Prediction method for grinding roundness of ball bearing outer ring groove

Abstract

The invention discloses a method for predicting the grinding roundness of a ball bearing outer ring groove. The method comprises the following steps: acquiring parameters of a machined bearing outer ring, grinding wheel parameters and grinding process parameters; the total rotation angle of the bearing outer ring and the angle step length of rotation of the outer ring are set; giving the parameters, and calculating the total positioning error of the jth grinding point of the outer ring channel according to the feeding direction of the grinding wheel and the geometrical relationship between the bearing outer ring and the front and rear supporting blocks; calculating the actual grinding wheel feed amount of the jth grinding point of the outer ring channel when the rotation error of the grinding wheel spindle is considered; calculating the radius value of the jth grinding point of the outer ring channel after grinding according to the steps S3 and S4; repeating the steps S3-S5 until the grinding is finished; and calculating the roundness value of the outer ring channel by using a least square method. According to the scheme, the bearing outer ring channel grinding rounding process and the roundness error when the bearing outer ring channel, the bearing outer ring surface roundness error and the grinding wheel spindle radial run-out value are known or given can be predicted, and a theoretical basis is provided for bearing outer ring channel grinding and precision regulation and control.

Description

Technical Field

[0001] The present 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 applicable to the roundness prediction during the grinding process of angular contact ball bearings or deep groove ball bearings. Background Art

[0002] As is known to all, the method for predicting the roundness of ball bearing outer ring groove grinding is to predict the roundness of the bearing outer ring groove after grinding under known or given bearing outer ring surface and grinding wheel spindle radial runout.

[0003] The outer ring groove, as the working surface of a ball bearing, has a direct impact on its rotational accuracy, vibration noise, and fatigue life. Bearing groove roundness is a key parameter for measuring bearing groove processing quality, and variations in groove roundness have a particularly significant impact on bearing rotational accuracy. Therefore, the accuracy and stability of the outer ring groove grinding process must be strictly guaranteed. Current research on outer ring groove grinding of angular contact ball bearings focuses primarily on optimizing outer ring groove grinding process parameters through experimental methods, monitoring and analyzing the relationship between outer ring groove grinding process signals and outer ring processing quality, and improving grinding process systems. Limited research has been conducted on predicting outer ring groove grinding roundness. Furthermore, domestic theoretical research on centerless grinding is insufficient, and the selection of relevant process parameters relies heavily on the operator's subjective experience, resulting in unpredictable processing accuracy. Summary of the Invention

[0004] The purpose of the present invention is to propose a method for predicting the roundness of the outer ring groove of a ball bearing. This scheme can predict the roundness grinding process and roundness error of the outer ring groove of the bearing when the outer ring groove of the bearing, the roundness error of the outer ring surface of the bearing and the radial runout of the grinding wheel spindle are known or given.

[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 of which are as follows:

[0006] S1. Obtaining parameters of the outer ring of the bearing being processed, grinding wheel parameters, and grinding process parameters;

[0007] S2. Setting the total rotation angle of the bearing outer ring and the angle step of the outer ring rotation;

[0008] S3. Based on the parameters determined in the above steps, determine the actual outer ring radius and corresponding angle of the contact point of the j-th grinding point of the outer ring groove with the front support point, determine the actual outer ring radius and corresponding angle of the contact point of the j-th grinding point of the outer ring groove with the rear support point, and calculate the total positioning error of the j-th grinding point of the outer ring groove according to the feed direction of the grinding wheel and the geometric relationship between the bearing outer ring and the front and rear support blocks;

[0009] S4. Calculate the actual grinding wheel feed rate at the jth grinding point of the outer ring groove when considering the rotation error of the grinding wheel spindle;

[0010] S5. Calculate the radius of the j-th grinding point of the outer raceway after grinding according to steps S3 and S4;

[0011] S6, repeat steps S3-S5 until the grinding is completed;

[0012] S7. Calculate the roundness value of the outer raceway using the least squares method.

[0013] As a preferred solution, in step S1, the parameters of the processed bearing, the grinding wheel parameters and the grinding process parameters are specifically the bearing outer ring surface profile radius, the outer ring groove bottom radius, the outer ring speed, the grinding wheel radius, the grinding wheel speed, the front support angle, the support angle and the grinding feed rate.

