Finite element analysis method for evaluating dynamic performance of angular contact ball bearing for machine tool

Abstract

A finite element analysis method for evaluating dynamic performance of angular contact ball bearing for machine tool is provided. According to the bearing design size provided by national standard, the three-dimensional solid model of inner ring, outer ring, rolling element and cage of angular contact ball bearing is established in mechanical design software SolidWorks, and the model is imported into finite element analysis software ABAQUS to carry out simulation. By using the cutting method of inner ring, outer ring and rolling element model, high-quality and high-precision finite element grid is divided, and the grid number of the whole model is reasonably controlled to reduce the calculation time of dynamic display, improve the calculation accuracy and efficiency. This method can accurately calculate the dynamic displacement response of machine tool bearing under high speed and the contact stress between rolling element and contact interface. Using the calculation results, the dynamic performance of machine tool bearing under service condition can be quickly evaluated, the failure mechanism of rolling contact fatigue in bearing raceway is analyzed, which provides help for improving the production process of bearing and improving the overall performance of machine tool.

Description

Technical Field

[0001] This invention relates to the field of dynamic performance research of angular contact ball bearings for machine tools, and in particular provides a finite element analysis method for evaluating the dynamic performance of angular contact ball bearings for machine tools. Background Technology

[0002] Bearings, as crucial components of machine tools, directly affect the machining accuracy, rigidity, and reliability of the machine tool, and have a significant impact on the performance of the machine tool's spindle system and the main machine itself. In recent years, machine tool spindle bearings have been developing towards higher speeds, higher precision, and longer lifespans, which places higher demands on the structural dynamic performance and material fatigue properties of machine tool bearings. Therefore, studying the dynamic response of machine tool bearings under service conditions is of great significance for evaluating their machining accuracy, rigidity, and material fatigue performance.

[0003] Under operating conditions, the main failure mode of machine tool bearings is rolling contact fatigue, which leads to peeling and cracking in the inner and outer raceways, resulting in a decrease in bearing accuracy. To study the failure mechanism of rolling contact fatigue in bearing materials and improve bearing service life, there is an urgent need for an analytical method capable of calculating the contact stress in the raceways of bearings at high speeds. Therefore, this invention proposes a finite element analysis method for evaluating the dynamic performance of angular contact ball bearings for machine tools. Summary of the Invention

[0004] The purpose of this invention is to provide a finite element analysis method for evaluating the dynamic performance of angular contact ball bearings used in machine tools. This method can help us measure the contact stress and dynamic displacement response of angular contact ball bearings used in machine tools at high speeds, and further evaluate the rolling contact fatigue failure mechanism of bearing materials, improve their manufacturing processes, and enhance the accuracy and lifespan of machine tool bearings.

[0005] This invention is mainly achieved through the following technical solution: a finite element analysis method for evaluating the dynamic performance of angular contact ball bearings for machine tools, comprising the following steps:

[0006] Step 1: Based on the national standard GB / T292-2007 for the external dimensions of angular contact ball bearings, establish a three-dimensional solid model of the inner ring, outer ring, rolling elements, and cage of the angular contact ball bearing:

[0007] First, a 3D solid model of the bearing was created using the mechanical design software SolidWorks. The model was built based on the bearing dimensional parameters specified in national standards and the selected bearing model. In the SolidWorks Parts module, 3D solid models of the inner ring, outer ring, and cage were created separately, while the rolling element models were generated using an array method. Then, the bearing components created in the SolidWorks Parts module were imported into the Assembly module to complete the assembly of the bearing parts. Finally, a Step file was exported for importing the model into the finite element software and for mesh generation.

[0008] Step 2: Import the exported bearing model file into the finite element analysis software Abaqus to complete the mesh generation of the bearing model:

[0009] The meshing of all bearing components was completed in the finite element analysis software Abaqus. First, because the contact area between the inner and outer ring raceways and the rolling elements is very small, approximating line contact, the meshes within the raceways and the rolling elements both require refinement. Second, since mesh refinement significantly increases computational complexity, the meshes of the inner and outer rings and rolling elements also need transition processing to reduce the number of meshes and improve computational efficiency.

