Pulling-out force analysis method considering centrifugal deformation of ball bearing retainer

Abstract

The invention provides a pull-out force analysis method considering centrifugal deformation of a ball bearing retainer. The pull-out force analysis method comprises the following steps: acquiring initial conditions of the ball bearing retainer and a rolling body; establishing a three-dimensional solid model of the retainer and the rolling body, dividing grids for the three-dimensional solid model, and endowing the model with material attributes; centrifugal force of the retainer is calculated, grid division is conducted on the retainer, and centrifugal force of grid units of the retainer is calculated; centrifugal deformation boundary conditions are set, and a tiny volume element method is adopted to apply corresponding loads to grid units of the retainer so as to simulate the actual working condition of the retainer in high-speed operation; and calculating centrifugal deformation conditions of the retainer under different retainer rotating speeds, on the basis of obtaining the centrifugal deformation of the retainer, importing a rolling body model, applying rigid displacement to a coupling point, drawing a corresponding curve of the displacement and the pulling-out force, and extracting the pulling-out force of the bearing under different working conditions. According to the method, the problem that a large deviation exists between a bearing pulling-out force calculation result and the actual bearing pulling-out force calculation result under the high-speed operation condition at present can be solved.

Description

Technical Field

[0001] The invention relates to the technical field of cage analysis, and in particular to a pull-off force analysis method considering the centrifugal deformation of a ball bearing cage. Background Art

[0002] At present, there is a lack of reasonable analysis methods for the pull-off force analysis of new energy electric drive ball bearings, and most of the calculated results have a large deviation from the actual results. The centrifugal deformation of the cage needs to be considered when the bearing is running at high speed, but most of the calculations do not consider the centrifugal deformation of the cage. When the bearing is running at high speed, the actual pull-off force of the bearing plays an important role in the design of the bearing. Summary of the invention

[0003] The purpose of the present invention is to provide a pull-off force analysis method taking into account the centrifugal deformation of a ball bearing cage, which can solve the problem that the calculated pull-off force of the bearing under high-speed operation conditions has a large deviation from the actual result.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is: a pull-off force analysis method considering the centrifugal deformation of a ball bearing cage, comprising the following steps: Step 1, obtaining the initial conditions of the ball bearing cage and rolling elements; Step 2: Establish a three-dimensional solid model of the cage and rolling element, divide the three-dimensional solid model into grids, and assign material properties to the model; Step 3: Calculate the centrifugal force of the cage, divide the cage into grids, and calculate the centrifugal force of the cage grid unit; Step 4: Set the centrifugal deformation boundary conditions, use the micro-element method, and apply corresponding loads to the cage grid unit to simulate the actual working conditions of the cage under high-speed operation; Step 5. Calculate the centrifugal deformation of the cage under different cage speeds. Based on the centrifugal deformation of the cage, import the rolling element model, set the steel ball in contact with the cage pocket surface, fix the steel ball, couple the grid unit node on the bottom surface of the cage to one point, apply rigid displacement to the coupling point, draw the corresponding curve between displacement and pull-off force, and extract the pull-off force of the bearing under different working conditions.

[0005] Preferably, the initial conditions of the ball bearing cage and rolling elements in step 2 include structural parameters, density, elastic modulus, Poisson's ratio, material properties, and cage rotation speed.

[0006] Preferably, in step 3, the cage is divided into N units, and the centrifugal force of the cage grid unit is calculated by formulas (1) to (4). F j =Δm j ω 2 r j (1) ω=2πn(2) Where, Fj is the centrifugal force of the jth block of the cage; Δm j is the mass of the jth block of the cage; ω is the angular velocity of the cage; r j is the radius of the jth block of the cage; D w D is the diameter of the bearing rolling element; pw is the bearing pitch diameter; α is the working contact angle; n c is the cage speed; n i is the inner ring rotation speed.

[0007] Preferably, in step 4, by using formulas (5) to (9), a micro-element method is used to apply corresponding loads to the cage grid unit to simulate the actual working condition of the cage under high-speed operation. σ ij =D ijkl ε kl (7) In the formula, σ ij,j The subscript in the equation represents the physical quantity σ ij Find the partial derivative in the j direction, σ ij Where i is the direction of the force, j is the normal direction of the force surface; is the unit volume force acting on the grid element along the i direction; ε ij is the strain component; u i,j The subscript in represents u i Find the partial derivative in the j direction, u i is the displacement component along the i direction; u j,i The subscript in represents u j Find the partial derivative in the i direction, u j is the displacement component along the j direction; D ijkl ε kl is the elasticity matrix; It is in S u The displacement along the i direction is specified above; n j is the direction cosine of the external normal at a boundary point; is the surface force acting along the i direction; S u is the given displacement boundary, S p is the given force boundary.

