In one case a rigid ellipsoidal die translates over the surface of a half-space. Because
of friction, both compression and shear force are required. In the other, a rigid sphere
rolls on the surface under a compressive force. Both motions occur along
a straight path at constant subcritical speed. A dynamic steady state is
treated, that is, the contact zone and its traction remain constant in the
frame of the die or sphere. Exact solutions for contact zone traction are
derived in analytic form, as well as formulas for the contact zone shape. Axial
symmetry is not required in the solution process. Cartesian coordinates are used,
but a system of quasipolar coordinates is introduced that allows problem
reduction to singular integral equations similar in form to those found in 2D
contact.
Keywords
sliding contact, ellipsoid, rolling contact sphere,
quasipolar
