Bearing mechanical property analysis method based on equivalent roller model

Abstract

The invention belongs to the field of computer aided design, and particularly provides a bearing mechanical property analysis method based on an equivalent roller model. The method comprises the steps that S1, a finite element model of contact of a roller and a raceway is established, the roller is an equivalent model composed of an inner-layer shell unit and an outer-layer entity unit, the shell unit and the entity unit are both cylindrical, and the shell unit is attached to the inner surface of the entity unit; and S2, adding constraint conditions and loads according to the actual load of the bearing, and running a simulation program to obtain a result. According to the method, the equivalent roller model formed by the shell units and the entity units can reduce the number of grids under the condition of small errors, so that the calculation amount is shortened, and the calculation efficiency is improved.

Description

Technical Field

[0001] The invention belongs to the field of computer-aided design, and in particular relates to a bearing mechanical performance analysis method based on an equivalent roller model. Background Art

[0002] Slewing bearings, especially three-row cylindrical roller slewing bearings, are widely used in large machinery such as cranes and shield machines because they can withstand large axial and radial loads and tipping moments. During operation, slewing bearings primarily withstand tipping moments and axial loads. Finite element modeling is a cost-effective and effective method for studying the load distribution of large slewing bearings.

[0003] In finite element analysis (FEA), the quality and quantity of mesh elements determine the convergence of the FEA calculations and the accuracy of the results. To ensure accurate results, a large number of meshes, sometimes even tens of millions, are often required, significantly increasing the cost of the FEA model. Furthermore, the increasing number of irregular mesh elements can sometimes affect the convergence of the FEA model. To improve computational efficiency, it is necessary to develop a FEA modeling method that can reduce the number of meshes while maintaining a certain level of accuracy.

[0004] To this end, many scholars have conducted relevant research. However, current research has largely focused on using nonlinear spring elements to replace rollers. For example, patent application publication number CN114139425A discloses a turntable bearing modeling and analysis method based on the coupling of rolling element entities with nonlinear springs. The key to this method is to use nonlinear spring elements to represent rolling elements in less loaded locations, thereby simplifying the finite element model, reducing the number of meshes, and shortening the calculation time.

[0005] However, the calculation accuracy of this method depends on the number of spring units, and the contact between the roller and the raceway is line contact. The nonlinear spring unit cannot accurately simulate the line contact behavior between the roller and the raceway, and the calculation results are less reliable. Summary of the Invention

[0006] The purpose of the present invention is to provide a bearing mechanical performance analysis method based on an equivalent roller model to solve the technical problems of large computational complexity and insufficient accuracy of the finite element model for bearing mechanical performance analysis in the prior art.

[0007] To achieve the above objectives, the technical solution of the bearing mechanical performance analysis method based on the equivalent roller model provided by the present invention is:

[0008] A bearing mechanical performance analysis method based on an equivalent roller model includes the following steps: S1: establishing a finite element model of roller and raceway contact, wherein the roller is an equivalent model composed of an inner shell unit and an outer solid unit, wherein the shell unit and the solid unit are both cylindrical, and the shell unit is attached to the inner surface of the solid unit; S2: adding constraints and loads according to the actual load of the bearing, running a simulation program, and obtaining results.

[0009] As a further improvement, in S1, the elastic modulus of the shell unit is determined by the following method: a roller finite element model of the full solid unit is established, a shell unit thickness of a certain set value is selected, the same constraints and loads as the full solid unit model are added, the elastic modulus is set as a variable, and the simulation result errors of the full solid unit model and the equivalent model under different elastic moduli are compared to determine the optimal value of the elastic modulus under the shell unit thickness.

[0010] As a further improvement, the shell element thickness and elastic modulus of the equivalent model are set as variables, and the simulation result errors of the full solid element model and the equivalent model under different elastic moduli and different shell element thicknesses are compared to determine the optimal value of the elastic modulus under different shell element thicknesses. The fitting equations for different shell element thicknesses and elastic moduli are fitted according to the simulation results to determine the shell element thickness and elastic modulus of the shell element in S1 according to the fitting equations.

[0011] As a further improvement, the fitting equations for shell element thickness and elastic modulus are: Where x is the thickness of the shell element, f1(x) is the elastic modulus, and a, b, c, and d are fitting parameters.

[0012] As a further improvement, the simulation results of the full solid element model and the equivalent model are compared to find the errors including the maximum roller contact stress error and the roller approach error.

[0013] As a further improvement, the shell element thickness and shell mid-surface radius of the equivalent model are set as variables, and the simulation result errors of the full solid element model and the equivalent model under different shell mid-surface radii and different shell element thicknesses are compared to determine the optimal value of the shell element thickness under different shell mid-surface radii. The fitting equations for different shell mid-surface radii and shell element thicknesses are obtained according to the simulation results, so as to determine the shell element thickness and shell mid-surface radius of the shell element in S1 according to the fitting equations.

[0014] As a further improvement, the fitting equation for the shell mid-surface radius and shell element thickness is: Where x is the radius of the shell mid-surface, f2(x) is the thickness of the shell element, and a i , b i , w are fitting parameters.

