Angular contact ball bearing rotation precision accurate prediction method

Abstract

The invention discloses an angular contact ball bearing rotation precision accurate prediction method, and belongs to the technical field of angular contact ball bearing rotation precision prediction methods, and the method comprises the steps: 1, analyzing error components and influence factors, i.e., a radial form and position error # imgabs0 # and an axial form and position error # imgabs1 # of an outer ring, and an axial form and position error # imgabs2 # and an axial form and position error # imgabs1 # of an outer ring; the radial form and position error # imgabs2 # and the axial form and position error # imgabs3 # of the inner ring, the roundness error # imgabs4 # of the outer ring and the roundness error # imgabs5 # of the inner ring, and the surface topography error # imgabs6 # of the ball; step 2, obtaining a radial clearance # imgabs7 # and an axial clearance # imgabs8 # according to the geometrical relationship of the bearing, and respectively calculating the influence coefficients of the channel roundness error on the axial run-out and the radial run-out; and 3, calculating the radial and axial rotation precision of the inner and outer rings of the bearing according to the roundness, the form and position error and the influence coefficient obtained in the step 2. On the basis of the error superposition principle, an angular contact ball bearing rotation precision error prediction and optimization model is established by considering the equipment machining capacity, and precise prediction and optimization control of the bearing rotation precision are carried out through the model.

Description

Technical Field

[0001] The invention relates to the technical field of bearing design and manufacturing, and in particular to a method for accurately predicting the rotation accuracy of an angular contact ball bearing. Background Art

[0002] As one of the key basic components, bearings play a vital role in wind power, high-speed rail, aerospace and other equipment. As the key rotating support in the equipment, the precision of rolling bearings directly determines the processing accuracy of the equipment. Precision is one of the performance properties of bearings and an important parameter in the bearing manufacturing process. It directly determines the performance, life and reliability of bearings. Choosing the right precision grade is crucial to ensure the normal operation and efficient performance of the equipment. In particular, rotational accuracy is the degree of accuracy that the bearing can achieve during operation. It reflects the stability and precision of the bearing when it is under load and rotating; There is little in-depth research on the maximum rotational accuracy error of angular contact ball bearings under measurement conditions and its control methods, as well as the variation law of accuracy error under working conditions and its control methods. Currently, the rotational accuracy of bearings is estimated only by roundness error, and the influencing factors are not fully considered, nor is the equipment processing capability. Moreover, the method of improving the processing accuracy of bearing components and thus the accuracy of bearings by investing a large amount of money is not applicable to mass production. Summary of the invention

[0003] To solve the above problems, the present invention provides a method for accurately predicting the rotation accuracy of angular contact ball bearings. Based on the error superposition principle, the bearing rotation accuracy is estimated by roundness error, form and position error, etc. The influencing factors are considered more comprehensively to improve the accuracy of the rotation accuracy prediction.

[0004] The present invention is achieved through the following technical solutions: The present invention provides a method for accurately predicting the rotation accuracy of an angular contact ball bearing, comprising the following steps: Step 1: Analyze the error components and influencing factors. The error components and influencing factors are the radial shape and position errors of the outer ring. and axial position error , radial shape and position error of the inner ring and axial position error , roundness error of outer ring And the roundness error of the inner ring , the surface topography error of the ball ; Step 2: Get radial clearance based on bearing geometry and axial clearance The roundness error has a bidirectional effect on the radial direction and a unidirectional effect on the axial direction. The influence coefficients of the groove roundness error on the axial runout and radial runout are calculated respectively. Step 3: Calculate the radial and axial rotation accuracy of the inner and outer rings of the bearing based on the roundness, form and position errors and the influence coefficient obtained in step 2.

[0005] Preferably, the components and influencing factors of the bearing rotation accuracy error in step 1 can be expressed as: Kia ( , , , ) Sia ( , , , ) Kea ( , , , ) Sea ( , , , ) ; in The radial runout of the inner ring of the bearing refers to the difference between the maximum and minimum radial distances of the inner hole surface at different angular positions of the inner ring relative to a fixed point on the outer ring. The axial runout of the inner ring of the bearing refers to the difference between the maximum and minimum axial distances between the inner ring reference end face and a fixed point on the outer ring at different angular positions of the inner ring at a radial distance from the inner ring axis equal to half the inner ring raceway contact diameter; It is the radial runout of the outer ring of the bearing; It is the axial runout of the bearing outer ring.