[0010] 1) The meshing and processing method for the bearing inner ring model is as follows: First, the inner ring is uniformly divided into 72 parts radially, each part occupying an angle of 5°. After division, only one part is retained, and the rest are deleted. At the same time, the retained part is divided again, with the main division area located on the outer side of the inner ring raceway. The divided model is as follows: Figure 1 As shown in (a), the segmented model exhibits a transitional morphology. Then, the segmented model is meshed, with the element type selected as C3D8R. The minimum mesh size for the inner circle after segmentation is 0.25 mm, and the maximum mesh size is 2 mm. The meshing result is shown below. Figure 1 (b) shows the process. Finally, the generated mesh components are imported into the assembly module, where they are arrayed to generate a complete bearing inner ring mesh model. Furthermore, to obtain more accurate stress results, the mesh at the location of maximum contact stress between the inner ring and the rolling element is further refined. In this case, the angle occupied by the re-divided mesh is 2.5°, the model segmentation method remains unchanged, and the minimum mesh size is 0.03 mm.

[0011] 2) The meshing method for the outer ring model of the bearing is the same as that for the inner ring. First, the outer ring is evenly divided into 90 parts radially, with each part occupying an angle of 4° (to ensure that the minimum mesh size is consistent with that of the inner ring). After division, only one part is retained, and the rest are deleted. At the same time, the retained part is divided again, with the main division area located outside the inner ring raceway. The divided model is as follows: Figure 2 As shown in (a), the segmented model exhibits a transitional morphology. Then, the segmented model is meshed, with the element type selected as C3D8R. The minimum mesh size on the outer edge after segmentation is 0.25 mm, and the maximum mesh size is 2 mm. The meshing result is shown below. Figure 2 (b) shows the process. Finally, the generated mesh components are imported into the assembly module, where they are arrayed to generate a complete bearing outer ring mesh model. Furthermore, to obtain more accurate stress results, the mesh at the location of maximum contact stress between the outer ring and the rolling element is further refined. In this case, the angle occupied by the re-divided mesh is 2°, the model segmentation method remains unchanged, and the minimum mesh size is 0.03 mm.

[0012] 3) The meshing of the rolling elements also needs to consider the overall computational efficiency of the model. Therefore, at the contact positions between the rolling elements and the inner and outer raceways, the rolling elements are divided radially along the bearing, and the mesh at the contact positions with the raceways is refined. The method of dividing the rolling elements is as follows: Figure 3 As shown in (a), and based on the motion trajectory of the rolling elements during bearing rotation, the rolling elements that come into contact with the outer ring after entering a steady state are selected, and their mesh is further refined to a minimum size of 0.03 mm, consistent with the mesh size of the inner and outer ring raceways. The refined mesh of the rolling elements is shown in Figure (a). Figure 3 As shown in (b);

[0013] 4) The bearing cage and rolling elements are in contact with each other to ensure the stability of the rolling elements during rolling. However, the contact stress between them is small, so the mesh is not refined and the mesh size is set to 0.2mm.

[0014] Step 3: Setting up contact between bearing components and inputting model parameters:

[0015] The contact type between the bearing components is selected as general contact. The normal direction of the contact interface is set to 'hard' contact, and the tangential direction is set to static-dynamic exponentially decaying friction contact. The static friction coefficient is set to 0.02, the dynamic friction coefficient is set to 0.01, and the decay coefficient is set to 0.01.

[0016] To meet the loading and constraint conditions of the bearing, two reference points are established at the center point of the bearing. Reference point 1 is coupled to the inner ring of the bearing, and reference point 2 is coupled to the bearing cage. The coupling type is continuous distributed coupling.

[0017] Based on the material of each component of the bearing, corresponding material parameters are assigned.

