Rolling and Sliding Friction of Polymeric Materials

Abstract

The coefficient of rolling friction for a hard sphere and a cylinder over a polymeric material are derived as a function of mechanical loss. A few assumptions were made to clarify the quantitative relation between rolling friction and dynamic modulus of polymeric material. Viscoelastic properties of polymeric material are represented by the generalized Voigt model. Contact deformation of base material owing to the rolling object is assumed to be a periodic phenomenon. From this assumption, the strain and stress for surface deformation is expressed by Fourier series and the stress is also obtained as a function of the dynamic modulus. Spectrum of the relaxation time of polymeric materials is assumed to be moderate and this leads to the correspondence between the rolling velocity and the angular frequency of the dynamic modulus.The coefficient of rolling friction for a rigid sphere is obtained as follows, λs=βs(W/E1)1/4r-3/4, where W, r, and E1 are the load, the radius of the sphere, and the real component of complex the dynamic modulus, respectively. βs is a function of mechanical loss. For a small range of mechanical loss, βs is linearly proportional to mechanical loss. λs is entirely proportional to mechanical loss. Temperature dependence of λs is explained by that of mechanical loss and modulus E1. The rolling velocity corresponds to the angular frequency of dynamic modulus and correspondence between them is obtained as follows v=0.7(Wr/E1)1/4ω. From these relations, the coefficient of rolling friction for any temperature or any rolling velocity can be calculated from the dynamic data, or the dynamic data can be presumed from the rolling friction measurement. Consistency of the rolling frictional measurement for several polymers and theoretical results is quantitatively very good.The coefficient of sliding friction for a hard sphere over a polymeric materials were measured. Temperature dependence of sliding friction of NBR resembles that of mechanical loss. Above glass temperature, however, it deviates from the tendency of mechanical loss curve. This may be due to the ploughing effect.