Ball bearing fatigue life calculation method considering residual stress distribution

Abstract

The invention provides a ball bearing fatigue life calculation method considering residual stress distribution, and the method comprises the steps: building a rolling bearing contact nonlinear finite element analysis model considering a bearing ring surface residual stress factor, and enabling the model to fully consider ring deformation and actual boundary conditions; the influence rule of the residual compressive stress on the surface of the bearing ring on the load and life of the rolling body is analyzed, and the calculation precision of the fatigue life of the ball bearing is greatly improved. Therefore, the fatigue life of the bearing can be prolonged by applying certain residual compressive stress to the bearing ring, the problem of prolonging the service life of the thin-wall angular contact ball bearing is solved, and the actual service life of the thin-wall angular contact ball bearing is prolonged. The depth and direction of the maximum shear stress of the bearing ring are extracted by utilizing a Perma finite element result, and on the basis, the service life of the angular contact ball bearing is further optimized, so that the service life of the bearing is prolonged, and the economic benefit and the social benefit are very huge.

Description

Technical Field

[0001] The invention relates to the technical field of bearing life calculation, and in particular to a method for calculating the fatigue life of a ball bearing taking residual stress distribution into consideration. Background Art

[0002] At present, most calculations of the rated life of ball bearings do not consider the effect of residual stress on the life of ball bearings. In fact, the surface residual stress of the bearing rings will affect the service life and performance of the ball bearings. For ball bearings used in aircraft, the residual compressive stress on the surface of the bearing rings will reduce the contact stress and contact half-width between the bearing rings and the rolling elements, reduce the rolling element load, and increase the fatigue life of the bearings. However, when calculating the life of ball bearings, the effect of the residual compressive stress on the surface of the bearing rings on the fatigue life of the ball bearings is not considered. Therefore, the calculation accuracy of the fatigue life of ball bearings still needs to be improved. Summary of the invention

[0003] The purpose of the present invention is to provide a method for calculating the fatigue life of a ball bearing taking into account the residual stress distribution, and to establish a nonlinear finite element analysis model of rolling bearing contact taking into account the residual stress factor on the surface of the bearing ring, thereby greatly improving the calculation accuracy of the fatigue life of the ball bearing.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is: a method for calculating the fatigue life of a ball bearing considering the residual stress distribution, comprising the following steps: Step 1, establishing a finite element model of an angular contact ball bearing, and dividing the finite element model of the angular contact ball bearing into a grid; Step 2, setting three contact surfaces of the inner ring, outer ring and steel ball of the angular contact ball bearing; Step 3: Set the constraints and loads of the angular contact ball bearing; Step 4, setting a residual stress layer of the angular contact ball bearing; Step 5, setting two analysis steps: unloaded residual stress and loaded residual stress; Step 6, using the full Newton-Raphson method to solve the nonlinear equations of the angular contact ball bearing to obtain the rolling element load; Step 7: Calculate the fatigue life of the angular contact ball bearing using the rolling element load.

[0005] Preferably, in step 1, Soildworks is used to establish a finite element model of the angular contact ball bearing, and mesh encryption is performed near the contact area.

[0006] Preferably, in step 2, three contact surfaces of the inner ring, outer ring and steel ball of the angular contact ball bearing are set by Hypermesh, the contact state between the inner ring, outer ring and steel ball of the angular contact ball bearing is defined as surface-to-surface contact, and symmetrical contact is applied on the symmetric surface of the finite element model of the angular contact ball bearing.

[0007] Preferably, in step 3, the grid nodes on the surfaces of the inner ring and outer ring of the angular contact ball bearing are coupled as rigid points MPC1 and MPC2 respectively, and the grid nodes on the outer ring of the angular contact ball bearing that apply force are coupled as the rigid point FORCE; the degrees of freedom of the rigid point MPC1 in the X and Y directions are constrained, and the degrees of freedom of the rigid point MPC2 in the X, Y and Z directions are constrained, and an axial load is applied to the rigid point FORCE.

[0008] Preferably, in step 4, the 2 mm grid units on the inner ring surface of the angular contact ball bearing are divided into 10 layers of unit sets by Hypermesh, and a load is applied to each layer of the grid unit set by Permas.

[0009] Preferably, in step 5, two analysis steps of unloaded residual stress and loaded residual stress are set by Permas.

[0010] Preferably, in step 6, the rolling element load Qj is the contact force between the j-th steel ball and the bearing ring, j∈[1,Z], and Z is the number of steel balls.