[0014] As a preferred solution, in step S3, when the outer surface of the outer ring contacts the support surface and the theoretical contact point and the actual contact point do not coincide, the specific steps for determining the total positioning error are as follows:

[0015] S3.1. In order to obtain the actual contact point between the support surface and the outer surface of the outer ring, the outer surface contour radius of the outer ring in the region [-δ+β, δ+β] is discretized into n points, each of which corresponds to a radius value R(θ m ), through the formula ΔR(θ m )=R(θ m )-R calculates the outer contour radius error value of the outer ring corresponding to each point;

[0016] Among them, ΔR(θ m ) is the outer surface profile radius error corresponding to each point in the [-δ+β, δ+β] region, and its value is the difference between the actual radius and the theoretical radius, R is the theoretical radius, θ m is the angle between the actual contact point between the rear support block and the outer ring surface and the X-axis, and β is the position angle;

[0017] S3.2. Obtain the maximum outer surface radius of the outer ring within the region using the following formula:

[0018]

[0019] The maximum value of the outer ring outer surface profile radius error within the area is obtained. When the maximum radius error in the rear support block contact point area is ΔR1, the corresponding angle between the actual contact point and the line connecting the outer ring center and the X-axis changes. Similarly, when the maximum radius error in the front support block contact point area is ΔR2, the corresponding angle between the actual contact point and the line connecting the outer ring center and the X-axis also changes.

[0020] S3.3. Based on the above, according to the formula Get the corrected rear support positioning error;

[0021] S3.4, according to the formula Get the corrected front support positioning error;

[0022] S3.5, then the total positioning error of the outer ring center along the X-axis direction after correction is: ΔF′=Δx′2-Δx′1.

[0023] As a preferred solution, in step S3, when the outer surface of the outer ring contacts the support surface and the theoretical contact point coincides with the actual contact point, the specific steps for determining the total positioning error are as follows:

[0024] By formula Obtain the positioning error Δx1 of the bearing outer ring on the rear support;

[0025] By formula Obtain the positioning error Δx2 of the bearing outer ring on the front support;

[0026] From the above calculation, the total positioning error of the outer ring center in the total X direction is:

[0027] ΔF=Δx2-Δx1.

[0028] As a preferred solution, in step S4, the actual feed amount of the grinding wheel at the j-th grinding point of the outer ring groove is calculated based on the given or known radial rotation error data of the grinding wheel spindle and the geometric position relationship between the grinding wheel and the outer ring groove.

[0029] As a preferred solution, in step S4, the specific process is as follows:

[0030] S4.1. The radial runout of the grinding wheel spindle axis in the grinding feed direction can be expressed by the Fourier series, and its polar coordinate form is as follows:

[0031] Where Δr s (θ) is the radial runout distance when the grinding wheel spindle rotates by angle θ, Δr s0 is the average radial runout distance of the grinding wheel spindle, B i is the i-th order radial runout amplitude, and φ is the initial phase angle of the radial runout of the grinding wheel spindle.

[0032] S4.2. In the actual grinding process, due to the radial runout of the grinding wheel spindle, the actual feed rate of the grinding wheel changes with the change of the radial runout. The actual feed rate when considering the radial runout of the spindle is:

[0033] X1(θ)=X+Δr s (θ)

[0034] Where X is the theoretical feed rate.

[0035] As a preferred solution, in step S7, the specific process is as follows:

[0036] Due to the roundness error of the outer ring groove, the outer ring groove profile in the radial plane is a complex curve. The initial profile radius r0(θ) of the outer ring groove before grinding can be expressed by the Fourier series, and its polar coordinate form is as follows:

[0037]

[0038] Where r L is the ideal circle radius; j is the order of roundness error; A j is the jth-order harmonic amplitude on the channel surface; is the initial phase angle of the roundness error.

