Modeling and Simulation of Backlash Dynamics of Worm-Wheel System and Its Gap Size Estimation Using Kalman Filters

Reduced weight, size, and maintenance cost, as well as quieter and eco-friendly operation of electro-mechanical actuators (EMA), gained profound attention in various sectors, particularly aerospace. As a result, hydraulic actuators are being replaced by EMA counterparts. However, EMA comprises mating gear systems used for power transmission, and these gears experience wear through time. Among widely known EMAs variants, worm-wheel gear system is quietest, smoothest, and compact with high gear ratio. Due to these advantages, worm-wheel is utilized in various devices that require high precision such as surgical robotic arms and 3D printers. Nevertheless, worm-wheel systems, alike other variants of mating gear systems in EMA, suffer friction wear that leads to a backlash in the system. Backlash induces non-linearity in the dynamics of the worm-wheel system, resulting in reduced EMA performance and complex control system design. Therefore, as a part of EMA prognostic and health management (PHM) approaches, we develop a mathematical model of the non-linear dynamic behavior of backlash in the worm-wheel system and derived equations from the model for backlash gap size estimation. This backlash gap size estimation can be employed not only for monitoring of worm-wheel system performance and reliability as a proactive measure but also for its compensation control system design. Simulations of backlash dynamic behavior and gap size estimation were conducted using the Matlab/simscape tool. Extended and unscented Kalman filters were implemented to estimate backlash gap size, and their performance was compared using root-mean-square error technique. Results show that both Kalman filters estimate a simulated gap size very well. However, the unscented Kalman filter performs relatively higher than that of the extended Kalman filter around sharp edges during the switching behavior.