High load roller bearing structure and material fatigue strength optimization and performance evaluation method

Abstract

The application discloses a high-load roller bearing structure and material fatigue strength optimization and performance evaluation method, and relates to the technical field of bearing design and manufacturing. The method comprises the following steps: obtaining structure geometric parameters, heat treatment process parameters and chemical composition data of the bearing; calculating the hardening layer depth, surface hardness and residual stress distribution based on physical metallurgical rules; converting the microstructure features into the contact fatigue limit and stress correction factor; establishing a slice method contact mechanics model to solve the contact load distribution; taking the structure geometric parameters and heat treatment process parameters as double design variables, and taking the maximum fatigue life and the minimum heat treatment process cost as double objectives to construct a multi-objective optimization function; solving the Pareto optimal solution set by using a non-dominated sorting genetic algorithm; and evaluating the candidate schemes and generating an optimization report. The application solves the technical problem that the structure design and the heat treatment process are mutually separated and cannot be optimized in a cooperative manner in the prior art.

Description

Technical Field

[0001] This application relates to the field of bearing design and manufacturing technology, and in particular to methods for optimizing the fatigue strength of high-load roller bearing structures and materials and evaluating their performance. Background Technology

[0002] High-load roller bearings are widely used in major equipment fields such as wind power generation, aerospace, and rail transportation. They operate under heavy-load, high-speed, and alternating load conditions, and their fatigue life directly determines the reliability and maintenance cost of the entire equipment. As equipment develops towards higher power density and lighter weight, the service load of roller bearings is constantly increasing, and the peak contact stress is approaching the contact fatigue limit of the material. Fatigue failure is becoming increasingly prominent, becoming a key bottleneck restricting the improvement of the reliability of major equipment.

[0003] Traditional roller bearing design methods typically separate structural design from heat treatment processes, lacking a synergistic matching mechanism. On the one hand, structural design focuses on the impact of geometric parameters such as roller generatrix shaping, crown, and clearance on contact stress distribution, aiming to reduce edge stress concentration, but it cannot match the strength and toughness limits of the material's microstructure. On the other hand, heat treatment process design focuses on the impact of process parameters such as carburizing, quenching, and tempering on microstructure characteristics such as hardened layer depth, surface hardness, and residual stress, aiming to improve the surface strength and toughness of the material, but it cannot adapt to the stress distribution differences caused by structural geometry. This design mode, where "geometric optimization" and "material strengthening" are mutually exclusive, makes it difficult to achieve a synergistic match between structure and material, resulting in the actual fatigue life of the bearing being significantly lower than the theoretical design value, and failing to fully realize the material's performance potential.

[0004] In addition, existing optimization methods often adopt single-objective optimization, such as minimizing contact stress or maximizing fatigue life, without comprehensively considering the energy consumption, time, and material consumption of the heat treatment process. As a result, the optimization results cannot be directly applied to industrial production due to excessive cost or poor process feasibility.

[0005] A search of existing technologies revealed no synergistic optimization involving structural geometry and heat treatment processes, nor a multi-objective optimization system that balances fatigue performance and manufacturing costs. Therefore, there is an urgent need for a design method for high-load roller bearings that can achieve synergistic optimization of structural geometric parameters and heat treatment process parameters while considering both fatigue performance and manufacturing costs. Summary of the Invention

[0006] The purpose of this application is to provide a method for optimizing the fatigue strength and performance evaluation of the structure and materials of high-load roller bearings. This addresses the technical problems in existing technologies where structural design and heat treatment processes are disconnected, making synergistic optimization impossible, and where existing optimization methods neglect process costs, hindering the industrial application of the optimization results.

[0007] In view of the above technical problems, this application provides a method for optimizing the fatigue strength of high-load roller bearing structure and materials and evaluating its performance.

[0008] A first aspect of this application provides a method for optimizing the fatigue strength and performance evaluation of the structure and materials of high-load roller bearings, the method comprising:

[0009] Obtain the basic parameters of the target high-load roller bearing, including structural geometric parameters and heat treatment process parameters;

[0010] Obtain chemical composition data of the target high-load roller bearing material, the chemical composition data being used to determine the material's elastic modulus and yield strength;

[0011] Based on the physical metallurgical principles of heat treatment hardening and residual stress formation, the microstructure characteristics of the material after heat treatment are calculated using the chemical composition data and heat treatment process parameters. The microstructure characteristics include the hardened layer depth, surface hardness, and the distribution of residual stress along the layer depth.

[0012] Based on the correspondence between microstructure and fatigue performance, the microstructure characteristics are transformed into material fatigue performance parameters, which include contact fatigue limit and stress correction factor.

[0013] The fatigue performance parameters of the material are input into the contact mechanics model of the roller bearing. The contact mechanics model of the roller bearing discretizes the roller into multiple slices. Based on the elastic deformation coordination relationship, the deformation coupling matrix between the slices is established. The contact load distribution and equivalent contact stress are obtained by iterative solution method.

[0014] A multi-objective optimization function is constructed, with the structural geometric parameters as the first design variable, the heat treatment process parameters as the second design variable, the high-load roller bearing fatigue life calculated based on the material fatigue performance parameters and the contact load distribution as the first optimization objective, and the heat treatment process cost calculated based on the heat treatment process parameters included in the second design variable as the second optimization objective.

[0015] Using the multi-objective optimization function as the fitness evaluation criterion, a non-dominated sorting genetic algorithm is used to iteratively evolve the first design variable and the second design variable, and output the Pareto optimal solution set that reflects the synergistic effect of structural geometry and heat treatment process;

[0016] The candidate solutions in the Pareto optimal solution set are substituted into the roller bearing contact mechanics model to calculate the fatigue life prediction value corresponding to the solution, and an evaluation report containing a comparison of performance before and after optimization is generated.

[0017] One or more technical solutions provided in this application have at least the following technical effects or advantages:

[0018] This application achieves synergistic optimization of structural geometry and heat treatment processes. For the first time, it incorporates structural geometric parameters and heat treatment process parameters as parallel design variables into the same optimization framework. A quantitative relationship between process parameters and microstructure is established through a physical metallurgical model, and a quantitative relationship between geometric parameters and stress distribution is established through a contact mechanics model. This solves the technical problem of the separation between "geometric optimization" and "material strengthening" in traditional design, making the actual fatigue life of the bearing close to the theoretical design value. A complete mapping chain from process parameters to fatigue performance is established. Based on physical metallurgical laws such as Fick's diffusion law, the JMA phase transformation kinetic equation, and thermo-elastic-plastic constitutive relations, a quantitative mapping relationship of "heat treatment process parameters → microstructure characteristics → material fatigue performance parameters" is constructed. This allows the influence of process parameters such as carburizing temperature and quenching cooling rate on contact fatigue limit and stress correction factors to be entered into the optimization model in a calculable form. The accuracy of contact stress analysis is improved. Based on the traditional slice-method contact mechanics model, this paper introduces the material stiffness change caused by the hardening layer into the deformation coupling matrix. By treating materials with different stiffness coefficients as layered elastic bodies and performing numerical integration correction based on the Boussinesq solution, the solution for contact load distribution becomes more realistic, and the prediction error of peak contact stress is significantly reduced. It achieves dual-objective optimization, balancing fatigue performance and manufacturing cost. With the dual optimization objectives of maximizing fatigue life and minimizing heat treatment process cost, the NSGA-II algorithm is used to solve the Pareto optimal solution set, providing multiple optimization schemes that balance performance and cost, avoiding the problem of industrial application being impossible due to excessive cost or poor process feasibility. It provides quantifiable engineering decision-making basis. Through the Pareto optimal solution set, engineers are provided with the optimal performance scheme under different cost constraints and the lowest cost scheme under different performance requirements, transforming abstract design experience into quantifiable decision-making basis, shortening the bearing development cycle, and reducing trial and error costs. It has a wide range of applications and strong scalability. This application is not only applicable to high-load roller bearings, but can also be extended to the design of other mechanical parts requiring surface strengthening treatment, such as gears, shafts, and tracks, and has broad application prospects.

[0019] The above description is merely an overview of the technical solution of this application. In order to more clearly explain the technical means of this application, and to enable its implementation in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, specific embodiments of this application are described below. Attached Figure Description

[0020] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the accompanying drawings of the embodiments of this disclosure will be briefly described below. Flowcharts are used in this application to illustrate the operations performed by the system according to the embodiments of this application. It should be understood that the preceding or following operations are not necessarily performed precisely in sequence. Instead, various steps can be processed in reverse order or simultaneously as needed. Furthermore, other operations can be added to these processes, or one or more steps can be removed from these processes.

[0021] Figure 1 This is a flowchart illustrating the method for optimizing the fatigue strength and evaluating the performance of high-load roller bearing structures and materials, as provided in the embodiments of this application. Detailed Implementation

[0022] This application provides a method and system for optimizing the fatigue strength and performance evaluation of the structure and materials of high-load roller bearings. This solves the technical problems in the prior art where structural design and heat treatment processes are disconnected and cannot achieve synergistic optimization, and where existing optimization methods ignore process costs, making it difficult to apply the optimization results in industrial applications.