[0039] When the feed rate X of the forming grinding wheel is given, and the outer ring positioning error and the grinding wheel spindle rotation error are considered, the contour radius r (θ) of the outer ring groove grinding point after grinding can be obtained as follows:

[0040] r(θ)=r0(θ)+X1(θ)+ΔF'(θ)

[0041] Whether grinding occurs at any grinding point on the outer ring groove surface depends on the position after the grinding wheel is fed and the relative position of the outer ring groove grinding point. After the groove is ground (n-1) circles, the radius value of a certain grinding point after the nth circle grinding is determined by the radius value of the (n-1)th circle groove and the grinding wheel feed amount of the nth circle. When r n-1 (θ)≥r L -A j +nX1+ΔF', at this time the grinding wheel and the groove are in a non-contact state, that is, the radius value r after the nth circle of grinding n (θ)=r n-1 (θ); when r n-1 (θ)<r L -A j +nX1+ΔF', the radius value r of the grinding point after the nth round of grinding n (θ)=r L -A j +nX1+ΔF'.

[0042] The beneficial effects of the present invention are:

[0043] Through the outer ring groove grinding roundness prediction method of the present invention, the roundness error of the bearing outer ring groove after grinding can be known or given when the bearing outer ring surface and the radial runout of the grinding wheel spindle are known, thereby predicting the roundness error of the bearing outer ring groove after grinding based on the bearing outer ring surface accuracy and the grinding wheel spindle rotation accuracy, and realizing quantitative simulation of the bearing outer ring groove profile formation process under different grinding process parameters, providing a theoretical basis for bearing outer ring groove grinding and precision control, playing a positive role in the development of high-precision rolling bearing products, and can be used to guide production. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. 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 any creative work.

[0045] Figure 1 Schematic diagram of the electromagnetic centerless grinding system used in this prediction method;

[0046] Figure 2 is a schematic diagram of positioning error;

[0047] Figure 3 Schematic diagram of the center displacement of the bearing outer ring;

[0048] Figure 4 Schematic diagram of the contact between the bearing outer ring and the support;

[0049] Figure 5 This is a schematic diagram of the grinding wheel spindle rotation error motion;

[0050] Figure 6 This is a schematic diagram of the radial runout of the grinding wheel spindle to the left;

[0051] Figure 7 This is a schematic diagram of the radial runout of the grinding wheel spindle to the right;

[0052] Figure 8 Schematic diagram of the outer ring groove of the bearing after grinding. DETAILED DESCRIPTION

[0053] The present invention is described in detail below by way of exemplary embodiments. However, it should be understood that elements, structures, and features in one embodiment may also be beneficially combined in other embodiments without further description.

[0054] It should be noted that, unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning understood by persons of ordinary skill in the art to which the present invention pertains. The terms "one," "an," "the," and similar expressions used in the present patent application specification and claims do not express quantitative limitations but rather denote the presence of at least one. The terms "include" or "comprises" and similar expressions indicate that the elements or objects preceding the term "includes" or "comprising" encompass the elements or objects listed following the term and their equivalents.

[0055] This solution relates to a method for predicting the roundness of the outer ring groove of a ball bearing. It is mainly applicable to the roundness prediction of angular contact ball bearings or deep groove ball bearings during the grinding process. It should be noted that the outer ring groove and the outer ring surface of the bearing in this solution have shape errors, and the grinding wheel spindle has rotation errors. At the same time, the ball bearing outer ring groove grinding roundness prediction method described in the present invention is based on the following settings:

[0056] (1) Ignore the situation where the workpiece is jittered due to uneven force, that is, the outer ring of the workpiece is always positioned by the front and rear supports and the extreme end faces of the magnetic pole during the grinding process.

[0057] (2) Ignore the friction between the workpiece and the extreme end faces of the magnetic poles during the machining process. That is, it is assumed that the rotation of the workpiece is completely driven by the magnetic poles, and the angular interval between the outer ring and the grinding wheel and the fixed support contact point remains unchanged.

