Developing a spatial model of a gear transmission with separate storage of the accumulated and extra turns for solving non-linear problems of aviation transmissions dynamics
Aviation transmissions ensure the torque transfer from the rotor to propeller or fan, and accessory box drive in the engines of various types, from the engine to the shaft of the main and tail rotors of the helicopter etc. [1-3]. Aviation transmissions should ensure high strength properties at small size. The dynamics analysis performing seems to be the best tool for these requirements compliance ensuring. Many scientific papers deal with the gear transmission dynamics. The most meaningful and interesting gear transmission models are represented in the works of Cardona [9], Spitas [12], Qiu [13], Margielewicz [14], and Kubo [19]. Nevertheless, most of them do not account for the linear wheels movement, variable stiffness, interaction between gears and other machine elements, and unfit for the non-stationary dynamics studies. The article presents a spatial model of the gear transmission capable of accounting for the aforementioned limitations and applicable for the non-stationary dynamics problem solving. The model is based on the Cardona's model [9]. The model employs Euler vector and the rotation tensor associated with it as rotations description. The final rotation is being decomposed into the accumulated rotation and a small incremental one. This technique allows avoiding the problems associated with achieving exceptional points near the 2p angle [15-17]. The presented model can be employed for performing analysis of the wide spectrum of gear transmissions, such as spur gears, helical gears, conical gears and internal gears. The model allows accounting for the gear mesh stiffness, gear mesh damping, kinematic error of the transmission and backlashes. The gear transmission model can conjoin with the models of other machine elements such as shafts, bearings, cases etc. The proposed model was verified by several well-known tests.