[0015] This invention is a groundbreaking innovation with the following beneficial effects: It proposes a novel equivalent roller model that combines shell and solid elements. During finite element simulation analysis, the contact between the roller and raceway remains that of the outer solid elements, more consistent with actual load conditions, while the shell elements represent the simulated roller's inner core. Compared to a solid roller model using only solid elements, this equivalent roller model reduces the number of meshes while minimizing errors, thereby shortening the computational effort and improving efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 Schematic diagram of the structure of a slewing bearing simulated by the embodiment of the bearing mechanical performance analysis method based on the equivalent roller model in the present invention;

[0017] Figure 2 Schematic diagram of the finite element model for mesh independence verification;

[0018] Figure 3 Added a way to verify the boundary conditions of finite element models for mesh independence;

[0019] Figure 4 Verify the maximum contact stress and error of the finite element model under different meshes for mesh independence;

[0020] Figure 5 Verify the finite element model and Hertz theory for mesh independence and calculate the maximum contact stress under different loads;

[0021] Figure 6 Verify the maximum contact stress error of the finite element model under different loads for mesh independence;

[0022] Figure 7 Schematic diagram of the roller and raceway contact finite element model of the full solid element model;

[0023] Figure 8 for Figure 7 Cross-sectional view of the finite element model;

[0024] Figure 9 The equivalent roller model of the bearing mechanical performance analysis method based on the equivalent roller model in the present invention;

[0025] Figure 10 for Figure 9 Schematic diagram of the shell element finite element model of the middle and inner layers;

[0026] Figure 11 Added methods for loads and boundary conditions for roller and raceway contact in full solid element models;

[0027] Figure 12Added methods for loads and boundary conditions for equivalent roller models and raceway contact;

[0028] Figure 13 Schematic diagram of node positions for calculating the roller load approach;

[0029] Figure 14 It is the roller normal contact stress cloud diagram of the full solid element model;

[0030] Figure 15 is the maximum contact stress value of the equivalent model under different shell element elastic moduli;

[0031] Figure 16 is the maximum contact stress error of the equivalent model under different shell element elastic moduli;

[0032] Figure 17 is the approximate value of the equivalent model under different shell element elastic moduli;

[0033] Figure 18 is the approximate error of the equivalent model under different shell element elastic moduli;

[0034] Figure 19 is the maximum contact stress value of the equivalent model and the full solid element model under different loads;

[0035] Figure 20 is the roller approach value of the equivalent model and the full solid element model under different loads;

[0036] Figure 21 is the calculation time of the equivalent model and the full solid element model under different loads;

[0037] Figure 22 Schematic diagram of the position of the shell element mid-surface of the shell element;

[0038] Figure 23 is the calculation result of the maximum contact stress of the shell element elastic modulus obtained according to the fitting formula;

[0039] Figure 24 is the calculation result of the roller approach of the shell element elastic modulus obtained according to the fitting formula;

[0040] Figure 25 is the calculation result of the maximum contact stress of the shell element mid-surface radius obtained according to the fitting formula;

[0041] Figure 26 is the calculation result of the roller approach of the shell element mid-surface radius obtained according to the fitting formula;

[0042] Figure 27 is the calculation result of the maximum contact stress of the shell element thickness obtained according to the fitting formula;

[0043] Figure 28 is the calculation result of the roller approach of the shell element thickness obtained according to the fitting formula;

[0044] Figure 29 Schematic diagram of the finite element model of the multi-roller equivalent model;

[0045] Figure 30 Schematic diagram of the finite element model of the multi-roller full solid unit model;

[0046] Figure 31 Schematic diagram of the finite element model of the multi-roller overall equivalent model;

[0047] Figure 32 Schematic diagram of the finite element model of the multi-roller overall solid unit model;

[0048] Figure 33 Schematic diagram of the overall finite element model with added boundary conditions;

[0049] Figure 34 It is the normal contact stress cloud diagram of the multi-roller overall equivalent model;

[0050] Figure 35 It is the normal contact stress cloud diagram of the multi-roller overall solid unit model;

[0051] Figure 36 It is the displacement cloud diagram of the multi-roller overall equivalent model;

[0052] Figure 37 It is the displacement cloud diagram of the multi-roller overall solid unit model;

[0053] Figure 38 Schematic diagram of the selected roller position;

[0054] Figure 39 The cross-section diagram of the finite element model of a three-row cylindrical roller bearing;

[0055] Figure 40 Schematic diagram of the finite element model of a three-row cylindrical roller bearing;

[0056] Figure 41 Schematic diagram of the roller finite element model of a three-row cylindrical roller bearing;

[0057] Figure 42 is a schematic diagram of loading;

[0058] Figure 43 Schematic diagram of the numbering direction of the main thrust rollers;

[0059] Figure 44 The maximum contact stress of the main thrust full solid element roller;

[0060] Figure 45The maximum contact stress of the main thrust full solid element roller model and the equivalent model. DETAILED DESCRIPTION

[0061] The basic technical concept of the present invention is to use an equivalent roller model with shell elements as the inner layer and solid elements as the outer layer when performing finite element analysis of bearing mechanics, so as to reduce the number of grids, reduce calculation time and improve efficiency while simulating conditions closer to the actual working conditions.

