A method for accurately predicting the rotational accuracy of angular contact ball bearings
Through the error superposition principle and equipment processing capability analysis, an angular contact ball bearing rotation accuracy prediction and optimization model was established, which solved the problems of inaccurate rotation accuracy prediction and uneconomical mass production in the existing technology, and achieved efficient and economical rotation accuracy control.
Patent Information
- Application Number
- CN202411783180.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-06
- Publication Date
- 2025-06-24
- Estimated Expiration
- 2044-12-06
AI Technical Summary
The prior art is difficult to accurately predict the rotational accuracy of angular contact ball bearings, the influencing factors are not comprehensive enough, and the method of improving processing accuracy during mass production is not economical.
Through the principle of error superposition, combined with roundness error, shape and position error, etc., the error components and influencing factors are analyzed, the rotation accuracy in the radial and axial directions are calculated, and the equipment processing capabilities are considered to establish a rotation accuracy error prediction and optimization model.
It improves the accuracy of the rotation accuracy prediction of angular contact ball bearings, realizes economical and efficient rotation accuracy control, and is suitable for large-scale production.
Smart Images
Figure CN119249775B_ABST
Abstract
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;
[0003] 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
[0004] 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.
[0005] The present invention is achieved through the following technical solutions:
[0006] The present invention provides a method for accurately predicting the rotation accuracy of an angular contact ball bearing, comprising the following steps:
[0007] 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 ;
[0008] Step 2: Get radial clearance based on bearing geometry and axial clearance , the influence of roundness error on the radial direction is two-way, and the influence on the axial direction is one-way. Calculate the influence coefficients of the raceway roundness error on the axial runout and radial runout respectively;
[0009] Step 3: Calculate the rotational accuracy of the inner and outer rings of the bearing in the radial and axial directions according to the roundness and geometric tolerance and the influence coefficients obtained in Step 2.
[0010] Preferably, the components and influencing factors of the bearing rotational accuracy error in Step 1 can be expressed as:
[0011] Kia ( 、 、 、 )
[0012] Sia ( 、 、 、 )
[0013] Kea ( 、 、 、 )
[0014] Sea ( 、 、 、 ) ;
[0015] Where is the radial runout of the inner ring of the bearing, which refers to the difference between the maximum and minimum radial distances between the inner hole surface at different angular positions of the inner ring and a fixed point on the outer ring; is the axial runout of the inner ring of the bearing, which refers to the difference between the maximum and minimum axial distances between the reference end face of the inner ring at different angular positions of the inner ring and a fixed point on the outer ring at a radial distance from the axis of the inner ring equal to half of the contact diameter of the inner ring raceway; is the radial runout of the outer ring of the bearing; is the axial runout of the outer ring of the bearing.
[0016] Preferably, according to the geometric relationship of the bearing in Step 2, it can be obtained that:
[0017] ;
[0018] Where is the diameter of the outer ring raceway of the bearing; is the diameter of the inner ring raceway; is the ball diameter; is the curvature radius of the inner ring raceway; is the curvature radius of the outer raceway groove;
[0019] Input and and and and , so as to calculate the influence coefficients of the groove roundness error on the axial runout and the radial runout.
[0020] Preferably, in step two, the influence coefficient of the groove roundness error on the radial runout is 1;
[0021] The influence coefficient of the roundness error on the axial runout is:
[0022] .
[0023] Preferably, in step three, the numerical calculation formulas for the rotational accuracy of the inner ring of the bearing in the radial and axial directions are respectively:
[0024] ;
[0025] The numerical calculation formulas for the rotational accuracy of the outer ring of the bearing in the radial and axial directions are respectively:
[0026] .
[0027] Preferably, it further includes step four, performing optimization control on the rotational accuracy, specifically:
[0028] According to the known rotational accuracy requirement indexes Kia0, Sia0, Kea0, Sea0 of the bearing and and and and and and selected initially according to the optimization model, on the premise of satisfying the process capability index Cp≥1 of the equipment processing ability, perform iterative optimization matching repeatedly, and select the optimal deviation group. During the production process, install the optimal deviation group for production, and then the finished bearing that meets the known rotational accuracy requirements can be obtained.
[0029] Preferably, the optimization model formula is:
[0030] .
[0031] Preferably, it further includes step five. When, on the premise of satisfying the process capability index Cp≥1 of the equipment processing ability, perform iterative optimization matching repeatedly. If the index requirements still cannot be met, select different contact angles for optimization.