[0018] Step 4: Based on the operating conditions of the bearing, complete the constraint and load settings for the bearing model:

[0019] In the bearing bench test, the outer ring of the bearing is fixed, while the inner ring is subjected to vertical and axial loads and rotates at high speed. Therefore, explicit dynamic analysis is selected in the simulation analysis, and two analysis steps are established: in analysis step 1), the vertical and axial loads and gravity loads on the bearing are applied at reference point 1 of the inner ring; in analysis step 2), the rotational speed of the bearing is applied at reference point 1. At the same time, degrees of freedom independent of the load and rotation direction are fixed in both analysis steps.

[0020] Furthermore, in step one, the contact angle of the angular contact ball bearing is 15°, the outer ring outer diameter D = 68mm, the inner ring inner diameter d = 40mm, and the number of rolling elements is 18.

[0021] Furthermore, in step two, the generation of the inner and outer ring mesh models of the bearing is achieved in the assembly module of Abaqus by merging the mesh components of the inner and outer rings using the mesh node merging function. At the same time, the locally refined mesh model also needs to be imported into the assembly module to merge the mesh nodes at the same positions.

[0022] Furthermore, in step three, the coupling type between the reference point and the inner ring and the cage can only be selected as continuous distributed coupling. This is because it is necessary to ensure that relative deformation can occur between the coupling nodes, while motion coupling will restrict the relative deformation of the nodes, thereby increasing the structural stiffness and producing a large error in the simulation results.

[0023] The material parameters are as follows: the inner and outer rings are made of bearing steel with a density of 7.8 g / cm³. 3 The elastic modulus is 206 GPa, and the Poisson's ratio is 0.3. The rolling element is made of ceramic material with a density of 3.2 g / cm³. 3 The elastic modulus is 320 GPa, and the Poisson's ratio is 0.26. The cage is made of nylon with a density of 1.35 g / cm³. 3 Its elastic modulus is 28.3 GPa and its Poisson's ratio is 0.35.

[0024] Furthermore, in step four, the loading amplitude type of the bearing vertical and axial loads is selected as smooth, and the speed amplitude type is also smooth. This loading method can reduce the oscillation caused by inertial force impact, so that the dynamic results can quickly stabilize.

[0025] The beneficial effects of this invention are:

[0026] This invention proposes a finite element analysis method for evaluating the dynamic performance of angular contact ball bearings used in machine tools. Based on the shape and dimensions of angular contact ball bearings for machine tools provided by national standards, this method accurately establishes a three-dimensional solid model and imports this model into commercial finite element analysis software for finite element simulation calculations. Addressing the issue of small contact areas between the inner and outer rings and rolling elements of machine tool bearings, and the high requirements for mesh size and calculation accuracy, this method proposes a segmentation method for the inner and outer ring and rolling element models. This segmentation method can generate high-quality, high-precision finite element analysis meshes and can reasonably control the number of meshes in the overall model, reducing the calculation time for dynamic display and improving calculation accuracy and efficiency. Finally, this method can accurately calculate the dynamic displacement response of machine tool bearings at high speeds, as well as the contact stress between the rolling elements and the contact interface. The calculation results can be used to quickly evaluate the dynamic performance of machine tool bearings under service conditions, analyze the failure mechanism of rolling contact fatigue in the bearing raceway, and provide assistance in improving bearing manufacturing processes and enhancing the overall performance of machine tools. Attached Figure Description

[0027] Figure 1 Schematic diagram of bearing inner ring segmentation method and mesh generation (a, segmentation method, b, mesh generation method);

[0028] Figure 2 Schematic diagram of bearing outer ring segmentation and mesh generation (a, segmentation method, b, mesh generation method);

[0029] Figure 3 Schematic diagram of rolling element segmentation and mesh generation (a, segmentation method, b, mesh generation method);

[0030] Figure 4 Schematic diagram of the overall mesh division of the bearing. Detailed Implementation

