An Approach to the Theory of Rolling Contact (3rd Report)

A theoretical approach is presented to the plane theory of rolling contact with friction. In the present paper, the existence of the stick area is considered, then the boundary conditions of this problem are derived and the analyses of elastic contact of two cylinders are given. When the contact area is constituted by the stick area alone, the boundary value problem results in the Hilbert problem in the theory of functions. If two cylinders have the same material properties, the stress field coincides with one of Hertz contact. If they have not the same material properties, the contact width becomes shorter and the maximum contact pressure becomes higher than those of Hertz contact. Then, the tangential force is not transmitted. In addition, the stress field is discussed on the assumption that two cylinders, having the same matertial properties, constitute the stick and slip areas. In this case, the contact pressure and the contact width coincide with those of Hertz contact. Then, the stick area can exist in the neighborhood of the leading edge and the length of the stick area is determined uniquely by the values of the normal force, the tangential force and the coefficient of friction in the slip area.