Angular contact ball bearing outer ring axial and radial runout prediction method

Abstract

The present application relates to a kind of angular contact ball bearing outer ring axial, radial runout prediction method, belong to angular contact ball bearing rotation precision calculation technical field.The method includes: the geometric parameter of angular contact ball bearing is collected, the rotation angle step and translation step of outer ring are set;Geometric parameter includes inner raceway curvature radius, inner raceway groove bottom diameter, outer raceway curvature radius, outer raceway groove bottom diameter, ball diameter, original contact angle and outer raceway roundness error;Establish three-dimensional coordinate system with the load center of angular contact ball bearing as origin, axial as Z axis, vertically upward as Y axis;Calculate the stable position of outer ring under each rotation angle step;According to the stable position of outer ring under each rotation angle step and the position change of inner ring, obtain the axial, radial runout value of outer ring.The present application predicts the axial, radial runout of outer ring of angular contact ball bearing by numerical calculation using the geometric parameter of angular contact ball bearing, improves the efficiency and accuracy of prediction.

Description

Technical Field

[0001] This invention relates to a method for predicting the axial and radial runout of the outer ring of an angular contact ball bearing, belonging to the technical field of angular contact ball bearing rotational accuracy calculation. Background Technology

[0002] Angular contact ball bearings are one of the most important support methods for high-speed rotating machinery and are widely used in high-speed machine tools, aero engines, electric motors, automobiles, high-speed centrifuges and other fields.

[0003] Bearing rotational accuracy is a key parameter for evaluating bearing performance. The main indicators for evaluating the rotational accuracy of angular contact ball bearings include the radial runout of the inner ring, the radial runout of the outer ring, and the axial runout. Currently, existing methods for measuring the radial and axial runout of the inner and outer rings of angular contact ball bearings can only be used to measure the finished bearings after machining and assembly through testing, resulting in low measurement efficiency and high cost. Summary of the Invention

[0004] The purpose of this application is to provide a method for predicting the axial and radial runout of the outer ring of an angular contact ball bearing, in order to solve the problems of low efficiency and high cost of existing methods.

[0005] To achieve the above objectives, this application proposes a technical solution for predicting the axial and radial runout of the outer ring of an angular contact ball bearing, comprising the following steps:

[0006] 1) Collect the geometric parameters of the angular contact ball bearing, and set the rotation angle step and translation step of the outer ring; the geometric parameters include the inner groove radius of curvature, the inner groove bottom diameter, the outer groove radius of curvature, the outer groove bottom diameter, the steel ball diameter, the original contact angle, and the outer groove roundness error;

[0007] 2) Establish a three-dimensional coordinate system with the load center of the angular contact ball bearing as the origin, the axial direction as the Z-axis, and the vertical upward direction as the Y-axis;

[0008] 3) Calculate the stable position of the outer ring at each rotation angle step:

[0009] a. Rotate the outer ring by one rotation angle step, and calculate the position of the center of the steel ball based on the diameter of the steel ball, the radius of curvature of the inner channel, the diameter of the bottom of the inner channel, and the original contact angle;

[0010] b. Calculate the outer channel profile curve for each translation step of the outer ring based on the outer channel bottom diameter, outer channel radius of curvature, inner channel bottom diameter, inner channel radius of curvature, original contact angle, and outer channel roundness error;

[0011] c. Calculate the distance between the point on the outer channel and the surface of the steel ball for each translation step to obtain the contact state between the outer channel and the steel ball; the contact state includes interference state, contact state, and separation state;

[0012] d. Based on the contact state between the outer groove and the steel ball, and combined with the stability criterion of the outer ring, the stable position of the outer ring at each rotation angle step is obtained;

[0013] 4) Based on the stable position of the outer ring and the position change of the inner ring under each rotation angle step, the axial and radial runout values ​​of the outer ring are obtained.

