A method for predicting the roundness of a groove of an outer ring of a ball bearing

Abstract

A kind of ball bearing outer ring raceway grinding roundness prediction method relates to bearing processing field, grinding wheel and outer ring raceway profile are respectively evenly dispersed into n And m Grinding points in circumferential direction, input grinding wheel parameters, outer ring parameters and grinding process parameters, determine raceway center displacement spindle displacement according to grinding process parameters, determine Newmark correction parameters and parameters;Judge whether the theoretical instantaneous grinding amount of time step is greater than zero, and bring unbalanced force and normal grinding force into grinding system structural dynamics equation group, solve dynamics equation group using Newmark-β method;Calculate the vibration displacement, velocity and acceleration of grinding wheel and sleeve ring in time step;Calculate the instantaneous wear of grinding wheel in time step;Calculate the actual grinding amount and the radius value after grinding of raceway in time step;Finally, calculate the roundness error of raceway in grinding process based on least square method.This scheme can predict the dynamic change of raceway profile in bearing outer ring raceway grinding process and the roundness error of raceway after grinding.

Description

Technical Field

[0001] This invention relates to the field of bearing processing technology, specifically a method for predicting the roundness of the outer ring groove of a ball bearing during grinding, which is mainly applicable to the roundness prediction during the grinding process of angular contact ball bearings or deep groove ball bearings. Background Technology

[0002] As is well known, the method for predicting the roundness of the outer ring of a ball bearing after grinding is to predict the roundness of the outer ring of the bearing after grinding, caused by known or given geometric errors of the bearing outer circle, such as center displacement, radial runout error of the grinding wheel spindle, imbalance between the grinding wheel and the ring, vibration displacement and contact deformation of the grinding wheel and the workpiece during grinding, grinding wheel wear, and initial profile error of the groove.

[0003] Ball bearings are crucial support components in mechanical transmission devices. The outer ring raceway is the working surface that bears the load when the bearing rings rotate. Its machining accuracy and surface quality directly affect the bearing's performance and lifespan. Improving the accuracy and surface quality of the outer ring raceway is of great significance for the overall performance and service life of the bearing. Currently, most research on bearing raceway grinding focuses on optimizing grinding process parameters through experiments, designing and optimizing grinding tools, and monitoring grinding signals. Furthermore, most models for grinding bearing outer raceways only consider the dynamics of the grinding system or the grinding process, without comprehensively considering both. Therefore, it is difficult to accurately reveal the formation mechanism of the bearing outer raceway grinding profile and the influence of grinding process parameters on the raceway roundness error. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the roundness of the outer ring groove of a ball bearing during grinding. This method can predict the dynamic changes in the groove profile during the grinding process of the outer ring groove of the bearing and the roundness error of the groove after grinding.

