Method for determining wear distribution of ball bearing rolling body
By acquiring the dynamic parameters and dynamic model of the rolling elements of the ball bearing, and calculating the contact point coordinates and wear increment, the problem of wear distribution prediction distortion in traditional methods is solved, and a more accurate wear distribution reconstruction is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XI AN JIAOTONG UNIV
- Filing Date
- 2026-01-29
- Publication Date
- 2026-05-12
AI Technical Summary
Existing technologies for measuring the wear of ball bearing rolling elements are insufficient to reflect the actual wear between the rolling elements and the raceway, because traditional methods ignore changes in the contact area during operation.
By acquiring target parameters at different times, including contact force, relative sliding speed, axial force, and radial force, and combining them with the ball bearing dynamics model, the contact angle and rotation speed are calculated. The fourth-order Runge-Kutta method is used to solve the differential equations to determine the coordinates of the contact point. The rolling element surface is discretized into multiple spherical cap meshes, and the wear increment is accumulated to determine the wear distribution.
This method enables precise reconstruction of the wear distribution of ball bearing rolling elements, improving the accuracy and intuitiveness of wear prediction and solving the problem of wear distribution prediction distortion in traditional methods.
Smart Images
Figure CN122016307A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of bearing wear detection technology, specifically a method for determining the wear distribution of rolling elements in a ball bearing. Background Technology
[0002] During operation, ball bearings experience adhesive wear due to the contact and relative sliding between the raceway and the rolling elements. This reduces the bearing's performance indicators, such as accuracy, and severely impacts its overall lifespan. Therefore, research on bearing wear is essential.
[0003] In the study of wear of objects, the Archard wear formula can quantitatively reveal the relationship between wear rate and parameters such as contact pressure, sliding speed, and material hardness. It is widely used in wear calculations in the mechanical field. The Archard wear formula is shown below: , in, W For wear rate, K For wear coefficient, P For the pressure in the contact area, V The relative sliding speed between contact surfaces, H The value represents the material hardness.
[0004] Because the contact points of the rolling elements in a ball bearing are constantly changing during operation, the area where wear occurs also changes over time. The traditional method of calculating and measuring the wear of the rolling elements in a ball bearing using the Archard wear formula only provides an overall wear condition, usually treating wear as a static or averaged process. This measurement process fails to consider the influence of changes in the contact area during bearing operation, and therefore cannot reflect the actual wear between the rolling elements and the raceway of the ball bearing. Summary of the Invention
[0005] The purpose of this invention is to provide a method for determining the wear distribution of the rolling elements of a ball bearing, in order to solve the problem that existing bearing wear measurement processes easily overlook the influence of changing wear areas, making it difficult to reflect the actual wear between the rolling elements and the raceway.
[0006] The technical solution of this invention is: A method for determining the wear distribution of rolling elements in a ball bearing includes the following steps: The target parameters are obtained at different times during the wear measurement period. The target parameters include the contact force between the ball bearing rolling element and the inner and outer raceways, the relative sliding speed between the ball bearing rolling element and the inner and outer raceways, the axial force and radial force on the ball bearing rolling element, and the rotational speed of the ball bearing drive end. Based on the obtained contact force and relative sliding velocity, the wear rate of the ball bearing rolling elements at different times is determined; Based on the axial force, radial force and rotational speed of the ball bearing drive end of the ball bearing rolling element, the contact angle between the ball bearing rolling element and the inner and outer raceways and the rotational speed of the ball bearing rolling element at different times are obtained by solving the ball bearing dynamics model. The contact point coordinates of the ball bearing rolling elements at different times are determined based on the obtained contact angle and rotation speed. The surface of the rolling element of the ball bearing is discretized into multiple spherical cap-shaped grids with equal area, and the coordinate interval corresponding to each spherical cap-shaped grid is recorded; For each moment within the wear measurement period, the wear increment at that moment is calculated based on the wear rate and the measurement time step. Based on the contact point coordinates at that moment, the corresponding spherical cap surface grid is determined, and the wear increment is accumulated to that spherical cap surface grid. By traversing all moments within the wear measurement period, the wear increment of each spherical cap surface grid is accumulated, thus obtaining the wear distribution of the entire spherical surface of the ball bearing rolling element.
