Rolling bearing reliability analysis method considering crystal plasticity and electronic equipment
By constructing crystal plasticity and continuous damage mechanics models, and combining Monte-Carlo sampling and finite element analysis, the problems of high cost and inaccurate results in rolling bearing reliability prediction are solved, and efficient and accurate reliability analysis is achieved.
Patent Information
- Application Number
- CN202511671712.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-14
- Publication Date
- 2026-02-10
AI Technical Summary
Existing technologies for predicting the reliability of rolling bearings require extensive life tests, which are costly and fail to reflect the microscopic impact of batch material variations on reliability, resulting in inaccurate predictions.
A constitutive model based on crystal plasticity and continuous damage mechanics is constructed. By combining Monte-Carlo sampling and finite element analysis, a grain distribution model is established. The evolution of rolling contact fatigue damage is predicted through simulation calculations, and a Weibull distribution map is plotted, enabling reliability analysis without the need for a large number of experiments.
It reduces the cost and time of reliability prediction, improves adaptability to different batches of materials, and provides high accuracy in prediction results, making it suitable for guiding the microstructure design of high-end rolling bearing materials.
Smart Images
Figure CN121502946A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of rolling bearing reliability prediction, specifically to a rolling bearing reliability analysis method and electronic device that takes into account crystal plasticity. Background Technology
[0002] Rolling bearings are the "joints" of rotating machinery and are widely used in key fields such as wind power, machine tools, high-speed rail, and aero engines. Their sudden failure may lead to equipment downtime, production line interruption, or even serious accidents such as fires and plane crashes. In order to avoid sudden bearing failure, it is necessary to analyze the reliability of rolling bearings and calculate their failure probability relative to the number of cycles using the Weibull distribution, so as to predict the service life and failure risk of the bearings.
[0003] Currently, reliability prediction for rolling bearings is primarily based on life tests, followed by the calculation of Weibull distributions using statistical methods to predict reliability. Life tests simulate real-world usage scenarios, applying loads to rolling bearings until failure occurs to examine the pattern of failure over time. Therefore, life tests require significant time and resources to obtain failure data. Furthermore, the Weibull distribution calculated using this method only analyzes life from a macroscopic statistical perspective and cannot reflect the essential impact of batch-to-batch material variations on reliability (such as roughness, grain distribution, and other microstructural characteristics). These microscopic features directly determine crystal plastic behavior (such as dislocation movement and local stress concentration), thus affecting the initiation and propagation of fatigue cracks in the bearing. Summary of the Invention
[0004] The purpose of this invention is to provide a method and electronic device for reliability analysis of rolling bearings considering crystal plasticity that does not require extensive experimentation, has low cost, and improves adaptability to different batches of materials.
[0005] To achieve the above objectives, the present invention adopts the following technical solution:
[0006] A reliability analysis method for rolling bearings considering crystal plasticity includes the following steps:
[0007] S1. Constructing the constitutive model: Construct a constitutive model based on crystal plasticity and continuous damage mechanics, and develop its corresponding UMAT subroutine; establish a representative volume element finite element model, and generate random orientations for different grains, and assign these representative volume elements; apply periodic boundary conditions and cyclic shear loads to obtain shear stress-strain curves; conduct torsional fatigue tests to obtain the shear stress-life curves of the material and obtain the fatigue damage parameters of the target material. S2. Testing materials: Test the corresponding batch of materials to obtain the random distribution range of grain size and the range of friction coefficient; S3. Sampling and establishing a grain distribution model: Set the sampling boundary according to the random distribution range obtained in step S2, and obtain multiple sets of sampled samples through Monte-Carlo sampling, and establish a grain distribution Voronoi model corresponding to different samples. S4. Establish a finite element prediction model: Establish a finite element model of the contact pair between the roller and the raceway, and replace the local contact area model in the original model with the Voronoi model established in step S3 to obtain a finite element prediction model of rolling contact fatigue damage evolution based on grain distribution characteristics. S5. Establish prediction models for different samples: Based on the random distribution range of friction coefficients obtained in step S2, set the corresponding friction coefficients in the model obtained in step S4 to establish prediction models for the evolution of rolling contact fatigue damage for different samples. S6. Observe the damage evolution characteristics: Based on the model established in step S5, apply cyclic rolling contact loads of different magnitudes to observe the damage evolution characteristics. S7. Calculate the maximum contact stress: By establishing a finite element model of the rolling bearing, calculate the maximum contact stress corresponding to different working conditions and input it into the model established in step S5. S8. Draw the Weibull distribution diagram: Calculate the failure probability of rolling contact fatigue life of different samples under different loads, draw the Weibull distribution diagram, and complete the prediction of the reliability of this batch of materials.
