Contact Of Multiple Surfaces
Author(s)
J. Jäger
Abstract
Contact problems of rough surfaces require the consideration of multiple contact
areas. Characteristic properties can be calculated with approximative models,
which are well documented in the literature on contact mechanics. Advanced
numerical methods are necessary for the calculation of accurate solutions. In this
paper, a recursive BEM method is presented, which is explained in a recently
published book. Some examples illustrate the solution of large multiple contact
areas and demonstrate the application of the so-called reduced friction method
that was developed by the author.
1 Introduction
Many contact problems do not permit analytical solutions in closed form. Under
certain assumptions, however, the frictional problem can be reduced to the
normal problem (Jäger, [3]). The reduced friction model assumes that each stick
area H is a smaller contact area C*. According to Coulomb’s law q = f p, the
tangential traction q in the slip area C – C* is proportional to the normal pressure
p of the actual contact area C. On this condition, an approximation for the
tangential traction q in the stick area C* is the difference of the slip stress of the
contact area and the stick area f (p-p*). For half-spaces and half-planes, the
proportionality between normal pressure and tangential traction carries over to
the tangential displacement ux and the normal displacement uz.
( *),
( )* x z z z
q f p p
u f u f u u κ κ
= −
= ∆ = −
(1)
Integration of (1) gives the equation for the forces Fx and Fz. The normal force
depends on the displacement ζ = uz(x0) of a datum point x0, usually the origin of
the coordinate system. The tangential displacement ξ = ux(x0) is given by (1)
Keywords
Related Book
Other papers in this volume
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