Dynamic characterization of hysteresis elements in mechanical systems. II. Experimental validation.

The industrial demand for machine tools with ever increasing speed and accuracy calls for a closer look at the physical phenomena that are present at small movements of those machine's slides. One of these phenomena, and probably the most dominant one, is the dependence of the friction force on displacement that can be described by a rate-independent hysteresis function with nonlocal memory. The influence of this highly nonlinear effect on the dynamics of the system has been theoretically analyzed in Part I of this paper. This part (II) aims at verifying these theoretical results on three experimental setups. Two setups, consisting of linearly driven rolling element guideways, have been built to specifically study the hysteretic friction behavior. The experiments performed on these specially designed setups are then repeated on one axis of an industrial pick-and-place device, driven by a linear motor and guided by commercial guideways. The results of the experiments on all the setups agree qualitatively well with the theoretically predicted ones and point to the inherent difficulty of accurate quantitative identification of the hysteretic behavior. They further show that the hysteretic friction behavior has a direct bearing on the dynamics of machine tools and its presence should therefore be carefully considered in the dynamic identification process of these systems.

Dynamic characterization of hysteresis elements in mechanical systems. I. Theoretical analysis.

The pre-sliding-pre-rolling phase of friction behavior is dominated by rate-independent hysteresis. Many machine elements in common engineering use exhibit, therefore, the characteristic of "hysteresis springs," for small displacements at least. Plain and rolling element bearings that are widely used in motion guidance of machine tools are typical examples. While the presence of a hysteresis element may mark the character of the resulting dynamics, little is to be found about this topic in the literature. The study of the nonlinear dynamics caused by such elements becomes imperative if we wish to achieve accurate control of such machines. In this Part I of the investigation, we examine a single-degree-of-freedom mass-hysteresis-spring system and show that, while the free response case is amenable to an exact solution, the more important case of forced response has no closed form solution and requires other methods of treatment. We consider harmonic-balance analysis methods (which are common analysis tools in engineering) suitable for frequency-domain treatment, in particular the approximate describing function (DF) method, and compare those results with "exact" numerical simulations. The DF method yields basically a linear equation with amplitude-dependent modal parameters. We find that agreement in the frequency response function, between DF and exact solution, is good for small excitation amplitudes and for very large amplitudes. Intermediate values, however, show high sensitivity to amplitude variations and, consequently, no regular solution is obtainable by either approach. This appears to be an inherent property of the system pointing to the need for developing further analysis methods. Experimental verification of the analysis outlined in this Part I is given in Part II of the paper.

Identification of pre-sliding friction dynamics.

The hysteretic nonlinear dependence of pre-sliding friction force on displacement is modeled using different physics-based and black-box approaches including various Maxwell-slip models, NARX models, neural networks, nonparametric (local) models and dynamical networks. The efficiency and accuracy of these identification methods is compared for an experimental time series where the observed friction force is predicted from the measured displacement. All models, although varying in their degree of accuracy, show good prediction capability of pre-sliding friction. Finally, we show that even better results can be achieved by using an ensemble of the best models for prediction.