Characterization of frictional hysteresis in ball-bearing guideways

Frictional hysteresis is a characteristic that may be found in many machine elements in common engineering use. Plain and rolling element bearings that are widely used in motion guidance of machine tools are typical examples. The study of the non-linear dynamics caused by such elements becomes imperative if we wish to achieve improved design and effective control of such machines. This paper extends the notion of ‘equivalent’ dynamic quantities, namely stiffness and damping, which describe linear systems to rolling element systems, which exhibit hysteretic friction. The dependency of these quantities on design parameters of the guideway such as preload, ball size an groove angle is furthermore examined experimentally on two set-ups. The first set-up is built to specifically study the hysteretic friction behavior, while the second set-up uses a commercial guideway. This study shows further that a single quantity, the equivalent damping ratio at resonance, is able to characterize the dynamics of systems exhibiting hysteretic friction. The greatest part of this paper is therefore dedicated to the experimental correlation of this characteristic damping ratio to the design parameters of rolling element bearings.