[0011] Preferably, in step 7, the fatigue life of the bearing is calculated by the following formula: Among them, C r is the radial basic dynamic load rating, D w is the nominal diameter of the ball, Q is the rolling element load, Q ce is the rolling element load corresponding to the basic dynamic load rating of the outer ring or race, Q ci is the rolling element load corresponding to the basic dynamic load rating of the inner ring or shaft ring, Q ee Q is the equivalent dynamic load of the rolling element on the outer ring or raceway, ei Q is the equivalent dynamic load of the rolling element on the inner ring or shaft ring, j is the load on rolling element j, r e is the outer ring or raceway radius, r i is the inner ring or shaft ring groove radius, α is the bearing nominal contact angle, L 10r is the basic rating life of the bearing.

[0012] The beneficial effects of the present invention are:

[0013] This scheme establishes a nonlinear finite element analysis model for rolling bearing contact that takes into account the residual stress factor on the bearing ring surface. The model fully considers the deformation of the ring and the actual boundary conditions, analyzes the influence of the residual compressive stress on the bearing ring surface on the rolling element load and life, and greatly improves the calculation accuracy of the fatigue life of the ball bearing. In addition, the fatigue life of the bearing can be improved by applying a certain residual compressive stress to the bearing ring, solving the problem of life extension of thin-walled angular contact ball bearings and extending the actual service life of thin-walled angular contact ball bearings. The depth and direction of the maximum shear stress of the bearing ring are extracted using the Permas finite element results. On this basis, the life of the angular contact ball bearing is further optimized, thereby extending the life of the bearing, with huge economic and social benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0015] Figure 1 It is a schematic diagram of the finite element model of the angular contact ball bearing of the present invention;

[0016] Figure 2 This is a schematic diagram of the model after mesh encryption is performed near the contact area in the present invention;

[0017] Figure 3 A schematic diagram of a model after the angular contact ball bearing of the present invention is provided with three contact surfaces;

[0018] Figure 4 A schematic diagram of a model after setting constraints for an angular contact ball bearing according to the present invention;

[0019] Figure 5 This is a schematic diagram of a model for simulating residual stress on the surface of a bearing ring according to the present invention;

[0020] Figure 6 Schematic diagram of contact stress of angular contact ball bearing under different working conditions of the present invention;

[0021] Figure 7 It is a schematic diagram of the life of the angular contact ball bearing under different working conditions of the present invention. DETAILED DESCRIPTION

[0022] The present invention is further described in detail below in conjunction with embodiments and with reference to the accompanying drawings.

[0023] The present invention discloses a method for calculating the fatigue life of a ball bearing considering the residual stress distribution. The finite element analysis software Hyperwork and Permas are used as a platform to establish a thin-wall rolling contact nonlinear finite element analysis model considering the residual stress on the surface of the bearing ring. The life of the thin-wall rolling bearing is obtained through calculation. The method mainly includes the following steps:

[0024] Step 1: Model establishment and meshing: Use Soildworks to establish the finite element model of the angular contact ball bearing, such as Figure 1 As shown in the figure, the finite element model of the angular contact ball bearing is meshed, and the mesh near the contact area is encrypted, as shown in the figure. Figure 2 shown.

[0025] Step 2, contact setting: Create three Setments through Hypermesh, select the three component contact surface mesh units of the inner ring, outer ring and steel ball, define the contact state between the inner and outer rings of the bearing and the steel ball as Surface-Surface contact in Permas, and apply symmetric contact on the symmetric surface of the finite element model of the angular contact ball bearing, such as Figure 3 shown.

[0026] Step 3, constraint and load setting: couple the mesh nodes on the inner and outer ring surfaces of the angular contact ball bearing as rigid points MPC1 and MPC2 respectively, and couple the mesh nodes that apply force to the outer ring of the angular contact ball bearing as rigid point FORCE; constrain the degrees of freedom of the rigid point MPC1 in the X and Y directions, and constrain the degrees of freedom of the rigid point MPC2 in the X, Y, and Z directions. Apply an axial load to the rigid point FORCE, such as Figure 4 shown.

[0027] Step 4: Setting the residual stress layer: Use Hypermesh to divide the 2mm mesh unit on the inner ring surface of the angular contact ball bearing into 10 layers of unit sets. At the same time, use the Disload function in Permas to apply loads to each layer of mesh unit set elemparts to simulate the residual stress of the angular contact ball bearing ring. For example: Figure 5 shown.

[0028] Step 5. Setting of analysis steps: Set two analysis steps: unloaded residual stress and loaded residual stress through Load History in Permas.

[0029] Step 6: Use Permas software to solve the nonlinear equations of the angular contact ball bearing using the full Newton-Raphson method to obtain the rolling element load Qj, where Qj is the contact force between the j-th steel ball and the bearing ring, j∈[1,Z], and Z is the number of steel balls.

