The Volume of Stressed Material Involved in the Rolling of a Ball

Abstract

The force necessary to roll a ball on a flat plate is experimentally determined as a function of the load for a number of different ball diameters and steel structures. Previously published data expressing rolling force as a power of the load and ball diameter are shown to be inadequate in describing the behavior of the rolling ball over the full-load range employed in this investigation. The rolling force is found to be negligible for contact stresses less than a certain “threshold” contact stress. Once the rolling force becomes measurable, it is shown to be proportional to the volume of significantly stressed material until a contact stress is attained which is sufficient to cause plastic deformation. The significantly stressed volume is determined from the distribution of the strain energy stored in the Hertzian stress field of a ball in contact with a flat plate. The threshold contact stress, the constant of proportionality between the rolling force and significantly stressed volume, and the contact stress at which plastic deformation is initiated are shown to be independent of the diameter of the rolling ball but dependent on steel structure. A model is introduced relating the volume of significantly stressed material to the elastic hysteresis processes responsible for the energy losses during rolling.