[0031] The technical solution of the present invention will be described and explained in detail below with reference to the accompanying drawings. A finite element analysis method for evaluating the dynamic performance of angular contact ball bearings for machine tools is described in detail below:

[0032] I. Based on the national standard GB / T292-2007 for the external dimensions of angular contact ball bearings, establish a three-dimensional solid model of the inner ring, outer ring, rolling elements, and cage of the angular contact ball bearing:

[0033] First, a 3D solid model of the bearing was created using the mechanical design software SolidWorks. The model was built based on the bearing dimensional parameters specified in national standards and the selected bearing model. In the SolidWorks Parts module, 3D solid models of the inner ring, outer ring, and cage were created separately, while the rolling element models were generated using an array method. Then, the bearing components created in the SolidWorks Parts module were imported into the Assembly module to complete the assembly of the bearing parts. Finally, a Step file was exported for importing the model into the finite element software and for mesh generation.

[0034] 2. Import the exported bearing model file into the finite element analysis software Abaqus to complete the mesh generation of the bearing model:

[0035] The meshing of all bearing components was completed in the finite element analysis software Abaqus. The meshes within the raceway and the rolling elements required refinement, and the meshes of the inner and outer rings and rolling elements also needed transition processing, as detailed below:

[0036] 1) The meshing and processing method for the bearing inner ring model is as follows: First, the inner ring is uniformly divided into 72 parts radially, each part occupying an angle of 5°. After division, only one part is retained, and the rest are deleted. At the same time, the retained part is divided again, with the main division area located on the outer side of the inner ring raceway. The divided model is as follows: Figure 1 As shown in (a), the segmented model exhibits a transitional morphology. Then, the segmented model is meshed, with the element type selected as C3D8R. The minimum mesh size for the inner circle after segmentation is 0.25 mm, and the maximum mesh size is 2 mm. The meshing result is shown below. Figure 1 (b) shows the process. Finally, the generated mesh components are imported into the assembly module, where they are arrayed to generate a complete bearing inner ring mesh model. Furthermore, to obtain more accurate stress results, the mesh at the location of maximum contact stress between the inner ring and the rolling element is further refined. In this case, the angle occupied by the re-divided mesh is 2.5°, the model segmentation method remains unchanged, and the minimum mesh size is 0.03 mm.

[0037] 2) The meshing method for the outer ring model of the bearing is the same as that for the inner ring. First, the outer ring is evenly divided into 90 parts radially, with each part occupying an angle of 4° (to ensure that the minimum mesh size is consistent with that of the inner ring). After division, only one part is retained, and the rest are deleted. At the same time, the retained part is divided again, with the main division area located outside the inner ring raceway. The divided model is as follows: Figure 2As shown in (a), the segmented model exhibits a transitional morphology. Then, the segmented model is meshed, with the element type selected as C3D8R. The minimum mesh size on the outer edge after segmentation is 0.25 mm, and the maximum mesh size is 2 mm. The meshing result is shown below. Figure 2 (b) shows the process. Finally, the generated mesh components are imported into the assembly module, where they are arrayed to generate a complete bearing outer ring mesh model. Furthermore, to obtain more accurate stress results, the mesh at the location of maximum contact stress between the outer ring and the rolling element is further refined. In this case, the angle occupied by the re-divided mesh is 2°, the model segmentation method remains unchanged, and the minimum mesh size is 0.03 mm.

[0038] 3) The meshing of the rolling elements also needs to consider the overall computational efficiency of the model. Therefore, at the contact positions between the rolling elements and the inner and outer raceways, the rolling elements are divided radially along the bearing, and the mesh at the contact positions with the raceways is refined. The method of dividing the rolling elements is as follows: Figure 3 As shown in (a), and based on the motion trajectory of the rolling elements during bearing rotation, the rolling elements that come into contact with the outer ring after entering a steady state are selected, and their mesh is further refined to a minimum size of 0.03 mm, consistent with the mesh size of the inner and outer ring raceways. The refined mesh of the rolling elements is shown in Figure (a). Figure 3 As shown in (b);

[0039] 4) The bearing cage and rolling elements are in contact with each other to ensure the stability of the rolling elements during rolling. However, the contact stress between them is small, so the mesh is not refined and the mesh size is set to 0.2mm.