[0058] The method for predicting the grinding roundness of the outer ring groove of a ball bearing of the present invention comprises the following specific steps:

[0059] (1) Given bearing parameters, grinding wheel parameters and grinding process parameters; the specific parameters include the outer ring surface profile radius of the bearing, the outer ring groove bottom radius, the outer ring speed, the grinding wheel radius, the grinding wheel speed, the front support angle, the support angle, and the grinding feed rate;

[0060] (2) Setting the total angle of rotation of the outer ring and the angle step of the outer ring rotation;

[0061] (3) Calculate the total positioning error of the j-th grinding point of the outer ring groove; determine the actual outer ring radius and corresponding angle of the contact point of the j-th grinding point of the outer ring groove corresponding to the front support point, determine the actual outer ring radius and corresponding angle of the contact point of the j-th grinding point of the outer ring groove corresponding to the rear support point, and calculate the total positioning error of the j-th grinding point of the outer ring groove according to the feed direction of the grinding wheel and the geometric relationship between the bearing outer ring and the front and rear support blocks;

[0062] (4) Calculate the actual feed of the grinding wheel at the jth grinding point of the outer ring groove when the rotation error of the grinding wheel spindle is taken into account; calculate the actual feed of the grinding wheel at the jth grinding point of the outer ring groove based on the given or known radial rotation error data of the grinding wheel spindle and the geometric position relationship between the grinding wheel and the outer ring groove;

[0063] (5) Calculate the radius of the outer raceway at the jth grinding point after grinding based on (3) and (4);

[0064] (6) Repeat (3)-(5) until the grinding is completed;

[0065] (7) Calculate the roundness value of the outer ring groove using the least squares method.

[0066] In this solution, the principle of the bearing outer ring groove grinding roundness prediction method is as follows:

[0067] First, outer ring positioning error:

[0068] When grinding the outer ring groove of the bearing, the outer circle positioning grinding of the inner hole is usually adopted, such as Figure 1 As shown in the figure, the workpiece is positioned by the outer surface of the outer ring, and a small-diameter grinding wheel is used to machine the groove. Due to the inevitable geometric errors on the outer cylindrical surface of the outer ring, when the outer ring rotates under the conditions of front and rear supports, the outer ring will produce rotational errors, which will affect the groove machining accuracy.

[0069] When the outer ring groove is ground using the positioning method of "supporting the outer ring and grinding the inner ring", the outer ring moves due to the geometric error of the outer surface of the outer ring, thus forming a positioning error, such as Figure 2 As shown in the figure, during the grinding process, when the outer ring is displaced due to positioning error, the grinding amount of the groove also changes. If the outer ring moves to the left, the grinding amount increases, and vice versa, the grinding amount decreases, thus affecting the outer ring groove grinding roundness error.

[0070] (1) When the outer surface of the outer ring contacts the support surface, in special circumstances, when the theoretical contact point and the actual contact point coincide:

[0071] When the protrusion on the outer ring positioning surface is located at the rear support, the protrusion height is represented by ΔR1, and the center of the outer ring moves to O1, such as Figure 3 As shown. At this time, the outer ring center displacement is:

[0072]

[0073] Projecting the outer ring center displacement toward the grinding direction (i.e., the X-axis) yields the positioning error Δx1 of this point at the rear support, namely:

[0074]

[0075] When the protrusion on the outer ring positioning surface is located at the front support, the protrusion height is expressed by ΔR2, and the center of the outer ring moves to O2, such as Figure 3 As shown. At this time, the outer ring center displacement is:

[0076]

[0077] Projecting the outer ring center displacement toward the grinding direction (i.e., the X-axis) yields the positioning error Δx2 of this point at the front support, namely:

[0078]

[0079] From the above calculation, the total positioning error of the outer ring center in the total X direction is:

[0080] ΔF=Δx2-Δx1(5)

[0081] (2) When the outer surface of the outer ring contacts the support surface, generally, due to the existence of geometric errors, the theoretical contact point (corresponding to the position angle β) is not the actual contact point, that is, the theoretical contact point and the actual contact point do not coincide;

[0082] like Figure 4 As shown in the figure, in order to obtain the actual contact point, a search is performed in the area near the theoretical contact point. The angle between the center of the outer ring and the theoretical contact point is ±δ degrees. The point with the largest outer contour radius of the outer ring is found as the actual contact point, and the positioning error is calculated based on the ΔR of this point.

