Modeling and dynamic response of parallel shaft gear transmission in non-inertial system

Gear transmissions play a critical role as a bridge between power elements and actuators. They are either fixed to the ground or operated in spatial motion, depending on the carrier to which they are attached. However, there are significant differences between the two. When the gear transmission is subjected to any transient motion with the carrier, its force mechanism and dynamic response should be studied in a non-inertial system. Assuming that the foundation is fixed, as in traditional studies, will result in a number of significant deviations in response results because of ignoring potential excitations. Therefore, a gear transmission dynamic model in non-inertial systems is established. Under non-inertial conditions, the effect of gravity on the carrier changes from constant to time-varying. Additional inertial forces and additional gyroscopic moments are derived. Typical translational and rotational motions of the carrier are the basic forms for synthesizing arbitrary spatial motions and are therefore selected as case studies. The force mechanism under different non-inertial conditions is shown. The results indicate that the non-inertial effect has a significant influence on the shafting deformation, trajectories, bearing force, and system stability. Transient motion of the carrier is also critical for gearing excitation. The influence ratio of each additional term is quantified. The study provides analytical models and data references for strength determination and optimization design of related structures, and lays a foundation for further studies on more detailed nonlinear behaviors under more diverse non-inertial conditions.