Dynamic behavior analysis method for segmented retainer of large thin-wall bearing

Abstract

The invention discloses a dynamic behavior analysis method for a segmented cage of a large thin-wall bearing. The method comprises the following steps: firstly, establishing a bearing coordinate system; secondly, according to the motion constraint condition of each element of the bearing, calculating to obtain the relative motion speed of each element; then solving the acting force among the output bearing elements and establishing a nonlinear dynamic differential equation set of each element of the bearing; and finally, solving the dynamic differential equation set by utilizing a GSTIFF variable step size integral algorithm, and if an error is within a convergence error and reaches a set time length, outputting a dynamic characteristic analysis result of the sectional type retainer. According to the method, the condition that the retainer is segmented in the bearing is considered, a multi-body dynamic analysis model is established, the condition that the rolling body is located in a complete pocket and a half pocket of the retainer is considered on the basis of a pure dynamic theory, collision and contact force of the rolling body and the retainer are analyzed, and research and analysis on dynamic behaviors of the segmented retainer are achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of bearing dynamics modeling and analysis, and in particular relates to a method for analyzing the dynamics behavior of a segmented cage of a large thin-walled bearing. Background Art

[0002] Double-row angular contact ball bearings are widely used in various fields, including aerospace, vehicle hub components, high-precision chemical equipment and various speed change devices. Because of their ability to simultaneously bear axial, radial combined loads and bending moment loads, they are extremely suitable for occasions that require high rigidity. Their unique thin-wall design structure effectively saves installation space and also effectively reduces the weight of the bearing. Therefore, the application of thin-wall double-row angular contact ball bearings is showing an increasingly widespread trend. As a key component of mechanical equipment, in-depth research and analysis of its dynamic performance provides a solid theoretical basis for predicting the potential failure risk of bearings and optimizing their structures.

[0003] In modern times, the research and analysis of bearings are mostly based on the following four analysis models: statics, quasi-statics, quasi-dynamics and bearing dynamics. By establishing a dynamic analysis model of the bearing, the dynamic performance of the bearing is analyzed, and the influence of the bearing structural parameters on its life under various working conditions is studied. The cage structure needs to be considered in the dynamic model of the rolling bearing, but in the prior art, the cages in the dynamic model of the rolling bearing are mostly complete cages or fully loaded bearings without cages, and there are fewer studies on ball bearings equipped with segmented cages. Segmented cage bearings divide a solid cage into multiple solid cages, resulting in a change in the motion relationship between the rolling element and the cage. Therefore, the mathematical model of the complete cage is not applicable to the segmented cage. In order to more accurately describe the dynamic behavior of ball bearings equipped with segmented cages, a method suitable for multi-body dynamics is needed, which can analyze the dynamic characteristics of such bearings according to their operating conditions. Summary of the invention

[0004] In view of this, in order to address the deficiencies of the above-mentioned prior art, the purpose of the present invention is to provide a method for analyzing the dynamic behavior of a segmented cage of a large thin-walled bearing. Different from the traditional dynamic analysis model of a ball bearing equipped with a complete cage, a multi-body dynamic analysis model is established, which can analyze the dynamic behavior of each bearing component according to its operating conditions and can more accurately describe the dynamic behavior of a ball bearing equipped with a segmented cage.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is: A method for analyzing the dynamic behavior of a segmented cage of a large thin-walled bearing comprises the following steps: S1. Obtain the initial conditions of the bearing and establish the bearing coordinate system; S2. Determine the position and motion parameters of each bearing component, analyze according to the motion constraint conditions of each bearing component, and obtain the relative motion speed between the components; S3. Solve the forces between the output bearing components, including the forces between the rolling element and the full pocket and the forces between the rolling element and the half pocket; S4. Establishing a group of nonlinear dynamic differential equations for each bearing component, including a group of equilibrium equations for rolling elements between complete pockets, a group of equilibrium equations for rolling elements between half pockets of a two-segmented cage, a group of equilibrium equations for the cage, and a group of equilibrium equations for the outer ring; S5. According to the bearing dynamics theory, the GSTIFF variable step size integration algorithm is used to solve the nonlinear dynamic differential equations. S6. Determine whether the error of the dynamic equation group satisfies the convergence error.

