Single-row four-point contact ball bearing simulation analysis method based on spring unit

Abstract

The invention discloses a single-row four-point contact ball bearing simulation analysis method based on a spring unit. The method is characterized by comprising the following implementation steps: (1) establishing a three-dimensional model of a single-row four-point contact ball bearing; (2) creating a spring connecting point at the ball position, and adding a spring unit to replace the ball; (3) defining nonlinear spring characteristics; (4) setting boundary conditions and load conditions; and (5) carrying out finite element statics analysis on the bearing. The rigidity of the spring unit is set according to the actual rigidity curve parameters of the balls. The rigidity curve parameter of the bearing ball is given to the spring unit, so that the deformation and the generated elastic force of the spring unit when the spring unit is stressed are similar to those of an actual ball, and the mechanical behavior of the ball in a bearing system is accurately simulated. The spring unit is adopted to simulate the ball, contact and separation of the ball and the inner ring and the outer ring can be simulated, the calculation amount of finite element analysis can be simplified, efficiency is improved, and the calculation precision is not lost.

Description

Technical Field

[0001] The present invention relates to the technical field of rolling bearings, and in particular to a structural simulation analysis method for a four-point contact ball bearing in which elastic elements are used instead of traditional balls. Background Art

[0002] Rolling bearings are essential mechanical components, widely used in automotive manufacturing, wind power generation, machine tool manufacturing, shipbuilding, aerospace, and other fields. Computer-aided design (CAD) is increasingly used in the design of large mechanical systems such as aircraft and automobiles, significantly reducing costs and cycle times. Finite element analysis, as the most important mechanical analysis method for mechanical systems, has been integrated into many large-scale software packages for widespread application.

[0003] Traditional bearing finite element analysis uses solid modeling, a method that suffers from high computational complexity and low efficiency. This is particularly true in large mechanical systems, where numerous bearings are involved. Therefore, it is crucial to find a method within finite element analysis software that can simplify bearings without compromising calculation accuracy. Summary of the Invention

[0004] In order to overcome the above-mentioned defects of the prior art, the present invention proposes a simplified method for a single-row four-point contact ball bearing in which spring units are used instead of balls. This method can simplify the calculation amount of finite element analysis and increase the efficiency of finite element analysis without losing its calculation accuracy.

[0005] The technical solution adopted in the present invention is:

[0006] A simulation analysis method for a single-row four-point contact ball bearing based on a spring unit is proposed. The method is based on a single-row four-point contact ball bearing structure in which spring units replace balls. The implementation steps of the method are as follows:

[0007] (1) Establish a three-dimensional model of a single-row four-point contact ball bearing with an inner diameter of 20 mm and an outer diameter of 40 mm;

[0008] (2) Create a spring connection point at the ball position and add a spring unit instead of the ball;

[0009] (3) Define nonlinear spring characteristics, with the spring pre-compression amount being 3% of the initial length;

[0010] (4) Set boundary conditions and load conditions, with the axial load being 500 N and the radial load being 200 N;

[0011] (5) Perform finite element static analysis on the bearing, and control the grid size to 0.5-2mm.

[0012] Furthermore, the addition of a spring unit instead of a ball reflects whether there is a contact effect based on the deformation of the spring itself. When the deformation of the spring unit is within a certain reasonable range, the corresponding simulated contact part is considered to be in a contact force state. If the deformation is zero or extremely small, it is considered to be in a non-contact state. As the external force changes, the deformation of the spring is a continuous process, and its force is proportional to the deformation. The linear correlation coefficient R between the spring deformation and the load is 2 ≥0.99.

[0013] Furthermore, when performing finite element static analysis on the bearing, the spring unit stiffness is set and adjusted according to the actual simulation requirements.

