Multivariate Damage-Based Reliability Assessment of Toothed Belts for Vehicle Steering Systems

Abstract

This study presents a comprehensive methodology for damage-based reliability assessment of safety-critical components, exemplified by a toothed belt within an automotive steering system. The proposed framework integrates multivariate lifetime modeling, fatigue damage accumulation, and probabilistic reliability evaluation to enable a data-driven and physically interpretable assessment of component reliability. Initially, a Design of Experiments (DoE)-based lifetime modeling approach is employed to identify and quantify the dominant influencing factors affecting component lifetime, utilizing a Generalized Linear Model (GLM) fitted via Maximum Likelihood Estimation (MLE). The approach allows lifetime estimation under varying combinations of operational stresses while accounting for interaction effects between stress variables. Subsequently, a Finite Element Method (FEM) analysis of the belt’s wrapping arc is used to derive load spectra through tooth-by-tooth stress classification and rainflow cycle counting. Stress-life relationships, such as the GLM-based lifetime model and a Wöhler Model, form the foundation for damage quantification using the linear damage accumulation hypothesis. Damage values are then statistically evaluated for individual teeth, enabling the identification of the most critical tooth and corresponding maximum fatigue damage. A nonparametric, bootstrap-based approach is introduced to quantify reliability and uncertainty. By generating $\boldsymbol{n_{\text{MC}} = 10^{4}}$ bootstrapped Weibull distributions and fitting the resulting reliability ensemble with a Beta distribution, the method yields confidence-informed reliability estimates. For the GLM-based model, a median reliability of $\boldsymbol{R = 81.05\%}$ is obtained, whereas the Wöhler model converges toward $\boldsymbol{R \to 100\%}$ for the prevailing failure mechanism. The result underscores that a multidimensional, load-representative GLM enables modeling of complex interactions and failure mechanisms beyond fatigue test data, preventing unduly conservative reliability evaluations. Overall, the integration of Lifetime-DoE, FEM-based load spectrum (LS) analysis, and damage-informed reliability modeling establishes a robust framework for predicting component reliability under multiaxial and uncertain loading conditions. The methodology bridges deterministic fatigue modeling and probabilistic reliability analysis, offering a transferable approach for the assessment of complex, safety-critical systems.