[0014] The beneficial effects of the technical solution of the axial and radial runout prediction method for the outer ring of the angular contact ball bearing of the present invention are as follows: The present invention predicts the axial and radial runout of the outer ring of the angular contact ball bearing by simulating the rotation process of the outer ring and using the geometric parameters of the angular contact ball bearing through numerical calculation, thereby improving the efficiency and accuracy of prediction and thus efficiently predicting the rotational accuracy of the angular contact ball bearing.

[0015] Furthermore, the stability criterion for the outer ring is:

[0016] a. The outer channel does not interfere with any steel ball;

[0017] b. The number of steel balls in contact with the outer channel is three or more;

[0018] c. The contact steel balls are distributed in at least three quadrants in the radial plane.

[0019] Furthermore, if there are multiple stable positions on the outer ring at each rotation angle step, then the position with the most contact steel balls is the stable position.

[0020] Furthermore, if there are multiple positions with the most contacting steel balls, then the position with the smallest displacement is the stable position.

[0021] Furthermore, several ideal contact points are determined among the points on the outer channel. A grid is then divided within a range centered on the ideal contact points. The intersections of the grids are the expansion points. The minimum distance between the expansion points, the ideal contact points, and the surface of the steel ball is used as the basis for judging the contact state between the outer channel and the steel ball.

[0022] Furthermore, the calculation process for the position of the steel ball's center is as follows:

[0023]

[0024]

[0025] Among them, (X) j Y j Z j ) represents the coordinates of the center of the j-th steel ball; β j Let be the position angle of the center of the j-th steel ball in the radial plane; D is the distance from the center of the steel ball to the axis; D w d is the diameter of the steel ball;i R is the diameter of the bottom of the inner channel; i α is the radius of curvature of the inner channel; α is the initial contact angle.

[0026] Furthermore, the roundness error of the outer channel is:

[0027]

[0028] Where ΔS(θ1) is the roundness error of the outer channel; θ1 is the position angle of the outer channel in the radial plane; m is the harmonic order; A m This represents the roundness error magnitude. This is the initial phase angle.

[0029] Furthermore, at each translation step, the outer channel profile curve is as follows:

[0030]

[0031] Among them, (X) c Y c Z c ) represents the coordinates of point c on the outer channel in the three-dimensional coordinate system; △x, △y, and △z are the components of the translation step size on the X, Y, and Z axes, respectively. The curvature center of the outer channel o e Coordinates in the axial plane Y1OZ1; R e θ1 is the radius of curvature of the outer channel; ΔS(θ1) is the roundness error of the outer channel; θ1 is the position angle of the outer channel in the radial plane; θ2 is the angle between the line connecting the point on the outer channel and the center of the steel ball and the Z1 axis.

[0032] Furthermore, the curvature center of the outer channel o e Coordinates in the axial plane Y1OZ1 for:

[0033]

[0034] Among them, D e R is the diameter of the bottom of the outer channel; e d is the radius of curvature of the outer channel; i R is the diameter of the bottom of the inner channel; i α is the radius of curvature of the inner channel; α is the initial contact angle.

[0035] Furthermore, when d 2min When |d <-ε, the outer channel and the steel ball are in an interference state; when |d 2min When |≤ε, the outer channel and the steel ball are in contact; when d 2min When ε > 0, the outer channel and the steel ball are separated; d 2min ε represents the minimum distance between several extended points, ideal contact points, and the surface of the steel ball; ε is the allowable interference error. Attached Figure Description

[0036] Figure 1 This is a three-dimensional structural diagram of the angular contact ball bearing of the present invention;

[0037] Figure 2 This is an axial planar schematic diagram of the initial state of the angular contact ball bearing of the present invention;

[0038] Figure 3 This is a geometric diagram showing the relationship between a point on the outer raceway of the angular contact ball bearing of the present invention and the axial plane;

[0039] Figure 4 This is a geometric diagram showing the relationship between a point on the outer raceway of the angular contact ball bearing of the present invention and the radial plane;

[0040] Figure 5 This invention is based on the outer groove profile curve that takes into account roundness error.

