Finite element simulation modeling method for joint part of angular contact ball bearing

Abstract

The invention discloses a finite element simulation modeling method for a joint part of an angular contact ball bearing, which comprises the following steps of: simplifying an angular contact ball bearing model in Creo software, carrying out implicit processing on all balls, storing a simplified geometric model, calculating a five-degree-of-freedom stiffness matrix of the angular contact ball bearing, opening Workbench software, and importing the geometric model. The method comprises the following steps: dividing a bearing inner ring and a bearing outer ring into hexahedral grids, selecting a Joint-Bushing kinematic pair to establish a contact relationship between raceways of the bearing inner ring and the bearing outer ring, clicking a Stiffness Coefficients matrix of a Joint-Bushing unit, and inputting a five-degree-of-freedom stiffness matrix. According to the modeling method provided by the invention, the rigidity characteristic of the joint part of the angular contact ball bearing can be effectively simulated, the calculation amount of finite element analysis is simplified, and meanwhile, the analysis precision is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical simulation CAE and relates to a finite element simulation modeling method for an angular contact ball bearing joint. Background Art

[0002] As the core functional component of the rotary mechanical system, the shaft system has an important impact on the functional realization of the rotary mechanical system. Angular contact ball bearings have the advantages of high rotation accuracy and the ability to withstand both axial and radial loads, so they are widely used in rotary mechanical systems.

[0003] When angular contact ball bearings are assembled, a certain preload is applied to them to eliminate bearing clearance and increase bearing stiffness. Under the action of the assembly preload, the bearing balls and the inner and outer ring raceways produce contact deformation. The stiffness of the bearing is closely related to the size of the preload.

[0004] The constant performance analysis of the bearing joint adopts the simulation analysis method. The existing method is to use the spring unit in the finite element software to simulate the stiffness of the bearing. Since the spring unit only has linear stiffness and no bending stiffness, it is impossible to simulate the bending stiffness characteristics of the bearing, resulting in distortion in the simulation of the static and dynamic characteristics of the bearing joint. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention provides a finite element simulation modeling method for an angular contact ball bearing joint to solve the problem that the existing finite element simulation modeling method for an angular contact ball bearing joint is difficult to effectively simulate the bearing bending stiffness and characterize the static and dynamic characteristics of the bearing joint.

[0006] The technical solution adopted by the present invention to solve the technical problem is: a finite element simulation modeling method for an angular contact ball bearing joint, comprising the following steps:

[0007] S1, simplify the angular contact ball bearing model in Creo software, implicitly process all the balls in the bearing, and save the simplified angular contact ball bearing geometry model in zhoucheng.xt format;

[0008] S2, establishing a five-degree-of-freedom stiffness matrix of the angular contact ball bearing including radial stiffness, axial stiffness and bending stiffness;

[0009] S3, open the Workbench software, import the zhoucheng.xt angular contact ball bearing geometry model, and divide the inner ring and outer ring of the bearing into hexahedral meshes;

[0010] S4, select the Joints-Bushing kinematic pair to establish a contact relationship between the inner ring of the bearing and the raceway of the outer ring of the bearing, select the raceway surface of the outer ring of the bearing as the Reference surface or the Mobile surface, and select the raceway surface of the inner ring of the bearing as the Mobile surface or the Reference surface;

[0011] S5, click the Stiffness Coefficients matrix of the Joints-Bushing unit, input the five-degree-of-freedom stiffness matrix of the bearing stiffness calculation result in step S2, and complete the finite element simulation modeling of the angular contact ball bearing joint.

[0012] Further, the step S2 is specifically as follows:

[0013] S2.1, according to Hertz contact stress theory, the relationship between the load and deformation of each ball in an angular contact ball bearing is: Where K n is a constant that depends only on the contact material properties and dimensions, is the load in the normal direction of the contact surface;

[0014] S2.2, the overall balance equation between the contact reaction force or contact reaction torque of each ball in the angular contact ball bearing and the external force is: Where F X 、F Y is the radial load of the bearing, N; F Z is the bearing axial load, N; M X 、M Y is the radial bending moment of the bearing, N·m; δ x , δ y is the radial relative displacement of the inner and outer rings of the bearing, m; δ z is the axial relative displacement of the inner and outer rings of the bearing, m; θ x ,θ y is the radial relative angular displacement of the inner and outer rings of the bearing, rad; R i is the radius of the center circle of the inner raceway curvature, m; is the ball position angle, rad;

[0015] S2.3, analytical expression of the five-degree-of-freedom stiffness matrix

[0016]

[0017] Expanding the elements in the matrix gives Similarly, we can get the expressions of other elements in the matrix;

[0018] S2.4, invert the five-degree-of-freedom stiffness matrix in Matlab software, and define the solution error e as e = norm(pinv(K)*(25-F));

[0019] S2.5, iterate the solution error e in Matlab software and define the solution accuracy to be better than 10 -8 , the solution is completed, and the calculation results of the five-degree-of-freedom stiffness matrix of the bearing are obtained.