[0014] Furthermore, the spring stiffness is set according to the stiffness curve parameters of the actual ball. By assigning the bearing ball stiffness curve parameters to the spring unit, the ball material is selected as 40CrMn bearing steel with an elastic modulus of 210GPa and a Poisson's ratio of 0.3, so that its deformation and the elastic force generated when subjected to force are similar to those of the actual ball, thereby accurately simulating the mechanical behavior of the ball in the bearing system.

[0015] Furthermore, the spring unit stiffness is set to 2000-10000 N / m.

[0016] The principle behind this invention is that, in actual bearing operation, when an external load is applied to the bearing, the balls transfer force between the inner and outer rings and deform. Spring elements, with appropriate stiffness parameters, simulate the deformation and force transfer characteristics of the balls under normal load. When the bearing inner ring is subjected to an external load, its position changes. The mesh nodes of the inner ring transfer the normal displacement to the intermediate nodes via axial constraint elements, filtering out the tangential displacement. The intermediate nodes then move axially, squeezing the elastic elements, which generate a force that simulates the elastic force generated by the deformation of the bearing balls.

[0017] The spring element's stiffness is set based on the stiffness curve parameters of the actual ball. By assigning the bearing ball stiffness curve parameters to the spring element, its deformation and resulting elastic force when subjected to force are similar to those of an actual ball, accurately simulating the mechanical behavior of the ball in the bearing system.

[0018] The characteristics and advantages of the present invention compared with the prior art are:

[0019] (1) The number of nodes in the spring unit model is much less than that in the solid ball model.

[0020] (2) The spring stiffness parameters are adjustable, which facilitates the simulation of different working conditions.

[0021] (3) The present invention uses a spring unit to simulate the ball, which can simulate the contact and separation between the ball and the inner and outer rings.

[0022] (4) The present invention can simplify the calculation amount of finite element analysis and increase efficiency without losing calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Schematic diagram of traditional bearing contact

[0024] Figure 2 It is the contact diagram of spring unit;

[0025] Figure 3 Meshing diagram for traditional ball contact;

[0026] Figure 4 Surface contact meshing diagram for springs;

[0027] Figure 5 This is the traditional ball contact stress cloud diagram;

[0028] Figure 6 、 Figure 7 It is the contact stress cloud diagram of the spring surface. DETAILED DESCRIPTION

[0029] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings.

[0030] The present invention provides a simulation analysis method for a single-row four-point contact ball bearing based on a spring unit. The method is implemented in the following steps:

[0031] (1) Establish a three-dimensional model of a single-row four-point contact ball bearing with an inner diameter of 20 mm and an outer diameter of 40 mm;

[0032] (2) Create a spring connection point at the ball position and add a spring unit instead of the ball;

[0033] (3) Define nonlinear spring characteristics, with the spring pre-compression amount being 3% of the initial length;

[0034] (4) Set boundary conditions and load conditions, with the axial load being 500 N and the radial load being 200 N;

[0035] (5) Perform finite element static analysis on the bearing, and control the grid size to 0.5-2mm.

[0036] In the present invention, the technical concept of adding a spring unit instead of a ball is:

[0037] Spring elements typically reflect the presence of "contact" based on their own deformation. When the deformation of a spring element is within a reasonable range, the corresponding simulated contact point can be considered to be in a state similar to contact force. If the deformation is zero or extremely small, it can be approximately considered to be in a non-contact state. As the external force changes, the spring's deformation changes continuously, and the force it receives also changes continuously according to Hooke's law (force is proportional to deformation). The transition from near contact force to almost no force is relatively smooth.

[0038] The spring unit has its own spring stiffness, which is an inherent property of the unit. As long as it is within the elastic range, its force and deformation always change according to the linear relationship corresponding to this stiffness. The spring stiffness can also be set and adjusted according to the actual simulation requirements.

[0039] Example 1

[0040] A single-row, four-point contact ball bearing (40CrMn) is used as an example. The 3D bearing model is imported into ABAQUS for static analysis. The bearing parameters are shown in Table 1 below.

