Reliability-Based Robust Design Optimization with Fourth-Moment Method for Ball Bearing Wear
Abstract
:1. Introduction
2. Materials and Methods
2.1. Kriging Surrogate Model of Mechanical Structural Response Based on FEM
2.2. Wear Reliability Model of Rolling Ball Bearing
2.3. Sensitivity Analysis and Reliability-Based Robust Design
3. Results
- The wear reliability target for ball bearings is set to , which means that the optimized reliability result obtained at the moment should be no less than . Therefore, the reliability constraint is expressed as follows:
- In order to ensure the point contact between the inner/outer raceway and the balls, the inner/outer raceway radius should be larger than the ball radius , and the inner raceway radius is usually larger than the outer raceway radius . According to the above principles to establish constraints as follows:
- Based on the structural design requirements of ball bearings and with reference to the various dimensional standards for ball bearings [46], the initial value constraints are established for the input parameters as follows:
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
References
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Inner Diameter (mm) | Radial Clearance (mm) | Axial Clearance (mm) |
---|---|---|
<30 | 4D/1000 | 0.2 |
35~70 | 3.5D/1000 | 0.3 |
75~100 | 3D/1000 | 0.3 |
>100 | <0.3 | 0.3 |
Bearing Parameters | Mean | Variance | Skewness | Kurtosis |
---|---|---|---|---|
Center circle diameter (mm) | 102.4874 | 2.5 × 10−5 | 9.96 × 10−2 | 2.87 |
Ball diameter (mm) | 13.4940 | 4.0 × 10−6 | 4.09 × 10−2 | 2.96 |
Inner ring groove radius | 7.1010 | 1.0 × 10−6 | −7.37 × 10−2 | 3.03 |
Outer ring groove radius (mm) | 6.9960 | 1.0 × 10−6 | 1.29 × 10−1 | 2.69 |
Elastic modulus (GPa) | 208 | 1.0 × 10−4 | −1.88 × 10−4 | 3.47 |
Poisson’s ratio | 0.3 | 1.0 × 10−8 | −1.53 × 10−1 | 2.85 |
Hardness | 200 | 1.0 × 10−4 | 8.35 × 10−2 | 2.88 |
Initial radial clearance | 0.0240 | 2.5 × 10−5 | 6.46 × 10−2 | 2.92 |
Methods | Relative Error | |||
---|---|---|---|---|
FOSM method | 635 h | −1.6567 | 95.12% | 0.7521% |
The proposed method | 635 h | −1.5985 | 94.50% | 0.0953% |
MCS method | 635 h | \ | 94.41% | \ |
Input Parameters | Reliability Sensitivity | Sensitivity Gradient | |
---|---|---|---|
Center circle diameter | 0.0037 | −1.06 × 10−6 | 40.4176 |
Ball diameter | 2.2782 | −0.1616 | |
Inner ring groove radius | −1.1763 | −0.0215 | |
Outer ring groove radius | −4.4164 | −0.3036 | |
Elastic modulus | −0.0028 | −1.21 × 10−6 | |
Poisson’s ratio | −0.3828 | −2.28 × 10−4 | |
Hardness | −0.0283 | −1.25 × 10−4 | |
Initial radial clearance | 20.9554 | −34.1776 |
Input Parameters | Before Optimization | After Optimization |
---|---|---|
Center circle diameter (mm) | 102.4874 | 102.4306 |
Ball diameter (mm) | 13.4940 | 13.4501 |
Inner ring groove radius | 7.1010 | 7.1499 |
Outer ring groove radius (mm) | 6.9960 | 7.05 |
Elastic modulus (GPa) | 208 | 208.0212 |
Poisson’s ratio | 0.3 | 0.3497 |
Hardness | 200 | 201.9952 |
Initial radial clearance | 0.0240 | 0.0235 |
Input Parameters | ||||
---|---|---|---|---|
Before optimization | 635 h | −1.5985 | 94.50% | 40.4176 |
After optimization | 635 h | −5.5483 | 99.99% | 8.4755 × 10−5 |
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Wang, Y.; E, S.; Yang, K.; Xie, B.; Lu, F. Reliability-Based Robust Design Optimization with Fourth-Moment Method for Ball Bearing Wear. Lubricants 2024, 12, 293. https://doi.org/10.3390/lubricants12080293
Wang Y, E S, Yang K, Xie B, Lu F. Reliability-Based Robust Design Optimization with Fourth-Moment Method for Ball Bearing Wear. Lubricants. 2024; 12(8):293. https://doi.org/10.3390/lubricants12080293
Chicago/Turabian StyleWang, Yanzhong, Shiyuan E, Kai Yang, Bin Xie, and Fengxia Lu. 2024. "Reliability-Based Robust Design Optimization with Fourth-Moment Method for Ball Bearing Wear" Lubricants 12, no. 8: 293. https://doi.org/10.3390/lubricants12080293