[0005] The technical solution adopted in this invention is: a method for predicting the roundness of the outer ring groove of a ball bearing after grinding, the steps of which are as follows: S1. The grinding wheel and the outer ring groove contour are uniformly discretized into n and m grinding points along the circumferential direction, respectively. The instantaneous radius of the grinding point during the rotation of the grinding wheel and the outer ring groove is respectively determined by r1(t). i ) and r2(t i This indicates that, in the iterative calculation model, the initial profile of the channel is used as the initial condition for the calculation. S2. Input grinding wheel parameters, bearing outer ring parameters, grinding system parameters, and grinding process parameters; S3. Calculate the time step Δt based on the grinding process parameters; calculate the groove center displacement Δu(t) caused by the geometric shape error of the outer circle of the bearing being machined at each time step during the groove grinding process. i), calculate the spindle displacement Δe(t) caused by radial runout error of the grinding wheel spindle at each time step during the grinding process. i ); S4. Determine the Newmark correction parameters γ and ξ; establish the mass matrix M, stiffness matrix K, and damping matrix C of the grinding system based on the Newmark-β method; calculate the unbalanced force F corresponding to each time step during the grinding process. ub (t i ); When S5 and t0 = 0, determine the initial vibration displacement, velocity, and acceleration of the grinding wheel and the outer ring of the bearing; S6, Calculate t i = The theoretical instantaneous grinding amount of the groove at time i·Δt; S7. Determine t in step S6. i =i·Δt time step theoretical instantaneous grinding amount δ w1 (t i Is it greater than zero? If the theoretical instantaneous grinding amount δ w1 (t i A value greater than zero indicates that the grinding wheel and the groove produce a grinding action at this time step, and the normal grinding force is calculated; the theoretical instantaneous grinding amount δ w1 (t i A value less than zero indicates that the grinding wheel is not in contact with the groove at this time step, and the normal grinding force at this time step is zero. S8, F ub (t i ) and F n (t i Substitute the equations of the grinding system's structural dynamics into the equations of motion and solve the system of dynamics using the Newmark-β method; calculate t. i =i·Δt time step, calculate the vibration displacement, velocity and acceleration of the grinding wheel and the grinding ring; calculate t i =i·Δt, the instantaneous wear of the grinding wheel at time step; calculate t i = i·Δt time step: actual grinding amount of the groove and the radius value after grinding; S9. Let i = i + 1, repeat steps S6 to S8, and solve the equation system for the next time step until the grinding ends; S10. Calculate the roundness error of the groove during the grinding process based on the least squares method. As a preferred embodiment, in step S2, the input parameters of the grinding wheel, the outer ring of the bearing to be processed, the grinding process parameters, and the grinding system parameters specifically include: the geometric dimensions of the grinding wheel and the outer ring of the bearing, the rotational speed and the grinding wheel feed time and feed rate, the front support angle α and the support angle β of the electromagnetic centerless chuck, the roundness error of the initial profile surface of the groove, the radial runout error of the grinding wheel spindle, the wear stiffness of the grinding wheel, and the stiffness of the contact area, etc. As a preferred option, the specific process for determining the channel center displacement in step S3 is as follows: S3.1 First, the contact position between the outer circle of the bearing outer ring and the fixed support should be accurately calculated. At time t, the theoretical contact point between the outer circle of the outer ring and the rear support is point k, and the outer circle radius is r. k Due to the existence of errors in the outer circle contour, the actual contact point is k', and the radius of point k' is r. k' At this point, the angle between ok and ok' is θ. k Then the included angle of the rear support is (β+θ) k The corresponding bearing outer ring at the rear support has a center displacement in the x-axis direction due to geometric errors of )°. In the formula, Δr1(t) i ) represents the radius error between the outer circle of the outer ring and the actual contact point of the rear support, and its value is the difference between the actual contact point radius and the ideal radius of the outer circle; S3.2, The displacement of the collar in the x-axis direction at the front support due to the geometric error of the outer circle is: In the formula, θ p Δr2(t) is the angle between the line connecting the outer circle of the outer ring to the center of the outer circle from the actual contact point of the outer ring and the front support, and the line connecting the theoretical contact point of the outer ring and the front support to the center of the outer circle; i The radius error is the actual contact point between the outer circle and the front support. S3.3, the center displacement of the bearing outer ring when there are geometric errors at both the front and rear fixed supports is: As a preferred option, the specific process in step S6 is as follows: The determination of t is based on factors such as grinding wheel feed rate, total grinding wheel wear, and total groove grinding amount. i The relative position of the grinding wheel and the groove at time i·Δt is determined using the following formula: δ w1 (t i ) = a p (t i )+Δu(t i )+Δr(t i )-Δ w (t i -T)-Δ s (t i -T)-Δe(t i ) Calculate t i = i·Δt time step theoretical instantaneous grinding amount. As a preferred option, in step S7, the normal grinding force F is calculated using the following formula. n (ti ), In the formula: U ch V represents the specific cutting energy. w δ represents the linear velocity of the workpiece. w1 (t) represents the amount of material removed from the workpiece, b represents the unit grinding width, and v s K represents the linear velocity of the grinding wheel. t The coefficient k represents the relationship between radial grinding force and tangential grinding force. w It can be defined as the grinding stiffness of the groove, which is the ratio of the normal grinding force on the groove to the instantaneous grinding depth of the groove. As a preferred option, in step S8, the set of equations for the structural dynamics of the grinding system is as follows: In the formula, m1 is the equivalent mass of the grinding wheel component, m2 is the mass of the bearing outer ring; c1 and c2 are the damping coefficients of the grinding wheel system and the workpiece system, respectively; k1 and k2 are the equivalent stiffness constants of the grinding wheel system and the workpiece system, respectively; x1(t i x2(t) represents the vibration displacement of the center point of the grinding wheel. i F represents the vibration displacement at the center point of the workpiece; ub1 (t i ) and F ub2 (t i These are the dynamic unbalance forces of the grinding wheel and the ferrule, respectively; F n (t i ) is the normal grinding force exerted on the grinding wheel and the groove. The beneficial effects of this invention are:

