Dynamic Reliability of a Permanent Magnet Planetary Gear Transmission System Considering Resonance and Tooth‐Surface Wear

ABSTRACT The planetary gear transmissions driven by permanent magnet synchronous motor (PMSM) are prone to coupled dynamic failure mechanisms arising from frequency resonance and long‐term tooth‐surface wear. This paper presents an MRGP‐based dynamic reliability framework for a permanent‐magnet planetary gear transmission system (PMPGTS) that explicitly accounts for these mechanisms. A unified electromechanical model is first established by integrating PMSM electromagnetic torque and current control with a planetary gear dynamic model and a wear‐dependent time‐varying mesh stiffness (TVMS). On this basis, a multi‐mode limit‐state vector is constructed to describe resonance and wear failures across discrete wear stages. To overcome the prohibitive cost of Monte Carlo simulation (MCS) on the high‐fidelity model, an active‐learning multi‐response Gaussian process (MRGP) surrogate is developed, which simultaneously approximates all limit‐state components and is adaptively refined using a combined U‐function and expected feasibility function (EFF). A benchmark example demonstrates that the proposed surrogate method attains a relative error of about 0.23% with only about 40.4 high‐fidelity evaluations. Application to the PMPGTS over a [0–20] year service interval shows that early‐life failure is dominated by resonance induced by high‐order mesh harmonics, whereas late‐life reliability is governed by tooth‐surface wear, with the wear failure probability approaching 0.97 at 20 years. The proposed MRGP‐based dynamic reliability framework provides an efficient tool for life‐cycle dynamic reliability assessment and for guiding the design of geometry in PMPGTS.