[0008] Preferably, the specific process of obtaining fatigue damage parameters in step S1 includes: S11. Establish a crystal plastic constitutive model and couple it with a continuous damage mechanics model to construct a crystal plastic constitutive model coupled with damage accumulation theory. S12. Based on the material constitutive subroutine development function of the finite element analysis software ABAQUS, develop the UMAT subroutine and embed the above model. S13. Fit the material parameters of the target material; S14. Use the open-source software Neper to establish representative volume elements of the target material, and establish a crystal plastic finite element model of the representative volume elements. S15. Apply periodic boundary conditions and shear loads based on the EasyPBC plugin of the finite element analysis software ABAQUS. S16. Input material constitutive parameters; S17. Conduct torsional fatigue tests to determine the material parameters for damage evolution; S18. Conduct simulation calculations to obtain shear stress-strain curves, compare them with torsion test curves, correct and determine constitutive parameters, and obtain a constitutive model based on crystal plasticity and continuous damage mechanics.
[0009] Preferably, the specific process of step S2 for detecting the material includes: detecting the micro-grain distribution characteristics of the corresponding batch of material to obtain the random distribution of the micro-grain size of the batch of material; detecting the surface roughness distribution of the corresponding batch of material and conducting a friction and wear test to obtain the random distribution range of the friction coefficient of the batch of material.
[0010] Preferably, the specific process of sampling and establishing a grain distribution model in step S3 includes: S31. Set the number of samples N, and use the probability density function. Random sample points were selected from the corresponding batch of materials. ; S32. The random sample points selected in step S31 Substitute these values into the function to calculate the function value. ; S33. Based on the function value Determine whether to sample; repeat steps S31-S33 before completing all sampling work. S34. When the sample size reaches the sample size N set in S31, then the sample proportion estimate is... Sample variance And end the sampling; S35. Based on the ABAQUS preprocessing module, and according to the obtained sample grain size, the corresponding model is built using the open-source software Neper, and an INP file is generated and imported into ABAQUS.
[0011] Preferably, the specific process of establishing the finite element prediction model in step S4 includes: further establishing a crystalline plastic finite element model of the roller and raceway contact pair based on the ABAQUS preprocessing module and sample model, and loading cyclic rolling contact load through a subroutine.
[0012] Preferably, the specific process of observing the damage evolution characteristics in step S6 includes: applying different maximum contact stresses according to the rolling bearing operating conditions, performing simulation calculations, obtaining damage evolution results, until the damage extends to the surface; defining the number of cycles corresponding to the damage extending to the surface as the rolling contact fatigue life.
[0013] Preferably, the specific process of drawing the Weibull distribution map in step S8 includes: S81. Calculate the cumulative distribution function F(N) and the failure probability density function f(N): , , in, The number of loops. For scale parameters, For shape parameters;
[0014] S82. Calculate the failure probability corresponding to each fatigue life value: , in, The order in which lifespan groups are sorted by size, where n is the total number of lifespan data samples; S83. Perform parameter fitting using the linearized Weibull equation, employing the least squares method: , S84. Calculate the bearing industry standard reliability index, i.e., the life L corresponding to a 10% failure probability. 10 : , S85. Finally, draw the Weibull distribution map.
[0015] An electronic device includes a memory and a processor, wherein a computer program is stored in the memory, and the processor executes the computer program to implement any step in any of the above-described methods for reliability analysis of rolling bearings considering crystal plasticity.
[0016] The beneficial effects of this invention are:
[0017] The rolling bearing reliability analysis method proposed in this invention does not require a large number of life tests to simulate and predict the bearing's life, which can greatly reduce the test cost and time cost of reliability prediction, thereby greatly improving the prediction efficiency.