[0041] Figure 6 This is a schematic diagram of the grid division of ideal contact points on the outer channel of the present invention;

[0042] Figure 7 This is a quadrant distribution diagram of the steel balls of the present invention in the radial plane;

[0043] Figure 8 This invention describes the radial runout process of the outer ring of the angular contact ball bearing.

[0044] Figure 9 This invention describes the axial runout process of the outer ring of the angular contact ball bearing.

[0045] In the diagram: 1 represents the outer ring, 2 the inner ring, and 3 the steel ball. Detailed Implementation

[0046] Example of a method for predicting axial and radial runout of the outer ring of an angular contact ball bearing:

[0047] The main concept of this invention lies in simulating the rotation process of the outer ring, calculating the stable position of the outer ring for each rotational angle step, and then obtaining the axial and radial runout values ​​of the outer ring based on the stable position of the outer ring and the position of the inner ring.

[0048] The three-dimensional structure of an angular contact ball bearing is as follows: Figure 1 As shown, it includes an outer ring 1, an inner ring 2, and several steel balls 3. The steel balls 3 are arranged between the outer groove of the outer ring 1 and the inner groove of the inner ring 2. The inner groove, the outer groove, and the surface of the steel balls 3 all have dimensional and roundness errors. The outer ring 1 rotates while the inner ring 2 is fixed.

[0049] Specifically, the method for predicting the axial and radial runout of the outer ring of an angular contact ball bearing includes the following steps:

[0050] 1) Collect the geometric parameters of the angular contact ball bearing to be predicted, and set the rotation angle step and translation step of the outer ring 1.

[0051] Angular contact ball bearing geometric parameters: inner raceway radius of curvature R i Diameter d of the bottom of the inner channel i Radius of curvature R of the outer channel e Diameter D of the outer channel bottom e , steel ball diameter D w Number of steel balls Z, initial contact angle α, radial clearance G r And the roundness error of the outer channel ΔS(θ1).

[0052] The outer ring 1 rotates in 1° increments, completing one revolution. The translation step is the step size by which the outer ring 1 moves towards the steel ball 3, and the maximum translation displacement is determined by the radial clearance G. r Sure.

[0053] 2) Establish a three-dimensional coordinate system with the load center T as the origin, and determine the initial state of the angular contact ball bearing.

[0054] Three-dimensional coordinate system as Figure 1 As shown, its origin O is the load center T. The load center T is the intersection point on the axis of all normals at the contact point between the steel ball 3 and the raceway when the steel ball 3 is in ideal contact with the inner and outer raceways. The coordinate axes are set as follows: the Z-axis coincides with the bearing axis, the Y-axis is vertically upward, and the X-axis is perpendicular to the YOZ plane. In this invention, only the roundness error of the outer raceway of the angular contact ball bearing is considered; other parts are ideal parts.

[0055] The initial state of the angular contact ball bearing is as follows: Figure 2 As shown, within the axial plane Y1OZ1, the origin of the three-dimensional coordinate system is also the origin of the axial plane. The rotation centers of the inner ring 2 and outer ring 1 of the angular contact ball bearing coincide, and the steel ball 3 is located on the bearing pitch circle diameter. The axial plane Y1OZ1 is a constantly changing plane, essentially a cross-sectional view of a point on the outer raceway along the axial direction.

[0056] 3) Calculate the stable position of outer ring 1 after each rotation angle step.

[0057] For every rotation of the outer ring 1 by a rotation angle step, all the steel balls 3 revolve to a new position as the outer ring 1 rotates. Then, the outer ring 1 moves toward the steel balls 3 according to the set translation step. The contact state of all the steel balls 3 with the outer channel is calculated for each translation. The stable position of the outer ring 1 is obtained according to the stability criterion of the outer ring 1.

