Accurate calculation method for rotation accuracy of angular contact ball bearing

Abstract

The application discloses a kind of angular contact ball bearing rotation precision accurate calculation method, comprising the following steps: S1, with O as the center of bearing outer ring outer diameter surface, O1 is bearing outer ring groove bottom, O2 is the contact point of ball and bearing outer ring, O3 is the contact point of ball and bearing inner ring, O4 is bearing inner ring groove bottom, O5 is the center of inner diameter surface;O Dw Ball center, m is bearing inner ring channel center, n is bearing outer ring channel center, alpha is contact angle, establish plane rectangular coordinate system at O.S2, measure bearing outer diameter D and steel ball diameter Dw, in circumferential direction, multiple uniform distribution measure bearing inner diameter d, inner ring groove bottom diameter d i , outer ring groove bottom diameter d e , inner ring groove curvature radius r i , outer ring groove curvature radius r e , the axial distance alpha between reference surface A and O1 point e And the axial distance alpha between reference surface B and O4 point i .S3, calculate radial rotation accuracy.S4, calculate axial rotation accuracy.The application can accurately calculate the rotation precision of angular contact ball bearing.

Description

Technical Field

[0001] This invention relates to the field of bearing analysis and design technology, specifically to a method for accurately calculating the rotational accuracy of angular contact ball bearings. Background Technology

[0002] Angular contact ball bearings (ACBBs) are widely used in various mechanical equipment and can withstand combined loads of axial force, radial force, and torque. Rotational accuracy is a crucial indicator of bearing manufacturing quality, including axial and radial rotational accuracy. The rotational accuracy of complete bearing sets is tested according to standard GB / T307.2-2005, measured by runout. For radial runout of the inner ring, the outer ring is fixed, the probe is positioned at O5, the inner ring rotates one revolution, the indicator reading is read, and the change is calculated. For axial runout, the outer ring is fixed, the probe is positioned at the inner ring reference plane B, the inner ring rotates one revolution, and the indicator reading is read. The above rotational accuracy tests must be performed on the entire bearing set. If the technical requirements cannot be met, the set must be disassembled and refitted, which not only reduces production efficiency but may also damage the precision of the parts. Furthermore, existing rotational accuracy testing methods do not consider ring positioning and reference planes, making it difficult to calculate the rotational accuracy of the complete bearing set based on the dimensions of the rings and balls. Summary of the Invention

[0003] The purpose of this invention is to solve the problems existing in the prior art and provide a method for accurately calculating the rotational accuracy of angular contact ball bearings.

[0004] To address the shortcomings of the aforementioned technical problems, the present invention provides a method for accurately calculating the rotational accuracy of angular contact ball bearings, comprising the following steps:

[0005] S1, Geometric Relationship Modeling

[0006] With O as the center of the outer diameter surface of the bearing outer ring, O1 as the bottom of the bearing outer ring groove, O2 as the contact point between the ball and the bearing outer ring, O3 as the contact point between the ball and the bearing inner ring, O4 as the bottom of the bearing inner ring groove, and O5 as the center of the inner diameter surface; Dw Let O be the center of the ball, m be the center of the inner ring groove of the bearing, n be the center of the outer ring groove of the bearing, and α be the contact angle. Establish a plane rectangular coordinate system at point O.

[0007] S2, Parameter Measurement

[0008] Fix the outer ring of the bearing and measure the outer diameter D of the bearing and the diameter D of the steel balls. w In the circumferential direction, the bearing inner diameter d and the inner ring groove bottom diameter d were measured multiple times in an evenly distributed manner. i d, the diameter of the outer groove bottom e Inner groove curvature radius r i Outer groove curvature radius r e The axial distance α between the outer ring machining reference surface A and point O1 eThe axial distance α between the outer ring machining reference surface B and point O4 i denoted as d(Z), d i (Z), d e (Z), r i (Z), r e (Z), α e (Z) and α i (Z), where Z = 1, 2, 3...n;

[0009] S3, Calculate radial rotation accuracy Substitute the multiple sets of measured values ​​from step S2 into formula (1) for iterative calculation, and calculate the radial runout value K using formula (2). ia

[0010] K = OO 5y =OO1+O1h+O2O3cosα+O4k+O4O5(1)

[0011] K ia =max(K)-min(K)(2)

[0012] in:

[0013] OO1 = 0.5(Dd) e )

[0014]

[0015]

[0016] O2O3 = D w

[0017]

[0018]

[0019] O4O5=0.5(d i -d);

[0020] S4. Calculate axial rotation accuracy Substitute the multiple sets of measured values ​​from step S2 into formula (3) for iterative calculation, and calculate the radial runout value K using formula (4). ia .

