Method for predicting grinding roundness of ball bearing outer ring groove

Abstract

A method for predicting the grinding roundness of an outer ring channel of a ball bearing relates to the field of bearing processing, and comprises the following steps: uniformly dispersing a grinding wheel and an outer ring channel profile into n grinding points and m grinding points in the circumferential direction, and inputting grinding wheel parameters, outer ring parameters and grinding process parameters; determining channel center displacement and main shaft displacement according to grinding process parameters, and determining Newmak correction parameters and parameters; whether the theoretical instantaneous grinding amount of the # imgabs0 # time step is larger than zero or not is judged, the unbalanced force and the normal grinding force are substituted into a structural dynamic equation set of the grinding system, and the dynamic equation set is solved through a Newmark-beta method; the vibration displacement, speed and acceleration of the grinding wheel and the ferrule in the # imgabs 1 # time step are calculated; the instantaneous abrasion loss of the grinding wheel in the # imgabs2 # time step is calculated; calculating the actual grinding amount of the # imgabs3 # time step channel and the radius value after grinding; and finally, calculating the roundness error of the channel in the grinding process based on a least square method. According to the scheme, the dynamic change of the channel profile in the bearing outer ring channel grinding process and the roundness error of the channel after grinding is finished can be predicted.

Description

Technical Field

[0001] The invention relates to the technical field of bearing processing technology, and in particular to a method for predicting the grinding roundness of a ball bearing outer ring groove, which is mainly suitable for predicting the roundness of an angular contact ball bearing or a deep groove ball bearing during the grinding process. Background Art

[0002] As we all know, the method for predicting the roundness of the outer ring groove of ball bearings is to predict the roundness of the outer ring groove of the bearing after grinding under the condition of known or given center displacement caused by the outer circle geometric shape error of the bearing, radial runout error of the grinding wheel spindle, imbalance of the grinding wheel and ring, vibration displacement and contact deformation of the grinding wheel and workpiece during grinding, grinding wheel wear, and initial groove profile error.

[0003] Ball bearings are important supporting components in mechanical transmission devices. The outer ring groove is the working surface that bears the load when the bearing ring rotates. Its processing accuracy and surface quality directly affect the working performance and life of the bearing. Improving the accuracy and surface quality of the outer ring groove is of great significance to the overall performance and service life of the bearing. At present, most of the research on bearing groove grinding focuses on optimizing grinding process parameters through experiments, designing and optimizing grinding tools, and monitoring grinding signals. Moreover, most of the models for bearing outer groove grinding only consider the dynamics of the grinding system or the grinding process, without considering the two comprehensively. Therefore, it is difficult to accurately reveal the formation mechanism of the bearing outer groove grinding profile and the influence of grinding process parameters on the groove roundness error. Summary of the invention

