Backlash Identification in Two-Mass Systems by Delayed Relay Feedback

Abstract

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 twoinertia motor bench that has coupling with backlash gap of about one degree.

Relay Feedback Systems — Established Approaches and New Perspectives for Application

“…In what follows, we will address such case of a two-mass, correspondingly two-inertia, system with backlash, while using only a one-side measurement for estimation of the backlash size via a relay feedback approach. The main principles will be discussed, together with some strengthening experimental results, while for more detailed developments of the method an interested reader is referred to (32) .…”

“…The utilized geared coupling between the motor and load contains a backlash. For further details on the experimental setup we refer to (32) . The reference measured input-output backlash map is shown in Fig.…”

“…switching to the engagement mode. Details on the relay parameterization and analytic solution of the limit cycle, in terms of the displacement amplitude and period of oscillations, can be found in (32) .…”

“…For instance, an approach for system mass measurement using the relay feedback with hysteresis has been reported in (31) . The most recently developed method (32) of backlash identification in two-mass systems, by using the non-ideal relay in feedback, cf. Fig.…”

“…This part largely orients on the established works (12) (13) (33) and, additionally, provides illustrative explanations to the use of relay feedback with related properties. In Section 3, an original approach (32) of identifying the unknown backlash nonlinearity, hidden inside of the two-mass systems, by using the drifting limit cycles is presented. An experimental case study is accompanying the proposed method and is also presented.…”