the finite element model of a spur gear planetary gear train with a time-varying friction coefficient is solved by using the BM critical plane method as shown below:

[0108]

[0109] In the formula, Δγ max is the maximum shear strain amplitude, S, A, and B are all material constants. Δε is the normal strain amplitude on the critical plane. σ n,m is the mean stress. f ′ is the fatigue strength coefficient. ε f ′ is the fatigue ductility coefficient. σ res is the residual stress. b is the fatigue strength index. c is the fatigue ductility index. E is the elastic modulus, N f is the fatigue life.

[0110] Embodiment 9:

[0111] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of embodiments 1 to 8. Further, the calculation formula for the fatigue life of each node of the gear in the finite element model of the spur gear planetary gear train with a time-varying friction coefficient is solved by using the FS critical plane method as shown below:

[0112]

[0113] In the formula, σ max is the maximum normal stress on the critical plane, k is the material constant, σ Y is the yield stress, v e 、v p are the elastic and plastic Poisson’s ratios of the material, respectively. max is the maximum shear strain amplitude, σ f ′ is the fatigue strength coefficient. ε f ′ is the fatigue ductility coefficient. σ res is the residual stress. b is the fatigue strength index. c is the fatigue ductility index. E is the elastic modulus, N f is the fatigue life.

[0114] Embodiment 10:

[0115] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of Embodiments 1 to 9. Further, the calculation formula for the fatigue life of each node of the gear in the finite element model of a spur gear planetary gear train with a time-varying friction coefficient is solved by using the SWT critical plane method as shown below:

[0116]

[0117] In the formula, σ max is the maximum normal stress on the critical plane, σ res is the residual stress. Δε is the normal strain amplitude on the critical plane. σ f ′ is the fatigue strength coefficient. ε f ′ is the fatigue ductility coefficient. b is the fatigue strength index. c is the fatigue ductility index. E is the elastic modulus, N f is the fatigue life.

[0118] Embodiment 11:

[0119] See also Figures 1 to 6 , a gear fatigue life simulation method based on ABAQUS secondary development, including the following steps:

[0120] 1) Construct a three-dimensional geometric model of the spur gear planetary gear train, simplify the three-dimensional geometric model of the spur gear planetary gear train, obtain a two-dimensional model of the spur gear planetary gear train, and divide the contact area along the involute of the tooth surface.

[0121] According to the basic parameters of the gear, such as the number of teeth, module, pressure angle, and modification coefficient, the SOLIDWORKS software is used to draw the three-dimensional model of the spur gear planetary gear train (sun gear-planetary gear-ring gear), generate the *.x_t file format and import it into the ABAQUS finite element software.

[0122] Since the imported gear model is a three-dimensional model, it is not conducive to meshing. Therefore, in ABAQUS, only the end face of the gear is taken as a two-dimensional plane model, and a certain area is divided along the involute of the tooth surface as the contact area.

[0123] 2) Pre-process the two-dimensional model of the spur gear planetary gear train;

[0124] 3) Extract the output variables of the two-dimensional model of the spur gear planetary gear train, and calculate the time-varying friction coefficient of the current gear node through the output variables.

[0125] 4) Assign the time-varying friction coefficient of the current gear node to the two-dimensional model of the spur gear planetary gear train, repeat step 3), and construct a finite element model of the spur gear planetary gear train with a time-varying friction coefficient.

[0126] Change the frictionless coefficient of tangential behavior in the contact properties in 2) to a penalty function (Penalty), and then import the corresponding time-varying friction coefficient into the penalty function table.

[0127] 5) In the contact area, the critical plane method is selected based on the gear failure situation, and the selected critical plane method is used to solve the fatigue life of each gear node in the finite element model of the spur gear planetary gear train with time-varying friction coefficient.

[0128] The fatigue life images of the tooth surface nodes solved by the critical plane method are plotted respectively.

[0129] a) Create a tooth surface display group to extract the tooth surface node number; select the contact area divided in step 1) as the area for solving the tooth surface node fatigue life and create a display group, output the node number information of the display group, use MATLAB programming to extract the node number, and store it in a *.txt file.

[0130] b) Use macro commands to complete the input and output of stress / strain components of each node on the tooth surface; in this step, use PYTHON to write 4 subroutines. The first subroutine is to read the tooth surface node number file and create a path for extracting stress / strain components from the tooth surface nodes; the second subroutine is to set the starting analysis step and the ending analysis step of the tooth surface node in a meshing cycle, and extract the stress / strain components under the tooth surface node path in this analysis step, specifically including S11, S12, S22, E11, E12, E22. If other components need to be extracted, just add content after the program; since the stress / strain components of each analysis step exist separately, the third subroutine is to integrate the stress / strain components of the same type into a file for storage, and obtain 6 stress / strain data summary results; the fourth subroutine is to output the above 6 total stress / strain component data to the specified working path, and output them as e11.rpt, e12rpt, e22.rpt, s11.rpt, s12.rpt, s22.rpt files respectively, and delete the text leading information in the file.

