*Article* **A Dynamic Wear Prediction Model for Studying the Interactions between Surface Wear and Dynamic Response of Spur Gears**

**Jinzhao Ren 1,\* and Huiqun Yuan 2**


**Abstract:** Surface wear, as a major failure mode of gear systems, is an unavoidable phenomenon during the whole life of gears. It also induces other gear damages, such as fatigue cracks, surface pitting and spalling. Ultimately, those defects may result in the sudden failure of a gearbox transmission system, which can lead to a serious accident and unexpected economic loss. Therefore, it can provide huge cost and safety benefits to industries to monitor gear wear and predict its propagation. Gear wear raises the error rate of gear transmission systems, typically leading to improvements in dynamic loads, vibration, and noise. In return, the increased load conversely aggravates wear, creating a feedback cycle between dynamic responses and surface wear. For this purpose, a wear prediction model was incorporated into a tribo-dynamic model for quantitatively investigating how surface wear and gear vibration are mutually affected by each other. To obtain more precise dynamic responses, the tribo-dynamic model integrates the time-varying mesh stiffness, load-sharing ratio and friction parameters. To improve the computational efficiency and guarantee the calculation precision, an improved and updated wear depth methodology is constructed in the wear prediction model. This paper demonstrates the capability of the proposed dynamic wear prediction model in the investigation of the interaction effects between gear dynamics and surface wear, allowing for the development of improved gear wear prediction tools. The obtained results indicate that the surface wear impacts the dynamic characteristics, even with slight wear. In the initial stage of wear, the friction coefficient decreases slightly, largely due to the reduction in surface roughness; but the friction force increases because of the improved dynamic meshing force. Although the initial wear depth distributions of a pinion under dynamic and static conditions are similar, the wear depth distributions under dynamic conditions becomes significantly different compared to the those under static conditions with the wear process. The maximum wear depth of a pinion under dynamic conditions is about 1.6 times as the corresponding static conditions, when the wear cycle comes to 4 × 104. Similarly, the maximum accumulative wear depth of a pinion under dynamic conditions reaches 1.2 times of that under static conditions. Therefore, the proposed dynamic wear prediction model is more appropriate to be applied to the surface wear of gears.

**Keywords:** coupling effects; dynamic model; gear wear; wear prediction
