The lubrication of rollers IV. Measurements of friction and effective viscosity

Abstract Measurements of friction with disk machines are described. The measurements have been made under conditions which fit them particularly for comparison with the theory of hydrodynamic lubrication of rollers and with the theory of frictional heating which has been developed in part III. The frictions due to rolling and sliding have been measured separately. It is shown that the frictional tractions T1 and T2 acting upon the surfaces of two disks can be expressed by — _ T _ where TR is the traction due to rolling and Ts is that due to sliding. If the disk 1 runs freely in frictionless bearings T1 must be zero and the disk runs in the condition TR = Ts. A four-disk machine is described in which the central disk, since it has no bearings, runs in the above condition unless some external torque is imposed upon it. External torques were applied by a band brake and from the curves of traction against sliding thereby obtained both and the way in which Ts increases with sliding speed were deduced. It is shown that in the elasto-hydrodynamic regime TR is independent of load and simply proportional to the thickness of the hydrodynamic film. It is also shown that this behaviour follows from the hydrodynamic theory and that the magnitudes of the rolling friction as predicted by theory and as deduced from experiment are substantially in accord. From experimental determinations of film thickness and from the linear increase of Ts with sliding speed over the range of sliding speeds employed ( ~ 1 cm s-1) values of the effective viscosity ( rjm) at the rolling point were deduced and are presented as a function of rolling speed {u as | ( mj +«2)). By effective viscosity is meant that constant viscosity throughout the conjunction of the disks which would give rise to the observed friction. It is shown that the values of so obtained when extrapolated to zero rolling speed are consistent with published results of experiments with dropping ball viscometers in high-pressure apparatus (Pressure Viscosity Report 1953) both with respect to the effects of pressure and of temperature. But the more important feature of the results from the disk experiments is that they show the effects of pressure and temperature upon the apparent viscosity of the oil to diminish as the rolling speed is increased, i.e. as the time for which the oil is under stress diminishes. This behaviour is interpreted in terms of a Maxwellian fluid and the required values of the elastic modulus in shear are deduced. However, although the visco-elastic hypothesis accounts for the observations it is stressed that it cannot yet be taken as the definitive explanation. In a further series of experiments a two-disk machine adapted for the direct measurement of friction independently of bearing frictions was used to explore sliding speeds up to 400 cm s-1. In contrast with the previous measurements, at such speeds of sliding frictional heating has a major effect upon effective viscosity, for example, in a particular instance the introduction of 400 cm s-1 sliding caused the effective viscosity to fall from ~ 3000 P at the rolling point to ~ 20 P. It is shown that the frictions and effective viscosities predicted by the theory of frictional heating (part III) and the measurements now reported are, in their larger aspects, substantially in accord. For example, in a particular instance theory predicted a coefficient of friction of 0-05 whereas experiment gave a coefficient of 0.03 and both experiment and theory show that as the sliding speed increases the friction rises to a maximum and then falls. But the theory of part III when applied to the experimental results leads to a value of the thermal conductivity of the oil of about half that to be expected from Bridgman’s work (1949). However, measurements in finer detail of friction up to a sliding speed of 30 cm s-1 indicate that an intrinsic effect (i.e. an effect at constant temperature) of rate of strain upon viscosity exists. By taking this into account the anomaly with respect to thermal conductivity can be resolved. The experimental results show clearly that in a lubricating system of widespread type (e.g. ballraces, gears) a mineral oil exhibits distinctive dynamic characteristics which are of significance with respect both to friction and to the thickness of the hydrodynamic oil film. The comparison of experiment and theory also emphasizes the importance of the thermal conductivity of the oil in relation to friction and to the temperatures in the oil film.