[0131] c) Use Scheme 1, Scheme 2, Scheme 3 and Scheme 4 to calculate the fatigue life of each node on the tooth surface; first, the e11.rpt, e12rpt, e22.rpt, s11.rpt, s12.rpt and s22.rpt files need to be rotated and transformed, with the base circle and tooth profile point as the x direction and the right-hand rule to determine the y direction. The rotation transformation formula is as follows, and the schematic diagram is as follows Figure 4 As shown;

[0132]

[0133] Where: x and σ y is the normal stress in the x / y direction, τ xy is the shear stress, ε x and ε y is the normal strain in the x / y direction, γ xy is the shear strain.

[0134] Then, MATLAB programming is used to implement four schemes. The program needs to input the number of teeth, module, normal pressure angle, tooth surface hardness, tooth surface core hardness, elastic modulus, Poisson's ratio and fatigue parameters in the scheme formula, etc. Figure 5 As shown, 6 total stress / strain files are read, and the fatigue life of the tooth surface node is solved by the Newton-iteration method. The tooth surface node number, x-coordinate, y-coordinate, fatigue life value, and crack angle under four schemes are output as a *.txt file with a total of 5 columns of data.

[0135] Four calculation results are obtained by calculating the four schemes separately, among which some methods are applicable to shear type failure, corresponding to tooth surface contact fatigue failure; some methods are applicable to tensile type failure, corresponding to tooth root bending fatigue failure. It should be noted that the fatigue life solved by the critical plane method is more accurate and needs to be based on experiments. At present, there is no unified and accurate method for calculating the fatigue life of gears, which is related to many factors such as gear materials, geometric structures, and processing technology. Therefore, the present invention provides four methods for calculating the fatigue life of gears. According to the comparison between the test life and the predicted life, it can be obtained that a certain critical plane method is more suitable for predicting the fatigue life of the gear.

[0136] Embodiment 12:

[0137] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content is shown in Example 11, further, the three-dimensional geometric model of the spur gear planetary gear system includes a three-dimensional geometric model of the sun gear, a three-dimensional geometric model of the planetary gear, and a three-dimensional geometric model of the ring gear.

[0138] The two-dimensional model of the spur gear planetary gear train is obtained by taking only the end faces of the gears of the three-dimensional geometric model of the spur gear planetary gear train as the two-dimensional plane model.

[0139] Embodiment 13:

[0140] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of Examples 11 to 12. Furthermore, the pre-processing of the two-dimensional model of the spur gear planetary gear train includes meshing, defining material properties, assembly, setting analysis steps and output variables, setting loads and boundary conditions, setting contact properties and constraints, and selecting threads.

[0141] The tangential behavior in the contact properties is set to no friction coefficient.

[0142] The spur gear planetary gear train model is meshed using ABAQUS finite element software; fine meshing is used in the contact area of ​​the tooth surface, 4 pairs of gear teeth are set in contact for external meshing, 5 pairs of gear teeth are set in contact for internal meshing, and coarse meshing is used for the remaining gears and areas. The mesh type is CPE4R, the mesh size of the gear involute is set to 0.01, the number of layers is set to 20, and it is obtained by scanning along the involute.

[0143] The material properties of the spur gear planetary gear train model are defined using ABAQUS finite element software; the default ABAQUS unit is mm-N-MPa, the elastic modulus of the gear is set to 206000, the Poisson's ratio is set to 0.3, and the material settings of the planetary gear train are the same.

[0144] The spur gear planetary gear train model is assembled using ABAQUS finite element software; in the assembly module, the principle of pure rolling of gears in contact at the nodes is used for external / internal meshing assembly, and then reference coupling points are set at the center of the sun gear, planet gear, and inner gear ring, named sun, planet, and gearring respectively. The spur gear planetary gear train assembly diagram is shown in the figure. Figure 2 shown.

[0145] The analysis steps and output variables are set for the spur gear planetary gear train model using ABAQUS finite element software. In order to ensure the convergence of the planetary gear train, it is necessary to set multiple analysis steps to apply boundary conditions step by step to ensure that the gears are in contact and meshing with each other. A total of three analysis steps are set, specifically:

[0146] Step-1: Turn on large deformation and set the time step size to 1; the purpose is to ensure that the inner and outer meshing gears are in contact with each other. It is necessary to constrain all degrees of freedom of the planetary gears and apply a small rotation angle to the sun gear and the inner ring gear.

[0147] Step-2: Turn on large deformation and set the time step size to 1; the purpose is to facilitate the application of load to the sun gear, release the rotational freedom of the sun gear around the Z axis, keep the planetary gears fixed, apply torque to the sun gear coupling point, and constrain all degrees of freedom with the inner ring gear;

[0148] Step-3: Turn on large deformation, set the time step size to 1, and the time increment to 0.005. If you need to speed up the simulation time, you can set a larger time increment. The purpose is to apply displacement to the planetary gear for gear meshing simulation. Only the arc of rotation of the planetary gear around the Z axis is modified, and the other boundary conditions remain unchanged as in Step-2.

[0149] The field output variables include contact pressure (CSTRESS), stress (S), strain (LE), displacement (U), and force (FORCE); the process output variables include resultant force (CFN), resultant moment (CMT), and center force displacement (XN).