[0007] Preferably, as a further improvement of the present invention, the method for obtaining the contact angle between the rolling elements of the ball bearing and the inner and outer raceways and the rotational speed of the rolling elements of the ball bearing at different times includes the following steps: The axial force, radial force, and rotational speed of the ball bearing drive end are obtained as input parameters into the ball bearing dynamic model. Based on the interaction and force analysis conditions between the components in the ball bearing dynamic model, a set of differential equations for the motion of the ball bearing rolling elements is constructed. The components include the ball bearing rolling elements, inner and outer raceways, cage, and lubricating oil. The forces include the centrifugal force on the ball bearing rolling elements, the contact force and drag force between the ball bearing rolling elements and the inner and outer raceways, the collision force between the ball bearing rolling elements and the cage, and the viscous resistance generated by the lubricating oil on the rolling elements and the cage. The fourth-order Runge-Kutta method was used to solve the differential equations of the motion of the ball bearing rolling elements, and the contact angle between the ball bearing rolling elements and the raceway and the rotation speed of the ball bearing rolling elements at different times during the wear measurement period were obtained.
[0008] Preferably, as a further improvement of the present invention, the method for determining the contact point coordinates of the rolling elements of a ball bearing at different times based on the acquired contact angle and rotational speed includes the following steps: With the center of the ball bearing rolling element as the origin, establish a body coordinate system fixed on the ball bearing rolling element and an azimuth coordinate system that revolves with the ball bearing rolling element. Determine the coordinates of the contact point of the ball bearing rolling elements in the azimuth coordinate system based on the contact angle between the rolling elements and the raceway of the ball bearing: In the azimuth coordinate system, the attitude of the ball bearing rolling element at a certain moment is used to determine the changed attitude of the ball bearing rolling element at the next moment by combining the following formula with the rotational speed of the ball bearing rolling element: In the formula, q n Let be the quaternion representation of the attitude of the rolling elements of a ball bearing at a certain moment. q n+1 The quaternion representation of the rolling element attitude of the ball bearing at the next moment. Let be the rotational speed of the rolling elements of the ball bearing, and =[ x , y , z ], Δ t The interval duration Using quaternions, the contact point coordinates of the ball bearing rolling elements are transformed from the azimuth coordinate system to the volume coordinate system, and the contact point coordinates at the next moment are extended into a quaternion format. P n+1 =[0, x , y , z Then, the coordinate quaternion after coordinate transformation is: , extract The imaginary part in the equation represents the coordinates of the contact point in the volume coordinate system.
[0009] Preferably, as a further improvement of the present invention, the determination of the contact point coordinates of the ball bearing rolling element in the azimuth coordinate system based on the contact angle between the ball bearing rolling element and the raceway is obtained by the following formula: , , in, p i These are the coordinates of the contact points between the rolling elements of the ball bearing and the inner raceway of the bearing in the azimuth coordinate system. p o These are the coordinates of the contact points between the rolling elements of the ball bearing and the outer raceway of the bearing in the azimuth coordinate system. D w The diameter of the rolling elements of the ball bearing. The contact angle between the rolling elements of the ball bearing and the inner raceway of the bearing. It is the contact angle between the rolling elements of the ball bearing and the outer raceway of the bearing.
[0010] Preferably, as a further improvement of the present invention, when discretizing the surface of the ball bearing rolling element into multiple spherical cap grids with equal area, the method of dividing the area into latitudinal zones is adopted.
[0011] Preferably, as a further improvement of the present invention, when determining the spherical cap grid to which the contact point belongs based on the contact point coordinates, the coordinates of the contact point of the ball bearing rolling element are matched with the latitude and longitude coordinate range of each spherical cap grid in the body coordinate system. If the contact point coordinates fall within the coordinate range of a certain grid, the spherical cap grid to which the contact point belongs is determined. If the contact point coordinates fall on the boundary between two adjacent grids, the grid with the smaller latitude and longitude value is assigned by default.
[0012] Preferably, as a further improvement of the present invention, the area of the divided spherical cap-shaped grid is 0.01 mm. 2 ~0.5mm 2 .