[0018] The method proposed in this invention takes into account the essential source of reliability, namely the randomness of microstructure and surface processing, thereby enabling reliability prediction for different batches of materials. The reliability analysis method proposed in this invention has high batch adaptability, and the prediction results still have good accuracy when facing different batches of materials. In application scenarios with high batch consistency requirements, such as materials for high-end rolling bearings, it has high predictive adaptability.
[0019] The method proposed in this invention can simultaneously study the impact of random distribution of microstructure on reliability under different operating conditions during the process of predicting bearing reliability, and thus has guiding significance for the design of microstructure of high-reliability rolling bearing materials. Attached Figure Description
[0020] Figure 1 This is an overall flowchart of the present invention; Figure 2 This is a logic diagram of the Monte-Carlo sampling method of the present invention; Figure 3 This is a local grain distribution diagram of the raceway contact pair in different sample groups of the present invention; Figure 4 This is a flowchart of the material parameter acquisition process for the present invention; Figure 5 This is a representative volume element model of the present invention; Figure 6 This is a diagram of the shear stress-strain curve of the present invention; Figure 7 This is the finite element model of the raceway contact pair of the present invention; Figure 8 The damage and spalling corresponding to the maximum contact stress of 1600 MPa in this invention; Figure 9 This is the Weibull distribution diagram of the present invention. Detailed Implementation
[0021] The following is a further explanation of the present invention in conjunction with specific embodiments, such as... Figure 1 As shown, this embodiment is a reliability analysis method for rolling bearings considering crystal plasticity, including the following steps: S1. Constructing the constitutive model: The specific process includes: S11. Establish a crystal plastic constitutive model and couple it with a continuous damage mechanics model to construct a crystal plastic constitutive model coupled with damage accumulation theory; the coupling method is as follows: a) Calculate the velocity gradient tensor, expressed as: , in, Let be the derivative of the deformation gradient tensor with respect to time; It is the inverse of the deformation gradient tensor.
[0022] b) The deformation gradient is decomposed into two parts: elastic and plastic components, expressed as follows: , in, The elastic deformation gradient; This represents the plastic deformation gradient.
[0023] c) The velocity gradient, tension tensor, and rotation tensor are also divided into elastic and plastic components, expressed as follows: , ,
[0024] d) Assuming that all plastic deformation originates from dislocation slip, the plastic velocity gradient... It is calculated from the shear rate of dislocation slip, and the expression is: , , , in, It is a slip system; The number of slip systems; For slip system The plastic shear rate; and They are the sliding surfaces The normal and tangential unit vectors; and These are the symmetric and asymmetric components of the plastic gradient, respectively. and These are the symmetric and asymmetric components of the Schmid tensor, respectively.
[0025] e) The plastic shear rate model is a nonlinear kinematic hardening model. Damage parameters are embedded in this model to introduce the effect of damage. The expression is as follows: , in, The sectional shear stress (RSS) after damage; For the back stress of the slip system; denoted as σs, where σs is the strength of the slip system
[0026] f) The strength calculation expression for the slip system is: , , , in, It is the hardening modulus of the slip system (including self-hardening and latent hardening). Represents a slip system; The total shear rate of the total slip system; and Material coefficient; Kronecker symbol; To provide saturated anti-slip resistance stress; This represents the initial slip resistance stress.
[0027] g) The expression for calculating RSS is: ,
[0028] , in, This is the second Piola-Kirchoff stress; This represents the local crystal anisotropic stiffness matrix; Let be the Green's strain tensor.
[0029] h) M50 steel has a cubic structure, therefore its stiffness matrix expression is: , ,
[0030] i) In the crystal plastic constitutive model, RSS is the main driving force for damage evolution. Therefore, this patent proposes a damage evolution theory based on RSS, expressed as follows: , , in, The maximum RSS in a cyclic load; The maximum cumulative plastic shear strain increment under one cyclic load; and is the material coefficient for the fatigue damage evolution model; E is Young's modulus; N is the number of load cycles.