[0020] Furthermore, the ball bearing outer ring finite element model and the inner ring finite element model are both three-dimensional solid mesh finite element models.

[0021] Furthermore, the step 2 of calculating the five-degree-of-freedom stiffness matrix of the angular contact ball bearing is implemented by MATLAB software.

[0022] Furthermore, steps S3 to S5 are implemented by finite element software.

[0023] Compared with the prior art, the present invention has the following beneficial effects: Based on the Hertz elastic body contact theory, the present invention uses the actual installation preload as input to solve the axial stiffness, radial stiffness and bending stiffness of the angular contact ball bearing, which can accurately reflect the stiffness characteristics of the bearing in the actual assembly state, and at the same time, the Joints-Bushing unit is used to simulate the contact relationship between the inner ring and the outer ring of the bearing, which can accurately and meticulously express the five-degree-of-freedom stiffness characteristics of the bearing joint. The modeling method proposed in the present invention can effectively simulate the stiffness characteristics of the angular contact ball bearing joint, and simplifies the calculation amount of the finite element analysis, while improving the analysis accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is a flow chart of the simulation modeling method of the present invention;

[0025] Figure 2 is a schematic diagram of bearing geometry;

[0026] Figure 3 is a schematic diagram of the bearing contact angle;

[0027] Figure 4 It is a schematic diagram of the force of a single ball;

[0028] Figure 5 This is the coordination diagram of shaft system deformation;

[0029] Figure 6 This is a simplified geometric model of angular contact ball bearing;

[0030] Figure 7 To mesh the inner and outer rings of the bearing in the finite element software;

[0031] Figure 8 Establish contact between the inner and outer rings of the bearing for the Joints-Bushing element simulation. DETAILED DESCRIPTION

[0032] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below in combination with specific embodiments and with reference to the accompanying drawings.

[0033] Reference Figure 1 As shown, the present embodiment discloses a finite element simulation modeling method for an angular contact ball bearing joint, comprising the following steps.

[0034] Step 1: Simplify the angular contact ball bearing model in Creo software, implicitly process all the balls in the bearing, and save the simplified angular contact ball bearing geometric model in zhoucheng.xt format.

[0035] Take angular contact ball bearing 71807C as an example. The bearing geometry is as follows: Figure 2 As shown, the bearing contact angle is Figure 3 As shown in Figure 2, the force on a single ball is as follows: Figure 4 As shown in the figure, the coordination relationship of the shaft system deformation is as follows: Figure 5 As shown in the figure, the bearing model is simplified in Creo software, and all balls are implicitly processed. The simplified model is as follows Figure 6 The bearing geometrical dimension parameters are shown in the following table.

[0036] parameter Numeric Bearing inner diameter (mm) 35 Bearing outer diameter (mm) 47 Ball diameter(mm) 3 Number of balls 26 Initial contact angle (°) 15 Inner ring raceway curvature radius coefficient 0.525 Outer ring raceway curvature radius coefficient 0.515 Axial preload (N) 25 .

[0037] Step 2: Use MATLAB software to establish the five-degree-of-freedom stiffness matrix of the angular contact ball bearing, where the bearing stiffness model includes radial stiffness, axial stiffness, and bending stiffness.

[0038] Step 2.1, according to Hertz contact stress theory, the relationship between the load and deformation of each ball of an angular contact ball bearing is: Where K n is a constant that depends only on the contact material properties and dimensions, is the load in the normal direction of the contact surface.

[0039] Step 2.2, the overall balance equation of the contact reaction force or contact reaction torque of each ball of the angular contact ball bearing and the external force is expressed as Where F X 、F Y is the radial load of the bearing, N; F Z is the bearing axial load, N; M X 、M Y is the radial bending moment of the bearing, N·m; δ x , δ y is the radial relative displacement of the inner and outer rings of the bearing, m; δ z is the axial relative displacement of the inner and outer rings of the bearing, m; θx ,θ y is the radial relative angular displacement of the inner and outer rings of the bearing, rad; R i is the radius of the center circle of the inner raceway curvature, m; is the ball position angle, rad.

[0040] Step 2.3, the analytical expression of the five-degree-of-freedom stiffness matrix is:

[0041]

[0042] Expanding the elements in the matrix gives Similarly, expressions for other elements in the matrix can be obtained.

[0043] Step 2.4, invert the five-degree-of-freedom stiffness matrix in Matlab software, and define the solution error e as e=norm(pinv(K)*(25-F)).

[0044] Step 2.5, iterate the solution error e in Matlab software and define the solution accuracy to be better than 10 -8 , the solution is completed, and the calculation results of the five-degree-of-freedom stiffness matrix of the bearing are obtained.

[0045] The solution error e is iterated in Matlab software, and the solution accuracy is defined to be better than 10 -8 , the solution is completed, and the calculation results of the five-degree-of-freedom stiffness matrix of the bearing are as follows.