[0058] The process of simulating the rotation of the outer ring 1 includes: complete rotation by one rotation angle step - steel ball 3 contacting the inner channel - outer channel contacting steel ball 3.

[0059] The contact state between the steel ball 3 and the outer channel includes three states: interference, contact, and separation. The contact state is obtained based on the position of the steel ball 3 and the contour curve of the outer channel.

[0060] Steel ball 3 revolves around the outer ring 1 as the outer ring 1 rotates, causing changes in its X and Y coordinates in a three-dimensional coordinate system. Since steel ball 3 is in ideal contact with the inner groove, its Z-axis coordinate remains unchanged. The coordinates of the steel ball's center depend on its position angle in the radial plane. The calculation process for the coordinates of steel ball 3 is as follows:

[0061]

[0062] Among them, (X) j Y j Z j ) represents the coordinates of the center of the j-th steel ball; β j Let be the position angle of the center of the j-th steel ball in the radial plane; D is the distance from the center of the steel ball to the axis.

[0063] Among them, D w d is the diameter of steel ball 3; i R is the diameter of the bottom of the inner channel; i α is the radius of curvature of the inner channel; α is the original contact angle of the bearing.

[0064] The profile curve of the outer channel takes into account the roundness error ΔS(θ1) of the outer channel. The specific process for determining the profile curve equation of the outer channel is as follows.

[0065] First, determine the roundness error ΔS(θ1) of the outer channel:

[0066] The roundness error at each point on the outer raceway of an angular contact ball bearing is along its respective normal direction. The roundness error of the outer raceway is expressed in the form of a Fourier series. The formula for calculating the roundness error of the outer raceway is:

[0067]

[0068] Where ΔS(θ1) is the roundness error of the outer channel; θ1 is the position angle of the outer channel in the radial plane (the radial plane is the X2O2Y2 plane, which is the plane with O2 as the origin); m is the harmonic order; A m This represents the roundness error magnitude. This is the initial phase angle.

[0069] Secondly, determine the outer channel profile curve that takes into account the roundness error of the outer channel.

[0070] like Figure 3 As shown, the center of curvature of the outer channel is o. eWhen outer ring 1 is in its initial position, the center of curvature o of the outer raceway can be determined based on the bearing's geometry. e Coordinates in the axial plane Y1OZ1 for:

[0071]

[0072] Among them, D e R is the diameter of the bottom of the outer channel; e d is the radius of curvature of the outer channel; i R is the diameter of the bottom of the inner channel; i α is the radius of curvature of the inner channel; α is the original contact angle of the bearing.

[0073] Taking point c on the outer channel as an example, by finding the three-dimensional coordinates of point c expressed by parametric equations, the parametric equations of the outer channel profile curve can be obtained. Considering the roundness error of the outer channel, the radius of curvature of a point on the outer channel will change in the Y1OZ1 plane; the change in radius of curvature is the roundness error corresponding to that point. The distance from point c on the outer channel to the center of curvature o of the outer channel... e The distance is equal to the sum of the radius of curvature of the outer channel and the roundness error at that point. Therefore, the coordinates of point c in the Y1OZ1 plane (Y 1c Z 1c )for:

[0074]

[0075] Where θ2 is the angle between the line connecting the point on the outer channel and the center of the steel ball and the Z1 axis.

[0076] like Figure 4 As shown, on the radial plane X2O2Y2 (the origin O2 of the radial plane is the bearing center, and the X2 axis is parallel to the X-axis, and the Y2 axis is parallel to the Y-axis), based on the position angle θ1 of point c on the outer ring 1 groove in the radial plane, and the distance from point c to the origin O2, which is Y... 1c Then, the coordinates of point c in the X2O2Y2 plane can be determined:

[0077]

[0078] Based on the coordinates of point c in the Y1OZ1 and X2O2Y2 planes obtained above, and the geometric relationships between the coordinate axes in the established local and three-dimensional coordinate systems, the parametric equation of point c on the outer channel profile curve in the three-dimensional coordinate system can be obtained:

[0079]

[0080] Among them, (X) c Y c Z cLet c be the coordinates of point c in the three-dimensional coordinate system.