[0013] Compared with the prior art, the beneficial effects of the present invention are: By acquiring the wear rate and contact point coordinates of the ball bearing rolling elements at different times during the wear measurement period, the surface of the ball bearing rolling elements is differentiated and discretized into multiple spherical cap surface grids with equal area. The contact points are then mapped to the discretized spherical cap surface grids for wear accumulation, ultimately obtaining the wear distribution of the ball bearing rolling elements. Since this method is no longer limited to a single total wear assessment but achieves a fine reconstruction of wear information in the spatial dimension, it solves the technical problem of wear distribution prediction distortion caused by neglecting the changes in the contact area in traditional methods. This significantly improves the simulation capability of non-uniform wear morphology on the rolling element surface, achieving a more accurate and intuitive reflection of the actual wear between the ball bearing rolling elements and raceways. Attached Figure Description
[0014] Figure 1 This is a schematic flowchart illustrating the steps of a method for determining the wear distribution of rolling elements in a ball bearing according to the present invention.
[0015] Figure 2 This is a schematic diagram of the ball bearing rolling element coordinate system established in the method for determining the wear distribution of the ball bearing rolling elements according to the present invention. Detailed Implementation
[0016] The following is combined with Figures 1-2The specific embodiments of the present invention will be described in detail below. In the description of the invention, it should be understood that the terms "center", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention.
[0017] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature; in the description of the invention, unless otherwise stated, "a plurality of" means two or more.
[0018] Example like Figures 1-2 As shown, this embodiment of the invention provides a method for determining the wear distribution of the rolling elements of a ball bearing. Includes the following steps: S1. Obtain target parameters at different times during the wear measurement period. The target parameters include the contact force between the ball bearing rolling element and the inner and outer raceways, the relative sliding speed between the ball bearing rolling element and the inner and outer raceways, the axial force and radial force on the ball bearing rolling element, and the rotational speed of the ball bearing drive end.
[0019] Among the aforementioned target parameters, the contact force between the rolling elements and the inner and outer raceways of the ball bearing, and the relative sliding velocity between the rolling elements and the inner and outer raceways, are dynamic response parameters that can be calculated using a dynamic simulation model. A multibody dynamics simulation software (such as ADAMS / Solver or SIMPACK) is selected to establish a multibody dynamics model of the ball bearing. Bearing geometric parameters are input, such as the nominal diameter of the rolling elements, the radius of curvature coefficients of the inner and outer raceways, and the nominal contact angle of the bearing. Material parameters include the elastic modulus, Poisson's ratio, and density of the rolling elements and raceways. A Hertzian elastic contact model is defined for the contact stiffness between the rolling elements and raceways. The simulation time (i.e., the wear measurement time period) is set, with the solution time step set to 0.001s~0.01s, adjusted according to the bearing speed to ensure the sampling accuracy of speed fluctuations. The simulation is run, and the time-domain data of the contact force and relative sliding velocity between the rolling elements and the inner and outer raceways at different times are output. Among the above target parameters, the axial and radial forces on the rolling elements of the ball bearing and the rotational speed of the ball bearing drive end are operating condition parameters, which are determined according to the bearing test conditions. The axial and radial forces are collected by strain gauge force sensors installed on the bearing housing, and the collection frequency is matched with the simulation time step. The rotational speed of the drive end is collected by photoelectric encoder installed on the drive shaft end, with a sampling frequency of 1kHz. After low-pass filtering to remove noise, a continuous rotational speed curve is obtained.
[0020] S2. Based on the obtained contact force and relative sliding speed, determine the wear rate of the ball bearing rolling elements at different times.
[0021] Specifically, within a set time step, the contact force P between the rolling elements of the ball bearing and the inner and outer raceways, as well as the relative sliding velocity V between the rolling elements and the inner and outer raceways, are collected at each moment. The product of these two values, PV, represents the instantaneous wear rate at that moment. Using PV avoids direct dependence on the difficult-to-obtain material wear coefficient k, instead modeling based on measurable or calculable mechanical parameters. This is particularly beneficial in actual working conditions with complex lubrication conditions (such as alternating elastohydrodynamic lubrication and boundary lubrication), where the K value in the traditional Archard model fluctuates significantly. Without relying on empirical wear coefficients... Under the premise of this, the wear rate between the rolling elements and raceways of a ball bearing is quantitatively described by using the product of the contact force P and the relative sliding velocity V, which can be obtained from dynamic analysis. Since both P and V can reflect the key physical mechanisms in the friction process (pressure-induced material deformation, sliding-induced energy dissipation), their product is naturally related to the driving force and motion conditions of wear. Therefore, it can more realistically depict the local wear trend at different positions and times. The contact force between the rolling elements and the inner and outer raceways of the ball bearing, as well as the relative sliding velocity between the rolling elements and the inner and outer raceways of the ball bearing, can be obtained from dynamic analysis.
