Automatic detection of clearance in mechanical systems: theory and simulation

This paper proposes a technique for the detection of clearance in mechanical systems under dynamic conditions with specific application to detecting backlash in gear systems of servomechanisms. The technique is based on a momentum transfer analysis that shows that the change in the speed (defined as the bounce) of the primary gear due to impact with the secondary gear is related to the magnitude of the backlash. An algorithm designed to monitor the bounce is developed. It is proposed that the standard bounce, determined by the standard deviation of the demodulated envelope of the speed of the primary gear, is a good measure of the bounce when the system is excited sinusoidally. The algorithm's accuracy and sensitivity are verified through computer simulation of an open loop DC servomechanism. An approximately linear relationship between the standard bounce and the backlash magnitude is observed. The detection technique is accurate, computationally simple, and requires no additional sensors if the servosystem to be monitored already has a conventional tachometer.