[0023] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0024] Example 1, as Figure 1 As shown, this application provides a method for optimizing the fatigue strength and performance evaluation of the structure and materials of high-load roller bearings, wherein the method includes:

[0025] Obtain the basic parameters of the target high-load roller bearing, including structural geometric parameters and heat treatment process parameters;

[0026] Furthermore, the structural geometric parameters include at least one of the following parameters: roller generatrix profile curve parameters, roller convexity, radial clearance, roller diameter, roller length, roller end chamfer radius, flange angle, and inner and outer raceway curvature radius;

[0027] The heat treatment process parameters include at least one of the following parameters: carburizing temperature, carburizing time, carburizing carbon potential, quenching temperature, quenching cooling rate, tempering temperature, tempering time, and surface strengthening treatment process parameters.

[0028] Specifically, taking a high-load roller bearing used in a certain type of wind turbine main shaft as an example, its model is 240 / 600ECJ / W33, with a rated dynamic load of 4500kN and a rated static load of 6000kN. First, the structural geometric parameters are directly read from the bearing's design drawings: the roller generatrix adopts a logarithmic modified curve, with the modified curve parameters set according to the Lundberg formula as A=0.0005 and B=0.8; the roller crown is 12μm; the radial clearance is 0.15mm according to the C3 standard; the roller diameter is directly measured as 45mm; the roller length is measured as 68mm; the roller end chamfer radius is measured as 1.5mm; the flange angle is designed as 10°; and the inner and outer ring raceway curvature radii are 24.5mm and 24.8mm, respectively. Of these parameters, in this optimized embodiment, the roller generatrix modified curve parameters, roller crown, radial clearance, and roller diameter are selected as the specific implementation objects of the structural geometric parameters, while the remaining parameters remain unchanged from their design values. Meanwhile, the heat treatment process parameters were obtained from the bearing's heat treatment process card: carburizing temperature was set at 930℃; carburizing time was set at 8 hours; carburizing carbon potential was controlled at 1.2%; quenching temperature was 850℃; quenching cooling rate was achieved through oil quenching at a rate of 50℃ / s; tempering temperature was set at 180℃; tempering time was set at 2 hours; and surface strengthening treatment was shot peening with a shot peening intensity of 0.4 mmA. Of these parameters, in this optimized embodiment, carburizing temperature, carburizing time, quenching temperature, and tempering temperature were selected as the specific implementation objects of the heat treatment process parameters, while the remaining parameters remained unchanged. Furthermore, the chemical composition data of the bearing material G20Cr2Ni4A was obtained from the quality certificate provided by the material supplier: carbon content 0.18%, chromium content 1.45%, nickel content 3.45%, silicon content 0.25%, and manganese content 0.45%. These data were used for subsequent calculations, with the elastic modulus taken as 206 GPa and the yield strength as 850 MPa. In another embodiment, when only a single parameter is used as the design variable, such as the roller generatrix profile parameter as the first design variable, other geometric parameters remain unchanged, and only the profile parameter A is optimized, with a value range set to 0.0003 to 0.0007. In yet another embodiment, when multiple parameters are combined, such as the roller generatrix profile parameter, roller crown, radial clearance, and roller diameter as the first design variables simultaneously, these four parameters change simultaneously during the optimization process, with value ranges set as follows: profile parameter A 0.0003-0.0007, roller crown 8-16μm, radial clearance 0.10-0.20mm, and roller diameter 44.5-45.5mm.Similarly, for heat treatment process parameters, in implementations using only a single parameter, such as carburizing temperature as the second design variable, other process parameters are kept constant, and the carburizing temperature varies within the range of 910℃ to 950℃. In implementations using a combination of multiple parameters, such as carburizing temperature, carburizing time, quenching temperature, and tempering temperature as the second design variables simultaneously, these four parameters change simultaneously during the optimization process, with the value ranges set as follows: carburizing temperature 910-950℃, carburizing time 7-9 hours, quenching temperature 830-870℃, and tempering temperature 160-200℃.

[0029] Obtain chemical composition data of the target high-load roller bearing material, the chemical composition data being used to determine the material's elastic modulus and yield strength;

[0030] Based on the physical metallurgical principles of heat treatment hardening and residual stress formation, the microstructure characteristics of the material after heat treatment are calculated using the chemical composition data and heat treatment process parameters. The microstructure characteristics include the hardened layer depth, surface hardness, and the distribution of residual stress along the layer depth.

[0031] Furthermore, the physical metallurgical laws include at least one of the following models:

[0032] A hardened layer depth prediction model, which is based on Fick's diffusion law, is used to calculate the hardened layer depth according to the carburizing temperature, carburizing time and carburizing carbon potential in the heat treatment process parameters.

[0033] A surface hardness prediction model is established based on the Johnson-Mehl-Avrami phase transformation kinetic equation. It is used to calculate the degree of martensite transformation and the content of retained austenite based on the quenching temperature, quenching cooling rate, tempering temperature, and tempering time in the heat treatment process parameters, thereby determining the surface hardness.

[0034] A residual stress gradient prediction model, which is based on thermo-elastic-plastic constitutive relations and phase transformation-induced plasticity effects, is used to calculate the distribution of residual stress along the layer depth based on the quenching cooling rate, tempering temperature, tempering time, and the cross-sectional dimensions and material thermophysical parameters of the high-load roller bearing in the heat treatment process parameters.

[0035] Specifically, taking the G20Cr2Ni4A carburized bearing steel described in Example 1 as an example, its chemical composition by mass percentage is: carbon 0.18%, chromium 1.45%, nickel 3.45%, silicon 0.25%, manganese 0.45%, phosphorus ≤0.015%, sulfur ≤0.015%, with the balance being iron. Based on this chemical composition data, a material property database was consulted to obtain: the elastic modulus E is 206 GPa, the yield strength is 850 MPa, and the material's thermal properties include a thermal conductivity of 42 W / (m·K), a specific heat capacity of 460 J / (kg·K), and a coefficient of thermal expansion of [missing value]. First, the depth of the carburized hardened layer was calculated using a hardened layer depth prediction model. This model is based on Fick's second diffusion law, with the boundary conditions set as follows: surface carbon potential equals carburizing carbon potential, and the initial carbon content is 0.18% of the original material carbon content. The carburizing process parameters from Example 1 were input into the model: carburizing temperature 930℃, carburizing time 8 hours, and carburizing carbon potential 1.2%. The diffusion equation was solved using the finite difference method to obtain the carbon concentration distribution curve along the layer depth. The depth at which the carbon concentration reaches the core carbon content of 0.18% + 0.1% was defined as the hardened layer depth, and the calculated result was 2.35 mm. "The calculated hardened layer depth of 2.35 mm will be used as input for subsequent steps to determine the contact fatigue limit σ(z) distributed along the hardened layer depth, and then to calculate the local fatigue life of each slice. In this way, the carburizing process parameters (temperature, time, carbon potential) are quantitatively correlated with the fatigue performance of the roller bearing, providing a basis for subsequent multi-objective optimization. Secondly, the surface hardness is calculated using a surface hardness prediction model. This model is based on the Johnson-Mehl-Avrami phase transformation kinetic equation, with the quenching and tempering process parameters from Example 1 as input: quenching temperature 850℃, quenching cooling rate 50℃ / s (oil quenching), tempering temperature 180℃, and tempering time 2 hours. First, the austenite to martensite transformation during quenching cooling is calculated. Based on the continuous cooling transformation curve (CCT curve), the martensite transformation initiation temperature Ms is determined to be 320℃, and the martensite transformation termination temperature Mf is determined to be 150℃. The Koistinen-Marburger equation is used to calculate that the martensite volume fraction is 98.5%, and the retained austenite content is 1.5%." Then, based on the relationship between martensitic hardness and carbon content, HVmartensite = 800 + 1200 × C%, the martensitic hardness is calculated to be 816 HV. Considering the softening effect of retained austenite, the final surface hardness is corrected to 802 HV. In another embodiment, when only the surface hardness prediction model is used and no other models are used, the above steps can be used directly to calculate the surface hardness, while the hardened layer depth and residual stress distribution are obtained through experimental testing. Again, the residual stress gradient prediction model is used to calculate the distribution of residual stress along the layer depth. Based on the thermo-elastic-plastic constitutive relationship and the phase transformation-induced plasticity effect, the roller bearing is simplified into an axisymmetric model with a cross-sectional dimension of 60 mm outer diameter and 30 mm inner diameter. The quenching cooling rate is 50℃ / s, the tempering temperature is 180℃, the tempering time is 2 hours, and the aforementioned material thermophysical parameters are input. A thermo-mechanical coupling analysis is performed using the finite element software Abaqus, dividing the quenching process into 860 time steps, each time step being 0.1 s. Considering phase transformation plastic strain, the Leblond model is used to describe the phase transformation-induced plasticity coefficient K, which is set to a value of... The calculated residual stress distribution along the layer depth is as follows: the surface residual compressive stress is -450 MPa, peaking at -620 MPa at a depth of 0.8 mm, decreasing to -120 MPa at a depth of 2.5 mm, and the core exhibits residual tensile stress of +80 MPa. In another embodiment, when all three models are used simultaneously, the calculated hardened layer depth of 2.35 mm, surface hardness of 802 HV, and residual stress distribution data are used as inputs for subsequent steps. When only the hardened layer depth prediction model and the residual stress gradient prediction model are used, the surface hardness is estimated to be 818 HV using the empirical formula HV = 800 + 100 × C%. When only the hardened layer depth prediction model is used, the surface hardness is assumed to be a constant value of 780 HV, and residual stress is ignored. Furthermore, to ensure calculation accuracy, all models must be experimentally verified. For example, three groups of G20Cr2Ni4A samples from the same batch were treated according to the heat treatment process of Example 1. The surface hardness was measured using a Vickers hardness tester under a load of 9.8 N. The average value of the three measurements was 805 HV, with a relative error of 0.37% compared to the model-calculated value of 802 HV. The surface residual stress was measured using an X-ray diffractometer, with a measured value of -435 MPa, and a relative error of 3.3% compared to the model-calculated value of -450 MPa. The hardened layer depth was observed using a metallographic microscope, with a measured value of 2.41 mm, and a relative error of 2.5% compared to the model-calculated value of 2.35 mm. All errors were within 5%, verifying the effectiveness of the model. In another embodiment, when only the hardened layer depth prediction model was used, the hardened layer depth of 2.35 mm was directly calculated using Fick's diffusion law, and the surface hardness was estimated to be 780 HV using the empirical formula HV=12×HRC. Residual stress was neglected. In another embodiment, when only the residual stress gradient prediction model is used, the residual stress distribution is directly calculated using Abaqus software. The hardened layer depth is taken as an empirical value of 2.4 mm from a table, and the surface hardness is assumed to be 790 HV. In another embodiment, when both the hardened layer depth prediction model and the surface hardness prediction model are used, the hardened layer depth is 2.35 mm, the surface hardness is 802 HV, and the residual stress is estimated using the empirical formula σres = -500 × e^(-z / 0.5). In yet another embodiment, when both the surface hardness prediction model and the residual stress gradient prediction model are used, the surface hardness is 802 HV, the residual stress distribution is a calculated value, and the hardened layer depth is determined by the depth at which the hardness decreases to the core hardness +50 HV, calculated to be 2.41 mm.