[0040] III. Contact settings between bearing components and input parameters for the model:

[0041] The contact type between the bearing components is selected as general contact. The normal direction of the contact interface is set to 'hard' contact, and the tangential direction is set to static-dynamic exponentially decaying friction contact. The static friction coefficient is set to 0.02, the dynamic friction coefficient is set to 0.01, and the decay coefficient is set to 0.01.

[0042] To meet the loading and constraint conditions of the bearing, two reference points are established at the center point of the bearing. Reference point 1 is coupled to the inner ring of the bearing, and reference point 2 is coupled to the bearing cage. The coupling type is continuous distributed coupling.

[0043] Based on the materials of each component of the bearing, corresponding material parameters are assigned. The inner and outer rings are made of bearing steel with a density of 7.8 g / cm³. 3 The elastic modulus is 206 GPa, and the Poisson's ratio is 0.3. The rolling element is made of ceramic material with a density of 3.2 g / cm³. 3The elastic modulus is 320 GPa, and the Poisson's ratio is 0.26. The cage is made of nylon with a density of 1.35 g / cm³. 3 Its elastic modulus is 28.3 GPa and its Poisson's ratio is 0.35.

[0044] IV. Based on the operating conditions of the bearing, complete the constraint and loading settings for the bearing model:

[0045] In the bearing bench test, the outer ring of the bearing is fixed, while the inner ring is subjected to vertical and axial loads and rotates at high speed. Therefore, explicit dynamic analysis is selected in the simulation analysis, and two analysis steps are established: in analysis step 1), the vertical and axial loads and gravity loads on the bearing are applied at reference point 1 of the inner ring; in analysis step 2), the rotational speed of the bearing is applied at reference point 1. At the same time, degrees of freedom independent of the load and rotation direction are fixed in both analysis steps.