[0041] Table 1 Bearing parameters

[0042] parameter Numerical Number of balls 16 Contact angle α(°) 15 <![CDATA[Ball radius R j (mm)]]> 40 bearing materials bearing steel <![CDATA[Axial external load F a (N)]]> 500 <![CDATA[Radial external load F r (N)]]> 200 Ball speed r(r / min) 2000 Elastic modulus E(GPa) 210 Poisson's ratio 0.3

[0043] (1) Build a three-dimensional model of a single-row four-point contact ball bearing and define its material properties such as elastic modulus and Poisson's ratio. The three-dimensional geometric model of the bearing is as follows: Figure 1 As shown;

[0044] (2) Apply loads and boundary conditions to the bearing;

[0045] (3) Perform grid division, such as Figure 3 As shown, it can be seen that the number of elements after traditional bearing mesh division is 13576 and the number of nodes is 18221;

[0046] (5) Perform static analysis of the bearing and check the stress cloud diagram, such as Figure 5 The cloud map shows that the simulation results show that the peak stress in the contact area reaches 904.9 MPa, and the stress is mainly concentrated in the contact between the ball and the raceway. According to the GB / T 4661-2020 standard, the yield strength of the bearing material (GCr15 quenched steel) is 1850 MPa, and the allowable stress is 1233 MPa when the safety factor is 1.5. The measured maximum stress is lower than the allowable value and meets the static strength requirements. In addition, it can be seen from the cloud map that the bearing was solved in 443 steps from the beginning to the end of the operation.

[0047] Example 2

[0048] Different from the ball modeling method adopted in Example 1, this embodiment replaces all balls with an equivalent spring unit group to establish a simplified calculation model and complete comparative analysis.

[0049] (1) Establish a three-dimensional model of the spring unit bearing, establish a node at the theoretical center point of the ball, and connect the corresponding coupling points of the inner ring and outer ring through the spring unit. Figure 2 As shown;

[0050] (2) Set appropriate spring unit parameters, and the spring unit stiffness is set to 10000N / m;

[0051] (3) Define nonlinear spring characteristics;

[0052] (4) Perform grid division, such as Figure 4 As shown, the number of elements is 2368 and the number of nodes is 4113;

[0053] (5) Set boundary conditions and load conditions according to actual working conditions;

[0054] (6) Perform static analysis on the bearing and check the stress results of the bearing, such as Figure 6 The cloud diagram shows that stress is primarily concentrated in the inner and outer raceways connected to the spring unit, with the maximum stress reaching , which does not exceed the allowable stress of the bearing. The incremental step size is only 121 steps, which greatly reduces the calculation time compared to traditional ball bearings. The maximum contact stress occurs in the connection area between the spring unit and the inner and outer rings, with the maximum equivalent stress being 917.3 MPa. Compared with Example 1, the calculated results of the spring unit model are 1.37% higher than those of the solid model. This may be due to the local stress concentration caused by the homogenization treatment of the spring unit.

[0055] According to the ISO / TS16281:2008 standard, "Calculation Methods for Rolling Bearings," the maximum stress difference between the two models (12.4 MPa) is less than the bearing material fatigue limit. The 95% confidence interval error is [-9.8, +14.6] MPa, meeting the engineering analysis tolerance (±5%).

[0056] The total number of increments was reduced to 121, a 72.7% reduction in increments, which significantly shortened the computational time. The spring element model avoids contact nonlinearity, making the iteration more stable.

[0057] Example 3

[0058] On the basis of Example 2, the spring unit stiffness setting parameters were changed to 2000N to simulate the mechanical response of the bearing under different stiffness conditions. The same constraints and loads as in Example 2 were maintained to ensure consistency of comparison.

