Robust Bayesian optimization design of the tension response of the yarn carrier of a carbon fiber braiding machine under parameter uncertainty

During the carbon fiber braiding process, stick–slip dynamics and impact loads induced by the carrier ratchet–pawl mechanism are key contributors to yarn tension instability. Conventional deterministic optimization approaches often neglect inherent parametric variability and time-dependent uncertainties, leading to optimal solutions that exhibit high sensitivity and limited robustness under manufacturing tolerances and environmental disturbances. To enhance tension stability in slider-type carriers, this study proposes a reliability-oriented structural parameter optimization framework that explicitly incorporates parametric uncertainty. Based on a nonlinear tension dynamic model, the stochastic characteristics of spring stiffness and friction coefficients are statistically quantified. A composite performance metric is formulated using the mean and dispersion of peak tension, and a sequential optimization strategy is implemented within a predefined computational budget. The optimized design achieves a 16.3% reduction in peak tension and a 3.9% decrease in tension standard deviation under nominal operating conditions. In 1000 Monte Carlo validation simulations, the width of the 95% confidence interval is reduced by 28.2%, the standard deviation of peak tension decreases by 31.8%, and the coefficient of variation is lowered by 17.6%. No yarn slackening failure is observed in the validation tests. Further analysis reveals a two-stage stiffness coordination mechanism, characterized by an initial low-stiffness energy-absorption phase followed by a high-stiffness support regime. These findings provide a theoretical foundation for reliability-oriented carrier design and tension stability optimization.