Dynamic characterization of hysteresis elements in mechanical systems

This paper considers the dynamic behavior of single degree of freedom systems consisting of a mass on a "non-linear hysteretic spring". Elements in common engineering use, in the form of plain or rolling element bearings for a variety of applications such as linear guideways in machine tools, exhibit predominately such "non-linear hysteretic spring" behavior. The highly non-linear effect caused by such elements has hitherto not been taken into consideration, by designers, in the control design for such machine tools. However, since more accurate and faster machines are required, these non-linear hysteresis effects should be identified and incorporated in the control design. The properties of this type of static hysteresis are first outlined. Thereafter, the dynamics of autonomous systems are deduced by an analytic solution. The problem of forced response is discussed and treated by using the approximate describing function approach, which is then validated by direct simulation. This analysis shows that for small excitation amplitudes an approximate linear behavior is obtained. For excitation amplitudes around the saturation value of the hysteretic spring, there is a region that is marked by high sensitivity of the displacement amplitude for a given excitation amplitude in which no satisfactory results are obtained, while concordant results are obtained over the greatest part of the Amplitude-Frequency plain. The results of the analysis are intended for use as input for the design process of appropriate controllers.