[0006] Furthermore, the initial conditions of S1 include structural parameters, material properties, operating conditions and lubrication parameters of the bearing, and a coordinate system including a geodetic coordinate system, an outer ring coordinate system, a cage coordinate system, a cage pocket center coordinate system and a rolling element coordinate system is constructed based on the above initial conditions.

[0007] Furthermore, when S2 solves the relative motion speed between the components, the slip speed of the rolling body between the half pockets of the two segmented cages and its relative motion speed with the half cages are solved according to the positions and motion parameters of the bearing components.

[0008] Furthermore, the S3 includes the following contents: Firstly, the position and motion parameters of each bearing component are solved as the initial values ​​according to the speed relationship in S2. Then, the collision force between the rolling elements and the cage between the complete pockets and half pockets of the segmented cage is determined according to the relative motion speed between the rolling elements and the cage between the complete pockets and half pockets of the segmented cage, and the force between the bearing components is solved.

[0009] Furthermore, in S5, the values ​​of dynamic parameters are solved according to the GSTIFF variable step size integration algorithm, including parameters such as the normal contact load between the rolling element and the ring, the rolling friction resistance on the rolling element surface, the sliding friction resistance on the rolling element surface, the acceleration of the cage, and the angular velocity of the cage.

[0010] Furthermore, the S6 includes the following contents: S61. Solve the dynamic differential equation at each moment and judge its error: If the error of the dynamic equations is within the convergence error, the position and motion parameters of each bearing component are output; Otherwise, the position and motion parameters of each part of the output bearing are solved as the initial values ​​of the next step length; S62, setting the time length of the position and motion parameters of each part of the output bearing: If the set time is reached, the dynamic characteristic analysis results of the segmented cage are output; Otherwise, the result is output to S2 as a parameter for the next cycle until the set time requirement is met and the cycle ends.

[0011] Furthermore, the convergence error is 10 -3 .

[0012] The beneficial effects of the present invention are: Based on the rolling bearing dynamics theory, the present invention constructs a ball bearing dynamics model equipped with a segmented cage. Based on the pure dynamics theory, the GSTIFF variable step-size integration method is used to iteratively calculate the dynamic differential equations of each bearing component, and finally outputs the dynamic behavior results between the segmented cage and the rolling element. This has obvious scientific application value for cage failure analysis of ball bearings equipped with segmented cages. During the modeling process, the present invention takes into account the situations where the bearing is located in a complete pocket and a half pocket, and solves the displacement, speed and force of each component of the output bearing by transmitting parameters such as the bearing structure, material properties, operating conditions and lubrication conditions. The force between the rolling element of the segmented cage and the complete pocket and the force between the rolling element and the half pocket are analyzed and solved respectively, and their dynamic characteristics are accurately analyzed. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] 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 present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0014] Figure 1 is a flow chart of the analysis method of the present invention; Figure 2 is a reference schematic diagram of the bearing coordinate system of the present invention; Figure 3 is a schematic diagram of a first segmented retainer in an embodiment of the present invention; Figure 4 is a schematic diagram of a second segmented retainer in an embodiment of the present invention; Figure 5 is a bearing assembly speed analysis model in an embodiment of the present invention; Figure 6Schematic diagram of the force of the rolling element in the embodiment of the present invention, wherein Figure a is a schematic diagram of the force in the xy plane, Figure b is a schematic diagram of the force in the xz plane, and Figure c is a schematic diagram of the force in the yz plane; Figure 7 Schematic diagram of the interaction between the rolling elements and the cage between the complete pockets of the two-segmented cage in the embodiment of the present invention; Figure 8 Schematic diagram of the interaction between the rolling elements and the cage between the half pockets of the two-segmented cage in the embodiment of the present invention; Fig. 9 This is a diagram of the simulation results of the collision force between the rolling element and the retaining frame output in an embodiment of the present invention. DETAILED DESCRIPTION

[0015] The following specific examples are given to further clearly, completely and in detail illustrate the technical solution of the present invention. This example is the best example based on the technical solution of the present invention, but the protection scope of the present invention is not limited to the following examples.