[0150] The contact and constraints of the spur gear planetary gear train model are set by ABAQUS finite element software; the adjacent teeth of the sun gear, planet gear and inner gear ring are tied together by Tie, all teeth of the sun gear are coupled to the reference point sun, all teeth of the planet gear are coupled to the reference point planet, and all teeth of the inner gear ring are coupled to the reference point gearring; set the contact, 4 pairs of teeth are in contact in the external meshing, 5 pairs of teeth are in contact in the internal meshing, the tangential behavior in the contact properties is set to no friction coefficient, and the normal contact is set to hard contact. The two endpoints of the sun gear axis are set to Beam connection, and the coupling point between the sun gear and the planet gear is set to MPC connection.

[0151] The load and boundary conditions are set for the spur gear planetary gear train model by using ABAQUS finite element software; the load is applied in Step-2, the application point is sun, a clockwise torque is applied along the Z axis, and the torque value is set to -4000N·mm; the boundary conditions are set as follows: in Step-1, the sun gear reference point sun is applied to rotate clockwise around the Z axis by -0.003rad, the planetary gear train constrains all degrees of freedom, and the ring gear reference point gearring is applied to rotate clockwise around the Z axis by -0.001rad; in Step-2, the sun gear releases the degrees of freedom around the Z axis, the ring gear remains fixed, and the planetary gear fixes all degrees of freedom; in Step-3, the sun gear releases the degrees of freedom around the Z axis, the ring gear remains fixed, and the planetary gear is hinged to rotate clockwise around the Z axis by -0.3rad.

[0152] Submit the job for calculation; select 16 threads to speed up the simulation calculation.

[0153] Embodiment 14:

[0154] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of Examples 11 to 13. Furthermore, the output variables of the two-dimensional model of the spur gear planetary gear train include field output variables and history output variables.

[0155] The field output variables include contact pressure variables, stress variables, strain variables, displacement variables, and force variables.

[0156] The process output variables include resultant force variables, resultant moment variables, and central force displacement variables.

[0157] The step of extracting the output variables of the two-dimensional model of the spur gear planetary gear train and calculating the time-varying friction coefficient of the current gear node through the output variables comprises:

[0158] 3.1) Extract the central force displacement variable and the resultant force variable, and calculate the maximum Hertz contact stress. First, open the history output in the post-processing ODB file of the planetary gear train model, and only extract the CFN1, CFN2, XN1, and XN2 variables of the external / internal meshing intermediate gear. The formula for the theoretical contact stress of the tooth surface is as follows:

[0159]

[0160]

[0161] Where, CFN1 and CFN2 are the resultant force variables of the external and internal meshing intermediate gears in the xy direction, respectively. XN1 and XN2 are the central force displacement variables of the external and internal meshing intermediate gears in the xy direction, respectively. E is the elastic modulus. his the maximum Hertzian contact stress. F(t) and R(t) are the intermediate functions of the resultant force variable and the central force displacement variable, respectively.

[0162] 3.2) MATLAB calculates the time-varying friction coefficient of the current gear node and imports it into the ABAQUS predefined field; MATLAB programming is used to implement the time-varying friction coefficient as follows

[0163] Show:

[0164]

[0165] f(ξ,P h ,μ0,S)=b1+b4|ξ|P h log 10 (μ0)+b5exp(-|ξ|P h log 10 (μ0))+b9exp(S) (4)

[0166] Where P h is the maximum Hertzian contact stress (GPa). μ0 is the dynamic viscosity of the lubricant (mPa·s). S is the root mean square of the gear surface roughness (μm). R is the comprehensive curvature radius at the meshing point. b1~b9 are all empirical coefficients, b i (i=1,2,...,9)=-8.92,1.03,1.04,-0.35,2.81,-0.10,0.75,-0.39,0.62. u(t) is the time-varying friction coefficient. f(ξ,P h ,μ0,S) is the intermediate function.

[0167] Among them, the entrainment speed (m / s)u at the meshing point is as follows:

[0168]

[0169] Where u1 and u2 represent the relative speeds of the driving wheel and the driven wheel respectively.

[0170] The sliding-rolling ratio ξ of the gear contact surface is given by:

[0171]

[0172] The relative speed of the driving wheel and the driven wheel can be calculated based on the curvature radius and the relative speed of the gear pair according to the geometric relationship.

[0173] Embodiment 15:

[0174] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of Examples 11 to 14. Further, when the gear failure condition is tooth surface contact fatigue failure, the selected critical plane methods include BM, FS, and Morrow.

[0175] When the gear failure condition is tooth root bending fatigue failure, the selected critical plane method includes SWT.

[0176] Embodiment 16:

[0177] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of Embodiments 11 to 15, and further, the step of selecting a critical plane method based on the gear failure condition comprises:

[0178] 5.1) Construct the mapping relationship between gear failure conditions and the critical plane method.

[0179] 5.1.1) Simulate the current gear failure situation and use the BM, FS, Morrow, and SWT methods to solve the fatigue life of each gear node in the finite element model of the spur gear planetary gear train with time-varying friction coefficient, and compare the solution results with the actual life.

[0180] 5.1.2) The critical plane method with the smallest error between the solution result and the true life and the current gear failure condition are used as a set of mappings.

[0181] 5.1.3) Repeat step 5.1.2) to construct the mapping relationship between different gear failure conditions and the critical plane method.

[0182] 5.2) In the mapping relationship between gear failure conditions and critical plane methods, find the critical plane method corresponding to the current gear failure condition.