[0062] Based on the above concept, the present invention is further described in detail below in conjunction with the embodiments.

[0063] When using the finite element method to analyze the mechanical properties of bearings, the finite element model of the roller and raceway contact is first established, where the roller uses an equivalent roller model, such as Figure 9 and Figure 10 As shown, the equivalent model consists of cylindrical shell elements and solid elements, with the shell elements attached to the inner surface of the solid elements. After the finite element model is established, constraints and loads are added based on the actual bearing load, and a simulation program (such as ANSYS or ABAQUS) is run to obtain analysis results.

[0064] That is to say, the key of the present invention is to use an equivalent roller model composed of shell elements and solid elements to analyze the mechanical properties of the bearing. Some specific embodiments are provided below to verify the effectiveness of the equivalent model.

[0065] First, let's review the Hertz contact theory. When the rollers and raceways are in external contact, in a three-row cylindrical roller slewing bearing, the contact between the rollers and raceways is line contact. The contact between the rollers and raceways is considered as the contact between two cylinders with parallel axes. The curvature radius of the raceway is infinite, satisfying the following formula:

[0066]

[0067] Wherein, σ represents the contact stress in MPa, F represents the normal load in N, L represents the contact length in mm, ρ1 and ρ2 represent the curvature radius of the two cylinders in mm, where the curvature radius of the raceway is +∞, E1 and E2 represent the elastic modulus of the materials of the two cylinders in MPa, and μ1 and μ2 represent the Poisson's ratio of the materials of the two cylinders.

[0068]

[0069] Where: a represents the half-width of the contact surface when the two cylinders are in contact, in mm; b represents the length of the two cylinders, in mm.

[0070] by Figure 1Taking the three-row cylindrical roller slewing bearing shown in FIG1 as an example, the structures such as the fillets of non-critical parts of the bearing are simplified. The number of main thrust rollers, radial rollers and reverse thrust rollers (also known as auxiliary thrust rollers) in the bearing are 272, 363 and 170 respectively. The main parameters are shown in Table 1.

[0071] Table 1

[0072]

[0073] When verifying the validity of the equivalent model, the comparison is with the roller model of the full solid element, or the simulation results of the solid roller model under the same conditions. In order to improve the calculation efficiency, when determining the number of grids of the solid roller model, the appropriate number of grids is determined based on the grid-independent finite element simulation results. Figure 2 As shown in the figure, when establishing the finite element model, in order to reduce the number of meshes in the finite element model and reduce the computational cost, the local mesh was refined in the contact area between the roller and the raceway. In order to select a finite element model with an appropriate mesh, finite element models with different numbers of meshes in the contact area were established for calculation and analysis.

[0074] Apply fixed constraints to all nodes on the bottom surface of the lower raceway, constrain the freedom of movement in the X and Z directions of all nodes on the uppermost busbar of the roller, release its freedom in the Y direction, and at the same time constrain the freedom of movement in the Z direction of all nodes on the contact line between the roller and the raceway. The load is applied to all nodes on the uppermost busbar of the roller in the negative direction of the Y axis in the form of concentrated force. Contact is established between the roller and the raceway. The mesh of the contact area of ​​the finite element model is encrypted multiple times, and a load of 200kN is evenly applied to the roller. The finite element model with boundary conditions is as follows Figure 3 shown.

[0075] The error Er between the finite element and Hertz contact theory calculation results can be expressed by Equation 3:

[0076]

[0077] Where Er represents the error, x represents the finite element calculation result, and T represents the Hertz contact theory calculation result.

[0078] Calculations were performed on multiple finite element models with different numbers of grids and compared with the maximum contact stress calculated by the Hertz contact theory. The maximum contact stress obtained by the Hertz contact theory was 2.342 GPa. The error between the results obtained by the finite element and the Hertz contact theory is as follows: Figure 4 As shown by Figure 4It can be seen that when the number of grids is small, the finite element results are quite different from the results calculated by the Hertz contact theory, and the error Er exceeds 80%. As the grid in the contact area is encrypted, the error between the results calculated by the finite element calculation and the results of the Hertz contact theory is also decreasing. The model with a roller grid number of 7760 is close to the results calculated by the Hertz contact theory, with an error of only 2.8%. Therefore, the relevant grid size parameters of the finite element model with a roller grid number of 7760 are selected for modeling and calculation of the main thrust roller.

