Reduction of friction by normal oscillations. II. In-plane system dynamics

Abstract

Abstract:The influence of out-of-plane oscillations on friction is a well-known phenomenon that has been studied extensively with various experimental methods, e.g., pin-on-disk tribometers. However, existing theoretical models have yet achieved only qualitative correspondence with experiment. Here we argue that this may be due to the system dynamics (mass and tangential stiffness) of the pin or other system components being neglected. This paper builds on the results of a previous study [19] by taking the stiffness and resulting dynamics of the system into account. The main governing parameters determining macroscopic friction, including a dimensionless oscillation amplitude, a dimensionless sliding velocity and the relation between three characteristic frequencies (that of externally excited oscillation and two natural oscillation frequencies associated with the contact stiffness and the system stiffness) are identified. In the limiting cases of a very soft system and a very stiff system, our results reproduce the results of previous studies. In between these two limiting cases there is also a resonant case, which is studied here for the first time. The resonant case is notable in that it lacks a critical sliding velocity, above which oscillations no longer reduce friction. Results obtained for the resonant case are qualitatively supported by experiments.

Critical Velocity of Controllability of Sliding Friction by Normal Oscillations in Viscoelastic Contacts

“…The model that will be analyzed in this paper is very similar to the one presented in [7]. It consists of a mass m that is pulled with a constant velocity v 0 through a system spring with a constant stiffness k x (see Fig.…”

“…Note the less than or equal in this formula, which breaks the proportionality and allows  to be less than  0 . To the author's knowledge, the possibility that the influence of normal oscillations on sliding friction may be explained entirely by the presence of intermittent stick phases has not been made explicit before the publication of the two part-study [6,7]. In these papers, the stick-induced reduction of friction force was studied in a displacementcontrolled setting with and without in-plane system dynamics.…”

“…This critical velocity also enters into the primary dimensionless parameter characterizing the behavior of the system, which makes accurate analysis of this quantity doubly important. If the model is augmented with a system spring and a contact mass, thus enabling inplane system dynamics, the expression for the critical velocity becomes [7]:…”

“…Numerical experiments show that in this case, the coefficient of friction reaches a plateau (which is less than  0 ) at fairly low sliding velocities and does not change thereafter. For the full analysis, the reader is referred to [6,7].…”

“…Active control of friction and system stability seems to be an underexplored topic when viscoelastic contacts are concerned, despite many possible applications in conjunction with the ubiquitous use of elastomers and the rising demands placed on devices in contact with biological tissues in medical technology. With this paper we would like to begin establishing a quantitative framework for the analysis of viscoelastic friction under oscillation, by proposing that the same methods used in [6,7] can be applied in viscoelastic contacts in order to calculate the critical velocity in closed form.…”