Reliability analysis of gear transmission with considering failure correlation

Gear is an important component of mechanical transmission. Gear transmission has been recognized as one of the most important mechanical transmission forms because it has a series of advantages, such as broad power and speed ratio in scope, high transmission efficiency, compact structure and so on. In recent years, with rapid development of machine tools, aircrafts, and automobiles, gear transmission has become an extremely important form of mechanical transmission [1, 4, 6, 8]. Reliability of mechanical transmission relies on the most critical component, e.g. gear, of the system [10]. The failure of gears in mechanical transmission will lead to a poor performance, sometimes even serious accidents and subsequently great economic loss. Therefore, developing an effective and accurate fatigue reliability evaluation model for gear transmission has been a hot topic in the gear engineering community [2, 3, 11]. Failure modes of gears are complicated, such as teeth broken, teeth surface pitting, teeth wear, teeth bonding and teeth plastic deformations and so on, because in most cases, gears work under high speed, heavy load and strong impulse conditions. Therefore, multiple failure modes should be considered simultaneously for analyzing reliability of gears. In this paper, the gear transmission of heavy machine tools is analyzed. Tooth bending fatigue, gear contact fatigue and flank adhesion are major failure modes of heavy duty gears. The failures of weak points are dependent of each other, because all the roots (with maximum bending stress) and surfaces (with maximum contact stress) in a gear subject to the same environmental conditions. Thus, the failure dependence of a gear in the transmission system should be considered. Reliability models of gear transmission with common cause failures are developed without the assumption of failure independence [5, 6, 12, 14, 15]. The paper is organized as follows. In Section 2, the strength calculation standards for gears and the copula theory as well as stressstrength interference theory are briefly introduced. Reliability calculation models are developed in Section 3. The proposed method is validated by a gear transmission of heavy machine tools with three failure modes in Section 4. Conclusions are dawn in Section 5.