Backlash Identification in Two-Mass Systems by Delayed Relay Feedback
The method addresses the practical problem of detecting and quantifying backlash in mechanical systems, which is critical for condition monitoring and fault detection, but the approach is domain-specific and incremental.
This paper proposes a novel method for identifying backlash in two-mass systems using delayed relay feedback with one-side sensing, enabling stable limit cycles within the backlash gap. Experimental results on a two-inertia motor bench with a one-degree backlash gap validate the approach.
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 machine elements. Generally, the backlash is nested between the moving parts 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 the components. This paper proposes a novel backlash identification method using one-side sensing of a two-mass system. The method is based on the delayed relay operator in feedback that allows stable and controllable limit cycles to be induced and operated 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 that has coupling with backlash gap of about one degree.