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

[0005] The technical solution adopted by the present invention is: a method for predicting the grinding roundness of the outer ring groove of a ball bearing, the steps are as follows: S1. The grinding wheel and outer ring groove profiles are evenly discretized into n and m grinding points respectively in the circumferential direction. The instantaneous radius of the grinding points during the rotation of the grinding wheel and outer ring groove is r1(t i ) and r2(t i ) indicates that in the iterative calculation model, the initial profile of the channel is used as the initial condition for calculation; S2, input grinding wheel parameters, outer ring parameters of the processed bearing, grinding system parameters and grinding process parameters; S3, calculate the time step Δt according to the grinding process parameters; calculate the groove center displacement Δu (t i), calculate the spindle displacement Δe(t i ); S4. Determine the Newmark correction parameter γ and parameter ξ; establish the grinding system mass matrix M, stiffness matrix K and damping matrix C based on the Newmark-β method; calculate the unbalanced force F corresponding to each time step in the grinding process ub (t i ); S5, when 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 = Theoretical instantaneous grinding amount of the groove at time i·Δt; S7, judging step S6 i = Theoretical instantaneous grinding amount δ at time step i·Δt w1 (t i ) is greater than zero, if the theoretical instantaneous grinding amount δ w1 (t i ) is greater than zero, indicating that the grinding wheel and the groove produce grinding action at this time step, and the normal grinding force is calculated; the theoretical instantaneous grinding amount δ w1 (t i ) is less than zero, indicating 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 ) into the structural dynamics equations of the grinding system, and the Newmark-β method is used to solve the dynamics equations; calculate t i = i·Δt time step vibration displacement, velocity and acceleration of grinding wheel and ring; calculate t i = i·Δt instantaneous wear of the grinding wheel; calculate t i = i·Δt time step actual grinding amount of the channel and the radius value after grinding; S9, let i=i+1, repeat steps S6-S8, and solve the solution of the equation group for the next time step until the grinding is completed; S10. Calculate the roundness error of the groove during the grinding process based on the least square method. As a preferred embodiment, in step S2, the input grinding wheel parameters, the parameters of the outer ring of the processed bearing, the grinding process parameters and the grinding system parameters are specifically: the geometric dimensions of the grinding wheel and the outer ring of the bearing, the rotation speed and the grinding wheel feed time and feed speed, the front support angle α and the support angle β of the electromagnetic centerless fixture, the surface roundness error of the initial contour of the groove, the radial runout error of the grinding wheel spindle, the grinding wheel wear stiffness and the contact area stiffness, etc. As a preferred solution, in step S3, the specific process of determining the channel center displacement is: 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 the outer circle contour error, the actual contact point is k', and the radius of k' is r k' , at this time the angle between ok and ok' is θ k , then the rear support angle is (β+θ k )°, the corresponding center displacement of the outer ring of the bearing in the x-axis direction due to the geometric error at the rear support is In the formula, Δr1(t i ) is the radius error of the actual contact point between the outer circle of the outer ring and the rear support, and its value is the difference between the radius of the actual contact point and the ideal radius of the outer circle; S3.2, the displacement of the ferrule in the x-axis direction due to the outer circle geometric error at the front support is In the formula, θ p The angle between the line connecting the outer circle of the outer ring and the actual contact point between the outer ring and the front support and the center of the outer circle and the line connecting the outer circle of the outer ring and the theoretical contact point between the outer ring and the front support and the center of the outer circle; Δr2(t i ) is the radius error of the actual contact point between the outer circle and the front support; S3.3, then 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 solution, in step S6, the specific process is as follows: Determine t based on factors such as grinding wheel feed, total grinding wheel wear, and total groove grinding amount. i = The relative position of the grinding wheel and the groove at time i·Δt, 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 =Theoretical instantaneous grinding amount in time step i·Δt. As a preferred solution, in step S7, the normal grinding force F is calculated using the following formula: n (ti ), Where: U ch represents specific cutting energy, v w Indicates the linear velocity of the workpiece, δ w1 (t) represents the material removal amount of the workpiece, b represents the unit grinding width, v s Indicates the linear speed of the grinding wheel, K t The coefficient that expresses the relationship between radial grinding force and tangential grinding force, k w It can be defined as the grinding stiffness of the channel, which is the ratio of the normal grinding force on the channel to the instantaneous grinding depth of the channel. As a preferred solution, in step S8, the grinding system structural dynamics equations are: Where m1 is the equivalent mass of the grinding wheel component, m2 is the mass of the outer ring of the bearing; 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 ) is the vibration displacement of the grinding wheel center point, x2(t i ) is the vibration displacement of the workpiece center; F ub1 (t i ) and F ub2 (t i ) are the dynamic unbalanced forces of the grinding wheel and the ring respectively; F n (t i ) is the normal grinding force acting on the grinding wheel and the groove. The beneficial effects of the present invention are:

[0006] Through the outer ring groove grinding roundness prediction method of the present invention, in order to predict the center displacement caused by the known or given bearing outer circle geometric shape error, the radial runout error of the grinding wheel spindle, the vibration displacement and contact deformation of the grinding wheel and the workpiece during the grinding process, the grinding wheel wear, and the roundness of the bearing outer ring groove after grinding, the quantitative simulation of the dynamic formation process of the bearing outer ring groove profile under different grinding system parameters and process parameters is realized, and a reliable analysis method is provided for effectively predicting the outer ring groove grinding roundness. Through synchronous simulation and test parameters, multi-condition angular contact ball bearing outer ring groove grinding tests were carried out, and the test results confirmed the rationality of the proposed outer ring groove grinding roundness prediction model. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work. Figure 1 Schematic diagram of the outer raceway grinding system used in this prediction method; Figure 2 It is a simplified schematic diagram of outer ring raceway support grinding; Figure 3 Schematic diagram of the center displacement of the bearing outer ring; Figure 4 It is a schematic diagram of the contact between the outer ring of the bearing and the rear support; Figure 5 Schematic diagram of the change of the center displacement of the outer ring of the bearing; Figure 6 Schematic diagram of the change of grinding force on the groove and grinding wheel; Figure 7 Schematic diagram of the channel after grinding; Figure 8 Schematic diagram of channel roundness change. DETAILED DESCRIPTION

[0008] The present invention is described in detail below by way of exemplary embodiments. However, it should be understood that, without further description, elements, structures and features in one embodiment may also be beneficially combined in other embodiments.

[0009] It should be noted that, unless otherwise defined, the technical terms or scientific terms used herein shall have the usual meanings understood by persons with ordinary skills in the field to which the present invention belongs. The words "one", "an" or "the" and the like used in the patent application specification and claims of the present invention do not express quantitative limitations, but indicate the existence of at least one. Words such as "include" or "comprise" indicate that the elements or objects appearing before "include" or "comprises" include the elements or objects listed after "include" or "comprises" and their equivalents.

[0010] Before describing this scheme, we first conduct a numerical analysis of the structural vibration differential equation. Currently, there are many algorithms that can be implemented, such as the central difference method, linear acceleration method, Newmark-β method, Wilson-θ method, etc. The present invention will use the Newmark-β method to solve the vibration displacement of the grinding wheel and the ring during the groove grinding process. The basic idea is to discretize the time, and the motion equation is only required to be satisfied at discrete time points. The detailed solution and steps of solving the structural dynamics equation of the outer ring groove grinding system using the Newmark-β method are as follows: (1) Time discretization. The grinding time n is divided into equal parts, the time step is Δt, the discrete points are (0, 1, 2, ..., n-1, n), and the time corresponding to the discrete point is 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 calculates the constants commonly used in integrals; (3) Input the mass matrix M, stiffness matrix K and damping matrix C of the dynamic equations; (4) Calculate the initial motion parameters of each time step, and obtain the vibration displacement x(t i ), vibration speed 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 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 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) until all time steps are calculated.