[0006] Preferably, in step 2, according to the bearing geometric relationship, it can be obtained that: ; in is the bearing outer ring groove diameter; is the inner raceway diameter; is the ball diameter; is the radius of curvature of the inner raceway; is the radius of curvature of the outer raceway; enter , , , , , thereby calculating the influence coefficient of the groove roundness error on the axial runout and radial runout.

[0007] Preferably, the influence coefficient of the groove roundness error on the radial runout in step 2 is is 1; The influence coefficient of roundness error on axial runout is: .

[0008] Preferably, in step 3, the numerical calculation formulas for the radial and axial rotation accuracy of the inner ring of the bearing are respectively: ; The numerical calculation formulas for the radial and axial rotation accuracy of the bearing outer ring are: .

[0009] Preferably, the method further comprises step 4 of optimizing and controlling the rotation accuracy, specifically: According to the known bearing rotation accuracy requirements Kia0, Sia0, Kea0, Sea0 and the initial selection of the optimization model , , , , , , under the premise of satisfying the process capability index Cp ≥ 1 of the equipment processing capacity, iterative optimization matching is repeated, and the optimal deviation group is selected. During the production process, the optimal deviation group is installed to produce finished bearings that meet the known rotation accuracy requirements.

[0010] Preferably, the optimization model formula is: .

[0011] Preferably, the method further includes step 5, in which, under the premise of satisfying the process capability index Cp≥1 for the equipment processing capability, the optimization matching is repeatedly iterated. If the index requirement is still not met, different contact angles are selected for optimization.

[0012] Preferably, the specific method for selecting different contact angles for optimization is: recalculate the influence coefficient of the groove roundness error on the axial runout and radial runout, where the input bearing outer ring groove diameter is The value is calculated based on the optimized contact angle, and the other parameters and steps remain unchanged until the finished product rotation accuracy is optimized to meet the target accuracy.

[0013] The beneficial effects of the present invention are: (1) The present invention estimates the bearing rotation accuracy by roundness error, form and position error, etc., and considers the influencing factors more comprehensively; (2) The present invention also takes into account the processing capacity of the equipment and establishes a prediction and optimization model for the rotation accuracy error of the angular contact ball bearing, so that the rotation accuracy of the angular contact ball bearing can be precisely controlled economically and efficiently; (3) The present invention can also determine the appropriate contact angle according to the rotation accuracy index requirements of the host equipment for the matching bearing. This rotation accuracy prediction and optimization model can meet actual production needs economically and efficiently. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 (a) and (b) are schematic diagrams showing the influence of radial and axial runout of roundness error, respectively; Figure 2 This is the flow chart of this application; Figure 3 (a) and (b) are schematic diagrams of measuring the radial runout and axial runout of the inner ring during the rotation accuracy measurement of the angular contact ball bearing, respectively; Figure 4 (a) and (b) are the top view and front view of the bearing inner ring wall thickness error measurement respectively; Figure 5 (a) and (b) are the top view and front view of the measurement of the parallelism error between the inner ring groove and the end face of the bearing, respectively. DETAILED DESCRIPTION

[0015] In order to make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the technical solution in the embodiments of the present invention will be clearly and completely described below according to the accompanying drawings.

[0016] Example 1 The present invention discloses a method for accurately predicting the rotation accuracy of an angular contact ball bearing. Firstly, the rotation accuracy measurement principle, the bearing inner ring wall thickness error measurement principle, the bearing inner ring groove parallelism error measurement principle, etc. are studied. Figures 3-5 ,in Figure 4 (b), 5 (b) where h is the pointer height during measurement; at the same time, the rotation accuracy and its error components and influencing factors are analyzed, such as Figure 1 This is a schematic diagram of the effect of roundness error on radial and axial runout, where Figure 1 (b) a is the bearing contact angle; secondly, calculate the influence coefficient of each factor error on the axial and radial runout; then, consider the equipment processing capability to establish a model to optimize the matching of each error to meet the index requirements; finally, form an operation process, such as Figure 2 As shown, the following functions can be completed according to the process: Step 1: Analyze the error components and influencing factors. The error components and influencing factors are the radial shape and position errors of the outer ring. and axial position error , radial shape and position error of the inner ring and axial position error , roundness error of outer ring And the roundness error of the inner ring , the surface topography error of the ball ; During implementation, select the outer ring and inner ring of the bearing, compile the corresponding serial numbers, and use high-precision measuring instruments to measure various parameters of the inner and outer rings; The components and influencing factors of bearing rotation accuracy error can be expressed as: Kia ( , , , ) Sia ( , , , ) Kea ( , , , ) Sea ( , , , ) ; in The radial runout of the inner ring of the bearing refers to the difference between the maximum and minimum radial distances of the inner hole surface at different angular positions of the inner ring relative to a fixed point on the outer ring. The axial runout of the inner ring of the bearing refers to the difference between the maximum and minimum axial distances between the inner ring reference end face and a fixed point on the outer ring at different angular positions of the inner ring at a radial distance from the inner ring axis equal to half the inner ring raceway contact diameter; It is the radial runout of the outer ring of the bearing; It is the axial runout of the bearing outer ring.