[0031] S12. Based on the material constitutive subroutine development function of the finite element analysis software ABAQUS, develop the UMAT subroutine and embed the above model. S13. Fit the material parameters of the target material; the process is as follows: Figure 4 As shown; S14. Using the open-source software Neper, establish representative volume elements of the target material, and build a crystalline plastic finite element model of the representative volume elements. The established model is as follows: Figure 5 As shown; S15. Apply periodic boundary conditions and shear loads based on the EasyPBC plugin of the finite element analysis software ABAQUS. S16. Input material constitutive parameters; S17. Conduct torsional fatigue tests to determine the material parameters for damage evolution; S18. Conduct simulation calculations to obtain shear stress-strain curves, compare them with torsion test curves, and correct and determine constitutive parameters, such as... Figure 6 As shown, a constitutive model based on crystal plasticity and continuous damage mechanics is obtained.
[0032] S2. Testing materials: Detect the micro-grain distribution characteristics of the corresponding batch of materials to obtain the random distribution of micro-grain size of the batch of materials; detect the surface roughness distribution of the corresponding batch of materials, and conduct friction and wear tests to obtain the random distribution range of the friction coefficient of the batch of materials.
[0033] S3. Sampling and establishing a grain distribution model: Based on the random distribution range obtained in step S2, set sampling boundaries and obtain multiple sets of samples using Monte Carlo sampling, then establish Voronoi models of grain distribution corresponding to different samples; for example... Figure 2 As shown, the specific process includes: S31. Set the number of samples N, and use the probability density function. Random sample points were selected from the corresponding batch of materials. ; S32. The random sample points selected in step S31 Substitute these values into the function to calculate the function value. ; S33. Based on the function value Determine whether to sample; repeat steps S31-S33 before completing all sampling work. S34. When the sample size reaches the sample size N set in S31, then the sample proportion estimate is... Sample variance And end the sampling; In this embodiment, no fewer than 10 groups of samples are extracted using this method, as shown in Table 1.
[0034] Table 1 Sampling Results Group Average grain size D (μm) Number of grains N coefficient of friction C 1 14.4 1470 0.191 2 14.3 1490 0.159 3 13.6 1640 0.098 4 13.5 1670 0.194 5 12.2 2040 0.033 6 10 3050 0.160 7 9.12 3680 0.183 8 6.79 6630 0.086 9 5.75 9250 0.192 10 5.57 9870 0.030
[0035] S35. Based on the ABAQUS preprocessing module, and according to the obtained sample grain size, the corresponding model is built using the open-source software Neper, and an INP file is generated and imported into ABAQUS.
[0036] S4. Establish a finite element prediction model: Establish a finite element model of the contact pair between the roller and the raceway, and replace the local contact area model in the original model with the Voronoi model established in step S3 to obtain a finite element prediction model of rolling contact fatigue damage evolution based on grain distribution characteristics.
[0037] Further, based on the ABAQUS preprocessing module and sample model, a crystalline plastic finite element model of the roller and raceway contact pair was established, and cyclic rolling contact loads were applied through a subroutine, such as... Figure 7 As shown.
[0038] S5. Establish prediction models for different samples: Based on the random distribution range of friction coefficients obtained in step S2, set the corresponding friction coefficients in the model obtained in step S4 to establish prediction models for the evolution of rolling contact fatigue damage for different samples.
[0039] S6. Observe the damage evolution characteristics: Based on the model established in step S5, apply cyclic rolling contact loads of different magnitudes to observe the damage evolution characteristics.
[0040] Based on the rolling bearing operating conditions, different maximum contact stresses were applied, and simulation calculations were performed to obtain the damage evolution results until the damage extended to the surface. The results corresponding to 1600 MPa are as follows. Figure 8 As shown; the number of cycles corresponding to the damage extending to the surface is defined as the rolling contact fatigue life.
[0041] Record the number of rolling contact load cycles that extend to the surface. The lifetime at this point is the lifetime corresponding to rolling contact fatigue pitting, as shown in Table 2.
