No abstract

A gear transmission system such as a gear train is a series system in sense of reliability evaluation, while it is different from a traditional series system such as a chain. Therefore, the conventional series system reliability model is not appropriate for gear transmission system. Based on the time-dependent configuration and the time-dependent loading path of a gear train, system specific reliability modeling technique is presented, by which a gear train is taken as a time-dependent series system, consisting of different components (gear teeth) in different time intervals. To illustrate the application of the reliability analysis method, several time-dependent series system reliability models are developed for different types of gear trains, the reliability estimation results are compared with those obtained by traditional series system reliability model.

A gear tooth or a gear is usually considered as an independent component in the traditional reliability research. However, gear trains are significantly different from the traditional series systems. Time-dependent configuration of the traditional series systems is fixed. But the meshing tooth-pairs of gear trains are changing all the time during operation. The failures of meshing tooth-pairs are dependent statistically under the common load action. In the paper, the reliability analysis considering time-domain meshing relation of tooth-pairs is studied and meshing relation equations are presented. Then, reliability analysis method of gear trains is developed based on the Monte Carlo simulation with dependent failure and time domain meshing relation. The differences of reliability results between time domain reliability analysis method and traditional series system reliability methods are illustrated by several examples.

The traditional reliability models of gear system were usually developed without considering strength degradation of gear tooth. Although some analysis methods considered strength degradation, but they ignored the uncertainty of strength degradation that is due to the random load. In order to consider the statistically dependent failure between the gears and the uncertainty of gear strength in the strength degradation process, the reliability models of gear system are developed based on the theory of stress - strength interference. The failure relationships between teeth are expressed by the minimum order statistics. The uncertainty of the strength degradation is expressed by the distribution of material parameter. Using the Monte Carlo simulation, the proposed model is validated. Taking a planetary gear system for a case study, the system reliabilities with strength degradation are analyzed. The results show that the strength degradation has a little influence on the gear system reliability at the early stage and it has a great influence on the gear system reliability at the middle and late stages.

Traditional reliability models of the gear system either simplify the gear system unreasonably or are too complicated to be applicable for some gear systems. Therefore, a reliability model of the gear system considering statistically dependent failure based on the theory of the order statistics is developed in this paper. Firstly, the gear bending fatigue test of small sample is implemented to obtain the P-S-N curves that are fitted by using the least square method and the linear regression method of the statistical parameters under the test stress levels. Then, according to stress-strength interference theory and the theory of the order statistics, the reliability models considering the number of load cycles from a gear to gear system are built, which indicates clear modeling process of the gear system. Finally, the proposed reliability model of gear system is validated by using the Monte Carlo Simulation (MCS) and the system reliability under special load history is analyzed qualitatively.