[0030] Step 7, life calculation: Use the rolling element load Qj to calculate the fatigue life of the angular contact ball bearing using the following formula: Among them, C r is the radial basic dynamic load rating, D w is the nominal diameter of the ball, Q is the rolling element load, Q ce is the rolling element load corresponding to the basic dynamic load rating of the outer ring or race, Q ci is the rolling element load corresponding to the basic dynamic load rating of the inner ring or shaft ring, Q ee Q is the equivalent dynamic load of the rolling element on the outer ring or raceway, ei Q is the equivalent dynamic load of the rolling element on the inner ring or shaft ring, j is the load on rolling element j, r e is the outer ring or raceway radius, r i is the inner ring or shaft ring groove radius, α is the bearing nominal contact angle, L 10r is the basic rating life of the bearing.

[0031] There are 14 rolling elements in the angular contact ball bearing. When the axial load is 100N, 300N, and 500N, the stress conditions of the inner ring and rolling elements of the bearing are as follows: Figure 6 shown.

[0032] According to the extracted rolling element load, the bearing life operation statement is written using MATLAB parameter expressions and functions to calculate the bearing fatigue life, such as Figure 7 As shown in the figure, applying a certain residual compressive stress on the inner ring of the bearing can increase the life of the bearing.

[0033] It should be noted that the parts not described in detail in the above embodiments are all prior art.

[0034] The above description is only a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for calculating the fatigue life of a ball bearing taking into account residual stress distribution, characterized in that: The following steps are involved: Step 1, establishing a finite element model of an angular contact ball bearing, and dividing the finite element model of the angular contact ball bearing into a grid; Step 2, setting three contact surfaces of the inner ring, outer ring and steel ball of the angular contact ball bearing; Step 3: Set the constraints and loads of the angular contact ball bearing; Step 4, setting a residual stress layer of the angular contact ball bearing; Step 5, setting two analysis steps: unloaded residual stress and loaded residual stress; Step 6, using the full Newton-Raphson method to solve the nonlinear equations of the angular contact ball bearing to obtain the rolling element load; Step 7: Calculate the fatigue life of the angular contact ball bearing using the rolling element load.

2. A method for calculating fatigue life of ball bearings taking residual stress distribution into consideration according to claim 1, characterized in that: In the step 1, Soildworks is used to establish a finite element model of the angular contact ball bearing, and mesh encryption is performed near the contact area.

3. The method for calculating fatigue life of a ball bearing considering residual stress distribution according to claim 1, characterized in that: In step 2, three contact surfaces of the inner ring, outer ring and steel ball of the angular contact ball bearing are set by Hypermesh, the contact state between the inner ring, outer ring and steel ball of the angular contact ball bearing is defined as surface-to-surface contact, and symmetric contact is applied on the symmetric surface of the finite element model of the angular contact ball bearing.

4. A method for calculating ball bearing fatigue life considering residual stress distribution according to claim 1, characterized in that: In the step 3, the mesh nodes on the inner ring and outer ring surfaces of the angular contact ball bearing are coupled as rigid points MPC1 and MPC2 respectively, and the mesh nodes on the outer ring of the angular contact ball bearing that apply force are coupled as rigid points FORCE; Constrain the degrees of freedom of the rigid point MPC1 in the X and Y directions, and constrain the degrees of freedom of the rigid point MPC2 in the X, Y, and Z directions, by applying an axial load to the rigid point FORCE.

5. A method for calculating fatigue life of ball bearings taking residual stress distribution into consideration according to claim 1, characterized in that: In the step 4, the 2 mm grid cells on the inner ring surface of the angular contact ball bearing are divided into 10 layers of cell sets by Hypermesh, and a load is applied to each layer of the grid cell set by Permas.

6. A method for calculating fatigue life of ball bearings taking residual stress distribution into consideration according to claim 1, characterized in that: In step 5, two analysis steps, namely, unloaded residual stress and loaded residual stress, are set by Permas.

7. A method for calculating fatigue life of ball bearings taking residual stress distribution into consideration according to claim 1, characterized in that: In step 6, the rolling element load Q j is the contact force between the jth steel ball and the bearing ring, j∈[1,Z], and Z is the number of steel balls.

8. A method for calculating fatigue life of ball bearings taking residual stress distribution into consideration according to claim 1, characterized in that: In step 7, the fatigue life of the bearing is calculated by the following formula: Among them, C r is the radial basic dynamic load rating, D w is the nominal diameter of the ball, Q is the rolling element load, Q ce is the rolling element load corresponding to the basic dynamic load rating of the outer ring or race, Q ci is the rolling element load corresponding to the basic dynamic load rating of the inner ring or shaft ring, Q ee Q is the equivalent dynamic load of the rolling element on the outer ring or raceway, ei Q is the equivalent dynamic load of the rolling element on the inner ring or shaft ring, j is the load on rolling element j, r e is the outer ring or raceway radius, r i is the inner ring or shaft ring groove radius, α is the bearing nominal contact angle, L 10r is the basic rating life of the bearing.

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