Modeling and optimization of high-temperature degradation in fuze coil springs using response surface methodology

Accelerated degradation testing (ADT) of safety-critical mechanical components like fuze coil springs remains challenging due to complex, nonlinear degradation mechanisms under thermal stress. This study presents a novel cubic-order Response Surface Methodology (RSM) framework to model and predict the simultaneous degradation of two key performance parameters, permanent deformation (compression set) and stress relaxation rate, under elevated temperature and time. A total of 18 experimental runs were conducted across 120–160 °C and 1–318 h, and statistically validated cubic models were developed with R² > 96% and adjusted R² > 92%. ANOVA and standardized-effect analysis showed that the degradation responses are governed predominantly by nonlinear exposure-time effects. For permanent deformation, the quadratic and cubic time terms were significant ( p = 0.0009 and p = 0.0134, respectively), while for stress loss the corresponding terms were also significant ( p = 0.0022 and p = 0.0149). In contrast, the linear time main effect was not significant for either response. Temperature and temperature–time interaction also contributed significantly to the degradation behavior. Independent confirmation tests demonstrated high predictive accuracy, with errors ≤ 8.8%. Multi-response desirability optimization identified an optimal condition of approximately 120.4 °C and 1.10 h for simultaneously minimizing permanent deformation and stress loss, with predicted responses of 8.14% and 13.82%, respectively. This work provides an empirical framework for characterizing nonlinear temperature–time effects on spring degradation and for predicting permanent deformation and stress loss within the experimentally investigated domain.