[0016] Example 1 A method for analyzing the dynamic behavior of a segmented cage of a large thin-walled bearing comprises the following steps: S1. Obtain the initial conditions of the bearing and establish the bearing coordinate system; The initial conditions include the structural parameters, material properties, working conditions and lubrication parameters of the bearing. A coordinate system including the earth coordinate system, the outer ring coordinate system, the cage coordinate system, the cage pocket center coordinate system and the rolling element coordinate system is constructed according to the initial conditions. Figure 1 shown.

[0017] Specifically, in this embodiment, the parameters are selected as follows: The structural parameters include: outer diameter, inner diameter, groove bottom diameter, rib diameter, width, number of rolling elements, rolling element diameter and cage structural parameters, as shown in Table 1; Table 1 Bearing structure parameters The material properties include: elastic modulus, Poisson’s ratio and density of each bearing component, as shown in Table 2; Table 2 Bearing component materials Working conditions include: radial force, axial force, overturning moment and rotation speed; lubrication parameters include: lubricant density, dynamic viscosity, viscosity-pressure coefficient and thermal conductivity coefficient, etc.

[0018] Furthermore, in order to describe the forces and motions between the components during operation, the coordinate systems of the bearing components are determined in the following manner: The geodetic coordinate system {O; X, Y, Z} is used to represent the motion between the various components of the bearing, with the X axis coinciding with the axis of the bearing ring; Outer circle coordinate system {O e ;X e ,Y e ,Z e}, the origin coincides with the centroid of the outer circle, X e The axis coincides with the X axis of the geodetic coordinate system; Cage coordinate system {o c ;x c ,y c ,z c}, x c The axis coincides with the X-axis of the earth coordinate system and is consistent with the movement of the cage; Cage pocket center coordinate system {o pj ;x pj ,y pj ,z pj}, consistent with the cage movement, the origin is located at the center of the pocket, the xpj axis is consistent with the X-axis of the geodetic coordinate system and remains parallel; Rolling element coordinate system {o bj ;x bj ,y bj ,z bj}, consistent with the movement of the rolling body, the origin is located at the center of mass of the rolling body, and the xbj axis is in the same direction as the X-axis of the inertial coordinate system.

[0019] S2. Determine the position and motion parameters of each bearing component, analyze according to the motion constraint conditions of each bearing component, and obtain the relative motion speed between the components; When solving the relative motion speed between the components, according to the position and motion parameters of the bearing components, the slip speed of the rolling element between the half pockets of the two segmented cages and its relative motion speed with the half cage are solved as follows: In the formula, Δv e and Δv i are the relative speeds of the rolling element and the inner and outer rings at the contact points; Δv m is the relative speed between the rolling element and the cage, according to Δv m The positive or negative value of determines whether the rolling element collides with the cage. m is the angular velocity of the cage revolution; e is the outer ring's angular velocity; ω b is the angular velocity of the rolling element; ω c is the angular velocity of the rolling element; d m is the bearing pitch diameter; d e and d iare the outer ring groove diameter and the inner ring groove diameter respectively; D w is the rolling element diameter.