[0032] Preferably, the specific method for optimizing by selecting different contact angles is as follows: recalculate the influence coefficients of the channel roundness error on the axial runout and the radial runout, where the diameter of the bearing outer ring channel is a value calculated according to the optimized contact angle, and the remaining parameters and steps remain unchanged until the finished product rotational accuracy meeting the target accuracy is optimized.
[0033] The beneficial effects of the present invention are as follows:
[0034] (1) The present invention estimates the bearing rotational accuracy through roundness error, geometric tolerance, etc., and comprehensively considers influencing factors;
[0035] (2) The present invention also considers the equipment processing capacity and establishes a prediction and optimization model for the rotational accuracy error of angular contact ball bearings, so as to economically and efficiently achieve precise control of the rotational accuracy of angular contact ball bearings;
[0036] (3) The present invention can also determine a suitable contact angle according to the requirements of the main engine equipment for the rotational accuracy index of the supporting bearings, and this rotational accuracy prediction and optimization model can economically and efficiently meet the actual production needs. Description of the Drawings
[0037] Figure 1 (a) and 1(b) are respectively schematic diagrams of the influence of roundness error on radial and axial runouts;
[0038] Figure 2 is the flow chart of this application;
[0039] Figure 3 (a) and 3(b) are respectively schematic diagrams of measuring the inner ring radial runout and axial runout during the measurement of the rotational accuracy of angular contact ball bearings;
[0040] Figure 4 (a) and 4(b) are respectively the top view and front view of the measurement of the wall thickness error of the bearing inner ring;
[0041] Figure 5 (a) and 5(b) are respectively the top view and front view of the measurement of the parallelism error of the bearing inner ring channel to the end face. Detailed Embodiments
[0042] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings.
[0043] Embodiment 1
[0044] The present invention discloses a method for accurately predicting the rotational accuracy of angular contact ball bearings. First, study the principles of rotational accuracy measurement, the measurement principle of the wall thickness error of the bearing inner ring, the measurement principle of the parallelism error of the bearing inner ring channel to the end face, etc., as Figures 3 to 5, where Figure 4 In (b), h in 5(b) is the pointer height during measurement; meanwhile, analyze the rotation accuracy, its error components, and influencing factors, such as Figure 1 is a schematic diagram of the influence of roundness error on radial and axial runout, where Figure 1 in (b), a is the bearing contact angle; secondly, calculate the influence coefficients of each factor error on axial and radial runout; subsequently, establish a model considering the equipment processing ability for the optimization and matching of each error to meet the index requirements; finally, form an operation process, such as Figure 2 shown, and the following functions can be completed according to the process specifically:
[0045] Step 1: Analyze the error components and influencing factors. The error components and influencing factors are the geometric and positional errors of the outer ring in the radial direction and the geometric and positional errors in the axial direction , the geometric and positional errors of the inner ring in the radial direction and the geometric and positional errors in the axial direction , the roundness error of the outer ring and the roundness error of the inner ring , the surface topography error of the ball ; during implementation, select the outer and inner rings of the bearing, number them correspondingly, and use high-precision measuring instruments to measure various parameters of the inner and outer rings;
[0046] The error components and influencing factors of the bearing rotation accuracy can be expressed as:
[0047] Kia ( , , , )
[0048] Sia ( , , , )
[0049] Kea ( , , , )
[0050] Sea ( , , , ) ;
[0051] Where 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 of the reference end face of the inner ring at different angular positions of the inner ring relative to a fixed point on the outer ring at a radial distance from the axis of the inner ring equal to half of the contact diameter of the inner ring raceway; is the radial runout of the outer ring of the bearing; is the axial runout of the outer ring of the bearing.
[0052] Secondly, since the roundness errors of the inner and outer rings are very small, it can be approximately considered the influence of the slight dimensional changes of the inner and outer ring raceways at the contact points on the rotation accuracy of the bearing. At the contact point O, there is a roundness deviation , which can be considered as the transient runout of the radial clearance and axial clearance caused by the slight dimensional changes of the raceway.
