Estimation of Gear Backlash: Theory and Simulation

Machine and product condition monitoring is important to product quality control, especially for unmanned manufacturing. This paper proposes a technique for the estimation of clearance in mechanical systems under dynamic conditions with specific application to the estimation of 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 bounce) of the primary gear due to impact with the secondary gear is related to the magnitude of the backlash. An algorithm is presented to estimate the bounce in real-time. The algorithm estimates the bounce by computing the standard bounce which is defined as the standard deviation of the demodulated envelope of the primary gear speed. The standard bounce is shown to be 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. This holds for backlash values exceeding recommended tolerances by ±100 percent. The algorithm is also shown to be insensitive to changes in the simulation model structure, model parameters as well as system and measurement noise. The estimation technique is accurate, computationally simple, and requires no additional sensors if the servosystem to be monitored already has a conventional tachometer.