[0008] Preferably, in step 2, Soildworks and UG three-dimensional design software are used to establish a three-dimensional solid model of the cage and the rolling element.

[0009] Preferably, in step 2, Hyperworks is used to mesh the three-dimensional solid model.

[0010] The beneficial effects of the present invention are:

[0011] This scheme is based on finite element theory and finite element analysis software. According to the relevant theories of space problems in the mechanical foundation of finite element analysis, the method of micro-element is used to apply loads to the cage grid unit, simulate the actual working conditions of the cage under high-speed operation, and analyze and calculate the cage pull-off force of the bearing under different working conditions on the basis of the centrifugal deformation of the cage. The present invention solves the problem of how to analyze the pull-off force of the bearing under high-speed operation considering the centrifugal deformation of the cage, and provides a technical reference for subsequent scholars to study the design of the cage, making the cage design more reasonable, with huge economic and social benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] 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.

[0013] Figure 1 Schematic diagram of a three-dimensional solid model of a retainer according to an embodiment of the present invention.

[0014] Figure 2 It is a schematic diagram of a three-dimensional solid model of a retaining rack and rolling elements according to an embodiment of the present invention.

[0015] Figure 3 It is a schematic diagram of a three-dimensional solid mesh model of a retaining frame and rolling elements according to an embodiment of the present invention.

[0016] Figure 4 It is a theoretical schematic diagram of a finite element space problem according to an embodiment of the present invention.

[0017] Figure 5 Schematic diagram of finite element analysis boundary conditions of an embodiment of the present invention.

[0018] Figure 6 Schematic diagram of centrifugal deformation of a retainer according to an embodiment of the present invention.

[0019] Figure 7 Schematic diagram of a rigid coupling point according to an embodiment of the present invention.

[0020] Figure 8 Schematic diagram of the bearing pull-off force according to an embodiment of the present invention.

[0021] Fig. 9The figure is a schematic diagram of the calculation results of the pull-off force of the bearing when the bearing speed is 10000r / min, 12000r / min and 15000r / min according to an embodiment of the present invention. DETAILED DESCRIPTION

[0022] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0023] The present invention discloses a pull-off force analysis method considering the centrifugal deformation of a ball bearing cage. The embodiment takes the 6209 new energy motor bearing cage as an example, based on finite element theory and finite element analysis software, the actual pull-off force of the bearing under high-speed working conditions is calculated, which mainly includes the following steps:

[0024] Step 1: Obtain the initial conditions of the bearing cage and rolling elements: structural parameters, density, elastic modulus, Poisson's ratio, material properties, and cage speed.

[0025] Step 2: Model establishment and mesh division: Use 3D design software such as Soildworks and UG to establish a 3D solid model of the cage, such as Figure 1 , 2 As shown. Finite element analysis software is used to divide the mesh of the three-dimensional solid model of the cage and rolling element, as shown Figure 3 As shown, the model is assigned material properties.

[0026] Step 3: Calculate the centrifugal force of the cage: The centrifugal force of the cage is the centrifugal load in the radial direction generated by its own rotation. The cage is divided into N units by meshing the cage, and the centrifugal force of the cage mesh unit is calculated using formulas (1) to (4). F j =Δm j ω 2 r j (1) ω=2πn(2)

[0027] Where, Fj is the centrifugal force of the jth block of the cage; Δm j is the mass of the jth block of the cage; ω is the angular velocity of the cage; r j is the radius of the jth block of the cage; D w D is the diameter of the bearing rolling element; pw is the bearing pitch diameter; α is the working contact angle; n c is the cage speed; n i is the inner ring rotation speed.

[0028] Step 4: Setting the centrifugal deformation boundary conditions: Based on the mechanical equations of spatial problems and the boundary condition related theories in the finite element analysis mechanics foundation, through formulas (5) to (9), the method of small volume elements is adopted, such as Figure 4 , 5 As shown, corresponding loads are applied to the cage grid units to simulate the actual working conditions of the cage under high-speed operation.

[0029] In the formula, σ ij,j The subscript in the equation represents the physical quantity σ ij Find the partial derivative in the j direction, σ ij Where i is the direction of the force, j is the normal direction of the force surface; is the unit volume force acting on the grid element along the i direction; ε ij is the strain component; u i,j The subscript in represents u i Find the partial derivative in the j direction, u i is the displacement component along the i direction; u j,i The subscript in represents u j Find the partial derivative in the i direction, u j is the displacement component along the j direction; D ijkl ε kl is the elasticity matrix; It is in S u The displacement along the i direction is specified above; n j is the direction cosine of the external normal at a boundary point; is the surface force acting along the i direction; S u is the given displacement boundary, S p is the given force boundary.

