The lubrication of rollers III. A theoretical discussion of friction and the temperatures in the oil film

Abstract

Measurements of the thickness of the oil film have shown that the lubrication of loaded rollers is hydrodynamic in character. But hitherto the theories of this lubrication have been isothermal; frictional heating has been ignored. For the understanding of the frictional behaviour and also to define the physical conditions met by the oil in its passage through the conjunction of the disks a knowledge of the temperatures in the film is required. It is from the shearing of the oil in the film that the frictional heat arises. In this paper the dissipation of the heat by conduction through the oil to the surfaces of the disks and by transport with the oil (i.e. convection) are both considered. The temperatures in the film are assessed from the balance between the rates of generation and dissipation of heat. It is shown that in pure rolling the temperatures arising from friction are confined to the entry side ahead of the region of high pressure and that for the range of conditions considered the tem ­peratures are too low to influence thickness. With sliding it is shown that conduction is the important mechanism of dissipation and that the temperatures due to the sliding rise with pressure. On the entry side where the pressures are low, so are the temperatures. This explains the insensitivity of film thickness to sliding which has been demonstrated experimentally. Within the pressure zone high temperatures occur (e.g. a temperature rise of 200 deg C ). The distributions of temperature and viscosity have been found and also the velocity profiles of the oil. These show the cooler oil close to the surfaces of the disks to act almost as a rigid extension of the disks themselves; a situation akin to that postulated in boundary lubrication. From the viscosity distributions, expressions for the effective viscosity within the pressure zone (i.e. that constant viscosity which would give the same frictional traction) and for the frictional traction have been developed. These display the factors of importance in relation to friction and provide a theoretical background to the experimental measurements of effective viscosity and friction which will be described in part IV.