[0081] When θ2 varies with a set step size near the ideal angle, multiple outer ring 1 upper channel profile curves can be obtained. These curves have the same roundness error form but different base circle radii r, such as... Figure 5 As shown.

[0082] Based on the above formula, the equation of the outer channel profile curve for each translation step is:

[0083]

[0084] Where △x, △y, and △z are the translation step components along the X, Y, and Z axes, respectively, and the radial clearance G... r .

[0085] The distance d1 from a point on the outer channel to the center of the steel ball is obtained by using the outer channel profile curve and the position of the steel ball 3, and then the distance d2 from a point on the outer channel to the surface of the steel ball is obtained:

[0086]

[0087] d2 = d1 - D w / 2.

[0088] For simplified calculation, several ideal contact points are selected on the outer raceway (ideal contact points are points calculated based on the geometry of the angular contact ball bearing without considering all errors; the calculation process is existing technology and will not be described in detail here), such as Figure 6 As shown, with the ideal contact point ( Figure 6 The ideal contact point (the square point in the diagram) is used as the center point for mesh generation. The angles of the ideal contact point in the radial and axial planes of the outer channel are θ1 and θ2, respectively. θ1 and θ2 are varied according to a set step size. After specifying the range of variation for θ1 and θ2, a mesh can be selected on the outer channel. The intersection of the meshes is... Figure 6 The triangle point in the diagram is the expansion point. For a given ideal contact point, the minimum distance between its expansion point, the ideal contact point, and the surface of the steel ball is used as the criterion for judging the contact state between the outer channel and the steel ball 3.

[0089] Specifically, based on multiple points obtained from the mesh generation (including ideal contact points and extension points), a series of d2 values ​​are calculated for each steel ball 3, and the minimum distance d between its extension point, ideal contact point, and the steel ball surface is obtained by comparison. 2min , with d 2min Determine the contact state between the outer channel and steel ball 3. Let ε be the allowable interference error, when d 2min When |d <-ε, the outer channel and steel ball 3 are in an interference state; when |d 2min When |≤ε, the outer channel and steel ball 3 are in contact; when d 2minWhen the value is greater than ε, the outer channel and the steel ball 3 are in a separated state.

[0090] The contact state between each steel ball 3 and the outer channel is obtained at each translation step. If the stability criterion of the outer ring 1 is satisfied at a certain translation step, then the position of the outer ring at that translation step is a stable position. The stability criterion of the outer ring 1 is:

[0091] a. The outer channel does not interfere with any steel ball 3;

[0092] b. The number of steel balls 3 in contact with the outer channel is 3 or more;

[0093] c. The contact steel balls 3 are distributed in at least three quadrants in the radial plane, and the distribution of the steel balls 3 in the quadrants is as follows: Figure 7 As shown.

[0094] 4) Find the optimal outer ring position from all stable positions of outer ring 1, calculate the rotation center position of the optimal outer ring position, and the changes in the Y and Z coordinates of the rotation center of the optimal outer ring position relative to the Y and Z coordinates of the rotation center of the inner ring are the radial runout and axial runout values ​​of outer ring 1 at that rotation angle.

[0095] With a rotation angle step of outer ring 1, there may be multiple stable positions of outer ring 1. When there are multiple positions, the optimal stable position of outer ring is found by the optimal stable contact state criterion of outer ring.

[0096] The criterion for the optimal stable contact state of the outer ring is:

[0097] a. Among all stable positions, compare the number of steel balls 3 in contact and select the position with the most steel balls 3 in contact as the optimal stable position of the outer ring;

[0098] b. If there are multiple positions where the number of contacting steel balls is the highest, the position with the smallest displacement relative to the initial position is taken as the optimal stable position of the outer ring.