[0022] S3. Based on the obtained axial force, radial force and rotational speed of the ball bearing drive end, the contact angle between the ball bearing rolling element and the inner and outer raceways and the rotational speed of the ball bearing rolling element at different times are obtained by solving the ball bearing dynamics model.
[0023] Specifically, this invention proposes a model for solving the contact trajectory of ball bearing rolling elements to address the changes in contact points. Analysis of the motion state of the ball bearing rolling elements reveals that they possess six degrees of freedom during actual operation: revolution around the axis, axial movement, radial movement, and rotation in three directions. The axial and radial movements of the rolling elements cause changes in the contact angle between the rolling elements and the raceway, while the rotation of the rolling elements alters their attitude. Therefore, determining the contact points of the ball bearing rolling elements requires calculating their contact angles and attitude angles.
[0024] The contact angle changes and rotation speed at different times can be obtained by solving the dynamics of the angular contact ball bearing, while the attitude angle needs to be further calculated based on the rotation speed.
[0025] The contact angle variation and rotation velocity at different times are solved using dynamics as follows: Assuming the outer raceway of the ball bearing is fixed, the ball bearing drive speed and external load are applied to the inner raceway of the ball bearing. The motion state of each component inside the ball bearing is analyzed and simplified. The inner raceway of the ball bearing has 5 degrees of freedom, the rolling elements of the ball bearing have 6 degrees of freedom, and the cage has 1 degree of freedom.
[0026] Obtain the operating parameters of the ball bearing rolling elements, including the axial force, radial force, and drive speed acting on the ball bearing rolling elements; Taking an angular contact ball bearing as an example, based on the dynamic model of an angular contact ball bearing, the interaction and force conditions between the rolling elements, raceways, cage, and lubricating oil are considered. These forces include the centrifugal force of the rolling elements, the contact and drag forces between the rolling elements and raceways, the collision forces between the rolling elements and cage, and the viscous resistance of the lubricating oil on the rolling elements and cage. Based on the operating parameters, interaction relationships, and force conditions, a set of differential equations for the motion of the ball bearing rolling elements is established. The process of establishing the differential equations is as follows: Based on Newton's equations of motion and Euler's equations of motion, the motion of the rolling elements of a ball bearing in various directions can be described: in For the mass of the rolling elements of the ball bearing, Let be the moment of inertia of the rolling elements of the ball bearing along the axis of rotation. For the rolling element in x Displacement in the direction, For the rolling elements of the ball bearing y Displacement in the direction, Let be the position angle of the rolling element of the ball bearing. x For the rolling elements of the ball bearing x Rotational speed in the direction, y For the rolling elements of the ball bearing y Rotational speed in the direction, zFor the rolling elements of the ball bearing z Rotational speed in the direction, The diameter of the rolling elements of the ball bearing is... D ro Let be the diameter of the outer contact area with respect to the center of the circle. D ri Let be the diameter of the inner contact area with respect to the center of the circle; β o The contact angle between the outer raceway and the rolling elements of the ball bearing. β i This is the contact angle between the inner raceway and the rolling elements of the ball bearing. Q o This refers to the contact force between the rolling elements and the outer raceway of the ball bearing. Q i This refers to the contact force between the rolling elements and the inner raceway of the ball bearing. For the rolling elements of the ball bearing x The drag force exerted on the rolling elements of the ball bearing by the outer contact area between the ball bearing and the raceway in the direction of the bearing. For the rolling elements of the ball bearing y The drag force exerted on the rolling elements of the ball bearing by the outer contact area between the ball bearing and the raceway in the direction of the bearing. For the rolling elements of the ball bearing x The drag force exerted on the rolling elements of the ball bearing by the inner contact area between the bearing and the raceway in the direction of travel. For the rolling elements of the ball bearing y The drag force exerted on the rolling elements of the ball bearing by the inner contact area between the bearing and the raceway in the direction of travel. M o The spin velocity on the outer raceway. M i The spin velocity on the inner raceway. Q c To maintain the impact force of the cage on the rolling elements of the ball bearing, This refers to the viscous resistance of the lubricating oil to the rolling elements of the ball bearing.