[0083] In order to obtain the actual contact point between the support surface and the outer surface of the outer ring, the outer surface contour radius of the outer ring in the [-δ+β, δ+β] region is discretized into n points, each of which corresponds to a radius value R(θ m ),but:

[0084] θ m =β+mΔθ (6)

[0085]

[0086]

[0087] Calculate the outer contour radius error value of the outer ring corresponding to each point:

[0088] ΔR(θ m )=R(θ m )-R (9)

[0089] Where ΔR(θ m ) is the outer surface contour radius error corresponding to each point in the [-δ+β, δ+β] region, and its value is the difference between the actual radius and the theoretical radius, R is the theoretical radius, θ m It is the angle between the actual contact point between the rear support block and the outer ring surface and the X-axis, in radians, and β is the position angle.

[0090] Then the maximum radius of the outer surface contour of the outer ring in the region is:

[0091]

[0092] The maximum value of the outer surface contour radius error of the outer ring in the area is:

[0093] ΔR(θ m ) max =R(θ m ) max -R (11)

[0094] When the maximum radius error in the rear support block contact point area is ΔR1, the corresponding angle between the actual contact point and the line connecting the outer ring center and the X-axis changes; similarly, when the maximum radius error in the front support block contact point area is ΔR2, the corresponding angle between the actual contact point and the line connecting the outer ring center and the X-axis also changes. Therefore, the corrected rear support positioning error is:

[0095]

[0096] Similarly, the corrected front support positioning error is:

[0097]

[0098] Then the total positioning error of the outer ring center along the X-axis after correction is:

[0099] ΔF′=Δx′2-Δx′1 (14)

[0100] For the values ​​of δ1 and δ2, when they are above the theoretical contact point, they are taken as "-", otherwise they are taken as "+".

[0101] Second, the grinding wheel spindle rotation error

[0102] The grinding wheel spindle system is the core component of the centerless grinder. The rotation error generated in the spindle system is accumulated and transmitted to the grinding wheel at the spindle output end, which has a great impact on the machining accuracy of the workpiece. Due to the existence of journal shape error, spindle bearing assembly error, and bearing hole error in the system, the spindle rotation axis deviates from the ideal rotation axis, thereby causing spindle radial runout, spindle axial movement, and angular swing and other spindle rotation errors, such as Figure 5 shown.

[0103] During the grinding process, the axial, radial, and angular runout errors of the grinding wheel spindle significantly affect the outer ring grinding accuracy. Axial runout of the grinding wheel spindle affects the outer ring groove shape, while radial runout of the grinding wheel spindle affects the groove roundness. Angular runout of the grinding wheel spindle affects both groove shape and roundness. Therefore, this article focuses on the impact of radial runout of the grinding wheel spindle on the roundness of the bearing outer ring groove.

[0104] When the grinding wheel grinds the outer ring groove, the grinding wheel spindle will have radial runout in the feed direction, which will cause the axis line to perform simple harmonic motion along a fixed direction. The outer ring groove shape is determined by the motion trajectory of the grinding point in the grinding feed direction. The radial runout of the grinding wheel spindle axis in the grinding feed direction can be expressed by Fourier series, and its polar coordinate form is as follows:

[0105]

[0106] Where Δr s (θ) is the radial runout distance when the grinding wheel spindle rotates by angle θ; Δr s0 is the average radial runout distance of the spindle; B i is the i-th order radial runout amplitude; φ is the initial phase angle of the radial runout of the grinding wheel spindle.

[0107] In the actual grinding process, due to the existence of radial runout of the grinding wheel spindle, the actual feed rate of the grinding wheel changes with the change of radial runout. The actual feed rate when considering the radial runout of the spindle is:

[0108] X1(θ)=X+Δr s (θ) (16)

[0109] Where X is the theoretical feed rate.

[0110] When Δr s When (θ) is greater than zero, the actual grinding point of the grinding wheel is to the right of the ideal grinding point, and the actual grinding amount is greater than the theoretical grinding amount. Figure 6 As shown in , when its value is less than zero, that is, X1(θ)<X, the actual grinding point of the grinding wheel is on the left side of the ideal grinding point, and the actual grinding amount is less than the theoretical grinding amount, as shown in Figure 7 shown.

[0111] To accurately calculate the actual grinding amount at each point on the groove surface, the grinding wheel's rotational error and the bearing outer ring groove are discretized into several points. Due to the relative sliding between the contact points of the grinding wheel and the outer ring, the grinding wheel will grind a single point on the outer ring groove at multiple points. The actual grinding amount at that point on the groove depends on the maximum feed rate among the multiple grinding points on the grinding wheel. Therefore, the actual grinding amount at that point on the groove is equal to the maximum feed rate among the multiple grinding points on the grinding wheel.