[0183] Embodiment 17:

[0184] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of Embodiments 11 to 16. Further, the calculation formula for the fatigue life of each node of the gear in the finite element model of the spur gear planetary gear train with a time-varying friction coefficient is solved by the Morrow critical plane method as follows:

[0185]

[0186] Where Δε is the normal strain amplitude on the critical plane. n,m is the mean stress. f ′ is the fatigue strength coefficient. ε f ′ is the fatigue ductility coefficient. σ resis the residual stress. b is the fatigue strength index. c is the fatigue ductility index. E is the elastic modulus, N f is the fatigue life.

[0187] Embodiment 18:

[0188] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of Embodiments 11 to 17. Further, the calculation formula for the fatigue life of each node of the gear in the finite element model of the spur gear planetary gear train with a time-varying friction coefficient is solved by the BM critical plane method as follows:

[0189]

[0190] In the formula, Δγ max is the maximum shear strain amplitude, S, A, and B are all material constants. Δε is the normal strain amplitude on the critical plane. σ n,m is the mean stress. f ′ is the fatigue strength coefficient. ε f ′ is the fatigue ductility coefficient. σ res is the residual stress. b is the fatigue strength index. c is the fatigue ductility index. E is the elastic modulus, N f is the fatigue life.

[0191] Embodiment 19:

[0192] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of Embodiments 11 to 18. Further, the calculation formula for the fatigue life of each node of the gear in the finite element model of the spur gear planetary gear train with a time-varying friction coefficient is solved by the FS critical plane method as follows:

[0193]

[0194] In the formula, σ max is the maximum normal stress on the critical plane, k is the material constant, σ Y is the yield stress, v e 、v p are the elastic and plastic Poisson’s ratios of the material, respectively. max is the maximum shear strain amplitude, σ f ′ is the fatigue strength coefficient. ε f ′ is the fatigue ductility coefficient. σ res is the residual stress. b is the fatigue strength index. c is the fatigue ductility index. E is the elastic modulus, N f is the fatigue life.

[0195] Embodiment 20:

[0196] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of Examples 11 to 19. Further, the calculation formula for the fatigue life of each node of the gear in the finite element model of the spur gear planetary gear train with a time-varying friction coefficient is solved by the SWT critical plane method as follows:

[0197]

[0198] In the formula, σ max is the maximum normal stress on the critical plane, σ res is the residual stress. Δε is the normal strain amplitude on the critical plane. σ f ′ is the fatigue strength coefficient. ε f ′ is the fatigue ductility coefficient. b is the fatigue strength index. c is the fatigue ductility index. E is the elastic modulus, N f is the fatigue life.

[0199] Embodiment 21:

[0200] A gear fatigue life simulation method based on ABAQUS secondary development, the main technical content of which is shown in any one of Examples 11 to 19. Furthermore, the method can be extrapolated to other mechanical parts, such as bearings, splines, etc., and other software can also be used to implement the above functions described in this example to perform finite element fatigue life analysis on these parts.

[0201] Embodiment 22:

[0202] See also Figures 1 to 6 , a gear fatigue life simulation method based on ABAQUS secondary development, including the following steps:

[0203] 1) Establish the geometric model of the spur gear planetary gear train. According to the basic parameters of the gear, such as the number of teeth, module, pressure angle, and displacement coefficient, use SOLIDWORKS software to draw the three-dimensional model of the spur gear planetary gear train (sun gear-planet gear-ring gear), generate the *.x_t file format and import it into the ABAQUS finite element software. Since the imported gear model is a three-dimensional model, it is not conducive to meshing. Therefore, in ABAQUS, only the end face of the gear is taken as a two-dimensional plane model, and a certain area is divided along the involute of the tooth surface as the contact area.

[0204] 2) Complete the pre-processing settings of the spur gear planetary gear train model through ABAQUS finite element software:

[0205] 2-1) The spur gear planetary gear train model is meshed using ABAQUS finite element software; fine meshing is used in the contact area of ​​the tooth surface, 4 pairs of gear teeth are set to contact in the external meshing, 5 pairs of gear teeth are set to contact in the internal meshing, and coarse meshing is used in the remaining gears and areas. The mesh type is CPE4R, the mesh size of the gear involute is set to 0.01, the number of layers is set to 20, and it is obtained by scanning along the involute.

[0206] 2-2) Define the material properties of the spur gear planetary gear train model using ABAQUS finite element software; the default ABAQUS unit is mm-N-MPa, the elastic modulus of the gear is set to 206000, the Poisson's ratio is set to 0.3, and the material settings of the planetary gear train are the same.

[0207] 2-3) Assemble the spur gear planetary gear train model using ABAQUS finite element software; in the assembly module, use the principle of pure rolling of gears in contact at the nodes to perform external / internal meshing assembly, and then set reference coupling points at the center of the sun gear, planet gear, and inner gear ring, named sun, planet, and gearring respectively. The spur gear planetary gear train assembly diagram is shown in Figure 2 shown.

[0208] 2-4) Set the analysis steps and output variables for the spur gear planetary gear train model through ABAQUS finite element software; in order to ensure the convergence of the planetary gear train operation, it is necessary to set multiple analysis steps to apply boundary conditions step by step to ensure that the gears are in contact and meshing with each other. A total of 3 analysis steps are set, specifically:

[0209] Step-1: Turn on large deformation and set the time step size to 1; the purpose is to ensure that the inner and outer meshing gears are in contact with each other. It is necessary to constrain all degrees of freedom of the planetary gears and apply a small rotation angle to the sun gear and the inner ring gear.