[0042] Table 2. Fatigue life of samples under different loads Group Average grain size D (μm) coefficient of friction C 1000 (MPa) 1600 (MPa) 2000 (MPa) 2500 (MPa) 1 14.4 0.191 7.12E13 5.85E10 9.85E7 1.85E7 2 14.3 0.159 1.50E14 7.92E10 1.67E8 6.62E7 3 13.6 0.098 1.14E14 1.38E10 2.73E8 5.70E7 4 13.5 0.194 1.77E14 1.41E11 1.24E8 4.46E7 5 12.2 0.033 1.01E14 3.89E10 1.94E9 3.70E7 6 10 0.160 1.10E13 9.96E10 1.54E8 4.31E7 7 9.12 0.183 1.25E13 7.21E10 4.43E7 4.56E7 8 6.79 0.086 2.23E14 6.70E10 1.89E8 5.34E7 9 5.75 0.192 1.46E13 8.57E10 5.92E8 4.13E7 10 5.57 0.030 6.99E13 7.54E10 1.23E8 2.50E7
[0043] S7. Calculate the maximum contact stress: By establishing a finite element model of the rolling bearing, calculate the maximum contact stress corresponding to different working conditions and input it into the model established in step S5.
[0044] S8. Draw the Weibull distribution diagram: Calculate the failure probability of rolling contact fatigue life for different samples under different loads, draw the Weibull distribution diagram, and predict the reliability of this batch of materials. The specific process includes: S81. Calculate the cumulative distribution function and the failure probability density function: , , in, The number of loops. For scale parameters, For shape parameters; S82. Calculate the failure probability corresponding to each fatigue life value: , in, The order in which lifespan groups are sorted by size, where n is the total number of lifespan data samples; S83. Perform parameter fitting using the linearized Weibull equation, employing the least squares method: , S84. Calculate the bearing industry standard reliability index, i.e., the lifespan corresponding to a 10% failure probability: , S85. Finally, draw the Weibull distribution map. The final Weibull distribution map is as follows: Figure 9 As shown.
[0045] The rolling bearing life under the same working conditions was calculated using the commercial software ROMAX, and the results were compared with those calculated by this method. The comparison results are shown in Table 3, and the error is within 10%.
[0046] Table 3 Comparison of lifetime between this model and Romax Maximum contact stress <![CDATA[L 10 Lifespan (in this model) <![CDATA[L 10 Lifespan (Romax) error 1600 MPa 1.297E10 1.42E10 8.66%
[0047] The above description is merely a further explanation of the present invention in conjunction with specific embodiments. All descriptions made do not imply any limitation on the scope of protection of the present invention. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A reliability analysis method for rolling bearings considering crystal plasticity, characterized in that, Includes the following steps: S1. Constructing the constitutive model: Construct a constitutive model based on crystal plasticity and continuous damage mechanics, and develop its corresponding UMAT subroutine; establish a representative volume element finite element model, and generate random orientations for different grains, and assign these representative volume elements; apply periodic boundary conditions and cyclic shear loads to obtain shear stress-strain curves; conduct torsional fatigue tests to obtain the shear stress-life curves of the material and obtain the fatigue damage parameters of the target material. S2. Testing materials: Test the corresponding batch of materials to obtain the random distribution range of their grain size and the range of their friction coefficient; S3. Sampling and establishing a grain distribution model: Set the sampling boundary according to the random distribution range obtained in step S2, and obtain multiple sets of sampled samples through Monte-Carlo sampling, and establish a grain distribution Voronoi model corresponding to different samples. S4. Establish a finite element prediction model: Establish a finite element model of the contact pair between the roller and the raceway, and replace the local contact area model in the original model with the Voronoi model established in step S3 to obtain a finite element prediction model of rolling contact fatigue damage evolution based on grain distribution characteristics. S5. Establish prediction models for different samples: Based on the random distribution range of friction coefficients obtained in step S2, set the corresponding friction coefficients in the model obtained in step S4 to establish prediction models for the evolution of rolling contact fatigue damage for different samples. S6. Observe the damage evolution characteristics: Based on the model established in step S5, apply cyclic rolling contact loads of different magnitudes to observe the damage evolution characteristics. S7. Calculate the maximum contact stress: By establishing a finite element model of the rolling bearing, calculate the maximum contact stress corresponding to different working conditions and input it into the model established in step S5. S8. Draw the Weibull distribution diagram: Calculate the failure probability of rolling contact fatigue life of different samples under different loads, draw the Weibull distribution diagram, and complete the prediction of the reliability of this batch of materials.
