Hysteresis curve analysis of a cycloid reducer using non-linear spring with a dead zone

Cycloid reducers are widely used for high-precision industrial instruments and robots because of many advantages: high efficiency, high stiffness and a high reduction ratio in a compact size. Nevertheless, the few studies that have investigated the hysteresis characteristics of a cycloid reducer used a time-consuming iterative procedure. This paper presents an efficient FE analysis procedure for the hysteresis characteristics of a cycloid reducer using a nonlinear spring with a dead zone. First, we introduced a cycloid reducer and performed a kinematic analysis of the cycloid disk with tolerance. Next, connecting elements of the cycloid reducer such as the input bearing, pin-roller and output roller were approximated as nonlinear springs with a dead zone. In particular, the dead zone for the nonlinear springs was introduced to represent the clearance of each connecting element. Then, a full FE model of the cycloid reducer was built incorporating the nonlinear springs, and the hysteresis characteristic of the cycloid reducer was directly evaluated at one time so as to significantly save its analysis effort and time. Results showed that tolerance had a great effect on torque and the torsional angle relationship of the cycloid reducer. such as lost motion, back lash and torsional rigidity.