[0210] Step-2: Turn on large deformation and set the time step size to 1; the purpose is to facilitate the application of load to the sun gear, release the rotational freedom of the sun gear around the Z axis, keep the planetary gears fixed, apply torque to the sun gear coupling point, and constrain all degrees of freedom with the inner ring gear;

[0211] Step-3: Turn on large deformation, set the time step size to 1, and the time increment to 0.005. If you need to speed up the simulation time, you can set a larger time increment. The purpose is to apply displacement to the planetary gear for gear meshing simulation. Only the arc of rotation of the planetary gear around the Z axis is modified, and the other boundary conditions remain unchanged as in Step-2.

[0212] The field output variables include contact pressure (CSTRESS), stress (S), strain (LE), displacement (U), and force (FORCE); the process output variables include resultant force (CFN), resultant moment (CMT), and center force displacement (XN).

[0213] 2-5) Use ABAQUS finite element software to set contacts and constraints for the spur gear planetary gear train model; the adjacent teeth of the sun gear, planetary gear, and inner gear ring are tied together by Tie, all teeth of the sun gear are coupled to the reference point sun, all teeth of the planetary gear are coupled to the reference point planet, and all teeth of the inner gear ring are coupled to the reference point gearring; set the contact, 4 pairs of teeth in external meshing contact, 5 pairs of teeth in internal meshing contact, the tangential behavior in the contact properties is set to no friction coefficient, and the normal contact is set to hard contact. The two endpoints of the sun gear axis are set to Beam connection, and the coupling point between the sun gear and the planetary gear is set to MPC connection.

[0214] 2-6) Use ABAQUS finite element software to set loads and boundary conditions for the spur gear planetary gear train model; the load is applied in Step-2, the application point is sun, and a clockwise torque is applied along the Z axis, and the torque value is set to -4000N·mm; the boundary conditions are set as follows: in Step-1, the sun gear reference point sun is applied to rotate clockwise around the Z axis by -0.003rad, the planetary gear train constrains all degrees of freedom, and the ring gear reference point gearring is applied to rotate clockwise around the Z axis by -0.001rad; in Step-2, the sun gear releases the degrees of freedom around the Z axis, the ring gear remains fixed, and the planetary gear fixes all degrees of freedom; in Step-3, the sun gear releases the degrees of freedom around the Z axis, the ring gear remains fixed, and the planetary gear is hinged to rotate clockwise around the Z axis by -0.3rad.

[0215] 2-7) Submit the job for calculation; select 16 threads to speed up the simulation calculation.

[0216] 3) Extract the output variables of the spur gear planetary gear train model and use MATLAB programming to obtain the time-varying friction coefficient of the tooth surface:

[0217] 3-1) Extract output variables XN and CFN, and calculate the maximum Hertzian contact stress; In this step, first open the process output in the post-processing ODB file of the planetary gear train model, and only extract the CFN1, CFN2, XN1, and XN2 variables of the external / internal meshing intermediate gears. The formula for the theoretical contact stress of the tooth surface is as follows:

[0218]

[0219]

[0220] Where: E is the comprehensive elastic modulus, Ph is the theoretical Hertzian contact stress.

[0221] 3-2) MATLAB calculates the time-varying friction coefficient and imports it into the ABAQUS predefined field; in this step, MATLAB programming is used to implement the time-varying friction coefficient, and the specific expression is as follows:

[0222]

[0223] Where: ξ is the sliding-rolling ratio of the gear contact surface, P h is the maximum Hertzian contact stress (GPa); μ0 is the dynamic viscosity of the lubricating oil (mPa·s); u is the entrainment velocity at the meshing point (m / s); S is the root mean square of the gear surface roughness (μm); R is the comprehensive curvature radius at the meshing point; b1~b9 are empirical coefficients, bi(i=1,2,...,9)=-8.92,1.03,1.04,-0.35,2.81,-0.10,0.75,-0.39,0.62.

[0224] The above entrainment velocity u and sliding-rolling ratio ξ are expressed as follows:

[0225]

[0226] Among them, u1 and u2 represent the relative speeds of the driving wheel and the driven wheel respectively, which can be calculated based on the curvature radius and the relative speed of the gear pair according to the geometric relationship.

[0227] The time-varying friction coefficient of the external / internal meshing is as follows Figure 3 As shown, Figure 3 a is the time-varying friction coefficient of external meshing, Figure 3 b is the time-varying friction coefficient of internal meshing. The friction-free coefficient of the tangential behavior of the external / internal meshing contact in 2-5) is changed to a penalty function (Penalty), and then the corresponding time-varying friction coefficient is imported into the penalty function table.

[0228] 3-3) Repeat step 3-2) and submit the Job to obtain the finite element model results of the spur gear planetary gear train with a time-varying friction coefficient; in this step, the UFIELD subroutine written in FORTRAN needs to be placed in the Job submitted by ABAQUS to read the predefined field in 3-2), thereby giving the tooth surface a time-varying friction coefficient and obtaining the calculation results.