[0006] The outer ring groove grinding roundness prediction method of this invention aims to predict the roundness of the bearing outer ring groove after grinding under known or given bearing outer circle geometric shape errors, including center displacement, radial runout error of the grinding wheel spindle, vibration displacement and contact deformation of the grinding wheel and workpiece during grinding, grinding wheel wear, and initial groove profile error. It achieves quantitative simulation of the dynamic formation process of the bearing outer ring groove profile under different grinding system parameters and process parameters, providing a reliable analytical method for effectively predicting the roundness of the outer ring groove after grinding. Through simultaneous simulation and experimental parameters, multi-condition angular contact ball bearing outer ring groove grinding experiments were conducted, and the experimental results confirmed the rationality of the proposed outer ring groove grinding roundness prediction model. Attached Figure Description

[0007] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Figure 1 A schematic diagram of the outer ring groove grinding system used in this prediction method; Figure 2 A simplified schematic diagram of outer ring groove support grinding; Figure 3 This is a schematic diagram of the displacement of the outer ring center of the bearing; Figure 4 This is a schematic diagram showing the contact between the bearing outer ring and the rear support. Figure 5 This is a schematic diagram showing the change in the center displacement of the bearing outer ring; Figure 6 A schematic diagram showing the changes in grinding force on the groove and grinding wheel; Figure 7 This is a schematic diagram of the groove after grinding; Figure 8 This is a schematic diagram showing the variation in the roundness of the channel. Detailed Implementation

[0008] The present invention will now be described in detail through exemplary embodiments. However, it should be understood that, without further description, elements, structures, and features in one embodiment may be advantageously incorporated into other embodiments.

[0009] It should be noted that, unless otherwise defined, the technical or scientific terms used herein should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "a," "an," or "the," and similar words used in the specification and claims of this patent application do not express a limitation of quantity, but rather indicate the presence of at least one. Terms such as "comprising" or "including" indicate that the elements or objects preceding "comprising" encompass the elements or objects listed following "comprising" or "including," and their equivalents.

[0010] Before describing this scheme, we first need to discuss the numerical analysis of the structural vibration differential equation. Currently, there are many algorithms that can be used, such as the central difference method, the linear acceleration method, the Newmark-β method, and the Wilson-θ method. This invention will use the Newmark-β method to solve the vibration displacement of the grinding wheel and the raceway during the groove grinding process. Its basic idea is to discretize the time, and the motion equation is only required to be satisfied at discrete time points. The detailed solution method and steps for solving the structural dynamics equations of the outer ring groove grinding system using the Newmark-β method are as follows: (1) Time discretization. The grinding time n under study is divided into equal parts, with a time step of Δt, and the discrete points are (0,1,2,…,n-1,n), with the time corresponding to each discrete point being t. i =iΔt, (i = 0, 1, 2, ..., n-1, n), starting time t0 = 0, ending time t m =nΔt; (2) Select the Newmark correction coefficients γ and ξ. When γ ≥ 1 / 2 and ξ ≥ γ / 2, the Newmark-β method is unconditionally stable and is a commonly used constant for calculating integrals; (3) Input the dynamic equations: mass matrix M, stiffness matrix K, and damping matrix C; (4) Calculate the initial motion parameters at each time step, obtained from the previous time step: vibration displacement x(t) i ), vibration velocity Vibration acceleration When i = 0, the initial vibration displacement x(t0) and initial vibration velocity of the grinding system are obtained from the initial conditions. Initial vibration acceleration and the initial grinding force F(t0); (5) Calculate the grinding force increment Δf(t) i+1 ), equivalent stiffness matrix Equivalent incremental load Δf(t i+1 )=F(t i+1 )-F(t i (2) (6) Calculate the displacement increment Δx(t) i+1 ) and speed increment (7) Calculate the displacement x(t) at the end of the current time step. i+1 ) and speed x(t i+1 )=x(t i )+Δx(t i+1 (7) (8) Calculate the acceleration at the end of the current time step. (9) Repeat steps (4) to (8) above until all time steps have been calculated.