[0030] Step 5: Analysis and calculation: In the finite element analysis software, enter different cage speeds, including 10000r / min, 12000r / min, 15000r / min, such as Figure 6 As shown in the figure, the centrifugal deformation of the cage is calculated. Then, based on the centrifugal deformation of the cage, the rolling element model is imported, as shown in the figure. Figure 2 As shown in the figure, the steel ball is set in contact with the pocket surface of the cage, the steel ball is fixed, the mesh unit node on the bottom surface of the cage is coupled to a point, and a rigid displacement is applied to the coupling point, as shown in Figure 7 As shown in the figure, the corresponding curves of displacement and pull-off force are drawn to extract the pull-off force of the bearing under different working conditions, such as Figure 8 shown.

[0031] Fig. 9This is a schematic diagram of the calculation results of the bearing pull-off force when the bearing speed is 10000r / min, 12000r / min, and 15000r / min.

[0032] It should be noted that the parts not described in detail in the above embodiments are all prior art.

[0033] 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 pull-off force analysis method considering the centrifugal deformation of a ball bearing cage, characterized in that: The following steps are involved: Step 1, obtaining the initial conditions of the ball bearing cage and rolling elements; Step 2: Establish a three-dimensional solid model of the cage and rolling element, divide the three-dimensional solid model into grids, and assign material properties to the model; Step 3, calculate the centrifugal force of the cage, divide the cage into grids, and calculate the centrifugal force of the cage grid unit; Step 4: Set the centrifugal deformation boundary conditions, and use the micro-element method to apply corresponding loads to the cage grid unit to simulate the actual working conditions of the cage under high-speed operation; Step 5. Calculate the centrifugal deformation of the cage under different cage speeds. Based on the centrifugal deformation of the cage, import the rolling element model, set the steel ball in contact with the cage pocket surface, fix the steel ball, couple the grid unit node on the bottom surface of the cage to one point, apply rigid displacement to the coupling point, draw the corresponding curve between displacement and pull-off force, and extract the pull-off force of the bearing under different working conditions.

2. A pull-off force analysis method considering centrifugal deformation of a ball bearing cage according to claim 1, characterized in that: The initial conditions of the ball bearing cage and rolling elements in step 2 include structural parameters, density, elastic modulus, Poisson's ratio, material properties, and cage rotation speed.

3. A pull-off force analysis method considering centrifugal deformation of a ball bearing cage according to claim 2, characterized in that: In step 3, the cage is divided into N units, and the centrifugal force of the cage grid unit is calculated by formulas (1) to (4). F j =Δm j oh 2 r j (1) ω=2πn(2) Where, Fj is the centrifugal force of the jth block of the cage; Δm j is the mass of the jth block of the cage; ω is the angular velocity of the cage; r j is the radius of the jth block of the cage; D w D is the diameter of the bearing rolling element; pw is the bearing pitch diameter; α is the working contact angle; n c is the cage speed; n i is the inner ring rotation speed.

4. A pull-off force analysis method considering centrifugal deformation of a ball bearing cage according to claim 3, characterized in that: In step 4, by using formulas (5) to (9), a micro-element method is used to apply corresponding loads to the cage grid unit to simulate the actual working conditions of the cage under high-speed operation. s ij =D ijkl e kl (7) In S u Previous (8) In S p Previous (9) In the formula, σ ij,j The subscript in the equation represents the physical quantity σ ij Find the partial derivative in the j direction, σ ij Where i is the direction of the force, j is the normal direction of the force surface; is the unit volume force acting on the grid element along the i direction; ε ij is the strain component; u i,j The subscript in represents u i Find the partial derivative in the j direction, u i is the displacement component along the i direction; u j,i The subscript in represents u j Find the partial derivative in the i direction, u j is the displacement component along the j direction; D ijkl ε kl is the elasticity matrix; It is in S u The displacement along the i direction is specified above; n j is the direction cosine of the external normal at a boundary point; is the surface force acting along the i direction; S u is the given displacement boundary, S p is the given force boundary.

5. The pull-off force analysis method considering the centrifugal deformation of the ball bearing cage according to claim 1, characterized in that: In the step 2, Soildworks and UG three-dimensional design software are used to establish a three-dimensional solid model of the cage and the rolling element.

6. A pull-off force analysis method considering centrifugal deformation of a ball bearing cage according to claim 1, characterized in that: In the step 2, Hyperworks is used to mesh the three-dimensional solid model.

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