[0017] Secondly, since the roundness error of the inner and outer rings is very small, it can be approximately considered that the influence of the small size change of the inner and outer ring grooves at the contact point on the bearing rotation accuracy. At the contact point O, there is a roundness deviation , which can be considered as the transient runout of radial clearance and axial clearance caused by slight changes in the groove size.

[0018] Step 2: The radial clearance can be obtained based on the bearing geometry and axial clearance : ; in is the bearing outer ring groove diameter; is the inner raceway diameter; is the ball diameter; is the radius of curvature of the inner raceway; is the radius of curvature of the outer raceway; Since the groove roundness error only affects the radial and axial directions of the bearing, it is assumed that , , Keeping it unchanged, taking partial derivative of the formula, we can get the outer ring groove diameter of the bearing , Inner raceway diameter The transient value is the groove roundness error. The influence coefficient formula of the groove roundness error on the radial clearance and axial clearance is: Therefore, the influence coefficient of the groove roundness error on the radial runout can be obtained: is 1, that is It should be emphasized that due to the existence of measurement pressure, the roundness deviation , The influence on the radial direction is bidirectional, but the influence on the axial direction is unidirectional. Therefore, the calculation formula for the influence coefficient of roundness error on axial runout is: Step 3: Calculate the radial and axial rotation accuracy of the inner and outer rings of the bearing based on the roundness, form and position errors and the influence coefficient obtained in step 2.

[0019] Combined with actual production, due to the high precision of bearing balls, the influence of surface topography error on rotation accuracy can be ignored.

[0020] The numerical calculation formulas for the radial and axial rotation accuracy of the bearing inner ring are: (1) (2) The numerical calculation formulas for the radial and axial rotation accuracy of the bearing outer ring are: (3) (4) Formulas (1)-(4) can be used to obtain the radial and axial runout model results of the inner and outer rings of the bearing, that is, the predicted value of the bearing's rotational accuracy.

[0021] Example 2 The difference from Example 1 is that: it also includes step 4, optimizing the rotation accuracy, and optimizing the matching of various errors according to the model to meet the index requirements. At this time, the equipment processing capability should be considered, and the equipment processing capability is represented by the process capability index Cp; as shown in Table 1: Table 1 Process capability index evaluation grading table The core of the bearing rotation accuracy optimization model is to achieve the highest possible Under the condition of satisfying the smallest possible deviation range (or meeting the target value), the rotation accuracy of the angular contact ball bearing can be precisely controlled economically and efficiently, specifically: According to the known bearing rotation accuracy requirements Kia0, Sia0, Kea0, Sea0 and the initial selection of the optimization model , , , , , , under the premise of satisfying the process capability index Cp ≥ 1 of the equipment processing capacity, iterative optimization matching is repeated, and the optimal deviation group is selected. During the production process, the optimal deviation group is installed to produce finished bearings that meet the known rotation accuracy requirements.

[0022] The optimization model formula is: (5).

[0023] Example 3 The difference from Example 2 is that: it also includes step 5, when the process capability index Cp≥1 of the equipment processing capability is satisfied, the optimization matching is repeatedly iterated. If the index requirement is still not met, different contact angles are selected for optimization.

[0024] The specific method for selecting different contact angles for optimization is: recalculate the influence coefficient of the groove roundness error on the axial runout and radial runout, where the input bearing outer ring groove diameter The value is calculated based on the optimized contact angle, and the other parameters and steps remain unchanged until the finished product rotation accuracy is optimized to meet the target accuracy.