[0021] S = a i +a e -mnsinα(3)

[0022] S ia =max(S)-min(S)(4)

[0023] in:

[0024] mn = r i +r e -D w .

[0025] As a further optimization of the method for accurately calculating the rotational accuracy of an angular contact ball bearing according to the present invention: in step S2, the bearing inner diameter d and the inner ring groove bottom diameter d are measured 9 times evenly in the circumferential direction. i d, the diameter of the outer groove bottom e Inner groove curvature radius r i Outer groove curvature radius r e The axial distance α between datum plane A and point O1 e The axial distance α between reference plane B and point O4 i Nine sets of data were obtained.

[0026] This invention can accurately calculate the rotational accuracy of angular contact ball bearings. Attached Figure Description

[0027] Figure 1 This is a diagram showing the contact state during bearing inspection.

[0028] Figure 2 for Figure 1 A diagram showing the relationship between line segments connecting all points in the diagram;

[0029] Figure 3 This is a geometric diagram of the angular contact ball bearing during measurement. Detailed Implementation

[0030] To better understand the present invention, the following embodiments further illustrate the content of the present invention, but the content of the present invention is not limited to the following embodiments.

[0031] A method for accurately calculating the rotational accuracy of an angular contact ball bearing includes the following steps:

[0032] S1, Geometric Relationship Modeling

[0033] like Figure 1 As shown, with O as the center of the outer diameter surface of the bearing outer ring, O1 as the bottom of the bearing outer ring groove, O2 as the contact point between the ball and the bearing outer ring, O3 as the contact point between the ball and the bearing inner ring, O4 as the bottom of the bearing inner ring groove, and O5 as the center of the inner diameter surface; O Dw Let O be the center of the ball, m be the center of the inner ring groove of the bearing, n be the center of the outer ring groove of the bearing, and α be the contact angle. Establish a plane rectangular coordinate system at point O. Figure 1 The relationship between the line segments connecting the points in the middle is as follows: Figure 2 As shown.

[0034] The change in radial runout at point O5 is the amount of variation in the y-direction between O5 and O. Therefore, based on geometric relationships, the runout value can be determined by the length of each line segment.

[0035] OO1 = 0.5(Dd) e )

[0036] Since nO1=nO2=r e

[0037] Therefore,

[0038] O2O3 = D w

[0039] Similarly, O1O2, O3O4 is...

[0040]

[0041] O4O5=0.5(d i -d)

[0042] O2h and O3k are perpendicular to the y-axis, therefore

[0043]

[0044]

[0045] but

[0046] K = OO 5y =OO1+O1h+O2O3cosα+O4k+O4O5(1)

[0047] Radial runout value K ia for

[0048] K ia =max(K)-min(K)(2)

[0049] Axial runout is the x-axis (axial) distance S between datum plane A and datum plane B. The axial distance between plane A and point O1 is called the groove position α. e The axial distance between surface B and point O4 is called the trench position α. i ,therefore:

[0050] S = a i +a e -mnsinα(3)

[0051] in

[0052] mn = r i +r e -D w

[0053] Axial runout value S ia for

[0054] S ia =max(S)-min(S)(4)

[0055] S2, Parameter Measurement

[0056] Fixed bearing outer ring, D w The change is very small and its impact on rotational accuracy is negligible. The bearing outer diameter D and the steel ball diameter D are measured. w In the circumferential direction, the bearing inner diameter d and the inner ring groove bottom diameter d were measured multiple times in an evenly distributed manner. i d, the diameter of the outer groove bottom e Inner groove curvature radius r i Outer groove curvature radius r e The axial distance α between datum plane A and point O1 e The axial distance α between reference plane B and point O4 i denoted as d(Z), d i (Z), d e (Z), r i (Z), r e (Z), α e (Z) and α i (Z), where Z = 1, 2, 3...n, and Z is the number of measurements;

[0057] S3, Calculate radial rotation accuracy

[0058] Substitute the multiple sets of measured values ​​from step S2 into formula (1) for iterative calculation, and calculate the radial runout value K using formula (2). ia ;

[0059] S4. Calculate axial rotation accuracy

[0060] Substitute the multiple sets of measured values ​​from step S2 into formula (3) for iterative calculation, and calculate the radial runout value K using formula (4). ia .