[0011] A method for predicting the roundness of the outer ring raceway after grinding in ball bearings, with detailed steps as follows: (1) The grinding wheel and the outer groove profile are uniformly discretized into n and m grinding points along the circumferential direction, respectively. The instantaneous radius of the grinding point during the rotation of the grinding wheel and the groove is respectively determined by r1(t i ) and r2(t i This indicates that the initial profile of the channel is used as the initial condition for the calculation in the iterative computation model. (2) Input grinding wheel parameters, bearing outer ring parameters, grinding system parameters, and grinding process parameters, etc. Specific parameters include the front support angle α and support angle β of the electromagnetic centerless chuck, the geometric dimensions of the grinding wheel and bearing outer ring, rotational speed and grinding wheel feed time and feed rate, initial profile surface roundness error of the groove, radial runout error of the grinding wheel spindle, grinding wheel wear stiffness, contact area stiffness, etc. (3) Calculate the time step Δt based on the grinding process parameters; calculate the groove center displacement Δu(t) caused by the geometric shape error of the bearing outer ring at each time step during the groove grinding process. i ), calculate the spindle displacement Δe(t) caused by radial runout error of the grinding wheel spindle at each time step during the grinding process. i ); (4) Determine the Newmark correction parameters γ and ξ; establish the mass matrix M, stiffness matrix K, and damping matrix C of the grinding system based on the Newmark-β method; calculate the unbalanced force F corresponding to each time step during the grinding process. ub (t i ); (5) When t0 = 0, determine the initial vibration displacement, velocity and acceleration of the grinding wheel and the outer ring of the bearing; (6) Calculate t i = i·Δt is the theoretical instantaneous grinding amount of the groove at time i. The value of t is determined based on factors such as the grinding wheel feed rate, total grinding wheel wear, and total groove grinding amount. i = i·Δt, the relative position of the grinding wheel and the groove at time t is calculated using equation (10). i = i·Δt time step theoretical instantaneous grinding amount; δ w1 (t i ) = a p (t i )+Δu(t i )+Δr(t i )-Δ w (t i -T)-Δ s (t i -T)-Δe(t i(10) (7) Determine t in (6) i =i·Δt time step theoretical instantaneous grinding amount δ w1 (t i Is it greater than zero? If the theoretical instantaneous grinding amount δ w1 (t i A value greater than zero indicates that the grinding wheel and the groove produce a grinding action at this time step. The normal grinding force is calculated based on equation (16); the theoretical instantaneous grinding amount δ w1 (t i A value less than zero indicates that the grinding wheel is not in contact with the groove at this time step, and the normal grinding force at this time step is zero. (8) F ub (t i ) and F n (t i Substitute the equations of the grinding system's structural dynamics into the equations of motion and solve the system of dynamics using the Newmark-β method; calculate t. i =i·Δt time step, calculate the vibration displacement, velocity and acceleration of the grinding wheel and the grinding ring; calculate t i =i·Δt, the instantaneous wear of the grinding wheel at time step; calculate t i = i·Δt time step: actual grinding amount of the groove and the radius value after grinding; (9) Let i = i + 1, repeat steps (6) to (8) to solve the equation system for the next time step until the grinding ends; (10) Calculate the roundness error of the groove during the grinding process based on the least squares method.

[0012] It should be described that the mathematical principles underlying the prediction method described in this scheme are as follows:

[0013] 1. Dynamic description of the outer ring groove grinding system: Angular contact ball bearing outer ring raceway grinding system, such as Figure 1 As shown, it mainly consists of a grinding wheel spindle 1, a ring 2, a grinding wheel 3, and a fixed support 4. In this paper, the grinding wheel spindle is supported by a hydrostatic bearing, and the workpiece (i.e., the outer ring of the bearing) is clamped and fixed by an electromagnetic centerless chuck. After the grinding wheel is fed, it comes into contact with the outer ring groove, generating a grinding force, which causes the grinding wheel and the groove to interact, thereby removing material from the outer ring groove. Grinding processes take many different forms depending on the workpiece shape and the kinematics of the grinding wheel. Supported grinding of the outer raceway is a basic form of machining the outer raceway of angular contact ball bearings. This paper focuses on the supported grinding process of bearing outer raceways. Figure 1It is known that the grinding process of the bearing outer ring groove is an interaction process of two shaft systems (i.e., the grinding wheel spindle system and the fixed support-ring-magnetic pole spindle system). However, for the bearing outer ring groove support type grinding, the grinding wheel only grinds the groove in the radial direction of the bearing ring groove. Without considering factors such as shaft torsional vibration and thermal deformation, the bearing outer ring groove grinding system can be simplified as two single-degree-of-freedom systems: the grinding wheel and the bearing outer ring. Figure 2 This is a simplified schematic diagram of bearing outer ring groove support grinding. According to vibration dynamics, there are dynamic equations for the grinding wheel and the raceway. In the formula, m1 is the equivalent mass of the grinding wheel component, m2 is the mass of the bearing outer ring; c1 and c2 are the damping coefficients of the grinding wheel system and the workpiece system, respectively; k1 and k2 are the equivalent stiffness constants of the grinding wheel system and the workpiece system, respectively; x1(t i x2(t) represents the vibration displacement of the center point of the grinding wheel. i F represents the vibration displacement at the center point of the workpiece; ub1 (t i ) and F ub2 (t i These are the dynamic unbalance forces of the grinding wheel and the ferrule, respectively; F n (t i ) is the normal grinding force exerted on the grinding wheel and the groove. For the grinding wheel and the raceway, the dynamic unbalance force can be expressed as: F ub (t i ) = G e mω*10 -3 cos(ωt i (13) In the formula, G e ω represents the dynamic balancing accuracy level; ω represents the rotational angular velocity. If the effects of tillage and friction are ignored, the formula for calculating grinding force can be expressed as follows: F n (t i ) = K t F t (t i (15) In the formula, F t (t i ) represents the tangential grinding force, U ch V represents the specific cutting energy. w δ represents the linear velocity of the workpiece. w1(t) represents the amount of material removed from the workpiece, b represents the unit grinding width, and v s F represents the linear velocity of the grinding wheel. n (t i ) represents the normal grinding force, K t The coefficient k represents the relationship between radial grinding force and tangential grinding force. w It can be defined as the grinding stiffness of the groove, which is the ratio of the normal grinding force on the groove to the instantaneous grinding depth of the groove.