[0079] Apply loads of different sizes to the finite element model determined above, such as Figure 5 and Figure 6 As shown, Figure 5 is the maximum contact stress obtained by finite element and Hertz contact theory under different loads. Figure 6 is the error between the two. Figure 5 It can be seen that when the mesh is fixed and the load is small, the contact stress results calculated by the finite element method and the Hertz contact theory differ greatly. This is because when the load is smaller, the contact width between the roller and the raceway is smaller, and the contact area requires a smaller mesh to ensure the accuracy of the results. Therefore, when the mesh is fixed, the smaller the load, the greater the error between the results calculated by the Hertz contact theory. Figure 6 It can be seen that after the load increases to a certain value, the error changes slightly and basically tends to be stable, with the error value within 5%.

[0080] The above results show that the error between the calculation results of the full-solid element roller model with a grid number of 7760 and the calculation results of the Hertz contact theory is within a small range. This full-solid element roller model can be used to verify the validity of the equivalent model.

[0081] In a specific embodiment:

[0082] Establish local finite element models of rollers and inner and outer raceways, such as Figure 7 and Figure 8 As shown in , firstly, a finite element model of the full solid unit roller, i.e., the solid roller and raceway contact is established. Similarly, the local mesh is encrypted in the roller and raceway contact area. The equivalent roller model is as follows Figure 9 and Figure 10 As shown, Figure 9 is the overall schematic diagram of the finite element model of the equivalent roller. Figure 10This is a schematic diagram of a shell element. Both the solid and shell elements are cylindrical, with the shell elements attached to the inner surface of the solid element cylinder. The solid and shell elements are connected as a single entity through shared nodes. The equivalent roller model has a total of 5120 shell and solid elements, while the solid roller model has 7120 solid elements, a 28.1% mesh saving. Furthermore, the models presented here all use mesh refinement in the contact area. For other meshing methods, the equivalent model may achieve even greater mesh savings.

[0083] The same boundary conditions are applied to the solid roller and the equivalent roller model. The boundary conditions are as follows: Figure 11 and Figure 12 As shown, fixed constraints are applied to all nodes on the bottom surface of the lower raceway. All nodes on the top surface of the upper raceway are constrained in the X and Z directions, while their Y degrees of freedom are released. At the same time, all nodes on the contact line between the roller and the raceway are constrained in the Z direction. A concentrated load of 200 kN is applied to all nodes on the top surface of the upper raceway, in the negative Y direction. Contact is established between the roller and the upper and lower raceways.

[0084] In order to simulate the contact stress between the solid roller and the raceway and the stiffness of the solid roller in the contact direction, it is necessary to analyze and adjust the relevant parameters of the equivalent model. The parameters of the solid mesh in the equivalent model are the same as those of the solid roller, and the material density is 7850 kg / m 3 , the elastic modulus is 210GPa, and the Poisson's ratio is 0.3. In the equivalent model, the shell element thickness is adjusted to 20mm, the Poisson's ratio is 0.3, and the different elastic moduli of the shell elements are adjusted. Under a load of 200kN, the contact stress results and the approach value of the roller after loading are extracted from the finite element software and compared with the results of the solid roller. The approach value of the roller is determined by the following formula:

[0085]

[0086] In the formula, δ represents the mean distance, μ represents the number of nodes, and k i Represents the distance between the i-th pair of nodes.

[0087] In this paper, i=3, k A 、k B 、k C are the distances between the three pairs of nodes A, B, and C on the contact line after the roller is loaded, such as Figure 13 As shown:

[0088] The maximum contact stress obtained using the solid roller is 2.664GPa. The cloud diagram of the result is as follows: Figure 14As shown in Figure 2, the maximum contact stress occurs at a position close to the fillet, which is due to the stress concentration at the edge of the roller.

[0089] The results obtained using the equivalent model are as follows Figure 15 As shown in the figure, when the load is constant, the maximum contact stress obtained is small when the elastic modulus of the shell element is small. As the elastic modulus of the shell element gradually increases, the maximum contact stress between the roller and the raceway also increases, but it stops increasing after reaching a certain level and stabilizes at a certain constant value. This is because when the elastic modulus of the shell element increases to a certain level, its influence on the deformation of the roller after being loaded gradually decreases.

[0090] Figure 16 = is the error between the maximum contact stress between the roller and raceway obtained by the equivalent model under different elastic moduli of the shell element and the result obtained for the solid roller. As shown in the figure, the error decreases with increasing elastic modulus of the shell element and gradually approaches zero. Furthermore, the overall trend of change is also decreasing, with large early-stage error variations. This may be because when the elastic modulus of the shell element is small, its stiffness is less than that of a solid cylinder, and the stiffness of the equivalent model is also less than that of a solid roller model. When loaded, the equivalent model deforms more than the solid roller model, and its contact area with the raceway is also larger, resulting in a lower contact stress for the equivalent model.