[0059] Stress cloud diagram Figure 7The results show that stress is concentrated at the connection between the spring unit and the inner and outer ring raceways. The maximum equivalent stress is 1576 MPa, a 71.8% increase compared to Example 2 (917.3 MPa). This indicates that the stress level under the current operating conditions is significantly higher than that in Example 2. This is due to the more severe loading conditions caused by the change in the spring unit stiffness parameters. However, the maximum equivalent stress must approach the yield strength of the bearing, 1850 MPa, requiring safety verification.

[0060] In the analysis step, the number of computational increments is 111, which is not much different from that in Example 2, indicating that the computational time of the spring element model is greatly reduced.

[0061] By comparing Example 2 with Example 1, it can be seen that the use of spring units to simulate the ball can simulate the contact and separation between the ball and the inner and outer rings. The number of nodes in the spring unit model after meshing is far less than that of the solid ball model, which can simplify the calculation amount of finite element analysis and increase efficiency without losing calculation accuracy.

[0062] By comparing Example 3 with Example 2, the mechanical response of the bearing under different stiffness conditions can be simulated by changing the stiffness parameters of the spring unit.

[0063] Some parts of the present invention are well-known technologies to those skilled in the art that are not described in detail.

[0064] Based on the above implementation, the present invention simplifies the ball bearing into a spring unit. During finite element modeling, spring units are created between corresponding nodes on the inner and outer races of the bearing, and the bearing ball stiffness curve parameters are assigned to simulate the ball bearing stiffness and deformation under load. The resulting finite element model, simulating contact between the ball bearing and the bearing, is then imported into the finite element analysis software ABAQUS for mechanical analysis of the bearing-containing mechanical system. This method significantly reduces model complexity and computational effort while maintaining accuracy.

[0065] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or replacements that can be understood and thought of by anyone familiar with the technology within the technical scope disclosed by the present invention should be included in the scope of the present invention.

Claims

1. A simulation analysis method for a single-row four-point contact ball bearing based on a spring unit, characterized by: The steps to implement this method are as follows: (1) Establish a three-dimensional model of a single-row four-point contact ball bearing with an inner diameter of 20 mm and an outer diameter of 40 mm; (2) Create a spring connection point at the ball position and add a spring unit instead of the ball; (3) Define nonlinear spring characteristics, with the spring pre-compression amount being 3% of the initial length; (4) Set boundary conditions and load conditions, with the axial load being 500 N and the radial load being 200 N; (5) Perform finite element static analysis on the bearing, and control the grid size to 0.5-2mm.

2. The simulation analysis method for a single-row four-point contact ball bearing based on a spring unit according to claim 1, characterized in that: The addition of a spring unit instead of a ball reflects whether there is a contact effect based on the deformation of the spring itself. When the deformation of the spring unit is within a certain reasonable range, the corresponding simulated contact part is considered to be in a contact force state. If the deformation is zero or extremely small, it is considered to be in a non-contact state. As the external force changes, the deformation of the spring is a continuous process. Its force is proportional to the deformation. The linear correlation coefficient R between the spring deformation and the load is 2 ≥0.

99.

3. The simulation analysis method for a single-row four-point contact ball bearing based on a spring unit according to claim 1 is characterized in that: When performing finite element static analysis on bearings, the spring unit stiffness is set and adjusted according to actual simulation requirements.

4. The simulation analysis method for a single-row four-point contact ball bearing based on a spring unit according to claim 3 is characterized in that: The spring stiffness is set according to the stiffness curve parameters of the actual ball. By assigning the bearing ball stiffness curve parameters to the spring unit, the ball material is selected as 40CrMn bearing steel with an elastic modulus of 210GPa and a Poisson's ratio of 0.

3. This makes its deformation and the elastic force generated when subjected to force similar to those of the actual ball, thereby accurately simulating the mechanical behavior of the ball in the bearing system.

5. The simulation analysis method for a single-row four-point contact ball bearing based on a spring unit according to claim 4 is characterized in that: The spring unit stiffness is set to 2000-10000N / m.

Images