[0011] A method for predicting the grinding roundness of the outer ring groove of a ball bearing, the detailed steps are as follows: (1) The grinding wheel and outer ring groove profiles are uniformly discretized into n and m grinding points respectively in the circumferential direction. The instantaneous radius of the grinding point during the rotation of the grinding wheel and the groove is r1(t i ) and r2(t i ) is expressed. In the iterative calculation model, the initial profile of the channel is used as the initial condition for calculation; (2) Input grinding wheel parameters, bearing outer ring parameters, grinding system parameters, and grinding process parameters. Specific parameters include the front support angle α and support angle β of the electromagnetic centerless fixture, the geometric dimensions of the grinding wheel and the bearing outer ring, the rotation speed and the grinding wheel feed time and feed speed, the surface roundness error of the initial profile of the groove, the radial runout error of the grinding wheel spindle, the wear stiffness of the grinding wheel, the stiffness of the contact area, etc.; (3) Calculate the time step Δt according to the grinding process parameters; calculate the groove center displacement Δu (t i ), calculate the spindle displacement Δe(t i ); (4) Determine the Newmark correction parameter γ and parameter ξ; establish the grinding system mass matrix M, stiffness matrix K and damping matrix C based on the Newmark-β method; calculate the unbalanced force F corresponding to each time step in 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 = Theoretical instantaneous grinding amount of the groove at time i·Δt. The grinding wheel feed, total grinding wheel wear, total groove grinding amount and other factors are used to determine t i = The relative position of the grinding wheel and the groove at time i·Δt, and t is calculated using formula (10) i = Theoretical instantaneous grinding amount at time step i·Δt; 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 = Theoretical instantaneous grinding amount δ at time step i·Δt w1 (t i ) is greater than zero, if the theoretical instantaneous grinding amount δ w1 (t i ) is greater than zero, indicating that the grinding wheel and the groove produce grinding action at this time step. The normal grinding force is calculated based on formula (16); the theoretical instantaneous grinding amount δ w1 (t i ) is less than zero, indicating 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 ) into the structural dynamics equations of the grinding system, and the Newmark-β method is used to solve the dynamics equations; calculate t i = i·Δt time step vibration displacement, velocity and acceleration of grinding wheel and ring; calculate t i = i·Δt instantaneous wear of the grinding wheel; calculate t i = i·Δt time step actual grinding amount of the channel and the radius value after grinding; (9) Let i = i + 1, repeat steps (6) to (8) to solve the equations for the next time step until the grinding is completed; (10) The roundness error of the groove during the grinding process is calculated 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 outer ring groove grinding system: Angular contact ball bearing outer ring groove grinding system Figure 1 As shown in the figure, it is mainly composed 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 liquid hydrostatic bearing, and the workpiece (i.e., the outer ring of the bearing) is clamped and fixed by an electromagnetic centerless clamp. After the grinding wheel is fed, it contacts the outer ring groove to generate a grinding force, so that the grinding wheel and the groove interact with each other, thereby causing material removal in the outer ring groove. There are many different forms of grinding, depending on the shape of the workpiece and the kinematics of the workpiece grinding wheel. Supporting external grinding is the basic form of machining the outer raceway of angular contact ball bearings. This paper studies the support grinding process of the outer raceway of the bearing. Figure 1It can be seen that the bearing outer ring groove grinding process is an interactive process of two shaft systems (i.e., the grinding wheel spindle system and the fixed support-ring-pole spindle system). However, for the bearing outer ring groove support grinding, the grinding wheel only grinds the groove in the radial direction of the bearing ring groove. Without considering factors such as shaft system torsional vibration and thermal deformation, the bearing outer ring groove grinding system can be simplified into two single-degree-of-freedom systems, namely the grinding wheel and the bearing outer ring. Figure 2 It is a simplified schematic diagram of bearing outer ring groove support grinding. From the vibration mechanics, we know that there is a dynamic equation for the grinding wheel and the ring: Where m1 is the equivalent mass of the grinding wheel component, m2 is the mass of the outer ring of the bearing; 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 ) is the vibration displacement of the grinding wheel center point, x2(t i ) is the vibration displacement of the workpiece center; F ub1 (t i ) and F ub2 (t i ) are the dynamic unbalanced forces of the grinding wheel and the ring respectively; F n (t i ) is the normal grinding force acting on the grinding wheel and the groove. For the grinding wheel and the ring, the dynamic unbalanced force can be expressed as F ub (t i )=G e mω*10 -3 cos(ωt i ) (13) In the formula, G e is the dynamic balancing accuracy grade; ω is the rotational angular velocity. If the effects of plowing and sliding are ignored, the calculation formula of grinding force can be expressed as: 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 represents specific cutting energy, v w Indicates the linear velocity of the workpiece, δ w1(t) represents the material removal amount of the workpiece, b represents the unit grinding width, v s Indicates the linear speed of the grinding wheel, F n (t i ) represents the normal grinding force, K t The coefficient that expresses the relationship between radial grinding force and tangential grinding force, k w It can be defined as the grinding stiffness of the channel, which is the ratio of the normal grinding force on the channel to the instantaneous grinding depth of the channel.