2. The rolling bearing reliability analysis method considering crystal plasticity according to claim 1, characterized in that: The specific process of obtaining fatigue damage parameters in step S1 includes: S11. Establish a crystal plastic constitutive model and couple it with a continuous damage mechanics model to construct a crystal plastic constitutive model coupled with damage accumulation theory. S12. Based on the material constitutive subroutine development function of the finite element analysis software ABAQUS, develop the UMAT subroutine and embed the above model. S13. Fit the material parameters of the target material; S14. Use the open-source software Neper to establish representative volume elements of the target material, and establish a crystal plastic finite element model of the representative volume elements. S15. Apply periodic boundary conditions and shear loads based on the EasyPBC plugin of the finite element analysis software ABAQUS. S16. Input material constitutive parameters; S17. Conduct torsional fatigue tests to determine the material parameters for damage evolution; S18. Conduct simulation calculations to obtain shear stress-strain curves, compare them with torsion test curves, correct and determine constitutive parameters, and obtain a constitutive model based on crystal plasticity and continuous damage mechanics.
3. The rolling bearing reliability analysis method considering crystal plasticity according to claim 2, characterized in that: The specific process of step S2 for detecting materials includes: detecting the micro-grain distribution characteristics of the corresponding batch of materials to obtain the random distribution of the micro-grain size of the batch of materials; detecting the surface roughness distribution of the corresponding batch of materials and conducting friction and wear tests to obtain the random distribution range of the friction coefficient of the batch of materials.
4. The rolling bearing reliability analysis method considering crystal plasticity according to claim 3, characterized in that: The specific process of sampling and establishing the grain distribution model in step S3 includes: S31. Set the number of samples and use the probability density function. Random sample points were selected from the corresponding batch of materials. ; S32. The random sample points selected in step S31 Substitute these values into the function to calculate the function value. ; S33. Based on the function value Determine whether to sample; repeat steps S31-S33 before completing all sampling work. S34. When the sample size reaches the sample size N set in S31, then the sample proportion estimate is... Sample variance And end the sampling; S35. Based on the ABAQUS preprocessing module, and according to the obtained sample grain size, the corresponding model is built using the open-source software Neper, and an INP file is generated and imported into ABAQUS.
5. The rolling bearing reliability analysis method considering crystal plasticity according to claim 4, characterized in that: The specific process of establishing the finite element prediction model in step S4 includes: further establishing a crystalline plastic finite element model of the roller and raceway contact pair based on the ABAQUS preprocessing module and sample model, and loading cyclic rolling contact load through a subroutine.
6. The rolling bearing reliability analysis method considering crystal plasticity according to claim 5, characterized in that: The specific process of observing the damage evolution characteristics in step S6 includes: applying different maximum contact stresses according to the rolling bearing operating conditions, performing simulation calculations, obtaining damage evolution results, until the damage extends to the surface; defining the number of cycles corresponding to the damage extending to the surface as the rolling contact fatigue life.
7. The rolling bearing reliability analysis method considering crystal plasticity according to claim 6, characterized in that: The specific process of drawing the Weibull distribution map in step S8 includes: S81. Calculate the cumulative distribution function F(N) and the failure probability density function f(N): ， ， in, The number of loops. For scale parameters, For shape parameters; S82. Calculate the failure probability corresponding to each fatigue life value: ， in, The order in which lifespan groups are sorted by size, where n is the total number of lifespan data samples; S83. Parametric fitting is performed using the linearized Weibull equation, with the least squares method as the fitting method: ， S84. Calculate the bearing industry standard reliability index, i.e., the life L corresponding to a 10% failure probability. 10 : ， S85. Finally, draw the Weibull distribution map.
8. An electronic device, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements any step in the rolling bearing reliability analysis method considering crystal plasticity as described in any one of claims 1-7.
9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a computer processor, implements any step in the rolling bearing reliability analysis method considering crystal plasticity as described in any one of claims 1-7.