[0025] Different contact angles can be selected for optimization. For example, when the contact angle is increased from 15° to 25°, the overall accuracy, especially the axial runout, is greatly improved. For example, the parameter Cer is equivalent to a 30% increase in equipment capacity. Therefore, a larger contact angle can better meet the processing requirements, significantly improve the equipment processing capability index, and improve production efficiency.

[0026] 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 accurately predicting the rotation accuracy of an angular contact ball bearing, characterized in that: The following steps are involved: Step 1: Analyze the error components and influencing factors. The error components and influencing factors are the radial shape and position errors of the outer ring. and axial position error , radial shape and position error of the inner ring and axial position error , roundness error of outer ring And the roundness error of the inner ring , the surface topography error of the ball ; Step 2: Get radial clearance based on bearing geometry and axial clearance The roundness error has a bidirectional effect on the radial direction and a unidirectional effect on the axial direction. The influence coefficients of the groove roundness error on the axial runout and radial runout are calculated respectively. Step 3: Calculate the radial and axial rotation accuracy of the inner and outer rings of the bearing based on the roundness, form and position errors and the influence coefficient obtained in step 2.

2. The method for accurately predicting the rotation accuracy of an angular contact ball bearing according to claim 1, characterized in that: The components and influencing factors of the bearing rotation accuracy error in step 1 can be expressed as: （ 、 、 、 ） （ 、 、 、 ） （ 、 、 、 ） （ 、 、 、 ） in The radial runout of the inner ring of the bearing refers to the difference between the maximum and minimum radial distances of the inner hole surface at different angular positions of the inner ring relative to a fixed point on the outer ring. The axial runout of the inner ring of the bearing refers to the difference between the maximum and minimum axial distances between the inner ring reference end face and a fixed point on the outer ring at different angular positions of the inner ring at a radial distance from the inner ring axis equal to half the inner ring raceway contact diameter; It is the radial runout of the outer ring of the bearing; It is the axial runout of the bearing outer ring.

3. The method for accurately predicting the rotation accuracy of an angular contact ball bearing according to claim 1, characterized in that: In step 2, according to the bearing geometry, we can get: ； in is the bearing outer ring groove diameter; is the inner raceway diameter; is the ball diameter; is the radius of curvature of the inner raceway; is the radius of curvature of the outer raceway; enter , , , , , thereby calculating the influence coefficient of the groove roundness error on the axial runout and radial runout.

4. The method for accurately predicting the rotation accuracy of an angular contact ball bearing according to claim 3, characterized in that: The influence coefficient of the groove roundness error on the radial runout in step 2 is 1; The influence coefficient of roundness error on axial runout is: 。 5. The method for accurately predicting the rotation accuracy of an angular contact ball bearing according to claim 1, characterized in that: In step 3, the numerical calculation formulas for the radial and axial rotation accuracy of the inner ring of the bearing are: ； The numerical calculation formulas for the radial and axial rotation accuracy of the bearing outer ring are: 。 6. The method for accurately predicting the rotation accuracy of an angular contact ball bearing according to claim 1, characterized in that: The fourth step is to optimize the rotation accuracy, which is as follows: According to the known bearing rotation accuracy requirements Kia0, Sia0, Kea0, Sea0 and the initial selection of the optimization model , , , , , , under the premise of satisfying the process capability index Cp ≥ 1 of the equipment processing capacity, iterative optimization matching is repeated, and the optimal deviation group is selected. During the production process, the optimal deviation group is installed to produce finished bearings that meet the known rotation accuracy requirements.

7. The method for accurately predicting the rotation accuracy of an angular contact ball bearing according to claim 6, characterized in that: The optimization model formula is: 。 8. The method for accurately predicting the rotation accuracy of an angular contact ball bearing according to claim 6, characterized in that: It also includes step five, when the process capability index Cp≥1 is met for the equipment processing capability, the optimization matching is repeatedly iterated. If the index requirements are still not met, different contact angles are selected for optimization.

9. The method for accurately predicting the rotation accuracy of an angular contact ball bearing according to claim 8, characterized in that: The specific method for selecting different contact angles for optimization is: calculate the deviation influence coefficient again, where the input bearing outer ring groove diameter The value is calculated based on the optimized contact angle, and the other parameters and steps remain unchanged until the finished product rotation accuracy is optimized to meet the target accuracy.

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