Height- Dependent Asperity Radii of Curvatures in a Contact and Friction Model

The effect of a height-dependent asperity radius of curvature is accounted for in a recently developed scaledependent model of contact and friction. The contact and friction model includes the effects of adhesion, using the Maugis model, and of scale-dependent friction, using the Hurtado and Kim single asperity friction model. This multiasperity model has been modified to include the effect of noncontacting asperities. The results indicate the types of conditions under which the effects of a height-dependent asperity radius of curvature affects friction. INTRODUCTION Contact and friction affect the operation of many machines and tools that we use every day, as well as some of the most basic activities in nature. Examples range from belt drives, brakes, tires, and clutches in automobiles and in other machines; gears, bearings and seals in a variety of mechanical systems; electrical contacts in motors; slider-disk interactions in a computer disk drive; various MEMS devices; a robotic manipulator joint; the motion of a human knee-joint (natural or artificial); and walking/running. The friction force F is the tangential force resisting the relative motion of two surfaces which are pressed against each other with a normal force P. Amontons, in 1699, and Coulomb in 1785, developed our phenomenological understanding of dry friction between two contacting bodies. Amontons-Coulomb friction states that the ratio of the friction force (during sliding) to the normal force is a constant called the coefficient of kinetic friction. Similarly the coefficient of static friction is the ratio of the maximum friction force F that the surfaces can sustain, without relative motion, to the normal force. These friction laws can be summarized by defining the coefficient of friction as F