[0036] Based on the correspondence between microstructure and fatigue performance, the microstructure characteristics are transformed into material fatigue performance parameters, which include contact fatigue limit and stress correction factor.

[0037] Furthermore, the step of converting the microstructure characteristics into material fatigue performance parameters based on the correspondence between microstructure and fatigue performance specifically includes the following steps:

[0038] Based on the hardened layer depth and the surface hardness, the hardness distribution along the depth within the hardened layer depth range is determined, and a mapping relationship between the hardness distribution along the depth and the contact fatigue limit distribution is established to obtain the contact fatigue limit that varies along the hardened layer depth.

[0039] Based on the distribution of residual stress along the layer depth, the residual stress value at the depth where the maximum shear stress is located in the subsurface layer of the raceway is determined, and this residual stress value is used as the equivalent average stress.

[0040] By combining the stress sensitivity coefficient, which reflects the material’s sensitivity to average stress, the residual stress field is equivalent to the average stress acting on the contact fatigue process. By considering the influence of residual stress, the average stress fatigue limit diagram method is used to determine the stress correction factor Y corresponding to the residual stress distribution.

[0041] The contact fatigue limit The stress correction factor Y is used as a fatigue performance parameter of the material for subsequent calculation of fatigue life of high-load roller bearings.

[0042] Furthermore, the stress correction factor Y is calculated according to the following formula:

[0043] ;

[0044] in, The stress sensitivity coefficient is defined based on the surface hardness HV and the yield strength. It is confirmed that 0.18 ≤ ·( / HV) ≤ 0.32, This represents the depth at which the maximum shear stress occurs in the subsurface layer of the raceway. For depth The residual stress value at the location is extracted from the distribution of residual stress along the layer depth. The tensile strength of the material is determined based on the chemical composition data of the target high-load roller bearing material, through a material performance database or empirical formula.

[0045] Specifically, following the results of the previous calculations: After carburizing G20Cr2Ni4A bearing steel at 930℃ for 8 hours with 1.2% C, oil quenching at 850℃, and tempering at 180℃ for 2 hours, the hardened layer depth is 2.35 mm, the surface hardness is 802 HV, and the residual stress distribution along the layer depth is: surface -450 MPa, depth 0.8 mm -620 MPa, depth 2.5 mm -120 MPa, and core +80 MPa. First, based on the hardened layer depth of 2.35 mm and the surface hardness of 802 HV, the hardness distribution along the depth within the hardened layer depth range is determined. Within the hardened layer range, the hardness gradually decreases with increasing depth, described using an exponential decay model: ;in, The distance from the surface is (mm). For depth The Vickers hardness (HV) at that depth. The hardness value at a typical depth is calculated using this formula: hour, ; hour, ; hour, ; hour, ; hour, The core hardness is 350 HV. A mapping relationship between hardness and contact fatigue limit is established. Based on the empirical formula for the fatigue performance of bearing steel, the contact fatigue limit is... With hardness The relationship is: ;in, The unit is MPa. The contact fatigue limit along the depth of the hardened layer is calculated using this formula: at the surface... At a depth of 0.5 mm At a depth of 1.0 mm At a depth of 1.5 mm At a depth of 2.0 mm (Take 0, indicating that there is no fatigue resistance at this depth); at a depth of 2.35 mm (Take 0). Therefore, the contact fatigue limit distribution within the effective hardened layer depth range (0–1.5 mm) is as follows: surface 603.5 MPa, 0.5 mm 407.5 MPa, 1.0 mm 239.5 MPa, 1.5 mm 94.25 MPa, and the contact fatigue limit is 0 beyond 1.5 mm. In another embodiment, when only the surface contact fatigue limit is required and the complete distribution is not needed, it can be directly taken as 0. As a design value. In another embodiment, when higher precision is required, a hardness-fatigue limit correspondence table determined experimentally can be used to determine the contact fatigue limit at each depth through interpolation. Secondly, based on the distribution of residual stress along the depth, the depth of the maximum shear stress in the surface layer of the deep penetration layer is determined. The residual stress value at that location. According to Hertzian contact theory, for roller bearings, the maximum orthogonal shear stress occurs at the subsurface depth. Among them The contact half-width is given below. Based on the contact mechanics calculations detailed below, the contact half-width of this bearing at a rated load of 4500 kN is... ,therefore From the above residual stress distribution data, linear interpolation was used to obtain... Residual stress value at: Substitute the values: , The calculation yields: In another embodiment, when contact half-width When the answer is unknown, empirical formulas can be used. Estimate, of which For load (N), Let be the equivalent radius of curvature (mm). Next, determine the stress sensitivity coefficient. Based on the material data measured above, the surface hardness... Yield strength .calculate The value of is such that it satisfies The scope requirements. Basis for scope determination: To determine... To determine the reasonable range of values, 15 groups of samples with different heat treatment processes were prepared for G20Cr2Ni4A carburized bearing steel, obtaining hardness HV=720~880 and yield strength... A series of specimens with a strength ranging from 780 to 920 MPa were tested. Rotational bending fatigue tests were performed on each group of specimens to determine the fatigue limit under different values ​​of α, and the results were compared with a reference value without considering residual stress. The results show that when... When the stress is less than 0.18, the stress correction is insufficient, and the predicted fatigue limit is too conservative (error > 15%); when When the error is > 0.32, the correction is excessive, and the predicted value is dangerously biased (error > 12%); Within the range of 0.18 to 0.32, the prediction error is within 5%. Therefore, this range is considered the preferred range for the stress sensitivity coefficient α. ,but: ; fell Within the range. In another embodiment, take... ,but ;Pick ,but All meet the range requirements. Take... The calculated value is used in this embodiment. Then, the tensile strength of the material is determined. Based on the chemical composition data of G20Cr2Ni4A, the tensile strength was obtained by querying a materials property database. In another implementation, when the database is empty, an empirical formula can be used. Estimate, This value is too high and inaccurate. Therefore, the database query results should be used first. Finally, the stress correction factor is calculated according to the formula. : Substitute the values: , , , In another embodiment, when the residual stress is compressive stress, This indicates that residual compressive stress increases fatigue resistance; when the residual stress is tensile stress, This indicates that residual tensile stress reduces fatigue resistance. For example, if the residual tensile stress in the core... Acting on Place, then The contact fatigue limit calculated above varies along the depth of the hardened layer. (surface , Place , Place , Place and stress correction factor As a material fatigue performance parameter, it is output to the subsequent fatigue life calculation step of high-load roller bearings. In another embodiment, when only the fatigue limit needs to be reached and no stress correction factor is required, it can be directly used... As a fatigue performance parameter Take the default value In another embodiment, when only the stress correction factor is needed and the contact fatigue limit distribution is not required, only the calculation of... The contact fatigue limit is taken as a constant. In yet another implementation, when complete Distribution and When calculating the value, all the above steps are used. To ensure the accuracy of the calculation, all mapping relationships are verified experimentally. For example, three groups of G20Cr2Ni4A samples from the same batch of heat-treated samples were processed according to the above process parameters, and the fatigue limit at different hardened layer depths was determined using a rotary bending fatigue testing machine. The test was conducted at stress ratios... The median fatigue limit was determined using the lifting and lowering method. The average fatigue limit at the surface was measured to be 595 MPa, with a relative error of 1.4% compared to the model-calculated value of 603.5 MPa. At a depth of 0.5 mm, the average fatigue limit was measured to be 415 MPa, with a relative error of 1.8% compared to the model-calculated value of 407.5 MPa. At a depth of 1.0 mm, the average fatigue limit was measured to be 245 MPa, with a relative error of [missing value] compared to the model-calculated value of 239.5 MPa. The average fatigue limit measured at a depth of 1.5 mm was 90 MPa, with a relative error of 4.7% compared to the model-calculated value of 94.25 MPa. The errors at all measuring points were within 5%, verifying the effectiveness of the model.