[0014] 2. Center displacement caused by errors in the outer circle's geometric shape: The outer ring raceway of ball bearings is often ground using a positioning method involving external grinding. Because the shape of the outer circular surface of the bearing outer ring is very complex, the center of the raceway cross-section is always moving, and its trajectory depends on the contact point between the outer circle and the fixed support. For example... Figure 3 As shown, during the grinding process, when the outer circle of the bearing outer ring is displaced due to geometric errors, the grinding amount of the groove also changes, thus affecting the roundness of the outer ring groove. To calculate the center displacement of the bearing ring during the grinding process, the contact position between the outer circle of the bearing outer ring and the fixed support must first be accurately calculated. Figure 4 As shown. At time t, the theoretical contact point between the outer circle and the rear support is point k, and the outer circle radius is r. k Due to the existence of errors in the outer circle contour, the actual contact point is k', and the radius of point k' is r. k' At this point, the angle between ok and ok' is θ. k Then the included angle of the rear support is (β+θ) k The corresponding bearing outer ring at the rear support has a center displacement in the x-axis direction due to geometric errors of )°. In the formula, Δr1(t) i ) represents the radius error between the outer circle of the outer ring and the actual contact point of the rear support, and its value is the difference between the actual contact point radius and the ideal radius of the outer circle. Similarly, the displacement of the collar in the x-axis direction at the front support due to the geometric error of the outer circle is... In the formula, θ p Δr2(t) is the angle between the line connecting the outer circle of the outer ring to the center of the outer circle from the actual contact point of the outer ring and the front support, and the line connecting the theoretical contact point of the outer ring and the front support to the center of the outer circle; i ) represents the radius error of the actual contact point between the outer circle and the front support. The center displacement of the bearing outer ring when there are geometric errors at both the front and rear fixed supports is: To obtain the radius error of the actual contact point, a search is performed in the angular region near the theoretical contact point k. This range is defined as the angle between the line connecting the center of the outer circle and the theoretical contact point. The outer circle's center is taken as the point furthest from the fixed support as the actual contact point, and the center displacement of the outer circle is calculated using the radius error Δr at this point. Taking the theoretical contact point k between the bearing outer ring and the rear support as an example, the bearing at the theoretical contact point k... The inner and outer circles within the angular region are discretized into n points, each point corresponding to a radius value r(θ). m Then, the corresponding outer circle radius error value at each point is... Δr(θ m )=r(θ m )-r (20) In the formula, r is the theoretical radius, and θ m It is the angle between "ok" and "ok'". The maximum value of the radius error between the inner and outer circles within the region is