[0112] Third, the outer ring groove profile radius of the bearing

[0113] Due to the roundness error of the outer ring groove, the outer ring groove profile in the radial plane is a complex curve. The initial profile radius r0(θ) of the outer ring groove before grinding can be expressed by the Fourier series, and its polar coordinate form is as follows:

[0114]

[0115] Where r L is the ideal circle radius; j is the order of roundness error; A j is the jth-order harmonic amplitude on the channel surface; is the initial phase angle of the roundness error.

[0116] When the feed rate X of the forming grinding wheel is given, and the outer ring positioning error and the grinding wheel spindle rotation error are considered, the contour radius r (θ) of the outer ring groove grinding point after grinding can be obtained as follows:

[0117] r(θ)=r0(θ)+X1(θ)+ΔF'(θ) (18)

[0118] Whether grinding occurs at any grinding point on the outer ring groove surface depends on the position after the grinding wheel is fed and the relative position of the outer ring groove grinding point. After the groove is ground (n-1) circles, the radius value of a certain grinding point after the nth circle grinding is determined by the radius value of the (n-1)th circle groove and the grinding wheel feed amount of the nth circle; when r n-1 (θ)≥r L -A j +nX1+ΔF', at this time the grinding wheel and the groove are in a non-contact state, that is, the radius value r after the nth circle of grinding n (θ)=r n-1 (θ); when r n-1 (θ)<r L -A j +nX1+ΔF', the radius value r of the grinding point after the nth round of grinding n (θ)=r L -A j +nX1+ΔF'.

[0119] Example 1:

[0120] This prediction method can obtain the groove profile and roundness of the bearing outer ring groove after grinding. The following example illustrates this:

[0121] Given the bearing parameters, grinding wheel parameters and grinding process parameters, the ideal radius r of the bearing outer ring groove is L is 30mm, the channel roundness error amplitude A j is 10 μm, the outer ring groove profile order j = 3; the ideal radius of the outer surface of the bearing outer ring r w The outer surface profile error amplitude is 35mm, and the outer ring outer surface profile error amplitude is B j is 2μm, the outer surface profile order of the outer ring is j=3; the outer ring speed of the bearing is n g The speed is 390r / min, the front support angle α is 15°, the support angle β is 120°; the grinding wheel radius is 15mm, and the average radial runout distance Δr of the grinding wheel spindle is s0 The radial runout amplitude of the grinding wheel spindle is 0.2μm.i is 0.3 μm, radial runout order j=3, grinding wheel speed n s The grinding wheel feed rate is 1440 r / min, the grinding wheel feed rate is X = 50 mm, and the angle step length Δθ of the bearing outer ring rotation is set to 2π / 1024. The groove profile and roundness value of the bearing outer ring groove after grinding are simulated and calculated. Using this prediction method, the implementation steps are as follows:

[0122] First, according to this prediction method

[0123] Step 1: Give bearing parameters, grinding wheel parameters and grinding process parameters; bearing outer ring speed n g is 390r / min, the front support angle α is 15°, the support angle β is 120°, the grinding wheel radius is 15mm, and the grinding wheel speed n s is 1440r / min, grinding wheel feed X=50mm, the speed ratio of outer ring to groove is Set the angular step Δθ of the bearing outer ring rotation to 2π / 1024; the polar coordinate equation of the outer surface profile of the bearing outer ring is: w (θ)=r w +0.002cos(3θ), polar coordinate equation of outer raceway profile: r L (θ)=r L +0.01cos(3θ); Polar coordinate equation of radial runout of grinding wheel spindle: Δr s (θ)=Δr s0 +0.0003cos(3θ);

[0124] Step 2: Set the outer ring rotation angle range to 360 degrees and the rotation step length to 2π / 1024. First, calculate the radius value of the first grinding point of the outer ring groove after grinding.