[0027] For the inner raceway of a ball bearing, its motion is mainly affected by the rolling elements of the ball bearing and external loads. The following describes its motion state: in, F x In order to be in x The force applied in the direction of the bearing raceway. F y In order to be in yThe force applied in the direction of the bearing raceway. F z In order to be in z The force applied in the direction to the inner raceway of the bearing. M y In order to be in y The torque applied in the direction to the inner raceway of the bearing. M z In order to be in z The torque applied in the direction of the bearing's inner raceway For the number of rolling elements, Where is the inner raceway radius. Q ij For the first j The contact force between the rolling elements of a ball bearing and the inner raceway of the bearing. For the first j The rolling elements of the ball bearing are in x The drag force exerted on the inner raceway of the bearing in the directional direction. For the first j The rolling elements of the ball bearing are in y The drag force exerted on the inner raceway of the bearing in the directional direction. β ij For the first j The contact angle between the rolling elements of a ball bearing and the inner raceway of the bearing.
[0028] For the cage, we have: in To maintain the moment of inertia of the cage about the axis of rotation, To maintain the rotational speed of the frame, To maintain the equivalent radius of the cage, The impact force of the rolling elements on the cage. This refers to the viscous resistance of the lubricating oil to the cage.
[0029] Based on the differential equations established in (1) to (12) above, the fourth-order Runge-Kutta method is used to solve them, and the contact angle between the ball bearing rolling element and the raceway and the rotation speed of the ball bearing rolling element at different times within a set time are obtained.
[0030] S4. Determine the contact point coordinates of the ball bearing rolling elements at different times based on the obtained contact angle and rotation speed.
[0031] Specifically, to analyze the attitude information of the rolling element, two coordinate systems are defined on the rolling element: a volume coordinate system fixed on the sphere and an azimuth coordinate system that revolves with the sphere. For example... Figure 2 As shown, where ( x , y , zThe bearing's overall coordinate system is established, with the center of the ball bearing's rolling elements as the origin. A volume coordinate system fixed on the ball bearing's rolling elements is then established. ， ， ) and the azimuth coordinate system that revolves with the rolling elements of the ball bearing ( x b , y b , z b Based on the contact angle between the rolling elements and the raceway of the ball bearing, the coordinates of the contact points of the rolling elements in the azimuth coordinate system are calculated.
[0032] , , in, p i These are the coordinates of the contact points between the rolling elements of the ball bearing and the inner raceway of the bearing in the azimuth coordinate system. p o These are the coordinates of the contact points between the rolling elements of the ball bearing and the outer raceway of the bearing in the azimuth coordinate system. D w The diameter of the rolling elements of the ball bearing. The contact angle between the rolling elements of the ball bearing and the inner raceway of the bearing. The contact angle between the rolling elements of the ball bearing and the outer raceway of the bearing; The attitude angle change is calculated based on the rotation speed, and the attitude of the rolling elements of the ball bearing at a certain moment is expressed using quaternions. q n When the rolling elements of the ball bearing rotate at their own speed =[ x , y , z Rotation time Δ t Then, the attitude of the rolling elements of the ball bearing at the next moment is represented by quaternions as follows: q n+1 ,but q n+1 and q n The relationship is as follows: , Using quaternions, the coordinate transformation of the contact point coordinates of the ball bearing rolling elements from the azimuth coordinate system to the volume coordinate system is performed, expanding the contact point coordinates at the next moment into a quaternion format. P n+1 =[0, x ,y , z Then, the coordinate quaternion after coordinate transformation is: , extract The imaginary part in the equation represents the coordinates of the contact point in the volume coordinate system.
[0033] The multiplication of quaternions is defined here, and the calculation process is as follows: for as well as Then there is in, w It is the real part, [ x y z [ is the imaginary part.]
[0034] S5. Discretize the rolling surface of the ball bearing into multiple spherical cap meshes with equal area, and record the coordinate interval corresponding to each spherical cap mesh.