[0014] 2. Center displacement caused by outer circle geometric shape error: The outer ring groove of the ball bearing is often ground by the positioning method of the outer grinding groove. Since the shape of the outer circle surface of the bearing outer ring is very complex, the cross-sectional center of the groove is always moving and its movement trajectory depends on the contact point between the outer circle and the fixed support. Figure 3 As shown in the figure, 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, thereby affecting the grinding roundness of the outer ring groove. In order to calculate the center displacement of the ring during the grinding process, the contact position between the outer circle of the bearing outer ring and the fixed support should be accurately calculated first, such as Figure 4 As shown. At time t, the theoretical contact 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 the outer circle contour error, the actual contact point is k', and the radius of k' is r k' , at this time the angle between ok and ok' is θ k , then the rear support angle is (β+θ k )°, the corresponding center displacement of the outer ring of the bearing in the x-axis direction due to the geometric error at the rear support is In the formula, Δr1(t i ) is the radius error of the actual contact point between the outer circle of the outer ring and the rear support, and its value is the difference between the radius of the actual contact point and the ideal radius of the outer circle. Similarly, the displacement of the ring in the x-axis direction due to the outer circle geometric error at the front support is In the formula, θ p The angle between the line connecting the outer circle of the outer ring and the actual contact point between the outer ring and the front support and the center of the outer circle and the line connecting the outer circle of the outer ring and the theoretical contact point between the outer ring and the front support and the center of the outer circle; Δr2(t i ) is the radius error of the actual contact point between the outer circle and the front support. Then the center displacement of the bearing outer ring when there are geometric errors at both the front and rear fixed supports is In order to obtain the radius error of the actual contact point, a search is performed in the angle area near the theoretical contact point k, which is the angle between the center of the outer circle and the theoretical contact point. The point farthest from the center of the outer circle to the fixed support is taken as the actual contact point, and the radius error Δr of this point is used to calculate the center displacement of the outer ring. Take the theoretical contact point k between the outer ring of the bearing and the rear support as an example. The outer circle in the angle region is discretized into n points, each of which corresponds to a radius value r(θ m ), then the outer circle radius error value corresponding to each point Δr(θ m )=r(θ m )-r (20) Where r is the theoretical radius, θ m It is the angle between ok and ok'. The maximum value of the outer circle radius error in the region is

[0015] 3. Outer ring groove grinding process model: The study of the rounding process of the bearing groove is to determine the relative position between the groove and the grinding wheel and the grinding condition of the groove surface by the grinding wheel to obtain the regenerated surface of the groove by analyzing the interaction between the groove and the grinding system. like Figure 2 As shown, during the grinding process, the outer ring groove and the grinding wheel always have the following position relationship in 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 ) is the distance from the grinding wheel center to the grinding contact point at time t; L2(t i ) is the distance from the center of the groove to the grinding contact point at time t; L(t i ) is the distance between the grinding wheel center and the groove center during the radial feeding process of the grinding wheel at time t. r1 is the outer radius of the grinding wheel before grinding; Δ s (t i ) is the total wear of the grinding wheel at time t; y k1 (t i ) is the contact deformation of the grinding wheel at time t; k a Indicates the contact stiffness between the grinding wheel and the groove. r2 is the groove radius before grinding; Δ w (t i ) is the total grinding amount of the groove at time t; y k2 (t i ) is the contact deformation of the channel at time t; Δu(t i ) is the positioning error of the ring; Δr(t i ) is the initial roundness error of the channel; Δe(t i ) is the grinding wheel rotation error; a p (t i ) is the nominal feed 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) Among them, δ w (t i ) is the instantaneous grinding amount of the groove; v f is the grinding wheel feed speed; s(t i ) can be approximated as the normal grinding force on the grinding wheel and the wear stiffness k of the grinding wheel s Ratio By integrating the above equations, we can get 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) From the above analysis, it can be seen that the mathematical expressions of the dynamic model of the grinding system are equations (10) and (11), and the geometric position relationship between the grinding wheel and the groove is equations (21) and (30). By solving the above equations, the instantaneous vibration displacement of the groove grinding process is obtained, and then the instantaneous grinding depth δ of the groove is calculated. w (t i ), and then calculate the total grinding depth Δ of each point on the groove profile w (t i ), the dynamic change process of the channel radius and the roundness error change can be obtained. Embodiment 1:

[0016] This prediction method can obtain the groove profile and roundness value of the bearing outer ring groove after grinding. The following example illustrates: The actual contour of the outer circle and groove of the bearing outer ring is a complex closed curve. Its roundness error can be expressed by Fourier series, and its polar coordinate form is as follows: In the formula, A j 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. In order to simplify the simulation model, the initial roundness errors of the outer circle and groove of the bearing outer ring are set to a single-order roundness error; the roundness error amplitude of the outer circle of the bearing outer ring is 0.20 μm, and the outer circle roundness error order j = 3; the roundness error amplitude of the groove of the bearing outer ring is 5 μm, and the groove roundness error order 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 Outer ring simulation parameters Table 2 Grinding wheel simulation parameters Table 3 Grinding process parameters

[0017] Using this prediction method, the implementation steps are as follows: First, according to the first step of this prediction method, the grinding wheel and ring groove profiles are evenly discretized into 10240 and 1024 grinding points along the circumferential direction, and the angular step lengths of the grinding wheel and the bearing outer ring are 2π / 10240 and 2π / 1024, respectively. In the second step, the bearing outer ring parameters, grinding wheel parameters and grinding process parameters are given, as shown in Tables 1 to 3. In the third step, the positioning method for the bearing outer ring groove grinding is to support the outer grinding groove. The geometric shape error of the outer circle of the bearing outer ring will cause the groove to be displaced relative to the grinding wheel during the grinding process. Therefore, the center displacement Δu(t) of the groove during the grinding process is calculated based on equation (18) in the prediction model, as shown in Figure 5 The figure shows the center displacement of the ring during the grinding process. The center displacement of the ring at the first grinding point is -0.1695 μm. The spindle displacement Δe (t i ), the radial runout error value of the grinding wheel spindle at the first grinding point is 0.05μm. The fourth step is to determine the parameters of the Newmark-β method, the time step Newmark correction coefficient γ = 1 / 2, ξ = 1 / 4, the unbalanced force of the grinding wheel and the ring is calculated based on formula (12). Step 5 The initial displacement and initial speed of the grinding wheel and the ring are both zero, and the initial grinding force F(t0) = F ub (t0)+F n (t0), and use equations (10) and (11) to calculate the initial acceleration of the grinding wheel and the ring. Step 6: Determine t based on factors such as grinding wheel feed, total grinding wheel wear, and total groove grinding amount. i = The relative position of the grinding wheel and the groove at time i·Δt, calculate t i = Theoretical instantaneous grinding amount in time step i·Δt. Step 7: Calculate the grinding force on the grinding wheel and the groove, such as Figure 6The figure shows the grinding force exerted on the grinding wheel and the groove during the grinding process. The eighth step is to substitute the grinding force obtained in the seventh step into the dynamic equations, and use the Newmark-β method to solve the vibration displacement, velocity and acceleration of the grinding system in the current time step; solve the actual instantaneous grinding amount in this time step, and then obtain the radius value of the groove after grinding. The ninth step is to repeat the sixth, seventh and eighth steps until the grinding is completed. The tenth step is to use MATLAB to draw the contour of the groove after the grinding is completed and use the least squares method to calculate its roundness value. The contour of the groove after grinding is as shown in the figure. Figure 7 As shown in Figure 2, the roundness change process is as follows: Figure 8 As shown, its final roundness value is 0.41 μm.