[0015] 3. Model of outer ring groove grinding process: The study of the rounding process of bearing grooves involves analyzing the interaction between the groove and the grinding system to determine the relative position between the groove and the grinding wheel and the grinding condition of the grinding wheel on the groove surface in order to obtain the regenerated surface of the groove. like Figure 2 As shown, during the grinding process, the outer ring groove and the grinding wheel always maintain the following positional relationship through their interaction. L2(t i )-L1(t i )=L(t i )-x1(t i )-x2(t i ) (twenty two) L1(t i )=r1-Δ s (t i )-y k1 (t i ) (twenty three) L2(t i )=r2+Δ w (t i )+y k2 (t i )-Δu(t i ) (twenty four) L(t i )=r2-r1+Δr(t i )-Δe(t i )+a p (t i (25) y k1 (t i )+y k2 (t i ) = F n (t i ) / k a (26) In the formula, L1(t) i L2(t) represents the distance from the center of the grinding wheel to the grinding contact point at time t. i L(t) represents the distance from the center of the groove to the grinding contact point at time t. i ) represents the distance between the center of the grinding wheel and the center of the groove during the radial feed of the grinding wheel at time t. r1 is the outer radius of the grinding wheel before grinding; Δ s (t i ) represents the total wear of the grinding wheel at time t; y k1 (t i ) represents the contact deformation of the grinding wheel at time t; k a This indicates the contact stiffness between the grinding wheel and the groove. r2 is the groove radius before grinding; Δ w (t i ) represents the total grinding amount of the groove at time t; y k2 (t i ) represents the contact deformation of the channel at time t; Δu(t) i ) represents the positioning error of the ring; Δr(t) i ) represents the initial roundness error of the channel; Δe(t) i ) represents the grinding wheel rotation error; a p (t i ( ) represents the nominal feed rate of the grinding wheel. The above parameters have the following relationship: Δ s (t i )=Δ s (t i -T)+δ s (t i (27) Δ w (t i )=Δ w (t i -T)+δ w (t i (28) a p (t i ) = v f ·t i (29) Where, δ w (t i ) represents the instantaneous grinding amount of the groove; v f δ is the feed rate of the grinding wheel. s(t i This can be approximated as the normal grinding force on the grinding wheel and the wear stiffness k of the grinding wheel. s ratio Integrating the above equations yields the following results: δ w (t i ) = a p (t i )+Δu(t i )+Δr(t i )-Δ w (t i -T)-Δ s (t i -T)-δ s (t i )-y k (t i )-Δe(t i )-x1(t i )-x2(t i (31) The above analysis shows that the mathematical expressions of the dynamic model of the grinding system are equations (10) and (11), and the geometric positional relationships between the grinding wheel and the groove are equations (21) and (30). By solving the above equations, the instantaneous vibration displacement of the groove grinding process can be obtained, and then the instantaneous grinding depth δ of the groove can be calculated. w (t i Then, the total grinding depth Δ at each point on the groove profile is calculated. w (t i This allows us to obtain the dynamic change process of the channel radius and the change in roundness error. Example 1:

[0016] This prediction method can obtain the groove profile and roundness value of the bearing outer ring after grinding. An example is given below: The actual profile of the outer circle of the bearing outer ring and the raceway is a complex closed curve, and its roundness error can be expressed by a Fourier series, with the following polar coordinate form: In the formula, A j φ is the amplitude of the roundness error when the order is j; j is the order of the roundness error; w is the rotational angular velocity of the ring; φ is the initial phase angle of the roundness error. To simplify the simulation model, the initial roundness error of the bearing outer ring and the raceway is set to a single-order roundness error; the roundness error amplitude of the bearing outer ring is 0.20 μm, and the order of the outer ring roundness error is j = 3; the roundness error amplitude of the bearing outer ring raceway is 5 μm, and the order of the raceway roundness error is j = 3; the simulation parameters of the bearing outer ring are shown in Table 1, the simulation parameters of the grinding wheel are shown in Table 2, and the grinding process parameters are shown in Table 3. Table 1. Simulation parameters of the outer ring Table 2. Grinding wheel simulation parameters Table 3 Grinding process parameters

[0017] The implementation steps for this prediction method are as follows: First, according to the first step of this prediction method, the grinding wheel and bearing raceway profiles are uniformly discretized into 10240 and 1024 grinding points along the circumferential direction, respectively. The angular step sizes of the grinding wheel and bearing outer ring rotation are 2π / 10240 and 2π / 1024, respectively. Second, the bearing outer ring parameters, grinding wheel parameters, and grinding process parameters are given, as shown in Tables 1 to 3. Third, the positioning method for grinding the bearing outer ring raceway is external grinding. The geometric shape error of the outer circle of the bearing outer ring will cause the raceway to be displaced relative to the grinding wheel during the grinding process. Therefore, the center displacement Δu(t) of the raceway during the grinding process is calculated based on formula (18) in the prediction model, as shown in Tables 1 to 3. Figure 5 The figure shows the center displacement of the grinding wheel ring during the grinding process. The center displacement of the grinding wheel ring at the first grinding point is -0.1695 μm. Calculate the spindle displacement Δe(t) caused by the radial runout error of the grinding wheel spindle at each time step during the grinding process. i The radial runout error of the grinding wheel spindle at the first grinding point was 0.05 μm. The fourth step was to determine the parameters of the Newmark-β method, including the time step. Newmark correction factors γ = 1 / 2, ξ = 1 / 4, and the unbalanced forces of the grinding wheel and the grinding ring are calculated based on equation (12). In the fifth step, the initial displacement and initial velocity of the grinding wheel and the grinding ring are both zero, and the initial grinding force F(t0) = F ub (t0)+F n (t0), calculate the initial acceleration of the grinding wheel and the raceway using equations (10) and (11). Sixth step, determine t based on factors such as the grinding wheel feed rate, total grinding wheel wear, and total groove grinding amount. i = i·Δt, the relative position of the grinding wheel and the groove at time t, calculate t. i =i·Δt, the theoretical instantaneous grinding amount at time step. Step 7: Calculate the grinding forces acting on the grinding wheel and the grooves, such as... Figure 6The image shows the grinding forces acting on the grinding wheel and the groove during the grinding process. Step 8: Substitute the grinding forces obtained in Step 7 into the dynamic equations and use the Newmark-β method to solve for the vibration displacement, velocity, and acceleration of the grinding system at the current time step; solve for the actual instantaneous grinding amount at this time step, and then obtain the radius value of the groove after grinding. Step 9: Repeat steps 6, 7, and 8 until grinding is complete. Step 10: Use MATLAB to draw the profile of the groove after grinding and use the least squares method to calculate its roundness value. The groove profile after grinding is shown below. Figure 7 As shown, its roundness change process is as follows Figure 8 As shown, its final roundness value is 0.41 μm.