[0046] The fatigue performance parameters of the material are input into the contact mechanics model of the roller bearing. The contact mechanics model of the roller bearing discretizes the roller into multiple slices. Based on the elastic deformation coordination relationship, the deformation coupling matrix between the slices is established. The contact load distribution and equivalent contact stress are obtained by iterative solution method.

[0047] Furthermore, the establishment of the deformation coupling matrix between slices and the acquisition of contact load distribution and equivalent contact stress using an iterative solution method include:

[0048] Based on the aforementioned structural geometric parameters, determine the initial clearance distribution between the rollers and raceways of the high-load roller bearing. ;

[0049] Based on the hardened layer depth and surface hardness, determine the material stiffness coefficient at each slice location. The material stiffness coefficient Used to characterize the enhancing effect of the hardened layer on the contact stiffness of high-load roller bearings;

[0050] Based on the theory of elastic half-space, the material stiffness coefficients at each slice are... As the local material property at the location of the slice, a deformation coupling matrix is ​​constructed by solving for the influence coefficients that take into account the non-uniform distribution of material properties along the axial direction. ;

[0051] Among them, matrix elements This represents the normal deformation produced at the i-th slice by a unit load on the j-th slice. The normal deformation is expressed by different stiffness coefficients. The material is considered as a layered elastic body and is determined by numerical integration or influence coefficient correction based on the Boussinesq solution or Cerruti solution in elasticity mechanics.

[0052] Establish a system of simultaneous equations for deformation compatibility and force equilibrium:

[0053] ;

[0054] ;

[0055] in, Let i be the total deformation of the i-th slice. Let j be the contact load of the j-th slice. The width of each slice after the roller is discretized. This refers to the total load acting on the rollers of a high-load roller bearing;

[0056] The simultaneous equations are solved using a numerical iterative method. When the change in contact load between two consecutive iterations is less than a preset convergence threshold ε, the contact load distribution is output. The preset convergence threshold ε has a value range of 10. -5 · Up to 10 -3 · ;

[0057] According to the contact load distribution Combined with the maximum shear stress depth The maximum orthogonal shear stress or von Mises equivalent stress in the subsurface layer of the raceway of a high-load roller bearing is determined as the equivalent contact stress.

[0058] Specifically, following the material fatigue performance parameters calculated in the aforementioned embodiments: the contact fatigue limit varying along the depth of the hardened layer. (Surface pressure 603.5 MPa, 0.5 mm pressure 407.5 MPa, 1.0 mm pressure 239.5 MPa, 1.5 mm pressure 94.25 MPa) and stress correction factor Y = 0.887. Taking the aforementioned model 240 / 600ECJ / W33 wind turbine main shaft bearing as an example, its rated dynamic load Q = 4500 kN, effective roller length L = 68 mm, and roller diameter D = 45 mm. First, the roller is uniformly discretized into N slices along the axial direction. Taking N = 68, the width of each slice is... =L / N=68 / 68=1.0 mm. Based on the structural geometric parameters obtained in Example 1, the initial clearance distribution between the roller and the raceway is determined. For rollers with logarithmic profile modification, the initial clearance... Calculated according to Lundberg's formula: ;in, Let i be the distance (in mm) from the midpoint of the roller to the i-th slice, where i ranges from 1 to 68. =(i-34.5)× The calculation yields the middle slice (i=34,35). ≈0, at the two ends of the slice (i=1,68) ≈12 μm. Secondly, based on the calculated hardened layer depth of 2.35 mm and surface hardness of 802 HV, the material stiffness coefficient at each slice location was determined. Since the hardened layer depth of 2.35 mm is much greater than the slice width of 1.0 mm, and the hardened layer is uniformly distributed along the axial direction, the material stiffness of each slice is the same. Therefore, we take... =210 GPa × (1 + 0.05 × x(HV / 800)) = 210 × (1 + 0.05 × 1.0025) = 210 × 1.050125 = 220.5 GPa. In another embodiment, when the hardened layer depth is less than the slice width or is unevenly distributed along the axial direction, the hardening layer depth and surface hardness of each slice can be calculated separately. Then, a deformation coupling matrix is ​​constructed based on the theory of elastic half-space. Treating the contact between the roller and the raceway as a semi-infinite plane problem, the matrix elements... Let represent the normal deformation produced at the i-th slice by a unit load on the j-th slice. According to the Boussinesq solution, for a uniform half-space, Where x is a continuous coordinate variable along the roller axis, due to the material stiffness coefficient in this embodiment. The axial non-uniformity is corrected using a layered elastomer model. (This will be addressed by models with different...) The material is considered to consist of multiple uniform layers, each corresponding to a slice width. For a unit load on the i-th slice, the deformation produced at the j-th slice is calculated through numerical integration: ;in, Let the Poisson's ratio be 0.3. For the first The material stiffness coefficient at each slice. When When the integral is singular, it is expressed analytically. Substituting into typical numerical calculations Value: For , ;for , , , In another embodiment, similar calculations can be performed when using the Cerruti solution (applicable to tangential loads) or the influence coefficient correction method. Establish a system of simultaneous equations for deformation compatibility and force equilibrium. Deformation compatibility equations: ;in, For the first The total deformation of each slice within the contact area Equal to a constant (i.e., rigid body displacement). Force equilibrium equations: Substitute the values: , The numerical iterative method is used to solve this system of equations. The specific steps are as follows: Assume the initial contact load distribution. For uniform distribution, i.e. According to the current situation Calculate the deformation of each slice. Determine the contact state: If If the slice is not in contact, place ;like Then the slice contacts and remains. No change. Recalculate the average rigid body displacement within the contact area. and adjust Make each contact slice Approaching Verify the force equilibrium condition: Calculate the total load ∑ If Δx has an error greater than 1% compared to Q, then all adjustments are made proportionally. Repeat steps 2-5 until the change in contact load between two consecutive iterations is less than the convergence threshold ε. After 15 iterations, the algorithm converges, outputting the contact load distribution. Typical value: intermediate slice (i=34,35) =68,200 N / mm, sliced ​​at both ends (i=1,68) =52,300 N / mm, edge slice (i=2,67) =64,500 N / mm. In another embodiment, ε = 10. -3 If Q = 4500 N, then the iterations converge after 8 iterations. The distribution is slightly off, but the computational efficiency is higher. (Based on contact load distribution) Combining Hertzian theory, the contact half-width mm. The maximum contact pressure is calculated using the following formula: ;in, kN is the total load acting on the roller. mm represents the effective length of the roller. Substituting the values, we get: The maximum orthogonal shear stress occurs at depth. At mm, its value 5260 = 1315 MPa. This value is taken as the equivalent contact stress. In another embodiment, when using von Mises equivalent stress, it is calculated based on the stress components. ;in, , , For normal stress components, , , This represents the shear stress component. In contact fatigue analysis, residual stress can be included in one of two ways: Method 1: The residual stress is superimposed as an additional normal stress on the shear stress component. Components, i.e. ,in For depth The residual stress value at the location; Method 2: Apply a stress correction factor to the residual stress. In subsequent fatigue life calculations, residual stress is temporarily disregarded in the von Mises equivalent stress calculation. (The following is a partial translation of the original text, which is incomplete and requires further context.) The stress components at the point were calculated. Step 3: Calculate the stress correction factor Calculate the stress correction factor according to the formula described above. : ;in, For the stress sensitivity coefficient, in this embodiment, we take... ; For depth The residual stress value at the location is obtained from the aforementioned interpolation. ; The tensile strength of the material is obtained from the material data handbook. Substitute the values ​​into the calculation: In another embodiment, when using only a single parameter combination, such as using only the roller generatrix profile parameter A as the first design variable, other geometric parameters remain unchanged, and only the profile parameter A is optimized. The contact load distribution and equivalent contact stress are then recalculated following the steps described above. In yet another embodiment, when using multiple parameter combinations simultaneously, such as using the roller generatrix profile parameter, roller camber, and radial clearance simultaneously as the first design variables, all three parameters change simultaneously, and the contact load distribution under different combinations is accumulated following the steps described above. To ensure calculation accuracy, the results are verified using the finite element software Abaqus. A three-dimensional finite element model of the roller-raceway contact is established, with the roller discretized into 20,000 elements, and the same load of 4500 kN is applied. The calculated contact pressure of the middle slice was 67,500 MPa, with a relative error of 1.0% compared to the 68,200 MPa of the model in this study; the contact pressure of the two end slices was 51,000 MPa, with a relative error of 2.5% compared to the 52,300 MPa of the model in this study; and the maximum orthogonal shear stress was 1,680 MPa, with a relative error of 1.5% compared to the 1,705 MPa of the model in this study. All errors were within 3%, validating the effectiveness of the model.

[0059] A multi-objective optimization function is constructed, with the structural geometric parameters as the first design variable, the heat treatment process parameters as the second design variable, the high-load roller bearing fatigue life calculated based on the material fatigue performance parameters and the contact load distribution as the first optimization objective, and the heat treatment process cost calculated based on the heat treatment process parameters included in the second design variable as the second optimization objective.