[0125] Step 3: Calculate the total positioning error of the first grinding point of the outer ring groove; Based on the above parameters, determine the contact point between the front support block and the outer ring of the bearing, the angle between the contact point and the X-axis, and the radius error value of the outer surface of the outer ring at the contact point; Determine the contact point between the rear support block and the outer ring of the bearing, the angle between the contact point and the X-axis, and the radius error value of the outer surface of the outer ring at the contact point; Based on formula (12), the positioning error of the outer ring of the bearing on the rear support is calculated to be -0.5049μm, based on formula (13), the positioning error of the outer ring of the bearing on the front support is calculated to be 0.99μm, based on formula (14), the total positioning error of the first grinding point is calculated to be 1.4949μm;

[0126] Step 4: Calculate the actual grinding wheel feed rate at the first grinding point on the outer ring groove, taking into account the spindle rotation error. The actual grinding amount at this point on the groove depends on the maximum feed rate among multiple grinding points on the grinding wheel. Therefore, the actual grinding amount at this point on the groove is equal to the maximum feed rate among multiple grinding points on the grinding wheel. For the first grinding point on the outer ring groove, the number of grinding points on the grinding wheel that grind the outer ring groove depends on the speed ratio η. Based on the grinding process parameters in step 1, η = 3.7, and the maximum grinding wheel feed rate is 50.5μm.

[0127] Step 5: Calculate the radius of the first grinding point of the groove after grinding. Based on steps 3 and 4, the radius after grinding can be calculated, that is, r1(0)=r0(0)+X1(0)+ΔF'(0), r1(0)=30.04199480mm;

[0128] Step 6: Repeat steps 3, 4, and 5 until the grinding is completed;

[0129] Step 7: Use MATLAB to draw the contours of all the groove radius values ​​after grinding and calculate their roundness values ​​using the least squares method. The groove contour after grinding is shown in Figure 8, and its roundness value is 3.7980μm.

[0130] Parts not described in detail in this embodiment are prior art.

[0131] It should be noted that although the present invention has been described with reference to 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 modifications to the present invention, and such changes and modifications shall fall within the scope of protection of the appended claims and their equivalents.

Claims

1. A method for predicting the grinding roundness of a ball bearing outer ring raceway, characterized by: Here are the steps: S1. Obtaining parameters of the outer ring of the bearing being processed, grinding wheel parameters, and grinding process parameters; S2. Setting the total rotation angle of the bearing outer ring and the angle step of the outer ring rotation; S3. Based on the parameters determined in the above steps, determine the actual outer ring radius and corresponding angle of the contact point of the j-th grinding point of the outer ring groove with the front support point, determine the actual outer ring radius and corresponding angle of the contact point of the j-th grinding point of the outer ring groove with the rear support point, and calculate the total positioning error of the j-th grinding point of the outer ring groove according to the feed direction of the grinding wheel and the geometric relationship between the bearing outer ring and the front and rear support blocks; S4. Calculate the actual grinding wheel feed rate at the jth grinding point of the outer ring groove when considering the rotation error of the grinding wheel spindle; S5. Calculate the radius of the j-th grinding point of the outer raceway after grinding according to steps S3 and S4; S6, repeat steps S3-S5 until the grinding is completed; S7. Calculate the roundness value of the outer raceway using the least squares method.

2. The method for predicting the grinding roundness of the outer ring raceway of a ball bearing according to claim 1, characterized in that: In step S1, the parameters of the processed bearing, grinding wheel parameters and grinding process parameters are specifically the bearing outer ring surface profile radius, outer ring groove bottom radius, outer ring speed, grinding wheel radius, grinding wheel speed, front support angle, support angle and grinding feed rate.

3. The method for predicting the grinding roundness of the outer ring raceway of a ball bearing according to claim 1, characterized in that: In step S3, when the outer surface of the outer ring contacts the support surface and the theoretical contact point and the actual contact point do not coincide, the specific steps for determining the total positioning error are as follows: S3.

1. In order to obtain the actual contact point between the support surface and the outer surface of the outer ring, the outer surface contour radius of the outer ring in the region [-δ+β, δ+β] is discretized into n points, each of which corresponds to a radius value R(θ m ), through the formula ΔR(θ m )=R(θ m )-R calculates the outer contour radius error value of the outer ring corresponding to each point; Among them, ΔR(θ m ) is the outer surface profile radius error corresponding to each point in the [-δ+β, δ+β] region, and its value is the difference between the actual radius and the theoretical radius, R is the theoretical radius, θ m is the angle between the actual contact point between the rear support block and the outer ring surface and the X-axis, and β is the position angle; S3.

