Dynamics of a Spur Gear Pair under Stochastic Internal and External Excitations

Abstract

Gear systems, which are one of the most widely adopted mechanical parts, receive lots of research attention. The dynamic modeling of gear systems under deterministic excitations has been widely investigated in existing studies. However, due to the diversity in both manufacturing processes and working environments, gear systems face stochastic internal and external excitations in reality, which result in the gear modeling to be complicated. In practical situations, the stochastic internal and external excitations should be considered when modeling gear systems. Besides the modeling complexity, stochastic excitations also lead to a large increase of time complexity when obtaining the statistic features of gear responses by numerical methods. Therefore, this thesis focuses on two aspects, including the modeling and the solving of gear dynamic models under stochastic excitations.The objective of this thesis is to investigate the dynamics of a spur gear pair, including analyzing the effects on dynamic characteristics from the stochastic excitations and investigating the solving techniques to stochastic dynamic models. First, a spur gear dynamic model considering one more internal stochastic excitation, friction, is proposed. The effects of friction are investigated in gear dynamic models under stochastic load for the first time. Then, one more external excitation factor (i.e., driving speed) is taken into account in gear models and its effects on the dynamic characteristics are also studied. The results of our work show that some excitations that have not yet been modeled cannot be ignored when modeling gear systems. After that, considering the large time complexity of numerical methods for solving gear models under stochastic excitations, an efficient method is proposed to obtain an approximate analytical solution of a spur gear pair model under stochastic load with one additional stochastic internal factor. Compared to the numerical methods, the proposed method can achieve similar accuracy responses but with much smaller time complexity.In summary, this thesis helps us understand the mechanism of a spur gear pair and gives insights into developing more realistic gear models for gear design and condition monitoring. Future works will explore other possible internal and external excitations in gear modeling. The gear models under different working conditions are also worthy to study.