A modified Hertzian foil rolling model: approximations based on perturbation methods

Fleck and Johnson (Int. J. Mech. Sci. 1987;29:507) have developed a foil rolling model, which has been used subsequently as a temper rolling model, based on a modification of the Hertzian contact problem. It removes the restrictive assumption that the rolls remain circular in profile. A perturbation approximation of the Fleck and Johnson model equations for small reductions has been developed. This enables good approximations to the roll torque and roll force to be obtained in a small fraction of the time required for the full iterative solution and has potential for use in on-line control.