[0091] Under the same boundary conditions, the calculated result of the approach distance of the solid roller model is δ = 0.0908 mm. Figure 17 is the approximate value of the equivalent model under different shell element elastic moduli. Figure 17 It can be seen that the roller approach amount decreases with the increase of the shell element elastic modulus, and as it further increases, the roller approach amount gradually tends to a certain value. Figure 18 is the error between the approximation of the equivalent roller model and the approximation of the solid model for different shell element elastic moduli. The figure shows that as the shell element elastic modulus increases, the approximation error of the equivalent roller model exhibits an overall V-shaped pattern, and there exists a modulus value where the error approaches zero. This is because, under a given load, as the shell element elastic modulus increases, the overall stiffness of the equivalent roller model increases, while its deformation under load decreases. When the shell element elastic modulus increases to a certain level, the stiffness and deformation of the equivalent model and the solid model become similar, and the error between the two approaches zero. As the shell element elastic modulus further increases, the deformation of the equivalent roller model decreases, and the difference in approximation from the solid model gradually increases, leading to a larger error. As the shell element elastic modulus further increases, its effect on the stiffness of the equivalent roller model decreases, the deformation of the equivalent roller decreases, and the approximation error between the equivalent roller and the solid roller stabilizes.

[0092] From the above results, it can be seen that when the boundary conditions are the same, taking into account the maximum contact stress and the roller approach value, when the elastic modulus of the shell element is 245GPa, the maximum contact stress and the approach value of the equivalent model and the solid roller are slightly different. The error of the maximum contact stress is 0.6%, and the error of the approach value is close to 0. In other words, the equivalent model with a shell element elastic modulus of 245GPa is selected for the mechanical analysis and calculation of the entire bearing.

[0093] The above embodiment provides a method for determining the elastic modulus of the shell unit in the equivalent roller model. The method is to establish a roller finite element model of a full solid unit, select a shell unit thickness of a certain set value, add the same constraints and loads as the full solid unit model, set the elastic modulus as a variable, compare the simulation result errors between the full solid unit model and the equivalent model under different elastic moduli, and determine the optimal value of the elastic modulus under the shell unit thickness.

[0094] In another specific embodiment:

[0095] Loads of K = [100, 200, 300, 400, 500] kN were applied to the equivalent roller model and the solid roller model, respectively. The error between the results of the roller equivalent model and the roller solid model under different load sizes was analyzed to verify the validity of the constructed roller equivalent model. The extracted results include the maximum contact stress between the roller and the raceway under load and the approach value δ of the roller after loading.

[0096] Figure 19 The results of the maximum contact stress of the equivalent roller model and the solid roller model under different loads are compared. Figure 19 It can be seen that as the load continues to increase, the contact stress between the roller and the raceway also continues to increase, and the contact stress results of the equivalent roller model and the solid roller model under different loads are highly similar.

[0097] Table 2 shows the error in the maximum contact stress obtained by the equivalent roller model relative to the solid roller model under different loads. The results show that the error in the equivalent roller model decreases with increasing load. This is likely because T increases with increasing load. Equation (3) shows that Er decreases with increasing T. Furthermore, the error in the equivalent model is generally small under different loads, remaining within 1%. Analysis of the maximum contact stress results demonstrates the effectiveness of the equivalent roller model.

[0098] Table 2

[0099]

[0100] Figure 20 The results of the approach of the equivalent roller model and the solid roller model under different loads are compared. Figure 20It can be seen that the roller approach amount increases with the increase of load, and the roller approach amount δ results of the equivalent roller model and the solid roller model are highly consistent.

[0101] Under different loads, the approach error of the equivalent roller model relative to the solid roller model is shown in Table 3. As can be seen from Table 3, the error between the two is very small, both maintained within 0.3%. The analysis of the roller approach result value proves the effectiveness of the equivalent roller model.

[0102] Table 3

[0103]

[0104] Figure 21 The calculation time for the equivalent single-roller model and the solid single-roller model, under the same boundary conditions and using the same computer, is shown in Table 4. The equivalent roller model can effectively reduce calculation time and improve efficiency. Table 4 shows the calculation time for the single-roller model. As shown in Table 4, the equivalent model can reduce the calculation time for the solid roller by up to 28.57%. This means that for slewing bearing models with a large number of rollers, a large amount of calculation, and a long calculation time, the equivalent model is more necessary.

[0105] Table 4

[0106]

[0107] The results of this embodiment show that, compared with the solid model of the equivalent roller model and the solid model of the full solid element, the calculation time can be shortened by about 1 / 4 when the results are similar, thereby improving the calculation efficiency.

[0108] As we know, the elastic modulus is the ratio of stress to strain in a material during its elastic deformation phase. It is a core parameter in the linear elastic constitutive relation that measures a material's resistance to elastic deformation. In finite element analysis, the elastic modulus directly contributes to the construction of the element stiffness matrix, directly influencing the deformation, stress distribution, and contact behavior of the roller under load. The shell element thickness of the roller model is the normal dimension of the shell model, representing the shell element's ability to simulate the thickness of the solid structure. Different thicknesses directly affect the stiffness and contact stress values ​​of the equivalent roller.

[0109] In order to make the equivalent roller model suitable for cylindrical rollers of different diameters, it is necessary to study the value of the elastic modulus of the shell element under different shell element thicknesses. The specific method is: set the shell element thickness and elastic modulus of the equivalent model as variables, compare the simulation result errors between the full solid element model and the equivalent model under different elastic moduli and different shell element thicknesses, determine the optimal value of the elastic modulus under different shell element thicknesses, and obtain the fitting equations for different shell element thicknesses and elastic moduli according to the simulation results, so as to obtain the shell element thickness and elastic modulus of the shell element according to the fitting equations.