[0046] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A finite element analysis method for evaluating dynamic performance of an angular contact ball bearing for machine tools, characterized by, The method comprises the following steps: Step one, according to the national standard "GB / T292-2007" rolling bearing angular contact ball bearing outer shape size, the three-dimensional solid model of the inner ring, outer ring, rolling body and cage of the angular contact ball bearing is established: The three-dimensional solid model of the bearing is created by using the mechanical design software SolidWorks. The model is established according to the bearing size parameters and the selected bearing type in the national standard. The three-dimensional solid models of the inner ring, outer ring and cage of the bearing are established in the part module of SolidWorks. The rolling body model of the bearing is generated by using the array method. The bearing parts established in the part module of SolidWorks are imported into the assembly module. The assembly of the bearing parts is completed. The file in Step format is exported. The file is used for importing the model into the finite element software and meshing. Step two, the exported bearing model file is imported into the finite element analysis software Abaqus to complete the meshing of the bearing model: The meshes in the bearing raceway and the rolling body need to be refined. The meshes of the inner ring, outer ring and rolling body of the bearing need to be transitioned. The specific methods are as follows: 1) The meshing and processing method of the inner ring model is as follows: firstly, the inner ring is evenly divided into 72 models along the radial direction. Each model occupies an angle of 5°. After the division, only one part is retained, and the remaining parts are deleted. At the same time, the retained part is divided again. The main division position is located outside the inner ring raceway. The divided model has a transition appearance. Then, the meshing of the divided model is performed. The unit type is C3D8R. The minimum mesh size of the inner ring after division is 0.25 mm, and the maximum mesh size is 2 mm. The meshes at the position with the maximum contact stress between the inner ring and the rolling body are refined again. At this time, the model of the meshing part occupies an angle of 2.5°. The model division method remains unchanged. The minimum mesh size is 0.03 mm. Finally, the generated mesh part is imported into the assembly module. The parts are arrayed in the assembly module to generate the complete inner ring mesh model of the bearing; 2) The meshing and processing method of the outer ring model is as follows: firstly, the outer ring is evenly divided into 90 models along the radial direction. Each model occupies an angle of 4°. After the division, only one part is retained, and the remaining parts are deleted. At the same time, the retained part is divided again. The main division position is located outside the inner ring raceway. The divided model has a transition appearance. Then, the meshing of the divided model is performed. The unit type is C3D8R. The minimum mesh size of the outer ring after division is 0.25 mm, and the maximum mesh size is 2 mm. The meshes at the position with the maximum contact stress between the outer ring and the rolling body are refined again. At this time, the model of the meshing part occupies an angle of 2°. The model division method remains unchanged. The minimum mesh size is 0.03 mm. Finally, the generated mesh part is imported into the assembly module. The parts are arrayed in the assembly module to generate the complete outer ring mesh model of the bearing; 3) The grid cutting and processing of the rolling elements are as follows: the rolling elements are cut along the bearing radial direction at the contact position of the rolling elements and the inner and outer ring raceways, and the grid at the contact position is refined; at the same time, according to the movement track of the rolling elements in the bearing rotation process, the rolling elements that contact the outer ring after entering the steady state are selected, and the grid of the rolling elements is further refined, so that the minimum size is 0.03 mm, which is consistent with the grid size of the inner and outer ring raceways; 4) The grid size between the bearing retainer and the rolling elements is set to 0.2 mm; Step three, the contact setting between the bearing parts and the input parameters of the model: The contact type between the bearing parts is selected as the general contact, the normal of the contact interface is set as 'hard' contact, and the tangential is set as the friction contact with static-dynamic exponential decay, in which the static friction coefficient is set to 0.02, the dynamic friction coefficient is set to 0.01, and the decay coefficient is set to 0.01; Two reference points are established at the center point position of the bearing, in which the reference point 1 is coupled with the inner ring of the bearing, the reference point 2 is coupled with the bearing retainer, and the coupling type is continuous distribution coupling; Step four, according to the service working condition of the bearing, the constraint and loading setting of the bearing model are completed: In the simulation analysis, the dynamic analysis is selected, and two analysis steps are established: in analysis step 1), the vertical and axial loads and the gravity load of the bearing are applied on the reference point 1 of the inner ring of the bearing; in analysis step 2), the rotation speed of the bearing is applied on the reference point 1, and the degrees of freedom irrelevant to the load and the rotation direction are fixed in the two analysis steps.

2. The method of analysis according to claim 1, characterized in that: In the step one, the contact angle of the angular contact ball bearing is 15°, the outer diameter of the outer ring is D=68 mm, the inner diameter of the inner ring is d=40 mm, and the number of rolling elements is 18.

3. The method of analysis of claim 1, wherein: In the step two, the generation of the grid model of the inner and outer rings of the bearing is in the assembly module of Abaqus, after the array of the grid components of the inner and outer rings, the grid nodes are merged to obtain, at the same time, the locally refined grid model also needs to be imported into the assembly module to merge the grid nodes at the same position.

4. The method of analysis of claim 1, wherein: The material parameters of the bearing parts in the third step are as follows: the inner and outer rings are bearing steel material, the density is 7.8 g / cm 3 , the elastic modulus is 206 GPa, and the Poisson's ratio is 0.3; the rolling element is ceramic material, the density is 3.2 g / cm 3 , the elastic modulus is 320 GPa, and the Poisson's ratio is 0.26; the retainer is nylon material, the density is 1.35 g / cm 3 , the elastic modulus is 28.3 GPa, and the Poisson's ratio is 0.

35.

5. The method of claim 1, wherein: In the step four, the loading amplitude type of the vertical and axial loads of the bearing is selected as smooth type, and the amplitude type of the rotation speed is also smooth type.

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