[0018] To verify the rationality and effectiveness of the proposed ball bearing raceway grinding roundness error prediction model, an experimental study on the grinding roundness error of angular contact ball bearing raceways was conducted. The details are as follows: 1. Experimental Objective To verify the rationality of the outer ring groove grinding roundness prediction model, grinding experiments with corresponding process parameters were conducted on a centerless grinder. The experiments mainly involved measuring the radial runout error of the grinding wheel spindle, the roundness error of the bearing outer ring, the initial profile of the outer ring groove, and the profile and roundness values ​​of the groove after grinding. The correctness of the proposed prediction model was verified by comparing the simulated and measured values ​​of the bearing outer ring groove roundness error. 2. Test Plan The experiment was conducted using existing grinding machines and testing tools. To facilitate the setting of experimental process parameters, the feeding device of the centerless grinder was changed from automatic to manual feeding. To ensure the stability of the grinding accuracy of the external groove grinder, the grinder was preheated for 30 minutes before the experiment to bring it to a thermal equilibrium state. To reduce the impact of grinding wheel wear on the groove grinding accuracy, the grinding wheel was dressed after each grinding cycle. The 7009C / P4 angular contact ball bearing ring was selected as the test object. The material was GCr15 bearing steel. The test procedure was the fine grinding process after the rough grinding of the groove. The grinding process conditions used in the experiment are shown in Tables 1 to 3. 3. Test equipment and instruments This experiment was conducted on a 3MK1410B external groove grinder of Luoyang Youpu Electromechanical Technology Co., Ltd., and the bearing ring raceway roundness error measuring instrument was a WALERA1000 roundness meter of Shaanxi Weier Electromechanical Technology Co., Ltd. 4. Analysis of Experimental Results Under the aforementioned grinding parameters, grinding tests on the outer rings of three 7009C / P4 angular contact ball bearings from the same batch showed that the roundness error of the raceway after grinding was between 0.30 and 0.48 μm, with an average of 0.39 μm; this value is consistent with... Figure 8The final roundness result of 0.41 μm shown is very close to the expected value. The experimental results confirm the rationality of the proposed outer ring groove grinding roundness prediction model.

[0019] The parts not described in detail in this embodiment are existing technologies.

[0020] It should be noted that although the present invention has been described through the above embodiments, the present invention may have many other embodiments. Without departing from the spirit and scope of the present invention, those skilled in the art can obviously make various corresponding changes and modifications to the present invention, but all such changes and modifications should fall within the scope of protection of the appended claims and their equivalents.