[0018] In order to verify that the ball bearing ring groove grinding roundness error prediction model proposed in the present invention is reasonable and effective, an angular contact ball bearing ring groove grinding roundness error test study was carried out, and the details are as follows: 1. Purpose of the experiment In order to verify that the outer ring groove grinding roundness prediction model is reasonable, a grinding test with corresponding process parameters is carried out on a centerless grinder. The test content mainly measures the radial runout error value of the grinding wheel spindle, the outer circle roundness error of the bearing outer ring, the initial profile of the outer ring groove, and the groove profile and roundness value after the outer ring groove grinding is completed. The correctness of the prediction model proposed in this paper is verified by comparing the simulation value and the measured value of the bearing outer ring groove roundness error. 2. Experimental plan The test was conducted using existing grinders and testing tools. To facilitate the setting of test process parameters, the feeding device of the centerless grinder was changed from automatic feeding 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 test to put it in a thermal equilibrium state. To reduce the influence of grinding wheel wear on the groove grinding accuracy, the grinding wheel was trimmed after each grinding. The bearing ring of angular contact ball bearing 7009C / P4 was selected as the test object. The material was GCr15 bearing steel. The test process was the fine grinding process after the rough grinding of the groove. The grinding process conditions used in the test are shown in Tables 1 to 3. 3. Test equipment and instruments This test was carried out on the 3MK1410B external groove grinder of Luoyang Youpu Electromechanical Technology Co., Ltd., and the bearing ring groove roundness error measuring instrument was the WALERA1000 roundness meter of Shaanxi Well Electromechanical Technology Co., Ltd. 4. Analysis of test results Under the above grinding parameters, the grinding test of the outer rings of three 7009C / P4 angular contact ball bearings from the same batch showed that the roundness errors of the grooves of the three bearing outer rings after grinding were 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 0.41μm is very close to the actual 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 prior art.

[0020] It should be noted that although the present invention is described by the above embodiments, the present invention may also have other various embodiments. Without departing from the spirit and scope of the present invention, it is obvious that those skilled in the art may make various corresponding changes and deformations to the present invention, but these changes and deformations should all fall within the scope of protection of the appended claims of the present invention and their equivalents.

Claims

1. A method for predicting the grinding roundness of a ball bearing outer ring raceway, characterized in that: Here are the steps: S1. The grinding wheel and outer ring groove profiles are evenly discretized into n and m grinding points respectively in the circumferential direction. The instantaneous radius of the grinding points during the rotation of the grinding wheel and outer ring groove is r1(t i ) and r2(t i ) indicates that in the iterative calculation model, the initial profile of the channel is used as the initial condition for calculation; S2, input grinding wheel parameters, outer ring parameters of the processed bearing, grinding system parameters and grinding process parameters; S3, calculate the time step Δt according to the grinding process parameters; calculate the groove center displacement Δu (t i ), calculate the spindle displacement Δe(t i ); S4, determining the Newmark correction parameter γ and parameter ξ; The mass matrix M, stiffness matrix K and damping matrix C of the grinding system are established based on the Newmark-β method. Calculate the unbalanced force F corresponding to each time step in the grinding process ub (t i ); S5, when 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 = Theoretical instantaneous grinding amount of the groove at time i·Δt; S7, judging step S6 i = Theoretical instantaneous grinding amount δ at time step i·Δt w1 (t i ) is greater than zero, if the theoretical instantaneous grinding amount δ w1 (t i ) is greater than zero, indicating that the grinding wheel and the groove produce grinding action at this time step, and the normal grinding force is calculated; the theoretical instantaneous grinding amount δ w1 (t i ) is less than zero, indicating 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 ) into the structural dynamics equations of the grinding system, and the Newmark-β method is used to solve the dynamics equations; calculate t i = i·Δt time step vibration displacement, velocity and acceleration of grinding wheel and ring; calculate t i = i·Δt instantaneous wear of the grinding wheel; calculate t i = i·Δt time step actual grinding amount of the channel and the radius value after grinding; S9, let i=i+1, repeat steps S6-S8, and solve the solution of the equation group for the next time step until the grinding is completed; S10. Calculate the roundness error of the groove during the grinding process based on the least square method.

