Rolling Friction on a Viscoelastic Surface

When a rigid sphere is pressed against a plane viscoelastic surface with a normal force and is rolled along with a small force parallel to the surface, the viscoelastic material undergoes deformation (combination of shear and compression, but mostly shear) followed by recovery. The parallel force required to maintain a constant velocity is related to the energy loss in the viscoelastic substratum.  

The coefficient of rolling friction, X, defined as the ratio of the vertical load (WO to the parallel rolling force, depends on the load, the sphere radius, and the viscoelastic properties of the substratum. The rather complicated relationships have been worked out by Atack and Tabor and Flom and Bueche. A measurement of X is roughly equivalent to a measurement of tan 5 at a radian frequency of the order of the angular velocity of the rolling sphere it passes through a maximum as a function of the velocity. The method has been applied to determinations of relative losses in a variety of rubbery and glassy polymers.  

Similarly, the coefficient of friction of a rolling cylinder on a viscoelastic surface has been treated by May, Morris, and Atack and Hunter. It also passes through a maximum as a function of the velocity. A more complete treatment by Minato and Takemura, together with experimental data over a wide range of temperature 

Some practical aspects of viscoelastic behavior in dilute solutions (Chapter 9, Section G) and in the terminal zone (Chapter 10, Section C5) have already been mentioned others are inherent in Chapters 16 and 17. We now call attention to some additional applications. 

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