# Robust design optimization of an angular contact ball bearing under manufacturing tolerance

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## Abstract

The performances of an angular contact ball bearing (ACBB) are influenced by its geometric dimensions that can have uncertainty due to manufacturing tolerances. Uncertainty of these geometric dimensions results in uncertainty of the performances. This study performed robust design optimization considering the uncertainty of the geometric dimensions which affect the performances of an ACBB, mounted on the main shaft of a grinder. Six geometric parameters and an axial preload were selected as design variables. Among these design variables, three geometric variables were regarded as random design variables that have significant uncertainty of geometric dimensions. To ensure manufacturing precision of the grinder, simultaneously maximizing means and minimizing standard deviations of both axial and radial stiffness values were defined as objective functions. Constraints were imposed to consider uncertainty of the performance functions. A quasi-static analysis was employed to evaluate the bearing performances. The means and standard deviations of the performances were evaluated by the enhanced dimensional reduction method. Robust design optimization was performed using the progressive quadratic response surface method. The robust optimum design revealed that the performance and robustness of both stiffness values were improved than the initial design of the ACBB while satisfying all constraints.

## Keywords

Robust design optimization Angular contact ball bearing Quasi-static analysis Enhanced dimensional reduction method Progressive quadratic response surface method## Notes

### Acknowledgments

This study was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (no. 20184010201710). The authors extend their gratitude to PIDOTECH Inc. for providing PIAnO, a commercial software for process integration and design optimization software for this study.

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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