Piecewise Nonlinear Dynamic Modeling for Gear Transmissions With Rotary Inertia and Backlash

Establishing an accurate dynamic model for gear transmission is challenging because of the complex dynamic mechanical behavior of the gear transmission, particularly under difficult working conditions such as heavy loads and frequent starts and stops. This feature significantly increases the difficulty level of the dynamic analysis, control, and real-time fault diagnosis of such a gear transmission, given that sufficiently accurate dynamic models are indispensable for them. Thus, this study proposes a piecewise nonlinear model for gear transmissions by considering rotary inertia, backlash, and friction in control applications under difficult working conditions. The model parameters of gear transmissions can be calculated by using analytical calculation formulas. The experiments are conducted for the gear transmission system of a heavy-duty manipulator in start–stop and continuous rotation conditions. The experimental results show that the proposed piecewise nonlinear model is in good agreement with the practical dynamic gear transmission behavior, which is feasible for the control applications of gear transmissions under difficult working conditions.