Gear trains are commonly used in many kinds of servomechanisms to amplify actuator torque as well as transmit power from one shaft to another. However, backlash between meshing gear teeth can cause impact, reduce system stability, and generate noise and undesired vibrations. Backlash is usually minimized by using precision gear, spring-loaded anti-backlash gears, and precise mechanical adjustment. Although these techniques can help reduce the backlash value, its production cost is relatively high and achievable accuracy is limited. Therefore, control strategies to compensate the effect of backlash are required. For these strategies, a control-oriented dynamic model for geared system with backlash must be proposed.
This paper proposes backlash model as a nonlinear spring which has a large torsional stiffness. Using this model, the entire gear systems are mathematically modeled. To analyze nonlinear system, the describing method is adopted. By this method the system is linearized and its dynamic characteristics, resonance and anti-resonance are predicted. According to the value of backlash, simulation are carried out for time responses and frequency responses and results are compared with experimental results.