2. The method for predicting the grinding roundness of the outer ring groove of a ball bearing according to claim 1, characterized in that: In step S2, the input grinding wheel parameters, the parameters of the outer ring of the processed bearing, the grinding process parameters and the grinding system parameters are specifically: the geometric dimensions of the grinding wheel and the outer ring of the bearing, the rotation speed and the grinding wheel feed time and feed speed, the front support angle α and the support angle β of the electromagnetic centerless fixture, the surface roundness error of the initial contour of the groove, the radial runout error of the grinding wheel spindle, the grinding wheel wear stiffness and the contact area stiffness, etc.

3. The method for predicting the grinding roundness of the outer ring groove of a ball bearing according to claim 1, characterized in that: In step S3, the specific process of determining the channel center displacement is: 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 the outer circle contour error, the actual contact point is k', and the radius of k' is r k' , at this time the angle between ok and ok' is θ k , then the rear support angle is (β+θ k )°, the corresponding center displacement of the outer ring of the bearing in the x-axis direction due to the geometric error at the rear support is In the formula, Δr1(t i ) is the radius error of the actual contact point between the outer circle of the outer ring and the rear support, and its value is the difference between the radius of the actual contact point and the ideal radius of the outer circle; S3.2, the displacement of the ferrule in the x-axis direction due to the outer circle geometric error at the front support is In the formula, θ p The angle between the line connecting the outer circle of the outer ring and the actual contact point between the outer ring and the front support and the center of the outer circle and the line connecting the outer circle of the outer ring and the theoretical contact point between the outer ring and the front support and the center of the outer circle; Δr2(t i ) is the radius error of the actual contact point between the outer circle and the front support; S3.3, then the center displacement of the bearing outer ring when there are geometric errors at both the front and rear fixed supports is 4. The method for predicting the grinding roundness of the outer ring groove of a ball bearing according to claim 1, characterized in that: In step S6, the specific process is as follows: Determine t based on factors such as grinding wheel feed, total grinding wheel wear, and total groove grinding amount. i = The relative position of the grinding wheel and the groove at time i·Δt, 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 =Theoretical instantaneous grinding amount in time step i·Δt.

5. The method for predicting the grinding roundness of the outer ring groove of a ball bearing according to claim 1, characterized in that: In step S7, the normal grinding force F is calculated using the following formula: n (t i ), Where: U ch represents specific cutting energy, v w Indicates the linear velocity of the workpiece, δ w1 (t) represents the material removal amount of the workpiece, b represents the unit grinding width, v s Indicates the linear speed of the grinding wheel, K t The coefficient that expresses the relationship between radial grinding force and tangential grinding force, k w It can be defined as the grinding stiffness of the channel, which is the ratio of the normal grinding force on the channel to the instantaneous grinding depth of the channel.

6. The method for predicting the grinding roundness of the outer ring groove of a ball bearing according to claim 1, characterized in that: In step S8, the structural dynamics equations of the grinding system are: Where m1 is the equivalent mass of the grinding wheel component, m2 is the mass of the outer ring of the bearing; 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 ) is the vibration displacement of the grinding wheel center point, x2(t i ) is the vibration displacement of the workpiece center point; F ub1 (t i ) and F ub2 (t i ) are the dynamic unbalanced forces of the grinding wheel and the ring respectively; F n (t i ) is the normal grinding force acting on the grinding wheel and the groove.

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