Backlash Identification in Two-Mass Systems by Delayed Relay Feedback

Backlash, also known as mechanical play, is a piecewise differentiable nonlinearity which exists in several actuated systems, comprising, e.g., rack-and-pinion drives, shaft couplings, toothed gears, and other elements. Generally, the backlash is nested between the moving elements of a complex dynamic system, which handicaps its proper detection and identification. A classical example is the two-mass system which can approximate numerous mechanisms connected by a shaft (or link) with relatively high stiffness and backlash in series. Information about the presence and extent of the backlash is seldom exactly known and is rather conditional upon factors such as wear, fatigue and incipient failures in components. This paper proposes a novel backlash identification method using one-side sensing of a twomass system. The method is based on the delayed relay operator in feedback that allows stable and controllable limit cycles to be induced, operating within the unknown backlash gap. The system model, with structural transformations required for the one-side backlash measurements, is given, along with the analysis of the delayed relay in velocity feedback. Experimental evaluations are shown for a two-inertia motor bench with gear coupling, with a low backlash gap of about one degree.