[0046] Stiffness Per Unit X(mm) Per Unit Y(mm) Per Unit Z(mm) Per UnitθX(°) Per Unitθy(°) △Force X(N) <![CDATA[8.7248×10 4 ]]> 0 0 0 <![CDATA[-0.9056×10 4 ]]> △Force Y(N) 0 <![CDATA[8.7248×10 4 ]]> 0 <![CDATA[0.9056×10 4 ]]> 0 △Force Z(N) 0 0 <![CDATA[1.5427×10 4 ]]> 0 0 △Moment X (N mm) 0 <![CDATA[0.9056×10 4 ]]> 0 <![CDATA[5.6817×10 4 ]]> 0 △Moment Y (N·mm) <![CDATA[-0.9056×10 4 ]]> 0 0 0 <![CDATA[5.6817×10 4 ]]> .

[0047] Step 3, open the Workbench software, import the zhoucheng.xt angular contact ball bearing geometry model, divide the inner ring and outer ring of the bearing into hexahedral meshes, and after the division is completed, the bearing finite element model is as follows Figure 7 shown.

[0048] Step 4. Select the Joints-Bushing kinematic pair to establish a contact relationship between the bearing inner ring and the bearing outer ring raceway, select the bearing outer ring raceway surface as the Reference surface or the Mobile surface, and select the bearing inner ring raceway surface as the Mobile surface or the Reference surface.

[0049] Step 5, click the Stiffness Coefficients matrix of the Joints-Bushing unit, input the five-degree-of-freedom stiffness matrix of the bearing stiffness calculation result in step 2, and establish the finite element of the bearing joint after completion. Figure 8 Steps 3 to 5 are implemented by finite element software.

[0050] The ball bearing outer ring finite element model and the inner ring finite element model are both three-dimensional solid mesh finite element models.

[0051] The above embodiments are only illustrative of the principles and effects of the present invention, as well as some embodiments of its application. For those skilled in the art, several modifications and improvements may be made without departing from the creative concept of the present invention, and all of these belong to the protection scope of the present invention.

Claims

1. A finite element simulation modeling method for an angular contact ball bearing joint, characterized in that: The following steps are included S1, simplify the angular contact ball bearing model in Creo software, implicitly process all the balls in the bearing, and save the simplified angular contact ball bearing geometric model; S2, establishing a five-degree-of-freedom stiffness matrix of the angular contact ball bearing including radial stiffness, axial stiffness and bending stiffness; S3, open the Workbench software, import the angular contact ball bearing geometry model, and divide the inner ring and outer ring of the bearing into hexahedral meshes; S4, select the Joints-Bushing kinematic pair to establish the contact relationship between the inner ring of the bearing and the raceway of the outer ring of the bearing; S5, click the Stiffness Coefficients matrix of the Joints-Bushing unit, and input the five-degree-of-freedom stiffness matrix in step S2.

2. The finite element simulation modeling method for an angular contact ball bearing joint according to claim 1, characterized in that: The specific steps of step 2 are as follows: S2.1, the relationship between the load and deformation of each ball in an angular contact ball bearing is: Where K n is a constant that depends only on the contact material properties and dimensions, is the load in the normal direction of the contact surface; S2.2, the overall balance equation between the contact reaction force or contact reaction torque of each ball in the angular contact ball bearing and the external force is: Where F X 、F Y is the radial load of the bearing, F Z is the bearing axial load, M X 、M Y is the radial bending moment of the bearing, δ x , δ y is the radial relative displacement of the inner and outer rings of the bearing, δ z is the axial relative displacement of the inner and outer rings of the bearing, θ x ,θ y is the relative radial angular displacement of the inner and outer rings of the bearing, R i is the radius of the center circle of the inner raceway curvature, is the ball position angle; S2.3, get the five-degree-of-freedom stiffness matrix Expanding the elements in the matrix gives S2.4, invert the five-degree-of-freedom stiffness matrix in Matlab software, and define the solution error e as e = norm(pinv(K)*(25-F)); S2.5, iterate the solution error e in Matlab software and define the solution accuracy to be better than 10 -8 , after the solution is completed, the calculation results of the five-degree-of-freedom stiffness matrix of the bearing are obtained.

3. The finite element simulation modeling method for an angular contact ball bearing joint according to claim 2, characterized in that: The ball bearing outer ring finite element model and the inner ring finite element model are both three-dimensional solid mesh finite element models.

4. A finite element simulation modeling method for an angular contact ball bearing joint according to claim 1, 2 or 3, characterized in that: The step S2 of calculating the five-degree-of-freedom stiffness matrix of the angular contact ball bearing is implemented by MATLAB software.

5. The finite element simulation modeling method for an angular contact ball bearing joint according to claim 4, characterized in that: The steps S3 to S5 are implemented by finite element software.

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