[0061] Taking a 7006 bearing as an example, calculate the rotational accuracy. (Except for D and D') w In addition, the design parameters were measured nine times evenly along the circumference. The measurement results are as follows (all units are mm):

[0062] D = 55;

[0063] D w =5.556;

[0064] d=[29.998; 29.998; 29.997; 29.997; 29.997; 29.996; 29.996; 29.996; 29.998];

[0065] D e = [48.071; 48.071; 48.071; 48.071; 48.072; 48.073; 48.073; 48.073; 48.073];

[0066] R i = [3.118; 3.117; 3.117; 3.117; 3.117; 3.116; 3.116; 3.118];

[0067] R e = [2.952; 2.952; 2.954; 2.954; 2.954; 2.953; 2.953; 2.952;] 2.952];

[0068] d i = [36.911; 36.911; 36.913; 36.913; 36.911; 36.911; 36.913; 36.913];

[0069] a i = [6.502; 6.501; 6.501; 6.503; 6.501; 6.499; 6.498; 6.5; 6.5];

[0070] a e = [6.642; 6.642; 6.644; 6.641; 6.64; 6.639; 6.639; 6.64; 6.641];

[0071] Calculation results:

[0072] K ia =0.001.

[0073] S ia =0.017.

[0074] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims, which do not affect the essence of the present invention.

Claims

1. A method for accurately calculating the rotational accuracy of an angular contact ball bearing, characterized in that, Includes the following steps: S1, Geometric Relationship Modeling With O as the center of the outer diameter surface of the bearing outer ring, O1 as the bottom of the bearing outer ring groove, O2 as the contact point between the ball and the bearing outer ring, O3 as the contact point between the ball and the bearing inner ring, O4 as the bottom of the bearing inner ring groove, and O5 as the center of the inner diameter surface; Dw Let O be the center of the ball, m be the center of the inner ring groove of the bearing, n be the center of the outer ring groove of the bearing, and α be the contact angle. Establish a plane rectangular coordinate system at point O. S2, Parameter Measurement Fix the outer ring of the bearing and measure the outer diameter D of the bearing and the diameter D of the steel balls. w In the circumferential direction, the bearing inner diameter d and the inner ring groove bottom diameter d were measured multiple times in an evenly distributed manner. i d, the diameter of the outer groove bottom e Inner groove curvature radius r i Outer groove curvature radius r e The axial distance α between the outer ring machining reference surface A and point O1 e The axial distance α between the inner ring machining reference surface B and point O4 i denoted as d(Z), d i (Z), d e (Z), r i (Z), r e (Z), α e (Z) and α i (Z), where Z = 1, 2, 3...n'; S3, Calculate radial rotation accuracy Substitute the multiple sets of measured values ​​from step S2 into formula (1) for iterative calculation, and calculate the radial runout value K using formula (2). ia ; （1） （2） This represents the change in the y-direction between O and O5; in: ； S4. Calculate axial rotation accuracy Substitute the multiple sets of measured values ​​from step S2 into formula (3) for iterative calculation, and calculate the axial runout value S using formula (4). ia （3） （4） in: 。 2. The method for accurately calculating the rotational accuracy of an angular contact ball bearing as described in claim 1, characterized in that, In step S2, the bearing inner diameter d and the inner ring groove bottom diameter d are measured nine times evenly in the circumferential direction. i d, the diameter of the outer groove bottom e Inner groove curvature radius r i Outer groove curvature radius r e The axial distance α between datum plane A and point O1 e The axial distance α between reference plane B and point O4 i Nine sets of data were obtained.

Images