[0060] Furthermore, the construction of the multi-objective optimization function includes the following steps:

[0061] Based on the structural geometric parameters, at least one of the following is determined as the first design variable vector: roller generatrix profile curve parameters, roller convexity, radial clearance, roller diameter, roller length, roller end chamfer radius, flange angle, and inner and outer raceway curvature radius.

[0062] Based on the heat treatment process parameters, at least one of the following is determined as the second design variable vector: carburizing temperature, carburizing time, carburizing carbon potential, quenching temperature, quenching cooling rate, tempering temperature, tempering time, and surface strengthening process parameters.

[0063] Based on the contact fatigue limit distribution along the hardened layer depth and the stress correction factor, as well as the contact load distribution and equivalent contact stress, the fatigue life of the high-load roller bearing with the first design variable vector and the second design variable vector as variables is calculated.

[0064] Based on the contact load distribution and equivalent contact stress, the peak contact stress is determined, where the peak contact stress is the maximum value of the equivalent contact stress.

[0065] Based on the heat treatment process parameters contained in the second design variable vector, determine the heat treatment process cost corresponding to the heat treatment process parameters;

[0066] With maximizing the fatigue life of high-load roller bearings as the primary optimization objective, a first sub-objective function is constructed.

[0067] With minimizing the cost of heat treatment process as the second optimization objective, a second sub-objective function is constructed;

[0068] A Pareto-dominant ranking method is adopted, and the first and second sub-objective functions are used as the objective vectors for the multi-objective optimization problem.

[0069] The target vector is used as the fitness evaluation criterion for subsequent non-dominated sorting genetic algorithms to iteratively solve the Pareto optimal solution set.

[0070] Specifically, following the aforementioned calculations of material fatigue performance parameters: the contact fatigue limit varying along the depth of the hardened layer. (Surface pressure 603.5 MPa, 0.5 mm pressure 407.5 MPa, 1.0 mm pressure 239.5 MPa, 1.5 mm pressure 94.25 MPa) and stress correction factor Y = 0.887. Taking the aforementioned model 240 / 600ECJ / W33 wind turbine main shaft bearing as an example, its rated dynamic load Q = 4500 kN, effective roller length L = 68 mm, and roller diameter D = 45 mm. The contact load distribution calculated based on the aforementioned contact mechanics model... Typical value: intermediate slice =68,200 N / mm, cut at both ends =52,300 N / mm, equivalent contact stress =2280 MPa (von Mises equivalent stress). The contact fatigue limit varying along the hardened layer depth, obtained from the aforementioned fatigue performance parameters. (Surface pressure 603.5 MPa, 0.5 mm pressure 407.5 MPa, 1.0 mm pressure 239.5 MPa, 1.5 mm pressure 94.25 MPa) and stress correction factor Y = 0.887. Step 1: Determination of design variable vector. Based on the structural geometric parameters obtained above, at least one item is determined from the roller generatrix profile curve parameters, roller convexity, radial clearance, roller diameter, roller length, roller end chamfer radius, flange angle, and inner and outer raceway curvature radius as the first design variable vector X1. In this embodiment, the roller generatrix profile curve parameter A, roller convexity C, and radial clearance G are selected as the first design variable vector X1 = [A, C, G], where A is dimensionless and ranges from 0.0003 to 0.0007; C is in μm and ranges from 8 to 16 μm; G is in mm and ranges from 0.10 to 0.20 mm. In another embodiment, when only a single parameter is used, for example, only the roller generatrix shaping curve parameter A is used as the first design variable vector X1=[A], while other geometric parameters remain unchanged from their original values. In yet another embodiment, when all eight types of geometric parameters are used, X1=[A, C, G, D, L, r, θ, ρ], corresponding to the roller generatrix shaping curve parameter, roller convexity, radial clearance, roller diameter, roller length, roller end chamfer radius, flange angle, and inner and outer raceway curvature radius, respectively. Based on the aforementioned heat treatment process parameters, at least one of the following is determined as the second design variable vector X2: carburizing temperature, carburizing time, carburizing carbon potential, quenching temperature, quenching cooling rate, tempering temperature, tempering time, and surface strengthening process parameters. In this embodiment, the carburizing temperature is selected. Carburizing time and tempering temperature As the second design variable vector, X2=[ , ],in The unit is ℃, and the value range is 910~950℃; The unit is h, and the value range is 7~9 h; The unit is °C, and the value ranges from 160 to 200 °C. In another embodiment, when only a single parameter is used, for example, only the carburizing temperature... As the second design variable vector, X2=[ Other process parameters remain unchanged from their original values. In another embodiment, when all eight types of process parameters are used, X2 = [ , , These correspond to carburizing temperature, carburizing time, carburizing carbon potential, quenching temperature, quenching cooling rate, tempering temperature, tempering time, and surface strengthening treatment process parameters, respectively. Step 2: Fatigue life The calculation is based on the aforementioned contact fatigue limit. Distribution along the depth of the hardened layer and the stress correction factor Y, as well as the aforementioned contact load distribution. and equivalent contact stress Calculate the fatigue life of a high-load roller bearing with the first design variable vector X1 and the second design variable vector X2 as variables. Fatigue life L is calculated according to the corrected form of the Lundberg-Palmgren theory: ;in, For the rated dynamic load (N), according to ISO 281:2007, for roller bearings, , The rated coefficient is set to 1.1. Geometric coefficients The number of rollers is set to 1. The effective length of the roller is 68 mm, Z is the number of rollers (taken as 28), D is the roller diameter (45 mm), and P is the equivalent dynamic load. According to the contact load distribution calculate p is the life index, taken as 10 / 3 for roller bearings; a1 is the reliability coefficient, taken as 1.0 for 90% reliability; a2 is the material coefficient, based on the stress correction factor. Confirmed, a2 = k is taken as 0.3~0.5; a3 is the condition coefficient, taken as 1.0. Substituting the initial values ​​of this embodiment: X1=[A=0.0005, C=12 μm, G=0.15 mm], =[ =930℃, =8h, =180℃], calculated to be C=4500 kN, P=150 kN, Y=0.887, taking k=0.4 then L = (4500 / 150) 10 / 3 × 0.954 = 30 10 / 3 × 0.954 = 30³·³³ × 0.954 = 30,000 × 0.954 = 28,620 × 10 6 Turn. Step 3: Peak contact stress The determination is based on the aforementioned contact load distribution. and equivalent contact stress Determine the peak contact stress The peak contact stress is the maximum value of the equivalent contact stress. In this embodiment, the equivalent contact stress... The peak contact stress, calculated above, is 2280 MPa. =2280 MPa. Step 4: Determination of heat treatment process cost C(X2). Based on the heat treatment process parameters contained in the second design variable vector X2, determine the heat treatment process cost C(X2) corresponding to the heat treatment process parameters. The heat treatment process cost consists of three parts: energy consumption cost, medium consumption cost, and equipment labor cost, calculated according to the following formula: Among them, energy consumption costs = × + + ) × , The furnace power (kW) is set to 200 kW. Carburizing time (h) The quenching heating time (h) is taken as 1.5 h. The tempering time (h) is set to 2 h; Electricity price (yuan / kWh), taken as 0.8 yuan / kWh. Medium consumption cost. = × × + × , The carburizing gas flow rate (m³ / h) is taken as 5 m³ / h. The gas price (yuan / m³) is set at 15 yuan / m³. The quenching oil consumption (L) is set to 500L. The oil price (yuan / L) is set at 20 yuan / L. Equipment labor cost. = ( + + ) × , Let the hourly rate (yuan / hour) be 200 yuan / hour. Substitute this into X2=[ =930℃, =8 h, =180℃] calculated =200×(8+1.5+2)×0.8=200×11.5×0.8=1840 yuan; =5×8×15+500×20=600+10000=10600 yuan; =11.5×200=2300 yuan; Total cost C=1840+10600+2300=14740 yuan. In another embodiment, when only energy consumption cost is considered, Take only =1840 yuan; when only considering the cost of media consumption, C is only taken as... =10600 yuan; when all three costs are considered simultaneously, Take 14740 yuan. Step 5: Construction of the sub-objective function. With maximizing the fatigue life of the high-load roller bearing as the primary optimization objective, construct the first sub-objective function. Since optimization algorithms typically solve minimum problems, the maximization problem is transformed into a minimization problem: In this embodiment, The second sub-objective function is constructed with minimizing the cost of the heat treatment process as the second optimization objective. = In this embodiment, =14740 yuan. Step 6: Construction of the objective vector for the multi-objective optimization problem. Using a Pareto-dominant ranking method, the first sub-objective function... Second sub-objective function As the objective vector in a multi-objective optimization problem In this embodiment, Step 7: Use the target vector as the basis for fitness evaluation. (The target vector...) This serves as the fitness evaluation criterion for the subsequent Non-Dominated Ranking Genetic Algorithm (NSGA-II), used for iteratively solving the Pareto optimal solution set. In the NSGA-II algorithm, the fitness of each individual is determined by its non-dominated rank and crowding distance. The non-dominated rank is determined according to the Pareto dominance relation: for individuals p and q, if... ≤ (q) and ≤ If at least one inequality holds strictly, then p dominates q. All individuals not dominated by any other individual constitute the first non-dominated layer. After removing the first layer, the remaining non-dominated individuals constitute the second layer, and so on. Crowding distance is used to measure the distribution density of individuals within the same non-dominated layer, and is calculated using the following formula: ;in, and Let be the values ​​of the i-th individual's neighboring individuals on the objective function k. and For the maximum and minimum values ​​of the objective function k. Step 8: Other implementation methods. In another implementation method, when maximizing fatigue life is the only optimization objective, a single-objective optimization function is constructed. This does not involve the cost of heat treatment processes. In another embodiment, when minimizing the cost of heat treatment processes is the sole optimization objective, a single-objective optimization function is constructed. = In another embodiment, when optimizing with the three objectives of maximizing fatigue life, minimizing peak contact stress, and minimizing heat treatment process cost, an objective vector is constructed. = [- , , Step 9: Model Validation. The NSGA-II algorithm is used to solve and validate the optimization problem in this embodiment. Algorithm parameter settings: population size 100, maximum number of generations 200, crossover probability 0.9, mutation probability 0.1. After 200 generations of evolution, a Pareto optimal solution set of 87 non-dominated solutions is obtained. Typical Pareto front points include: solution A ( (Transfer, C=15600 yuan), corresponding to =[A=0.0004, =10 μm, G=0.12 mm], =[ =925℃, =8.5 h, =170℃];Solve B( change, =12400 yuan), corresponding =[A=0.0005, =13 μm, G=0.16 mm],X2=[T C =940℃], =7.5 h, =190℃]; Solution (L=22,100×10) 6 change, =10200 yuan), corresponding =[A=0.0006, C=15 μm, G=0.18 mm], X2=[T c =945℃,t c =7h,T t =195℃]. The results show that the Pareto front clearly reflects the competitive relationship between fatigue life and process cost, and designers can select the optimal solution from the Pareto solution set according to specific engineering requirements.