[0229] 4) Calculate the fatigue life of gear nodes based on ABAQUS and MATLAB and draw images;

[0230] a) Create a tooth surface display group to extract the tooth surface node number; select the contact area divided in step 1) as the area for solving the tooth surface node fatigue life and create a display group, output the node number information of the display group, use MATLAB programming to extract the node number, and store it in a *.txt file.

[0231] b) Use macro commands to complete the input and output of stress / strain components of each node on the tooth surface; In this step, use PYTHON to write 4 subroutines. The first subroutine is to read the tooth surface node number file in step a) and create a path for extracting stress / strain components from the tooth surface nodes; The second subroutine is to set the starting analysis step and the ending analysis step of the tooth surface node in a meshing cycle, and extract the stress / strain components under the tooth surface node path in this analysis step, including S11, S12, S22, E11, E12, E22. If other subroutines need to be extracted Components, just add content at the end of the program; since the stress / strain components of each analysis step exist independently, the third subroutine is to integrate the stress / strain components of the same type into one file for storage, and obtain 6 stress / strain data summary results; the fourth subroutine is to output the above 6 total stress / strain component data to the specified working path, and output them as e11.rpt, e12rpt, e22.rpt, s11.rpt, s12.rpt, s22.rpt files respectively, and delete the text leading information in the file.

[0232] c) Use Scheme 1, Scheme 2, Scheme 3 and Scheme 4 to calculate the fatigue life of each node on the tooth surface; first, the e11.rpt, e12rpt, e22.rpt, s11.rpt, s12.rpt and s22.rpt files need to be rotated and transformed, with the base circle and tooth profile point as the x direction and the right-hand rule to determine the y direction. The rotation transformation formula is as follows, and the schematic diagram is as follows Figure 4 As shown;

[0233]

[0234] Where: x and σ y is the normal stress in the x / y direction, τ xy is the shear stress, ε x and ε y is the normal strain in the x / y direction, γ xy is the shear strain.

[0235] Then, MATLAB programming is used to implement four schemes. The program needs to input the number of teeth, module, normal pressure angle, tooth surface hardness, tooth surface core hardness, elastic modulus, Poisson's ratio and fatigue parameters in the scheme formula, etc. Figure 5As shown, 6 total stress / strain files are read, and the fatigue life of the tooth surface node is solved by the Newton-iteration method. The tooth surface node number, x-coordinate, y-coordinate, fatigue life value, and crack angle under four schemes are output as a *.txt file with a total of 5 columns of data.

[0236] The first scheme uses the following formula to calculate the fatigue life value of each node on the tooth surface:

[0237]

[0238] Where Δε is the normal strain amplitude on the critical plane, σ n,m is the mean stress, σ f ′ is the fatigue strength coefficient, ε f ′ is the fatigue ductility coefficient, b is the fatigue strength index, and c is the fatigue ductility index. E is the elastic modulus, N f is the fatigue life;

[0239] The second scheme uses the following formula to calculate the node fatigue life:

[0240]

[0241] Where: Δγ max is the maximum shear strain amplitude, S, A, and B are material constants, A = 1.65, B = 1.75;

[0242] The third scheme uses the following formula to calculate the node fatigue life:

[0243]

[0244] Where: max is the maximum normal stress on the critical plane, k is the material constant, k = 1, σ Y is the yield stress, v e and v p are the elastic and plastic Poisson's ratios of the material, v e =0.3, v p =0.5;

[0245] The fourth scheme uses the following formula to calculate the node fatigue life:

[0246]

[0247] Finally, the fatigue life values ​​obtained by the above four schemes, that is, the fourth column of data, are extracted separately and named as Life_Morrow.txt, Life_BM.txt, Life_FS.tx, and Life_SWT.txt files respectively.

[0248] d) Submit the job and draw the fatigue life image of the tooth surface node based on the ABAQUS predefined field. In this step, add the predefined field (Predefined Field) in 2-6), select the contact area of ​​the external / internal meshing intermediate gear, select User-defined, and then use FORTRAN to write the UFIELD subroutine to read the Life_Morrow.txt, Life_BM.txt, Life_FS.tx, Life_SWT.txt files. Only the first analysis step needs to be retained in the analysis step, and then select the subroutine in the submitted job. The post-processing results will display the numerical results of the tooth surface nodes; finally, the schematic diagram of the fatigue life of the tooth surface nodes under Scheme 2 and Scheme 3 is given, as shown below: Figure 6 shown.

[0249] The method described in this example can be applied to other mechanical parts, such as bearings, splines, etc., and other software can also be used to implement the above functions described in this example to perform finite element fatigue life analysis on these parts.