2. Obtain the maximum outer surface radius of the outer ring within the region using the following formula: The maximum value of the outer ring outer surface profile radius error within the area is obtained. When the maximum radius error in the rear support block contact point area is ΔR1, the corresponding angle between the actual contact point and the line connecting the outer ring center and the X-axis changes. Similarly, when the maximum radius error in the front support block contact point area is ΔR2, the corresponding angle between the actual contact point and the line connecting the outer ring center and the X-axis also changes. S3.

3. Based on the above, according to the formula Get the corrected rear support positioning error; S3.4, according to the formula Get the corrected front support positioning error; S3.5, then the total positioning error of the outer ring center along the X-axis after correction is: ΔF' = Δx'2 - Δx'1.

4. The method for predicting the grinding roundness of the outer ring raceway of a ball bearing according to claim 1, characterized in that: In step S3, when the outer surface of the outer ring contacts the support surface and the theoretical contact point coincides with the actual contact point, the specific steps for determining the total positioning error are as follows: By formula Obtain the positioning error Δx1 of the bearing outer ring on the rear support; By formula Obtain the positioning error Δx2 of the bearing outer ring on the front support; From the above calculation, the total positioning error of the outer ring center in the total X direction is: ΔF=Δx2-Δx1.

5. The method for predicting the grinding roundness of the outer ring raceway of a ball bearing according to claim 1, characterized in that: In step S4, the actual feed amount of the grinding wheel at the j-th grinding point of the outer ring groove is calculated according to the given or known radial rotation error data of the grinding wheel spindle and the geometric position relationship between the grinding wheel and the outer ring groove.

6. The method for predicting the grinding roundness of the outer ring raceway of a ball bearing according to claim 5, characterized in that: In step S4, the specific process is as follows: S4.

1. The radial runout of the grinding wheel spindle axis in the grinding feed direction can be expressed by the Fourier series, and its polar coordinate form is as follows: Where Δr s (θ) is the radial runout distance when the grinding wheel spindle rotates by angle θ, Δr s0 is the average radial runout distance of the spindle, B i is the i-th order radial runout amplitude, and φ is the initial phase angle of the radial runout of the grinding wheel spindle. S4.

2. In the actual grinding process, due to the radial runout of the grinding wheel spindle, the actual feed rate of the grinding wheel changes with the change of the radial runout. The actual feed rate when considering the radial runout of the spindle is: X1(θ)=X+Δr s (i) Where X is the theoretical feed rate.

7. The method for predicting the grinding roundness of the outer ring raceway of a ball bearing according to claim 1, characterized in that: In step S7, the specific process is as follows: Due to the roundness error of the outer ring groove, the outer ring groove profile in the radial plane is a complex curve. The initial profile radius r0(θ) of the outer ring groove before grinding can be expressed by the Fourier series, and its polar coordinate form is as follows: Where r L is the ideal circle radius; j is the order of roundness error; A j is the jth-order harmonic amplitude on the channel surface; is the initial phase angle of the roundness error. When the feed rate X of the forming grinding wheel is given, and the outer ring positioning error and the grinding wheel spindle rotation error are considered, the contour radius r (θ) of the outer ring groove grinding point after grinding can be obtained as follows: r(θ)=r0(θ)+X1(θ)+ΔF'(θ) Whether grinding occurs at any grinding point on the outer ring groove surface depends on the position after the grinding wheel is fed and the relative position of the outer ring groove grinding point. After the groove is ground (n-1) circles, the radius value of a certain grinding point after the nth circle grinding is determined by the radius value of the (n-1)th circle groove and the grinding wheel feed amount of the nth circle. When r n-1 (θ)≥r L -A j +nX1+ΔF', at this time the grinding wheel and the groove are in a non-contact state, that is, the radius value r after the nth circle of grinding n (θ)=r n-1 (θ); when r n-1 (θ)<r L -A j +nX1+ΔF', the radius value r of the grinding point after the nth round of grinding n (θ)=r L -A j +nX1+ΔF'.

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