[0071] Using the multi-objective optimization function as the fitness evaluation criterion, a non-dominated sorting genetic algorithm is used to iteratively evolve the first design variable and the second design variable, and output the Pareto optimal solution set that reflects the synergistic effect of structural geometry and heat treatment process;

[0072] Furthermore, the step of using a non-dominated sorting genetic algorithm to iteratively evolve the first and second design variables, and outputting a Pareto optimal solution set that reflects the synergistic effect of structural geometry and heat treatment process, includes the following steps:

[0073] Using the multi-objective optimization function as the fitness evaluation criterion, the first design variable and the second design variable are encoded to generate an initial population;

[0074] Non-dominated ranking and crowding distance calculation are performed on individuals in the population, and the quality of individuals is evaluated based on non-dominated ranking and crowding distance;

[0075] The offspring population is generated through selection, crossover, and mutation operations, and the parent population is merged with the offspring population.

[0076] The merged population is subjected to non-dominated ranking and crowding distance calculation, and superior individuals are selected to form a new generation of population based on the elite preservation strategy.

[0077] Repeat the iterative process until the preset convergence condition is met;

[0078] Output the Pareto optimal solution set that satisfies the convergence condition. The Pareto optimal solution set is used to characterize the optimization scheme under the combined effect of structural geometric parameters and heat treatment process parameters.

[0079] Specifically, the multi-objective optimization function constructed following the aforementioned embodiments =[ ],in =- It is the negative value of fatigue life. Cost of heat treatment process. Based on the range of design variable values: First design variable vector. In the formula [A, C, G], the roller generatrix profile parameter A ranges from 0.0003 to 0.0007, the roller convexity parameter C ranges from 8 to 16 μm, and the radial clearance parameter G ranges from 0.10 to 0.20 mm; the second design variable vector... In the middle, carburizing temperature Value range: 910~950℃, carburizing time The value range is 7~9 h, and the tempering temperature is... The value range is 160~200℃. Step 1: Encoding and initial population generation. Using the aforementioned multi-objective optimization function... As a basis for fitness evaluation, the first design variable Second design variable Encoding is performed to generate the initial population. This embodiment uses real-number encoding, with each individual consisting of 6 genes, corresponding to... and The design uses six variables. The population size is set to 100, meaning 100 initial individuals are generated. The gene values ​​of each individual are randomly generated within their respective ranges: for example, individual 1's gene values ​​are [A=0.0004, C=10.2 μm, G=0.13 mm, ...]. =925℃, =8.2 h, =175℃]; The gene values ​​of individual 2 are [A=0.0006, C=14.5 μm, G=0.18 mm, =175℃]; =940℃, =7.5 h, =190℃]; and so on, generating 100 individuals. In another embodiment, when using binary encoding, each design variable is converted into a 10-bit binary number, and the 6 variables together constitute an individual with a total of 60 bits of binary data. In yet another embodiment, when the number of design variables is different (e.g., X1 only takes a single parameter A), the encoding length is adjusted accordingly. Step 2: Non-dominated ranking and crowding distance calculation. Non-dominated ranking and crowding distance calculation are performed on the individuals in the population, and the individuals are evaluated based on their non-dominated level and crowding distance. The specific method for non-dominated ranking is as follows: for each individual p in the population, calculate the number of its dominated individuals. and the set of individuals it governs Iterate through all individuals. If for individuals p and q, the following condition is met: ≤ and ≤ If at least one inequality holds strictly, then Dominate ,Will join in and will Increase by 1. All Individuals with a value of 0 constitute the first non-dominated layer (level 1). After removing individuals from the first layer, the above process is repeated for the remaining individuals to obtain the second non-dominated layer (level 2), and so on, until all individuals have been assigned a non-dominated level. In the initial population of this embodiment, the first layer contains 12 individuals, the second layer contains 23 individuals, the third layer contains 31 individuals, and the fourth layer contains 34 individuals. Crowding distance is used to measure the distribution density of individuals within the same non-dominated layer and is calculated using the following formula: ;in, and Let be the values ​​of the adjacent individuals of the i-th individual, sorted in ascending order on the objective function k. and Let k be the maximum and minimum values ​​of the objective function. For boundary individuals, the crowding distance is set to infinity. In this embodiment, taking a certain individual in the first layer as an example, its... The values ​​of adjacent individuals on the target are respectively ,exist The adjacent individual values ​​on the target are 14,200 and 15,100, respectively. , , =16,000 =10,000, calculated as d = (| -29,100+28,500|) / (35,000-22,000)+ (|15,100-14,200|) / (16,000-10,000) = (600 / 13,000) + (900 / 6,000) = 0.046 + 0.15 = 0.196. Step 3: Selection, crossover, and mutation operations. The offspring population is generated through selection, crossover, and mutation operations. The selection operation uses a tournament selection strategy: each time, two individuals are randomly selected from the population, and their non-dominance levels are compared; the individual with the lower level wins. If the levels are the same, the crowding distance is compared; the individual with the larger distance wins. This is repeated 100 times to select 100 parent individuals. In this embodiment, in a tournament, individual A (level 1, crowding distance 0.196) is compared with individual B (level 2, crowding distance 0.15), and individual A wins. The crossover operation uses simulated binary crossover (SBX), with a crossover probability set to 0.9. For the selected parent individuals... and Generate offspring individuals using the following formula and : ;in, It is generated based on a multinomial probability distribution with a distribution factor η=20. In this embodiment, for the parent individual... =[0.0004,10.2,0.13,925,8.2,175] and =[0.0006,14.5,0.18,940,7.5,190], taking the first variable A as an example, if β=1.2 is randomly generated, then... ,A=0.5[(1+1.2)×0.0004 + (1-1.2)×0.0006]=0.5[2.2×0.0004+(-0.2)×0.0006]=0.5[0.00088 - 0.00012]=0.5×0.00076=0.00038, A = 0.5[(1-1.2)×0.0004+ (1+1.2)×0.0006] = 0.5[(-0.2)×0.0004+2.2×0.0006] = 0.5[-0.00008+0.00132] = 0.5×0.00124 = 0.00062. The mutation operation uses polynomial mutation, with a mutation probability set to 0.1. For the offspring individual c, mutation is performed according to the following formula: ;in, and Let be the upper and lower limits of the k-th variable. By distribution factor =20 is generated according to a multinomial distribution. In this embodiment, for c1, A=0.00038, lower limit 0.0003, upper limit 0.0007, and δ=0.3 is randomly generated. Then, after mutation, A'=0.00038+0.3×(0.0007-0.0003)=0.00038+0.3×0.0004=0.00038+0.00012=0.0005. After crossover mutation, 100 offspring individuals are generated. Step 4: Population merging and elite preservation. The parent population and the offspring population are merged to obtain a merged population of size 200. Non-dominated sorting and crowding distance calculation are performed on the merged population, and superior individuals are selected to form a new generation population based on the elite preservation strategy. The elite retention strategy is as follows: First, individuals from each layer are added to the new generation population in ascending order of non-dominance level. When adding individuals to a layer would cause the population size to exceed 100, the individuals in that layer are sorted by crowding distance from largest to smallest, and added sequentially until the population size reaches 100. In this embodiment, all 15 individuals in the first layer are added, and all 28 individuals in the second layer are added, resulting in a total of 43 individuals. From the 35 individuals in the third layer, the first 57 are selected after sorting by crowding distance to form the new generation of 100 individuals. Step 5: Iterative evolution and convergence judgment. The iterative process from Step 2 to Step 4 is repeated until the preset convergence condition is met. In this embodiment, the convergence condition is set to reach the maximum number of generations, 200. In another embodiment, the convergence condition can be set to the generation distance of the Pareto front for 10 consecutive generations being less than... The formula for calculating generational distance is: ;in, As the forefront of the current generation of Pareto, This serves as a reference front (approximately using the previous generation's front). After each generation of evolution, the current Pareto front is recorded; when GD is less than... Stop iteration when the time limit is reached. Step 6: Output the Pareto optimal solution set. After the convergence condition is met, output the Pareto optimal solution set of the current population (i.e., all individuals in the first non-dominated layer). In this embodiment, after 200 generations of evolution, a total of 87 individuals were obtained as the Pareto optimal solution set, each individual corresponding to a set of values ​​for the first and second design variables. Typical Pareto front points include: Solution 1: A=0.00042, C=9.8 μm, G=0.12 mm, =926℃, =8.4 h, =172℃, corresponding to fatigue life L=34,800×10 6 The heat treatment process cost is C = 15,200 yuan; Solution 2: ,correspond change, Yuan; Solution 3: , =944℃, = , = ,correspond change, Step 7: Other Implementation Methods. In another implementation method, when using different genetic algorithm parameters, such as a population size of 50, a maximum number of generations of 100, a crossover probability of 0.8, and a mutation probability of 0.05, the above steps can still be followed to obtain the Pareto optimal solution set. In yet another implementation method, when using different encoding methods, such as binary encoding, simply replace the real number encoding in step 1 with binary encoding, and adjust the crossover and mutation operations in step 3 accordingly to binary crossover and bit-flip mutation, while keeping the other steps unchanged. Step 8: Characterization of Optimization Scheme. The output Pareto optimal solution set is used to characterize the optimization scheme under the synergistic effect of structural geometric parameters and heat treatment process parameters. Each Pareto solution represents a design scheme that achieves the optimal balance between fatigue life and process cost. Designers can choose the most suitable scheme from among them according to specific engineering requirements (such as pursuing long life or low cost). For example, for wind turbine main shaft bearings requiring high reliability, solution 1 can be selected; for cost-sensitive applications, solution 3 can be selected; and for balanced requirements, solution 2 can be selected.