[0250] Embodiment 23:

[0251] See also Figures 1 to 6 , a gear fatigue life simulation method based on ABAQUS secondary development, including the following steps:

[0252] 1) Establish the geometric model of the spur gear planetary gear train, use SOLIDWORKS software to generate the three-dimensional model of the spur gear planetary gear train (sun gear-planet gear-ring gear), and import it into ABAQUS finite element software;

[0253] 2) Complete the pre-processing settings of the spur gear planetary gear train model through ABAQUS finite element software:

[0254] 2-1) Use ABAQUS finite element software to mesh the spur gear planetary gear train model;

[0255] 2-2) Define the material properties of the spur gear planetary gear train model using ABAQUS finite element software;

[0256] 2-3) Assemble the spur gear planetary gear train model using ABAQUS finite element software;

[0257] 2-4) Set the analysis steps and output variables for the spur gear planetary gear train model using ABAQUS finite element software;

[0258] 2-5) Set contacts and constraints for the spur gear planetary gear train model using ABAQUS finite element software;

[0259] 2-6) Set loads and boundary conditions for the spur gear planetary gear train model using ABAQUS finite element software;

[0260] 2-7) Submit the job for calculation;

[0261] 3) Extract the output variables of the spur gear planetary gear train model and use MATLAB programming to obtain the time-varying friction coefficient of the tooth surface:

[0262] 3-1) Extract output variables XN and CFN and calculate the maximum Hertzian contact stress;

[0263] 3-2) MATLAB calculates the time-varying friction coefficient and imports it into the ABAQUS predefined field;

[0264] 3-3) Repeat step 3-2) and submit the job to obtain the finite element model results of the spur gear planetary gear train with time-varying friction coefficient;

[0265] 4) Calculate the fatigue life of gear nodes based on ABAQUS and MATLAB and draw images;

[0266] a) Create a tooth surface display group to extract the tooth surface node number;

[0267] b) Use macro commands to complete the input and output of stress / strain components at each node on the tooth surface;

[0268] c) Calculate the fatigue life of each node on the tooth surface using Scheme 1, Scheme 2, Scheme 3 and Scheme 4;

[0269] d) Submit the job and draw the fatigue life image of the tooth surface node based on the predefined field in ABAQUS.

[0270] In step 3-3), the written UFIELD subroutine needs to be placed in the Job submitted by ABAQUS.

[0271] In step a), it is necessary to extract the node coordinate numbers in the display group based on MATLAB and create a node path.

[0272] The macro commands in step b) are written based on PYTHON language, and include a subroutine for creating a node path, a subroutine for extracting stress / strain components within a cycle, a subroutine for integrating stress / strain components, and a subroutine for outputting stress / strain components.

[0273] In step c), the stress / strain components in step b) need to be rotationally transformed.

[0274] The solution 1 in step c) uses the following formula to calculate the node fatigue life:

[0275]

[0276] Where Δε is the normal strain amplitude on the critical plane, σ n,m is the mean stress, σ f ′ is the fatigue strength coefficient, ε f ′ is the fatigue ductility coefficient, σ res is the residual stress, b is the fatigue strength index, c is the fatigue ductility index. E is the elastic modulus, N f is the fatigue life;

[0277] The second scheme uses the following formula to calculate the node fatigue life:

[0278]

[0279] Where: Δγ max is the maximum shear strain amplitude, S, A, and B are material constants, A = 1.65, B = 1.75;

[0280] The third scheme uses the following formula to calculate the node fatigue life:

[0281]

[0282] Where: max is the maximum normal stress on the critical plane, k is the material constant, k = 1, σ Y is the yield stress, v e and v p are the elastic and plastic Poisson's ratios of the material, v e =0.3, v p =0.5;

[0283] The fourth scheme uses the following formula to calculate the node fatigue life:

[0284]

[0285] In step d), a UFIELD subroutine is written in FORTRAN to read the node fatigue life value and submit it to the Job.

Claims

1. A gear fatigue life simulation method based on ABAQUS secondary development, characterized in that: The following steps are involved: 1) Construct a three-dimensional geometric model of a spur gear planetary gear train, simplify the three-dimensional geometric model of the spur gear planetary gear train, obtain a two-dimensional model of the spur gear planetary gear train, and extract the contact area along the involute of the tooth surface; 2) Pre-process the two-dimensional model of the spur gear planetary gear train; 3) Extract the output variables of the two-dimensional model of the spur gear planetary gear train, and calculate the time-varying friction coefficient of the current gear node through the output variables; The output variables of the two-dimensional model of the spur gear planetary gear train include field output variables and process output variables; The field output variables include contact pressure variables, stress variables, strain variables, displacement variables, and force variables; The process output variables include resultant force variable, resultant moment variable, and central force displacement variable; The steps of extracting the output variables of the two-dimensional model of the spur gear planetary gear train and calculating the time-varying friction coefficient of the current gear node through the output variables are as follows: 3.1) Extract the central force displacement variable and the resultant force variable and calculate the maximum Hertzian contact stress as follows: Where, CFN1 and CFN2 are the resultant force variables of the outer and inner meshing intermediate gears in the xy direction, respectively; XN1 and XN2 are the central force displacement variables of the outer and inner meshing intermediate gears in the xy direction, respectively; E is the elastic modulus; P h is the maximum Hertzian contact stress; F(t) and R(t) are the intermediate functions of the resultant force variable and the central force displacement variable, respectively; 3.2) Calculate the time-varying friction coefficient of the current gear node as follows: f(ξ,P h ,μ0,S)=b1+b4|ξ|P h log 10 (μ0)+b5exp(-|ξ|P h log 10 (μ0))+b9exp(S) (4) Where P h is the maximum Hertzian contact stress; μ0 is the dynamic viscosity of the lubricant; S is the root mean square of the gear surface roughness; R is the comprehensive curvature radius at the meshing point; b1~b9 are all empirical coefficients; u(t) is the time-varying friction coefficient; f(ξ,P h ,μ0,S) is the intermediate function; The entrainment velocity u at the meshing point is as follows: In the formula, u1 and u2 represent the relative speed of the driving wheel and the driven wheel respectively; The sliding-rolling ratio ξ of the gear contact surface is given by: 4) assigning the time-varying friction coefficient of the current gear node to the two-dimensional model of the spur gear planetary gear train, repeating step 3), and constructing a finite element model of the spur gear planetary gear train with a time-varying friction coefficient; 5) In the contact area, the critical plane method is selected based on the gear failure situation, and the selected critical plane method is used to solve the fatigue life of each gear node in the finite element model of the spur gear planetary gear train with time-varying friction coefficient.

