Rate independent hysteresis seems to be the dominant frictional characteristic found in many machine elements in common engineering use, such as plain and rolling element guideways. The study of the non-linear dynamics caused by such elements becomes imperative if we wish to achieve improved design and, in particular, effective control of such machines. This paper reviews systematic analysis, which we have carried out to characterize the dynamics of rolling element guideways. The dependency of hysteresis characteristics on the bearing design parameters is first investigated and the notion of ‘equivalent’ dynamic quantities, namely stiffness and damping, is introduced. Secondly, a frequency domain, harmonic analysis method for mass-“hysteresis spring” systems, via application of the Describing Function method, is developed and discussed. We checked the validity and applicability of this approach by direct numerical simulation as well as by experiment. The results showed that the (amplitude dependent) Frequency Response Maps invariably contain an “anomalous” region where the response is very sensitive to systems parameter variations. This manifests itself in practice in jump-like phenomena, which thus appear to be inherent features of this type of system. Finally, appropriate control structures for systems with this type of hysteresis elements are proposed and discussed.

This content is only available via PDF.
You do not currently have access to this content.