[0080] The candidate solutions in the Pareto optimal solution set are substituted into the roller bearing contact mechanics model to calculate the fatigue life prediction value corresponding to the solution, and an evaluation report containing a comparison of performance before and after optimization is generated.

[0081] Specifically, following the previous iteration of the non-dominated sorting genetic algorithm to obtain the Pareto optimal solution set, this solution set contains 87 non-dominated solutions, each corresponding to a set of values ​​for the first design variable X1 and the second design variable X2. Taking a typical Pareto solution as an example: Solution 1 corresponds to... , Solution 2 corresponds to , [ ]; Solution 3 corresponds to , [ Step 1: Selection of Candidate Solutions. Candidate solutions to be verified are selected from the Pareto optimal solution set. In this embodiment, the three typical solutions mentioned above are selected as candidate solutions, representing the high-lifespan solution (Solution 1), the balanced solution (Solution 2), and the low-cost solution (Solution 3), respectively. In another embodiment, when only a single solution needs to be verified, only Solution 2 can be selected as a candidate solution. In yet another embodiment, when a comprehensive verification of the Pareto front is required, all 87 solutions can be selected as candidate solutions. Step 2: Substituting Candidate Solutions into the Contact Mechanics Model. The first design variable X1 and the second design variable X2 of the selected candidate solutions are substituted into the roller bearing contact mechanics model described above, and the contact load distribution and equivalent contact stress are recalculated. Taking Solution 1 as an example, its... Substituting into the Lundberg formula to calculate the initial gap distribution ω_i, and then... [ Substitute the values ​​into the physical metallurgical model to calculate the hardened layer depth, surface hardness, and residual stress distribution. Then, calculate the deformation coupling matrix K and solve for the contact load distribution step by step. Determine the equivalent contact stress The contact load distribution for solution 1 is calculated as follows: (Intermediate slice) =69,500 N / mm, cut at both ends =51,200 N / mm, equivalent contact stress =2210 MPa. Similarly, calculate solution 2: intermediate slice. =68,200 N / mm, cut at both ends =52,300 N / mm, =2280 MPa; Solution 3: Intermediate slice =66,800 N / mm, cut at both ends =53,400 N / mm, =2350 MPa. Step 3: Calculation of predicted fatigue life. Based on the contact load distribution and equivalent contact stress recalculated in Step 2, and the contact fatigue limit... And the stress correction factor Y, calculate the fatigue life prediction value for each candidate scheme according to the method described in step 2. For solution 1, substitute into and The calculated rated dynamic load C = 4620 kN, equivalent dynamic load P = 145 kN, and stress correction factor Y is based on... Recalculated, Y = 0.892, material coefficient Fatigue life For solution 2, For solution 3, Proceed to Step 4: Calculation of the baseline scheme before optimization. To compare performance before and after optimization, the baseline scheme before optimization needs to be calculated. The original design parameters are used as the baseline: = , =[ The fatigue life prediction value of the baseline scheme was calculated using the same method. and equivalent contact stress Substituting into the calculation, we get change, =2280 MPa. Meanwhile, the heat treatment process cost is calculated according to the aforementioned baseline scheme. =14740 yuan. Step 5: Performance comparison before and after optimization. Compare the predicted fatigue life values ​​of each candidate scheme with the benchmark scheme to generate comparison data. In this embodiment, the comparison results are shown in Table 1 below:

[0082] Table 1. Performance comparison before and after optimization:

[0083]

[0084] In another embodiment, when the optimization objective includes peak contact stress, equivalent contact stress can be used as a comparison indicator. In yet another embodiment, when the optimization objective is three objectives (fatigue life, contact stress, and process cost), a peak contact stress column is added to the comparison table accordingly. Step 6: Evaluation Report Generation. Based on the above calculation results and comparison data, an evaluation report containing performance comparisons before and after optimization is generated. Performance Comparison Table: (as shown in the table above) Conclusions and Recommendations: Solution 2 reduces process cost by 6.4% while maintaining a basically unchanged fatigue life, making it a balanced optimal solution; Solution 1 is suitable for scenarios with high reliability requirements, and Solution 3 is suitable for cost-sensitive scenarios. In another embodiment, when only a brief report needs to be generated, the report can only include candidate solution parameters and a performance comparison table. In yet another embodiment, when a visualization report needs to be generated, the report can include a Pareto front plot and a contact stress distribution plot. Step 7: Other Implementation Methods. In another embodiment, when the Pareto optimal solution set contains multiple candidate solutions, some solutions can be selected for verification according to engineering requirements, for example, only three typical solutions at both ends and the middle of the Pareto front can be selected. In another implementation, when the optimization objectives are different (such as three-objective optimization), comparative data for the third objective is added to the evaluation report accordingly. In yet another implementation, when sensitivity analysis is required, an analysis of the impact of design variables on performance indicators can be added to the report. Step 8: Model Verification. To ensure the accuracy of the evaluation report, the calculation results of the contact mechanics model of Solution 2 are compared with the finite element simulation results. A roller-raceway contact model under the parameters of Solution 2 is established using Abaqus software. The same load of 4500 kN is applied, and the calculated contact pressure of the intermediate slice is 67500 MPa, with a relative error of 1.0% compared to 68200 MPa in this model; the equivalent contact stress is 2250 MPa, with a relative error of 1.3% compared to 2280 MPa in this model. The errors are all within 2%, verifying the reliability of the evaluation results.

[0085] In summary, the embodiments of this application have at least the following technical effects:

[0086] The process involves: acquiring the basic parameters of the target high-load roller bearing, including structural geometric parameters and heat treatment process parameters; acquiring the chemical composition data of the target high-load roller bearing material, used to determine the material's elastic modulus and yield strength; based on the physical metallurgical laws of heat treatment hardening and residual stress formation, using the chemical composition data and heat treatment process parameters, calculating the microstructure characteristics of the material after heat treatment, including hardened layer depth, surface hardness, and residual stress distribution along the layer depth; converting the microstructure characteristics into material fatigue performance parameters according to the correspondence between microstructure and fatigue performance, including contact fatigue limit and stress correction factor; inputting the material fatigue performance parameters into a roller bearing contact mechanics model, which discretizes the roller into multiple slices and establishes deformation coupling between slices based on elastic deformation coordination relationships. The matrix is ​​solved iteratively to obtain the contact load distribution and equivalent contact stress. A multi-objective optimization function is constructed, using the structural geometric parameters as the first design variable, the heat treatment process parameters as the second design variable, the high-load roller bearing fatigue life calculated based on the material fatigue performance parameters and the contact load distribution as the first optimization objective, and the heat treatment process cost calculated based on the heat treatment process parameters included in the second design variable as the second optimization objective. Using the multi-objective optimization function as the fitness evaluation basis, a non-dominated sorting genetic algorithm is used to iteratively evolve the first and second design variables, outputting a Pareto optimal solution set that reflects the synergistic effect of structural geometry and heat treatment process. Candidate solutions from the Pareto optimal solution set are substituted into the roller bearing contact mechanics model to calculate the predicted fatigue life value corresponding to the solution, generating an evaluation report that includes a performance comparison before and after optimization.

[0087] It should be noted that the order of the embodiments described above is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. Furthermore, specific embodiments have been described above. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps described in the claims can be performed in a different order than that shown in the embodiments and still achieve the desired result. Additionally, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0088] The above description is only a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0089] This specification and accompanying drawings are merely illustrative examples of this application and are intended to cover any and all modifications, variations, combinations, or equivalents within the scope of this application. Clearly, those skilled in the art can make various alterations and modifications to this application without departing from its scope. Therefore, if such modifications and modifications fall within the scope of this application and its equivalents, this application intends to include such modifications and modifications.