[0110] In a specific embodiment:

[0111] The relationship between the shell element thickness of the equivalent roller model and the elastic modulus of the shell element is studied when the thickness is 4mm to 40mm. The parameters such as the Poisson's ratio of the shell element are the same as those of the solid mesh. The curve fitting is performed using Matlab. The data values ​​of the shell thickness and the shell elastic modulus are shown in Table 5:

[0112] Table 5

[0113]

[0114] The data were fitted using the S-shaped fitting type to obtain the following formula, where x is the shell element thickness, f1(x) is the elastic modulus, and a, b, c, and d are fitting parameters. The specific values ​​are shown in Table 6:

[0115] Table 6

[0116]

[0117] In order to verify the fitting equation, x=6, x=21 and x=38 are substituted into the fitting formula to obtain: the shell elastic modulus is 8.8732e+11Pa when the shell element thickness is 6mm, the elastic modulus is 2.326e+11Pa when the shell element thickness is 21mm, and the elastic modulus is 1.2364e+11Pa when the shell element thickness is 38mm. The three sets of data are substituted into the finite element model and recorded as roller 1, roller 2 and roller 3. The loads of K=[100, 200, 300, 400, 500] kN are applied to the three rollers respectively. The finite element results of the equivalent roller model are extracted and compared with the solid roller model. The results are shown as follows: Figure 23 、 Figure 24 As shown, Figure 23 、 Figure 24 are the maximum contact stress of the roller and the value of the roller approach δ extracted by finite element analysis. It can be seen from the figure that with the continuous increase of load, the maximum contact stress and approach of the solid roller and equivalent roller models are constantly increasing, and the result value of the equivalent model is highly consistent with the result value of the solid roller, and the error does not exceed 1%, which effectively verifies the validity of the fitting formula.

[0118] That is to say, the above embodiment determines the shell element thickness and elastic modulus by calculating and comparing the maximum roller contact stress error and the roller approach error of the full solid element model and the equivalent model, and it has been verified that the fitting equation is valid, which provides a reference for the analysis of rollers of different diameters.

[0119] like Figure 22 As shown in the figure, the mid-surface of the shell element is the geometric center plane in the thickness direction, and its position can be changed by adjusting the offset of the shell element. In finite element analysis, the change of the shell element offset will affect the geometric error of the model structure, and thus have an important impact on the result value of the contact stress.

[0120] The shell element thickness and shell mid-surface radius of the equivalent model are set as variables. The simulation result errors between the full solid element model and the equivalent model under different shell mid-surface radii and different shell element thicknesses are compared to determine the optimal value of the shell element thickness under different shell mid-surface radii. The fitting equations for different shell mid-surface radii and shell element thicknesses are obtained according to the simulation results, so as to determine the shell element thickness and shell mid-surface radius of the shell element according to the fitting equations.

[0121] In a specific embodiment, a finite element calculation is performed using the main thrust roller model of a slewing bearing. The radius of the shell element mid-surface is changed by changing the shell element offset value. The shell element material parameters are consistent with the solid element settings. When the shell element is equivalent, the relationship between the shell element mid-surface radius in the range of 3 mm to 40 mm and the shell element thickness is studied. Curve fitting is performed using Matlab, where the data values ​​of the shell element mid-surface radius and the shell element thickness are shown in Table 7:

[0122] Table 7

[0123]

[0124] Using the "Fourier" fitting type for fitting, we get the following equation:

[0125]

[0126] Where x is the radius of the shell mid-surface, f2(x) is the thickness of the shell element, and a i , b i , w are fitting parameters, and the specific values ​​of the parameters are shown in Table 8:

[0127] Table 8

[0128]

[0129] Formula 4 is verified by substituting x=9, 22 and 38 into Formula 4 respectively. The shell thicknesses are 22.8259mm, 30.376mm and 39.1675mm when the mid-surface radius of the shell element is 9mm, 22mm and 38mm respectively. The corresponding parameters are substituted into the equivalent roller model and recorded as roller 1, roller 2 and roller 3 respectively. The loads of K=[100, 200, 300, 400, 500]kn are applied to the three roller models. The finite element results of the equivalent roller model are extracted and compared with the solid roller model. The results are shown as follows: Figure 25 、 26 As shown, Figure 25 、 Figure 26 They are the maximum contact stress and roller approach value of the equivalent roller model and the solid roller model respectively. It can be seen from the figure that the result values ​​​​between the two are very similar, with very small errors, which limitedly verifies the effectiveness of the fitting formula.