[0035] When discretizing the rolling element surface of a ball bearing into multiple spherical cap-shaped meshes with equal area, a latitudinal zone equal area division method is used, and the area of each spherical cap-shaped mesh is 0.01 mm². 2 ~0.5mm 2 When the area of the divided spherical cap mesh exceeds this range, the model accuracy decreases, affecting the final calculation results; conversely, when the area of the divided spherical cap mesh is less than this range, more memory and time are consumed in the calculation, resulting in unnecessary resource waste. The total number of meshes is determined based on the area of the divided spherical cap mesh and the total area of the sphere. Then, a series of latitudinal boundaries are solved numerically to ensure that the spherical zone areas between adjacent latitude lines are equal. Within each spherical zone, longitude is evenly divided according to the perimeter of the zone, forming approximately equal-area quadrilateral or triangular meshes.
[0036] S6. For each moment within the wear measurement period, calculate the wear increment at that moment based on the wear rate and the measurement time step. Based on the contact point coordinates at that moment, determine the corresponding spherical cap grid and add the wear increment to that spherical cap grid. Repeat this process for all moments within the wear measurement period to accumulate the wear increment for each spherical cap grid and obtain the wear distribution of the entire spherical surface of the ball bearing rolling element.
[0037] Specifically, within each simulation time step, the contact force P(t) at a certain moment is collected in real time. n ) and relative sliding velocity V (t n ), calculate the wear rate PV(t) corresponding to that moment. n) = P(t) n )×V(t n The wear rate remains essentially constant within this simulation time step, and the wear increment ΔW generated within this time step... n =PV(t) n )*Δt n In the formula t n It is the nth simulation time, Δt n It is the nth time step, PV(t) n () represents the wear rate at that moment.
[0038] Then, the coordinates of the contact points of the ball bearing rolling elements at each time point are matched with the latitude and longitude coordinate intervals of each spherical cap grid. If the coordinates of the contact point fall within the coordinate interval of a certain grid, the spherical cap grid to which the contact point belongs is determined. If the coordinates of the contact point fall on the boundary between two adjacent grids, it is assigned to the grid with the smaller latitude and longitude value by default. Thus, the wear increment is accumulated to the spherical cap grid. The above process is repeated until the wear increments of the contact point coordinates corresponding to the spherical cap grids at all times during the measurement period are accumulated to obtain the wear distribution of the entire spherical surface of the ball bearing rolling elements.
[0039] The above-disclosed embodiments are merely preferred embodiments of the present invention. However, the embodiments of the present invention are not limited thereto, and any variations that can be conceived by those skilled in the art should fall within the protection scope of the present invention.
Claims
1. A method for determining the wear distribution of rolling elements in a ball bearing, characterized in that, Includes the following steps: The target parameters are obtained at different times during the wear measurement period. The target parameters include the contact force between the ball bearing rolling element and the inner and outer raceways, the relative sliding speed between the ball bearing rolling element and the inner and outer raceways, the axial force and radial force on the ball bearing rolling element, and the rotational speed of the ball bearing drive end. Based on the obtained contact force and relative sliding velocity, the wear rate of the ball bearing rolling elements at different times is determined; Based on the axial force, radial force and rotational speed of the ball bearing drive end of the ball bearing rolling element, the contact angle between the ball bearing rolling element and the inner and outer raceways and the rotational speed of the ball bearing rolling element at different times are obtained by solving the ball bearing dynamics model. The contact point coordinates of the ball bearing rolling elements at different times are determined based on the obtained contact angle and rotation speed. The surface of the rolling element of the ball bearing is discretized into multiple spherical cap-shaped grids with equal area, and the coordinate interval corresponding to each spherical cap-shaped grid is recorded; For each moment within the wear measurement period, the wear increment at that moment is calculated based on the wear rate and the measurement time step. Based on the contact point coordinates at that moment, the corresponding spherical cap surface grid is determined, and the wear increment is accumulated to that spherical cap surface grid. By traversing all moments within the wear measurement period, the wear increment of each spherical cap surface grid is accumulated, thus obtaining the wear distribution of the entire spherical surface of the ball bearing rolling element.