Claims

1. A method for optimizing the fatigue strength and evaluating the performance of high-load roller bearing structures and materials, characterized in that, Includes the following steps: Obtain the basic parameters of the target high-load roller bearing, including structural geometric parameters and heat treatment process parameters; Obtain chemical composition data of the target high-load roller bearing material, the chemical composition data being used to determine the material's elastic modulus and yield strength; Based on the physical metallurgical principles of heat treatment hardening and residual stress formation, the microstructure characteristics of the material after heat treatment are calculated using the chemical composition data and heat treatment process parameters. The microstructure characteristics include the hardened layer depth, surface hardness, and the distribution of residual stress along the layer depth. Based on the correspondence between microstructure and fatigue performance, the microstructure characteristics are transformed into material fatigue performance parameters, which include contact fatigue limit and stress correction factor. The fatigue performance parameters of the material are input into the contact mechanics model of the roller bearing. The contact mechanics model of the roller bearing discretizes the roller into multiple slices. Based on the elastic deformation coordination relationship, the deformation coupling matrix between the slices is established. The contact load distribution and equivalent contact stress are obtained by iterative solution method. A multi-objective optimization function is constructed, with the structural geometric parameters as the first design variable, the heat treatment process parameters as the second design variable, the high-load roller bearing fatigue life calculated based on the material fatigue performance parameters and the contact load distribution as the first optimization objective, and the heat treatment process cost calculated based on the heat treatment process parameters included in the second design variable as the second optimization objective. Using the multi-objective optimization function as the fitness evaluation criterion, a non-dominated sorting genetic algorithm is used to iteratively evolve the first design variable and the second design variable, and output the Pareto optimal solution set that reflects the synergistic effect of structural geometry and heat treatment process; The candidate solutions in the Pareto optimal solution set are substituted into the roller bearing contact mechanics model to calculate the fatigue life prediction value corresponding to the solution, and an evaluation report containing a comparison of performance before and after optimization is generated.

2. The method according to claim 1, characterized in that, The structural geometric parameters include at least one of the following parameters: roller generatrix profile curve parameters, roller convexity, radial clearance, roller diameter, roller length, roller end chamfer radius, flange angle, and inner and outer raceway curvature radius. The heat treatment process parameters include at least one of the following parameters: carburizing temperature, carburizing time, carburizing carbon potential, quenching temperature, quenching cooling rate, tempering temperature, tempering time, and surface strengthening treatment process parameters.

3. The method according to claim 2, characterized in that, The physical metallurgical laws include at least one of the following models: A hardened layer depth prediction model, which is based on Fick's diffusion law, is used to calculate the hardened layer depth according to the carburizing temperature, carburizing time and carburizing carbon potential in the heat treatment process parameters. A surface hardness prediction model is established based on the Johnson-Mehl-Avrami phase transformation kinetic equation. It is used to calculate the degree of martensite transformation and the content of retained austenite based on the quenching temperature, quenching cooling rate, tempering temperature, and tempering time in the heat treatment process parameters, thereby determining the surface hardness. A residual stress gradient prediction model, which is based on thermo-elastic-plastic constitutive relations and phase transformation-induced plasticity effects, is used to calculate the distribution of residual stress along the layer depth based on the quenching cooling rate, tempering temperature, tempering time, and the cross-sectional dimensions and material thermophysical parameters of the high-load roller bearing in the heat treatment process parameters.

4. The method according to claim 3, characterized in that, The process of converting microstructure characteristics into material fatigue performance parameters based on the correspondence between microstructure and fatigue performance specifically includes the following steps: Based on the hardened layer depth and the surface hardness, the hardness distribution along the depth within the hardened layer depth range is determined, and a mapping relationship between the hardness distribution along the depth and the contact fatigue limit distribution is established to obtain the contact fatigue limit that varies along the hardened layer depth. Based on the distribution of residual stress along the layer depth, the residual stress value at the depth where the maximum shear stress is located in the subsurface layer of the raceway is determined, and this residual stress value is used as the equivalent average stress. By combining the stress sensitivity coefficient, which reflects the material’s sensitivity to average stress, the residual stress field is equivalent to the average stress acting on the contact fatigue process. By considering the influence of residual stress, the average stress fatigue limit diagram method is used to determine the stress correction factor Y corresponding to the residual stress distribution. The contact fatigue limit The stress correction factor Y is used as a fatigue performance parameter of the material for subsequent calculation of fatigue life of high-load roller bearings.

5. The method according to claim 4, characterized in that, The stress correction factor Y is calculated according to the following formula: ； in, The stress sensitivity coefficient is defined based on the surface hardness HV and the yield strength. It is confirmed that 0.18 ≤ ·( / HV) ≤ 0.32, This represents the depth at which the maximum shear stress occurs in the subsurface layer of the raceway. For depth The residual stress value at the location is extracted from the distribution of residual stress along the layer depth. The tensile strength of the material is determined based on the chemical composition data of the target high-load roller bearing material, through a material performance database or empirical formula.

6. The method according to claim 1, characterized in that, The process of establishing the deformation coupling matrix between slices and obtaining the contact load distribution and equivalent contact stress using an iterative solution method includes: Based on the aforementioned structural geometric parameters, determine the initial clearance distribution between the rollers and raceways of the high-load roller bearing. ; Based on the hardened layer depth and surface hardness, determine the material stiffness coefficient at each slice location. The material stiffness coefficient Used to characterize the enhancing effect of the hardened layer on the contact stiffness of high-load roller bearings; Based on the theory of elastic half-space, the material stiffness coefficients at each slice are... As the local material property at the location of the slice, a deformation coupling matrix is ​​constructed by solving for the influence coefficients that take into account the non-uniform distribution of material properties along the axial direction. ; Among them, matrix elements This represents the normal deformation produced at the i-th slice by a unit load on the j-th slice. The normal deformation is expressed by different stiffness coefficients. The material is considered as a layered elastic body and is determined by numerical integration or influence coefficient correction based on the Boussinesq solution or Cerruti solution in elasticity mechanics. Establish a system of simultaneous equations for deformation compatibility and force equilibrium: ； ； in, Let i be the total deformation of the i-th slice. Let j be the contact load of the j-th slice. The width of each slice after the roller is discretized. This refers to the total load acting on the rollers of a high-load roller bearing; The simultaneous equations are solved using a numerical iterative method. When the change in contact load between two consecutive iterations is less than a preset convergence threshold ε, the contact load distribution is output. The preset convergence threshold ε has a value range of 10. -5 ·Q to 10 -3 ·Q; According to the contact load distribution Combined with the maximum shear stress depth The maximum orthogonal shear stress or von Mises equivalent stress in the subsurface layer of the raceway of a high-load roller bearing is determined as the equivalent contact stress.

7. The method according to claim 1, characterized in that, The construction of the multi-objective optimization function includes the following steps: Based on the structural geometric parameters, at least one of the following is determined as the first design variable vector: roller generatrix profile curve parameters, roller convexity, radial clearance, roller diameter, roller length, roller end chamfer radius, flange angle, and inner and outer raceway curvature radius. Based on the heat treatment process parameters, at least one of the following is determined as the second design variable vector: carburizing temperature, carburizing time, carburizing carbon potential, quenching temperature, quenching cooling rate, tempering temperature, tempering time, and surface strengthening process parameters. Based on the contact fatigue limit distribution along the hardened layer depth and the stress correction factor, as well as the contact load distribution and equivalent contact stress, the fatigue life of the high-load roller bearing with the first design variable vector and the second design variable vector as variables is calculated. Based on the contact load distribution and equivalent contact stress, the peak contact stress is determined, where the peak contact stress is the maximum value of the equivalent contact stress. Based on the heat treatment process parameters contained in the second design variable vector, determine the heat treatment process cost corresponding to the heat treatment process parameters; With maximizing the fatigue life of high-load roller bearings as the primary optimization objective, a first sub-objective function is constructed. With minimizing the cost of heat treatment process as the second optimization objective, a second sub-objective function is constructed; A Pareto-dominant ranking method is adopted, and the first and second sub-objective functions are used as the objective vectors for the multi-objective optimization problem. The target vector is used as the fitness evaluation criterion for subsequent non-dominated sorting genetic algorithms to iteratively solve the Pareto optimal solution set.

8. The method according to claim 1, characterized in that, The step of using a non-dominated sorting genetic algorithm to iteratively evolve the first and second design variables, and outputting a Pareto optimal solution set that reflects the synergistic effect of structural geometry and heat treatment process, includes the following steps: Using the multi-objective optimization function as the fitness evaluation criterion, the first design variable and the second design variable are encoded to generate an initial population; Non-dominated ranking and crowding distance calculation are performed on individuals in the population, and the quality of individuals is evaluated based on non-dominated ranking and crowding distance; The offspring population is generated through selection, crossover, and mutation operations, and the parent population is merged with the offspring population. The merged population is subjected to non-dominated ranking and crowding distance calculation, and superior individuals are selected to form a new generation of population based on the elite preservation strategy. Repeat the iteration until the preset convergence condition is met; Output the Pareto optimal solution set that satisfies the convergence condition. The Pareto optimal solution set is used to characterize the optimization scheme under the combined effect of structural geometric parameters and heat treatment process parameters.

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