This article describes the mechanism of precursor events; the mechanism was determined through an experiment and simulation by considering non-uniform normal loading. In the experiment, real-time observations of a contact zone were performed using a longitudinal line contact of PMMA specimens (i.e., a slider on a stationary base block) under a total normal load of 400 N. Partial propagations of the detachment front were considered as precursor events, and it was found that non-uniform normal loading influences the occurrence frequency of the precursor events and the increasing rate of the propagation length. In the simulation, the time evolution of a multidegree-of-freedom system with Coulomb friction was studied. The model considered in the simulation comprised multiple masses serially connected by linear springs on a stationary rigid plane. By regarding the precursor in the experiment to correspond to a partial slip (i.e., simultaneous slip of some of the masses) in the simulation, the influence of non-uniform normal loading on the precursor events can be explained to a certain extent. Additionally, it was found that the apparent static friction coefficient (i.e., the ratio of the maximum tangential load to the total normal load) could be lesser than the real static friction coefficient due to the residual strain in the slider.
The sliding of a solid object on a solid substrate requires a shear force that is larger than the maximum static friction force. It is commonly believed that the maximum static friction force is proportional to the loading force and does not depend on the apparent contact area. The ratio of the maximum static friction force to the loading force is called the static friction coefficient µM, which is considered to be a constant. Here, we conduct experiments demonstrating that the static friction force of a slider on a substrate follows a novel friction law under certain conditions. The magnitude of µM decreases as the loading force increases or as the apparent contact area decreases. This behavior is caused by the slip of local precursors before the onset of bulk sliding and is consistent with recent theory. The results of this study will develop novel methods for static friction control.
The condition for the occurrence of stick-slip motion is examined analytically based on a 1-DOF system with Coulomb friction which includes seven independent parameters. There exist two dimensionless parameters which control the occurrence of stick-slip motion, one denotes the easiness for the occurrence of stick-slip motion and the other is the damping ratio acting to suppress the motion. A simple non-occurrence inequality of stick-slip motion is derived with the two dimensionless parameters through dimensionless analysis and numerical simulation, which has both high accuracy and high usability. Its validity is confirmed by the comparison with the experimental results reported by Singh. Nomenclature c viscous damping coefficient [Ns/m] F frictional force [N] F k kinetic friction (=l k W) [N] F s static friction [N] F smax maximum static friction (=l s W) [N] k stiffness [N/m] m mass [kg] t time [s] V moving velocity of the floor surface [m/s] W normal load [N] x position of the object [m] x 0position of the object when the spring is in its natural length (= )F k /k) [m] c ratio of friction coefficients (=l k /Dl) dimensionless mechanical energy f damping ratio (=c/2(mk) 1/2 ) D dimensionless dissipative energy Dl difference of friction coefficients (= l s )l k ) k dimensionless parameter (= DlW/(mk) 1/2 V) l k kinetic friction coefficient l s static friction coefficient n dimensionless position (=x n x/V) s dimensionless time (=x n t) x n natural angular frequency (=(k/m) 1/2 ) ( AE ) derivative with respect to time (=d/dt) ( 0 ) derivative with respect to dimensionless time (=d/ds)
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