[0099] The following uses an angular contact ball bearing as an example to predict the axial and radial runout history of the outer ring of the angular contact ball bearing using the method of the present invention.

[0100] The collected geometric parameters of the angular contact ball bearing are as follows: inner raceway radius of curvature is 3.17 mm, inner raceway bottom diameter is 36.927 mm, outer raceway radius of curvature is 2.94 mm, outer ring raceway diameter is 48.079 mm, ball diameter is 5.556 mm, number of balls is 18, radial clearance is 0.04 mm, and contact angle is 16°.

[0101] Set the outer ring 1 to rotate 360°, with a rotation step of 1°, for a total of 360 rotations;

[0102] In the outer channel profile curve equation, the roundness error order m is taken as 2, and the roundness error amplitude A m The value is 0.002mm, meaning the outer groove profile is approximately elliptical with two peaks and two troughs, and the roundness error is 0.004mm.

[0103] In the initial state, after the outer ring 1 rotates by 1°, the equation of the outer channel profile curve and the coordinates of the center of the steel ball 3 after contact with the inner channel are obtained through the calculation process in step 3). The contact situation between the outer ring 1 and all steel balls 3 under all translation steps is determined, and the optimal position of the outer ring when the outer ring 1 is in stable contact with the steel balls is found. The coordinates of the outer ring rotation center at the optimal position are calculated. The changes in the Y and Z coordinates of the outer ring rotation center relative to the Y and Z coordinates of the inner ring rotation center are the radial runout and axial runout values ​​of the outer ring 1 under that rotation angle.

[0104] Next, outer ring 1 continues to rotate 1°, and the radial runout and axial runout values ​​of outer ring 1 at this rotation angle are calculated; this process is repeated until the radial and axial runout values ​​of the outer ring corresponding to all rotation angles are obtained. Figure 8 The radial runout process shown, and as Figure 9 The axial runout process is shown.

[0105] From the radial and axial runout values ​​calculated above for one revolution of outer ring 1, find the maximum and minimum values. The difference between them is the radial and axial runout of the bearing outer ring. The calculation results show that the maximum radial runout is 0.00242mm and the minimum is 0, with a radial runout of 0.00242mm = 2.42μm. The maximum axial runout is 0.03721mm and the minimum is 0.03687mm, with an axial runout of 0.00034mm = 0.34μm.

[0106] This invention simulates the rotation process of the outer ring 1 and uses the geometric parameters of the angular contact ball bearing to predict the axial and radial runout of the outer ring of the angular contact ball bearing through numerical calculation, thereby achieving the prediction of the rotational accuracy of the angular contact ball bearing.

Claims

1. A method for predicting the axial and radial runout of the outer ring of an angular contact ball bearing, characterized in that, Includes the following steps: 1) Collect the geometric parameters of the angular contact ball bearing, and set the rotation angle step and translation step of the outer ring; the geometric parameters include the inner groove radius of curvature, the inner groove bottom diameter, the outer groove radius of curvature, the outer groove bottom diameter, the steel ball diameter, the original contact angle, and the outer groove roundness error; 2) Establish a three-dimensional coordinate system with the load center of the angular contact ball bearing as the origin, the axial direction as the Z-axis, and the vertical upward direction as the Y-axis; 3) Calculate the stable position of the outer ring at each rotation angle step: a. Rotate the outer ring by one rotation angle step, and calculate the position of the steel ball's center based on the steel ball's diameter, the inner channel's radius of curvature, the inner channel's bottom diameter, and the original contact angle; b. Calculate the outer channel profile curve for each translation step of the outer ring based on the outer channel bottom diameter, outer channel radius of curvature, inner channel bottom diameter, inner channel radius of curvature, original contact angle, and outer channel roundness error; c. Calculate the distance between the point on the outer channel and the surface of the steel ball for each translation step to obtain the contact state between the outer channel and the steel ball; the contact state includes interference state, contact state, and separation state; d. Based on the contact state between the outer groove and the steel ball, and combined with the stability criterion of the outer ring, the stable position of the outer ring at each rotation angle step is obtained; 4) Based on the stable position of the outer ring and the position change of the inner ring under each rotation angle step, the axial and radial runout values ​​of the outer ring are obtained.

