DETERMINATION OF LIMITING RADII OF THE CONTACT AREA IN AXISYMMETRICALCONTACT PROBLEMS WITH FRICTIONAL HEAT-GENERATION

Axi-symmetric contact problems for a half-space with frictional heat g eneration have been considered by Barber, [(1975) Thermoelastic contac t of a rotating sphere and a half-space. Wear 35, 283-289; (1976) Some thermoelastic contact problems involving frictional heating. Q. J. Me ch. Appl. Math. 29, 1-13], Generalov et al [(1976) The contact problem of thermoelasticity for rotating bodies. Izvestija AN USSR. Mechanika Tverdogo Tela. 3, 46-52] and Grilitski and Kulchytsky-Zhyailo [(1991) The axi-symmetrical contact problem of thermoelasticity for the bodie s of rotating. Physicochem. Mech. Mater. 3, 93-97]. The problems have been treated by different methods and their solutions included estimat es of the critical values of the dimensionless contact area radius. Th e present paper gives closed form expressions for these limiting radii by the application of Atkinson's result [(1976) A Survey of Numerical Methods for the Solution of Fredholm integral Equations of the Second Kind. SIAM, Philadelphia (SIAM Monograph)] to the governing Fredholm integral equations, rather than using a full solution as was done by p revious authors.