[0130] To further illustrate the universal applicability of the equivalent roller, the equivalent roller model can be applied to multiple applications with different roller radii, obtain the equivalent roller model parameter values ​​for different roller radii, and study the relationship between roller radius and shell element thickness. The material parameters of the shell element of the equivalent roller are consistent with those of the solid element. By repeatedly modeling the main thrust roller of the slewing bearing to obtain finite element models of different radii and performing calculations, the corresponding data for roller radius of 10mm to 30mm and shell thickness were obtained, as shown in Table 9:

[0131] Use the exponential fitting type to fit the data in the table and get the following formula:

[0132] f3(x)=ae bx +ce dx

[0133] Where f3(x) is the shell element thickness, x is the roller radius, a, b, c, and d are fitting parameters. The specific values ​​are shown in Table 10:

[0134] Table 9

[0135]

[0136] Table 10

[0137]

[0138] Substituting x=11, 21, and 29 into the fitting equation, we obtain the shell element thicknesses of 7.8891mm, 22.5717mm, and 32.3825mm for roller radii of 11mm, 21mm, and 29mm, respectively. The rollers are denoted as roller 1, roller 2, and roller 3 in order. The three equivalent roller models are calculated and compared with the calculation results of the solid rollers with the same roller radius. The results are shown in Figure 2. Figure 27 、 Figure 28 As shown, Figure 27 is the maximum result value of roller contact stress, Figure 28 is the roller approach value. As can be seen from the figure, the calculation results of the three equivalent roller models with different roller radii are highly consistent with the solid roller model, with a very small error. The main reason for the error is that the number and method of mesh division in the middle of the solid roller are different from the actual ones.

[0139] In the above embodiments, the effectiveness of the full solid unit model and the equivalent model of a single roller is mainly analyzed. In the following embodiments, the effectiveness of the equivalent model of multiple rollers is mainly analyzed.

[0140] In one embodiment:

[0141] Establish a multi-roller finite element model of equivalent roller model and solid roller model, where the multi-roller equivalent model is as follows Figure 29 As shown, the solid roller model is as follows Figure 30 As shown, the size of the rollers is consistent with Table 1, and the number is 18.

[0142] The overall model of rollers and raceways is as follows Figure 31 and Figure 32 As shown, Figure 31 is the overall model of the multi-roller equivalent model and the raceway, Figure 32 It is the overall model of multiple solid roller models and raceways.

[0143] Fixed constraints are applied to all nodes on the bottom surface of the lower raceway, and the freedom of movement of all nodes on the top surface of the upper raceway in the X and Z directions is constrained. The rollers are constrained by low-stiffness spring elements. The load is applied to all nodes on the top surface of the upper raceway in the form of a concentrated force of 3600 kN in the -Y direction. The finite element model with boundary conditions is as follows: Figure 33 shown.

[0144] Extract the contact stress results from the two finite element models and conduct comparative analysis. Figure 34 、 Figure 35 These are the normal contact stress cloud diagrams of the two models. The maximum values ​​are 2.667 GPa and 2.682 GPa respectively. The result of the equivalent roller model is slightly smaller than that of the solid roller model, with a difference of 0.559%.

[0145] Extract the displacement contours of the two finite element models, such as Figure 36 、 Figure 37 As shown in the figure, the maximum values ​​of the results are consistent, both are 0.1932 mm.

[0146] In the two finite element models, a roller is selected respectively, and the specific position is as follows Figure 38As shown in the figure, the approach amount of this roller is extracted. The approach amounts of the equivalent roller model and the solid roller model are 0.0905mm and 0.09047mm respectively. The result is only 0.0368% different from the approach amount of the solid roller model.

[0147] The results of the above embodiments show that the error between the results of the equivalent roller in the multi-roller model and the calculation results of the solid roller of the full solid element is still small, which further verifies the effectiveness of the equivalent roller model.

[0148] Furthermore, in some embodiments, a finite element model of a three-row cylindrical roller bearing is created. Here, two finite element models of a solid roller model and an equivalent roller model are also created. Specifically:

[0149] The finite element model of a three-row cylindrical roller bearing using solid roller elements is as follows: Figures 39-41 As shown in the figure, in order to ensure the calculation accuracy, all mesh units use hexahedral meshes, with a total number of meshes of 42502840. From top to bottom, they are the finite element models of the main thrust roller, radial roller, and reverse thrust roller. The mesh is encrypted at the contact point between each roller and the inner and outer rings. The material density of the bearing unit is 7850kg / m 3 , the elastic modulus is 2.1e11Pa, and the Poisson's ratio is 0.3. In order to improve the calculation efficiency, only half of the bearing is calculated, and a 180° cyclic symmetry is set.

[0150] The boundary conditions set for the bearing are: constrain the degrees of freedom of all nodes on the bottom surface of the inner ring in the x, y and z directions, use low-stiffness spring units to constrain all rollers, establish point stiffness coupling, couple all nodes on the top surface of the outer ring with the main node, add the axial force and tilting moment of the bearing to the main node in the form of nodal force, constrain the displacement of the main node in the x and z directions and the rotational degrees of freedom in the x and y directions, and apply the axial force F to the main node. Z =3243800N, the direction is the negative direction of the y-axis, the tipping moment M = 66868.3kN·m, the direction is the z-axis rotation, such as Figure 42 shown.