2. The method for predicting axial and radial runout of the outer ring of an angular contact ball bearing according to claim 1, characterized in that, The stability criterion for the outer ring is: a. The outer channel does not interfere with any steel ball; b. The number of steel balls in contact with the outer channel is three or more; c. The contact steel balls are distributed in at least three quadrants in the radial plane.

3. The method for predicting axial and radial runout of the outer ring of an angular contact ball bearing according to claim 1 or 2, characterized in that, If there are multiple stable positions on the outer ring at each rotation angle step, then the position with the most contact steel balls is the stable position.

4. The method for predicting axial and radial runout of the outer ring of an angular contact ball bearing according to claim 3, characterized in that, If there are multiple positions with the most contact with the steel balls, then the position with the smallest displacement is the stable position.

5. The method for predicting axial and radial runout of the outer ring of an angular contact ball bearing according to claim 1, characterized in that, Several ideal contact points are determined among the points on the outer channel. A grid is divided within a range centered on the ideal contact points. The intersection of the grid is the extension point. The minimum distance between the extension points, the ideal contact points and the surface of the steel ball is used as the basis for judging the contact state between the outer channel and the steel ball.

6. The method for predicting axial and radial runout of the outer ring of an angular contact ball bearing according to claim 1, characterized in that, The calculation process for the position of the center of the steel ball is as follows: Among them, (X) j Y j Z j ) represents the coordinates of the center of the j-th steel ball; β j Let be the position angle of the center of the j-th steel ball in the radial plane; D is the distance from the center of the steel ball to the axis; D w d is the diameter of the steel ball; i R is the diameter of the bottom of the inner channel; i α is the radius of curvature of the inner channel; α is the initial contact angle.

7. The method for predicting axial and radial runout of the outer ring of an angular contact ball bearing according to claim 1, characterized in that, The roundness error of the outer channel is: Where ΔS(θ1) is the roundness error of the outer channel; θ1 is the position angle of the outer channel in the radial plane; m is the harmonic order; A m This represents the roundness error magnitude. This is the initial phase angle.

8. The method for predicting axial and radial runout of the outer ring of an angular contact ball bearing according to claim 1, characterized in that, At each translation step, the outer channel profile curve is as follows: Among them, (X) c Y c Z c ) represents the coordinates of point c on the outer channel in the three-dimensional coordinate system; △x, △y, and △z are the components of the translation step size on the X, Y, and Z axes, respectively. The curvature center of the outer channel o e Coordinates in the axial plane Y1OZ1; R e θ1 is the radius of curvature of the outer channel; ΔS(θ1) is the roundness error of the outer channel; θ1 is the position angle of the outer channel in the radial plane; θ2 is the angle between the line connecting the point on the outer channel and the center of the steel ball and the Z1 axis.

9. The method for predicting axial and radial runout of the outer ring of an angular contact ball bearing according to claim 8, characterized in that, outer channel curvature center o e Coordinates in the axial plane Y1OZ1 for: Among them, D e R is the diameter of the bottom of the outer channel; e d is the radius of curvature of the outer channel; i R is the diameter of the bottom of the inner channel; i α is the radius of curvature of the inner channel; α is the initial contact angle.

10. The method for predicting axial and radial runout of the outer ring of an angular contact ball bearing according to claim 5, characterized in that, When d 2min When |d <-ε, the outer channel and the steel ball are in an interference state; when |d 2min When |≤ε, the outer channel and the steel ball are in contact; when d 2min When ε > 0, the outer channel and the steel ball are separated; d 2min ε represents the minimum distance between several extended points, ideal contact points, and the surface of the steel ball; ε is the allowable interference error.

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