2. The gear fatigue life simulation method based on ABAQUS secondary development according to claim 1 is characterized in that: The three-dimensional geometric model of the spur gear planetary gear train includes a three-dimensional geometric model of the sun gear, a three-dimensional geometric model of the planetary gear, and a three-dimensional geometric model of the ring gear; The two-dimensional model of the spur gear planetary gear train is obtained by taking only the end faces of the gears of the three-dimensional geometric model of the spur gear planetary gear train as the two-dimensional plane model.

3. The gear fatigue life simulation method based on ABAQUS secondary development according to claim 1 is characterized in that: The pre-processing of the two-dimensional model of the spur gear planetary gear train includes meshing, defining material properties, assembly, setting analysis steps and output variables, setting loads and boundary conditions, setting contact properties and constraints, and selecting threads; The tangential behavior in the contact properties is set to no friction coefficient.

4. The gear fatigue life simulation method based on ABAQUS secondary development according to claim 1 is characterized in that: When the gear failure is tooth surface contact fatigue failure, the selected critical plane methods include BM, FS, and Morrow; When the gear failure condition is tooth root bending fatigue failure, the selected critical plane method includes SWT.

5. The gear fatigue life simulation method based on ABAQUS secondary development according to claim 1 is characterized in that: The steps of selecting the critical plane method based on gear failure conditions include: 5.1) Construct the mapping relationship between gear failure conditions and critical plane method; 5.1.1) Simulate the current gear failure situation and use the BM, FS, Morrow, and SWT methods to solve the fatigue life of each gear node in the finite element model of the spur gear planetary gear train with time-varying friction coefficient, and compare the solution results with the actual life; 5.1.2) The critical plane method with the smallest error between the solution result and the actual life and the current gear failure condition are used as a set of mappings; 5.1.3) Repeat step 5.1.2) to construct the mapping relationship between different gear failure conditions and the critical plane method; 5.2) In the mapping relationship between gear failure conditions and critical plane methods, find the critical plane method corresponding to the current gear failure condition.

6. The gear fatigue life simulation method based on ABAQUS secondary development according to claim 4 is characterized in that: The calculation formula for the fatigue life of each node of the gear in the finite element model of the spur gear planetary gear train with time-varying friction coefficient is solved by the Morrow critical plane method as follows: Where Δε is the normal strain amplitude on the critical plane; σ n,m is the mean stress; σ f ′ is the fatigue strength coefficient; ε f ′ is the fatigue ductility coefficient; σ res is the residual stress; b is the fatigue strength index; c is the fatigue ductility index; E is the elastic modulus, N f is the fatigue life.

7. The gear fatigue life simulation method based on ABAQUS secondary development according to claim 4 is characterized in that: The calculation formula for the fatigue life of each node of the gear in the finite element model of the spur gear planetary gear train with time-varying friction coefficient using the BM critical plane method is as follows: In the formula, Δγ max is the maximum shear strain amplitude, S, A, and B are all material constants; Δε is the normal strain amplitude on the critical plane; σ n,m is the mean stress; σ f ′ is the fatigue strength coefficient; ε f ′ is the fatigue ductility coefficient; σ res is the residual stress; b is the fatigue strength index; c is the fatigue ductility index; E is the elastic modulus, N f is the fatigue life.

8. The gear fatigue life simulation method based on ABAQUS secondary development according to claim 4 is characterized in that: The calculation formula for the fatigue life of each node of the gear in the finite element model of the spur gear planetary gear train with time-varying friction coefficient is solved by the FS critical plane method as follows: In the formula, σ max is the maximum normal stress on the critical plane, k is the material constant, σ Y is the yield stress, v e 、v p are the elastic and plastic Poisson's ratios of the material respectively; Δγ max is the maximum shear strain amplitude, σ f ′ is the fatigue strength coefficient; ε f ′ is the fatigue ductility coefficient; σ res is the residual stress; b is the fatigue strength index; c is the fatigue ductility index; E is the elastic modulus, N f is the fatigue life.

9. The gear fatigue life simulation method based on ABAQUS secondary development according to claim 4 is characterized in that: The calculation formula for the fatigue life of each node of the gear in the finite element model of the spur gear planetary gear train with time-varying friction coefficient using the SWT critical plane method is as follows: In the formula, σ max is the maximum normal stress on the critical plane, σ res is the residual stress; Δε is the normal strain amplitude on the critical plane; σ f ′ is the fatigue strength coefficient; ε f ′ is the fatigue ductility coefficient; b is the fatigue strength index; c is the fatigue ductility index; E is the elastic modulus, N f is the fatigue life.

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