[0151] The overall model of the slewing bearing with equivalent rollers is established. The main thrust solid rollers of the three-row cylindrical roller slewing bearing are all replaced by equivalent rollers. The material parameters of the solid mesh of the equivalent rollers are the same as those of the solid rollers, and the material density of the shell element is 7850 kg / m 3 , elastic modulus is 2.45e11Pa, thickness is 20mm. The other boundary conditions are consistent with those of the integral slewing bearing whose main thrust roller is a solid roller.

[0152] When analyzing the results, in order to clearly describe the position of the rolling elements, the main thrust rollers are numbered, such as Figure 43As shown, they are numbered clockwise from small to large.

[0153] The calculation results of the finite element model of the slewing bearing with solid main thrust rollers are extracted. Figure 44 is the maximum stress of the inner and outer ring rollers of the main thrust. The result value of the roller is extracted every five rollers. Figure 44 It can be seen that when the slewing bearing is subjected to a certain axial force and tilting moment, as the roller number increases, the main thrust inner and outer ring rollers tend to gradually decrease as a whole, and the result value of the main thrust outer ring roller is generally higher than that of the inner ring roller.

[0154] The calculation results of the slewing bearing with the main thrust rollers as equivalent rollers are extracted and compared with the results of the slewing bearing with the main thrust rollers as solid rollers. Figure 45 is the maximum contact stress of the solid roller model and the equivalent roller model under the same conditions, given by Figure 45 It can be seen that as the roller number increases, the maximum contact stress of the main thrust roller shows an overall decreasing trend, but it increases in local areas, and the curve is "hump-shaped". The result value of the equivalent roller model is highly consistent with that of the solid roller, verifying the effectiveness of the equivalent roller model.

[0155] In summary, this invention pioneered the use of an equivalent roller model composed of shell elements and solid elements to perform finite element analysis and calculation of bearings, and verified in different ways that the results of the equivalent roller model are highly consistent with the results of the full solid element roller model. After actual calculations, the equivalent roller model can greatly reduce the number of grids, thereby improving the efficiency of the calculation and providing new ideas for the analysis of bearing mechanical properties.

[0156] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments without inventive effort, or replace some of the technical features therein with equivalents. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A bearing mechanical performance analysis method based on an equivalent roller model, characterized in that: The following steps are involved: S1: Establish a finite element model of the contact between the roller and the raceway, in which the roller is an equivalent model consisting of an inner shell element and an outer solid element. The shell element and the solid element are both cylindrical, and the shell element is attached to the inner surface of the solid element. S2: According to the actual load of the bearing, constraints and loads are added, and the simulation program is run to obtain the results.

2. The bearing mechanical performance analysis method based on the equivalent roller model according to claim 1 is characterized in that: In S1, the elastic modulus of the shell element is determined by the following method: a roller finite element model of a full solid element is established, a shell element thickness of a certain set value is selected, the same constraints and loads as the full solid element model are added, the elastic modulus is set as a variable, the simulation result error between the full solid element model and the equivalent model under different elastic moduli is compared, and the optimal value of the elastic modulus under the shell element thickness is determined.

3. The bearing mechanical performance analysis method based on the equivalent roller model according to claim 2 is characterized in that: The shell element thickness and elastic modulus of the equivalent model are set as variables. The simulation result errors between the full solid element model and the equivalent model under different elastic moduli and different shell element thicknesses are compared to determine the optimal elastic modulus under different shell element thicknesses. The fitting equations for different shell element thicknesses and elastic moduli are obtained based on the simulation results, so as to determine the shell element thickness and elastic modulus of the shell element in S1 according to the fitting equations.

4. The bearing mechanical performance analysis method based on the equivalent roller model according to claim 3 is characterized in that: The fitting equations for shell element thickness and elastic modulus are: In this equation, x is the thickness of the shell element, f1(x) is the elastic modulus, and a, b, c, and d are fitting parameters.

5. The bearing mechanical performance analysis method based on the equivalent roller model according to any one of claims 2 to 4 is characterized in that: Comparing the simulation results of the full solid element model and the equivalent model, the errors include the maximum roller contact stress error and the roller approach error.

6. The bearing mechanical performance analysis method based on the equivalent roller model according to any one of claims 2 to 4 is characterized in that: The shell element thickness and shell mid-surface radius of the equivalent model are set as variables. The simulation result errors between the full solid element model and the equivalent model under different shell mid-surface radii and different shell element thicknesses are compared to determine the optimal shell element thickness under different shell mid-surface radii. The fitting equations for different shell mid-surface radii and shell element thicknesses are obtained according to the simulation results, so as to determine the shell element thickness and shell mid-surface radius of the shell element in S1 according to the fitting equations.

7. The bearing mechanical performance analysis method based on the equivalent roller model according to claim 6 is characterized in that: The fitting equation for the shell mid-surface radius and shell element thickness is: In this equation, x is the radius of the shell mid-surface, f2(x) is the thickness of the shell element, and a i , b i , w are fitting parameters.

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