2. The method for determining the wear distribution of rolling elements in a ball bearing according to claim 1, characterized in that, The method for obtaining the contact angle between the rolling elements of a ball bearing and the inner and outer raceways, as well as the rotational speed of the rolling elements of the ball bearing at different times, includes the following steps: The axial force, radial force, and rotational speed of the ball bearing drive end are obtained as input parameters into the ball bearing dynamic model. Based on the interaction and force analysis conditions between the components in the ball bearing dynamic model, a set of differential equations for the motion of the ball bearing rolling elements is constructed. The components include the ball bearing rolling elements, inner and outer raceways, cage, and lubricating oil. The forces include the centrifugal force on the ball bearing rolling elements, the contact force and drag force between the ball bearing rolling elements and the inner and outer raceways, the collision force between the ball bearing rolling elements and the cage, and the viscous resistance generated by the lubricating oil on the rolling elements and the cage. The fourth-order Runge-Kutta method was used to solve the differential equations of the motion of the ball bearing rolling elements, and the contact angle between the ball bearing rolling elements and the raceway and the rotation speed of the ball bearing rolling elements at different times during the wear measurement period were obtained.
3. The method for determining the wear distribution of rolling elements in a ball bearing according to claim 1, characterized in that, The method for determining the contact point coordinates of the rolling elements of a ball bearing at different times based on the acquired contact angle and rotation speed includes the following steps: With the center of the ball bearing rolling element as the origin, establish a body coordinate system fixed on the ball bearing rolling element and an azimuth coordinate system that revolves with the ball bearing rolling element. Determine the coordinates of the contact point of the ball bearing rolling elements in the azimuth coordinate system based on the contact angle between the rolling elements and the raceway of the ball bearing: In the azimuth coordinate system, the attitude of the ball bearing rolling element at a certain moment is used to determine the changed attitude of the ball bearing rolling element at the next moment by combining the following formula with the rotational speed of the ball bearing rolling element: In the formula, q n Let be the quaternion representation of the attitude of the rolling elements of a ball bearing at a certain moment. q n+1 The quaternion representation of the rolling element attitude of the ball bearing at the next moment. Let be the rotational speed of the rolling elements of the ball bearing, and =[ x , y , z ], Δ t The interval duration Using quaternions, the contact point coordinates of the ball bearing rolling elements are transformed from the azimuth coordinate system to the volume coordinate system, and the contact point coordinates at the next moment are extended into a quaternion format. P n+1 =[0, x , y , z Then, the coordinate quaternion after coordinate transformation is: ， extract The imaginary part in the equation represents the coordinates of the contact point in the volume coordinate system.
4. The method for determining the wear distribution of rolling elements in a ball bearing according to claim 3, characterized in that, The contact point coordinates of the ball bearing rolling elements in the azimuth coordinate system, determined based on the contact angle between the ball bearing rolling elements and the raceway, are obtained using the following formula: ， ， in, p i These are the coordinates of the contact points between the rolling elements of the ball bearing and the inner raceway of the bearing in the azimuth coordinate system. p o These are the coordinates of the contact points between the rolling elements of the ball bearing and the outer raceway of the bearing in the azimuth coordinate system. D w The diameter of the rolling elements of the ball bearing. The contact angle between the rolling elements of the ball bearing and the inner raceway of the bearing. It is the contact angle between the rolling elements of the ball bearing and the outer raceway of the bearing.
5. The method for determining the wear distribution of rolling elements in a ball bearing according to claim 3, characterized in that, When discretizing the rolling element surface of a ball bearing into multiple spherical cap-shaped grids with equal area, the method of dividing the area into latitudinal zones is adopted.
6. The method for determining the wear distribution of rolling elements in a ball bearing according to claim 5, characterized in that, When determining the spherical cap grid to which the contact point belongs based on the contact point coordinates, the coordinates of the ball bearing rolling element contact point are matched with the latitude and longitude coordinate range of each spherical cap grid in the volume coordinate system. If the contact point coordinates fall within the coordinate range of a certain grid, the spherical cap grid to which the contact point belongs is determined. If the contact point coordinates fall on the boundary between two adjacent grids, it is assigned to the grid with the smaller latitude and longitude value by default.
7. The method for determining the wear distribution of rolling elements in a ball bearing according to claim 5, characterized in that, The area of the divided spherical cap grid is 0.01 mm. 2 ~0.5mm 2 .