[0020] S3. Solve the forces between the output bearing components, including the forces between the rolling element and the full pocket and the forces between the rolling element and the half pocket; According to the relative movement speed between the rolling elements and the cage in the complete pockets and half pockets of the segmented cage, the collision force between the rolling elements and the cage in the complete pockets and half pockets of the segmented cage is determined and calculated as follows: The nonlinear dynamic differential equation of the rolling element between the complete pockets in the inertial coordinate system {O; X, Y, Z} is as follows: The nonlinear dynamic differential equation of the rolling element between the half pockets of the segmented cage in the inertial coordinate system {O; X, Y, Z} is as follows: Among them, α lij , α lej are the inner and outer contact angles respectively; Q lij , Q lej is the normal contact load between the rolling element and the inner and outer raceways; Q lcj is the normal contact load between the rolling element and the pocket; T lηij , T lηej , T lξij , T lξej are the drag forces of the rolling element and the groove in the contact area; F lηj 、F lτj is the inertia force component of the rolling element; P lRξj , P lRηj is the rolling friction resistance of the rolling element surface; P lSξj , P lSηj F is the sliding friction resistance of the rolling element surface; lHηij 、F lHηej 、F lHξej 、F lHξij F is the horizontal component of the fluid dynamic pressure at the center of the rolling element; lRηij 、F lRηej 、F lRξej 、F lRξij J is the fluid dynamic pressure friction force in the contact entrance area between the rolling element and the groove; lx , J ly , J lz is the moment of inertia of the rolling body; G lyj , G lzj is the rolling element inertia moment in y bj 、z bjDirectional component; F lDj is the fluid resistance on the rolling element; I is the revolution speed of the rolling element; lb is the moment of inertia of the rolling body; is the component of the rolling body's center of mass acceleration in the inertial coordinate system; ω lbx ,ω lby ,ω lbz is the angular velocity component of the rolling body in the inertial coordinate system; is the angular acceleration component of the rolling body in the inertial coordinate system; is the angular acceleration component of the rolling body in the rolling body coordinate system.

[0021] S4. Establish a group of nonlinear dynamic differential equations for each bearing component, including the balance equations for rolling elements between complete pockets, the balance equations for rolling elements between half pockets of a two-segmented cage, the cage balance equations, and the outer ring balance equations, as follows: The nonlinear dynamic differential equation of the cage in the inertial coordinate system {O; X, Y, Z} is as follows: The nonlinear dynamic differential equation of the outer ring in the inertial coordinate system {O; X, Y, Z} is as follows: In the formula, is the rolling element position angle; Q lcxj , Q lcyj , Q lczj It is the component of the force between the rolling element and the cage pocket; is the acceleration of the cage; ω lcx ,ω lcy ,ω lcz is the angular velocity of the left cage; is the angular acceleration of the left cage; r j is the trajectory radius of the contact point between the rolling element and the outer raceway L is the bearing outer ring groove spacing; is the component of the outer circle particle acceleration in the geodetic coordinate system; M y 、M z is the component of the external torque in the geodetic coordinate system; ω ex ,ω ey ,ω ez is the angular velocity component of the outer ring; is the angular acceleration component of the outer ring.

[0022] S5. According to the bearing dynamics theory, the GSTIFF variable step-size integration algorithm is used to solve the nonlinear dynamic differential equations to obtain the values ​​of dynamic parameters including the normal contact load between the rolling element and the ring, the rolling friction resistance on the rolling element surface, the sliding friction resistance on the rolling element surface, the acceleration of the cage, and the angular velocity of the cage.

[0023] S6. Determine whether the error of the dynamic equations meets the convergence error, including the following: S61. Solve the dynamic differential equation at each moment and judge its error: If the error of the dynamic equations is within the convergence error (10 -3 ) within the range of 10000 to 20000, and output the position and motion parameters of each bearing part; Otherwise, the position and motion parameters of each part of the output bearing are used as the initial values ​​of the next step length to solve, and the nonlinear equations are solved iteratively again; S62, setting the time length of the position and motion parameters of each part of the output bearing: If the set time is reached, the dynamic characteristic analysis results of the segmented cage are output; Otherwise, the result is output to step 2 as a parameter for the next loop until the set time requirement is met and the loop ends.

[0024] The simulation results are as follows: According to the above parameter settings in this embodiment, the simulation results refer to Fig. 9 , which is the collision force between the rolling element and the full pocket and half pocket of the segmented cage solved by the present invention, rolling elements 2 to 7 are located between the full pockets, and rolling elements 1 and 8 are located between the half pockets. Fig. 9 It can be seen that the present invention can output the collision behavior between the rolling elements and different pockets of the segmented cage under specified working conditions of the bearing, check the collision force between the rolling elements and the pockets at different positions according to the output results, and predict the weak links of the segmented cage. With the help of the present invention, multiple simulations can be performed by changing the structure and material parameters of each component of the bearing, and the cage can be optimized and analyzed based on the output collision behavior results between the rolling elements and the cage pockets, thereby reducing mechanical failures caused by cage failure during the actual operation of the bearing.

