Experimental identification and robust optimization of spindle–bearing systems with reliability constraints

Effective vibration control and dynamic behavior management in the presence of parameter uncertainties are critical for high-speed motorized spindles. Although traditional robust design optimization minimizes dynamic response variability, it lacks explicit control over failure probabilities. To address these limitations, this study utilizes data from 1000 experimental runs to drive a reliability-based robust optimization investigation. Instead of assuming ideal distributions, uncertainties in bearing stiffness and damping are quantified using the Multi-Innovation Stochastic Gradient (MISG) method. These empirically identified distributions are propagated via Monte Carlo simulation and integrated with the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to analyze the trade-offs between vibration suppression and reliability across target failure probabilities of 1 %, 5 %, and 10 %. The results indicate that tightening the target failure constraint from 5 % to 1 % yields diminishing returns, necessitating a 7.0 % increase in preload for only a marginal gain in response robustness. Comprehensive experimental validation across the spectrum of 1000–24 000 rpm confirms the full-range efficacy of the proposed framework. Specifically, statistical validation via 20 independent physical replications at the rated speed of 24 000 rpm demonstrates that the optimized design reduces the experimental mean peak vibration by 16.84 % and the response standard deviation by 29.78 % while successfully curtailing the failure probability from 55.44 % to 0.35 %. These findings demonstrate that integrating experimental identification with robust optimization improves both dynamic performance and engineering reliability in spindle-bearing systems.