Claims

1. A method of predicting the roundness of a groove of an outer ring of a ball bearing, characterized in that: The steps are as follows: S1. Discrete the grinding wheel and the outer groove profile evenly in the circumferential direction. n One and m The instantaneous radii of the grinding points during the rotation of the grinding wheel and the outer groove are respectively composed of: and This means that in the iterative calculation model, the initial profile of the channel is used as the initial condition for the calculation. S2. Input grinding wheel parameters, bearing outer ring parameters to be machined, grinding system parameters, and grinding process parameters; the input grinding wheel parameters, bearing outer ring parameters to be machined, grinding process parameters, and grinding system parameters specifically include: the geometric dimensions of the grinding wheel and bearing outer ring, rotational speed and grinding wheel feed time and feed rate, the front support angle α and support angle β of the electromagnetic centerless chuck, the initial profile surface roundness error of the groove, the radial runout error of the grinding wheel spindle, the wear stiffness of the grinding wheel, and the stiffness of the contact area; S3. Calculate the time step based on the grinding process parameters. ; Calculate the displacement of the raceway center at each time step during the raceway grinding process caused by the geometric shape error of the outer circle of the bearing being machined. Calculate the spindle displacement caused by radial runout error of the grinding wheel spindle at each time step during the grinding process. ; S4. Determine the Newmark correction parameters and parameters ; A mass matrix M , a stiffness matrix K and a damping matrix C of the grinding system are established based on the Newmark-β method calculating an unbalance force corresponding to each time step in the grinding process ; S5 t 0 When =0, determine the initial vibration displacement, velocity, and acceleration of the grinding wheel and the outer ring of the bearing; S6, Calculation The theoretical instantaneous grinding amount of the groove at any given moment; S7, judging whether the theoretical instantaneous grinding amount in step S6 is greater than zero theoretical instantaneous grinding amount of the time step whether greater than zero, if the theoretical instantaneous grinding amount is greater than zero greater than zero indicates that the grinding wheel and the groove produce grinding action at this time step, and the normal grinding force is calculated theoretical instantaneous grinding amount less than zero indicates that the grinding wheel and the groove are not in contact at this time step, and the normal grinding force of this time step is zero S8、will be and into the grinding system structure dynamics equations, using Newmark-β method to solve the dynamics equations; calculate time step grinding wheel and the outer ring of the vibration displacement, velocity and acceleration; calculate time step grinding wheel instantaneous wear; calculate time step channel of the actual grinding and grinding after the radius value; S9, let S6, S7, and S8 are repeated to solve the solution of the next time step equation set until the grinding is finished. S10. Calculate the roundness error of the groove during the grinding process based on the least squares method.

2. The method of claim 1, wherein: In step S3, the specific process of determining the displacement of the channel center is as follows: S3.1 First, the contact position between the outer circle of the bearing outer ring and the fixed support should be accurately calculated. t The theoretical contact point between the outer circle of the outer ring and the rear support at any given moment is... k The outer radius is r k Due to the existence of errors in the outer circle contour, the actual contact is a point. k' , k' The radius of the point is r k' ,at this time OK and OK The included angle is θ k Then the included angle of the rear support is ( β + θ k )°, the corresponding bearing outer ring at the rear support is at a geometric error of . x The center displacement in the axial direction is In the formula, This is the radius error between the outer circle of the outer ring and the actual contact point of the rear support, and its value is the difference between the actual contact point radius and the ideal radius of the outer circle. S3.2, the outer ring at the front support has geometric errors due to the outer circle. x The displacement in the axial direction is In the formula, The angle between the line connecting the outer circle of the outer ring to the center of the outer circle from the actual contact point of the outer ring and the front support and the line connecting the theoretical contact point of the outer ring and the front support to the center of the outer circle; This represents the radius error at the actual contact point between the outer circle and the front support; S3.3, the center displacement of the bearing outer ring when there are geometric errors at both the front and rear fixed supports is: 。 3. The method for predicting the roundness of the outer ring raceway of a ball bearing according to claim 1, characterized in that: In step S6, the theoretical instantaneous grinding amount The calculation formula is as follows: calculate Theoretical instantaneous grinding amount per time step; In the formula, This is the nominal feed rate of the grinding wheel. This refers to the initial roundness error of the channel. for( t - T Total grinding amount of the groove at any given time. for( t - T The total grinding amount of the grinding wheel at any given time.

4. The method for predicting the roundness of the outer ring raceway of a ball bearing according to claim 1, characterized in that: In step S7, the normal grinding force is calculated using the following formula. , In the formula: Indicates specific cutting energy. Indicates the linear velocity of the workpiece. Indicates the amount of material removed from the workpiece. Indicates the unit grinding width. This indicates the linear velocity of the grinding wheel. A coefficient representing the relationship between radial grinding force and tangential grinding force. It is defined as the grinding stiffness of the groove, which is the ratio of the normal grinding force on the groove to the instantaneous grinding depth of the groove.

5. The method for predicting the roundness of the outer ring groove of a ball bearing as described in claim 1, characterized in that: In step S8, the set of equations for the structural dynamics of the grinding system is as follows: In the formula, For the equivalent mass of the grinding wheel component, The mass of the bearing outer ring; and These are the damping coefficients of the grinding wheel system and the workpiece system, respectively. and These are the equivalent stiffness constants of the grinding wheel system and the workpiece system, respectively; This represents the vibration displacement of the grinding wheel's center point. This represents the vibration displacement at the center point of the workpiece. and These are the dynamic unbalance forces of the grinding wheel and the outer ring, respectively. It is the normal grinding force exerted on the grinding wheel and the groove.

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