[0025] In summary, the present invention proposes a method for analyzing the dynamic behavior of a segmented cage of a large thin-walled bearing, establishes its multi-body dynamic analysis model, and analyzes the dynamic behavior of each bearing component according to the operating conditions of the thin-walled bearing, thereby judging the cage failure of the ball bearing equipped with a segmented cage.

[0026] The above shows and describes the main features, basic principles and advantages of the present invention. The present invention is not limited to the above model, and can be analyzed and calculated for different number of segments and different types of cages; technicians in this industry should understand that the present invention is not limited to the above embodiment, and the above embodiment and description are only to illustrate the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will also have various changes and improvements according to actual conditions, and these changes and improvements fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for analyzing the dynamic behavior of a segmented cage of a large thin-walled bearing, characterized in that: The following steps are involved: S1. Obtain the initial conditions of the bearing and establish the bearing coordinate system; S2. Determine the position and motion parameters of each bearing component, analyze according to the motion constraint conditions of each bearing component, and obtain the relative motion speed between the components; S3. Solve the forces between the output bearing components, including the forces between the rolling element and the full pocket and the forces between the rolling element and the half pocket; S4. Establishing a group of nonlinear dynamic differential equations for each bearing component, including a group of equilibrium equations for rolling elements between complete pockets, a group of equilibrium equations for rolling elements between half pockets of a two-segmented cage, a group of equilibrium equations for the cage, and a group of equilibrium equations for the outer ring; S5. According to the bearing dynamics theory, the GSTIFF variable step size integration algorithm is used to solve the nonlinear dynamic differential equations. S6. Determine whether the error of the dynamic equation group satisfies the convergence error.

2. A method for analyzing dynamic behavior of a segmented cage of a large thin-walled bearing according to claim 1, characterized in that: The initial conditions of S1 include structural parameters, material properties, operating conditions and lubrication parameters of the bearing. A coordinate system including a geodetic coordinate system, an outer ring coordinate system, a cage coordinate system, a cage pocket center coordinate system and a rolling element coordinate system is constructed based on the above initial conditions.

3. The method for analyzing dynamic behavior of a large thin-walled bearing segmented cage according to claim 1 is characterized in that: When S2 solves the relative motion speed between the components, the slip speed of the rolling body between the half pockets of the two segmented cages and the relative motion speed with the half cages are solved according to the positions and motion parameters of the bearing components.

4. The method for analyzing dynamic behavior of a large thin-walled bearing segmented cage according to claim 3 is characterized in that: The S3 includes the following: Firstly, the position and motion parameters of each bearing component are solved as the initial values ​​according to the speed relationship in S2. Then, the collision force between the rolling elements and the cage between the complete pockets and half pockets of the segmented cage is determined according to the relative motion speed between the rolling elements and the cage between the complete pockets and half pockets of the segmented cage, and the force between the bearing components is solved.

5. The method for analyzing dynamic behavior of a large thin-walled bearing segmented cage according to claim 1 is characterized in that: In S5, the values ​​of dynamic parameters are solved according to the GSTIFF variable step size integration algorithm, including the normal contact load between the rolling element and the ring, the rolling friction resistance on the rolling element surface, the sliding friction resistance on the rolling element surface, the acceleration of the cage and the angular velocity of the cage.

6. The method for analyzing dynamic behavior of a large thin-walled bearing segmented cage according to claim 1 is characterized in that: The S6 includes the following contents: S61. Solve the dynamic differential equation at each moment and judge its error: If the error of the dynamic equations is within the convergence error, the position and motion parameters of each bearing component are output; Otherwise, the position and motion parameters of each part of the output bearing are solved as the initial values ​​of the next step length; S62, setting the time length of the position and motion parameters of each part of the output bearing: If the set time is reached, the dynamic characteristic analysis results of the segmented cage are output; Otherwise, the result is output to S2 as a parameter for the next cycle until the set time requirement is met and the cycle ends.

7. A method for analyzing dynamic behavior of a large thin-walled bearing segmented cage according to claim 6, characterized in that: The convergence error is 10 -3 .

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