[0053] Step 2: According to the geometric relationship of the bearing, the radial clearance and the axial clearance are obtained as follows:
[0054] ;
[0055] where is the diameter of the outer ring raceway of the bearing; is the diameter of the inner ring raceway; is the ball diameter; is the radius of curvature of the inner ring raceway; is the radius of curvature of the outer ring raceway;
[0056] Since the roundness error of the raceway only affects the radial and axial directions of the bearing, assuming , , remain unchanged, taking the partial derivative of the formula to obtain the transient values of the diameter of the outer ring raceway of the bearing and the diameter of the inner ring raceway, which are the roundness errors of the raceway. The influence coefficient formulas of the roundness error of the raceway on the radial clearance and axial clearance are as follows:
[0057]
[0058]
[0059]
[0060]
[0061] Therefore, the influence coefficient of the roundness error of the raceway on the radial runout can be obtained, which is 1, that is
[0062]
[0063] It should be emphasized that due to the existence of the measured pressure, the influence of roundness deviation , on the radial direction is two-way, but the influence on the axial direction is one-way. Therefore, the calculation formula for the influence coefficient of roundness error on axial runout is:
[0064]
[0065] Step 3: Calculate the rotational accuracy of the inner and outer rings of the bearing in the radial and axial directions according to the roundness and geometric tolerance and the influence coefficient obtained in Step 2.
[0066] Combined with the actual production, due to the high precision of the bearing balls, the influence of surface topography error on rotational accuracy can be ignored.
[0067] The numerical calculation formulas for the rotational accuracy of the inner ring of the bearing in the radial and axial directions are respectively:
[0068] (1)
[0069] (2)
[0070] The numerical calculation formulas for the rotational accuracy of the outer ring of the bearing in the radial and axial directions are respectively:
[0071] (3)
[0072] (4)
[0073] From formulas (1)-(4), the results of the radial and axial runout models of the inner and outer rings of the bearing can be obtained, that is, the predicted numerical values of the rotational accuracy of the bearing.
[0074] Example 2
[0075] The difference from Example 1 is that it further includes Step 4: Optimize and control the rotational accuracy. The optimization matching of each error can be carried out according to the model to meet the index requirements. At this time, the machining ability of the equipment needs to be considered, and the machining ability of the equipment is represented by the process capability index Cp; specifically as shown in Table 1:
[0076] Table 1 Rating and classification table of process capability index
[0077]
[0078] The core of the bearing rotational accuracy optimization model is to meet the smallest deviation range (or meet the target value) under the condition of as high as possible , so as to economically and efficiently achieve the precise control of the rotational accuracy of angular contact ball bearings. Specifically:
[0079] According to the known rotational accuracy requirement indexes Kia0, Sia0, Kea0, Sea0 of the bearing and , , , , , , on the premise that the process capability index Cp≥1 for meeting the equipment processing capacity is satisfied, repeatedly iterate and optimize the matching, and select the optimal deviation group. During the production process, install the optimal deviation group for production, and then the finished product bearing that meets the known rotational accuracy requirements can be obtained.
[0080] Among them, the optimization model formula is:
[0081] (5).
[0082] Example 3
[0083] The difference from Example 2 is that it further includes Step Five. When, on the premise that the process capability index Cp≥1 for meeting the equipment processing capacity is satisfied, repeatedly iterate and optimize the matching, and if the index requirements still cannot be met, select different contact angles for optimization.
[0084] The specific method for selecting different contact angles for optimization is: recalculate the influence coefficients of the groove roundness error on the axial runout and radial runout, where the input bearing outer ring groove diameter is the value calculated according to the optimized contact angle, and the remaining parameters and steps remain unchanged until the finished product rotational accuracy that meets the target accuracy is optimized.
[0085] Different contact angles can be selected for optimization. For example, increasing the contact angle from 15° to 25°, its overall accuracy, especially the axial runout, is improved greatly. For parameters such as Cer, the equipment capacity is equivalent to an increase of 30%. Therefore, a larger contact angle can better meet the processing requirements, significantly improve the equipment processing capacity index, and improve production efficiency.
[0086] It should be noted that although the present invention has been described through the above embodiments, the present invention can also have many other embodiments. Without departing from the spirit and scope of the present invention, those skilled in the art can obviously make various corresponding changes and deformations to the present invention, but these changes and deformations should all fall within the scope protected by 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. Influence coefficient of groove roundness error on radial runout is 1; The influence coefficient of roundness error on axial runout is: ； 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; 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: Okay. ( 、 、 、 ) Is ( 、 、 、 ) 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.
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: ； 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 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: 。 5. 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.
6. The method for accurately predicting the rotation accuracy of an angular contact ball bearing according to claim 5, characterized in that: The optimization model formula is: 。 7. The method for accurately predicting the rotation accuracy of an angular contact ball bearing according to claim 5, 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 cannot be met, different contact angles are selected for optimization.
8. The method for accurately predicting the rotation accuracy of an angular contact ball bearing according to claim 7, 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.