Traction measurements for two kinds of synthetic naphthenic traction oils were carried out, using a two-roller machine. The Eyring stress and shear modulus of test oils were estimated simultaneously by a curve-fitting procedure based on the nonlinear viscoelastic model introduced by Johnson and Tevaarwerk. As a consequence, it has been found that the Eyring stress decreases with an increase in contact pressure, and it increases with oil temperature. It has been also clarified that the effective shear modulus, including the effect of the roller compliance, decreases with an increase in contact pressure. At higher pressure it decreases as the oil temperature increases, whereas at lower pressure it increases with the oil temperature. In addition, the influences of operating conditions such as the kind of oil, pressure, and oil temperature upon the Eyring stress, shear modulus, and traction coefficient were also investigated. It has been shown that under the operating conditions where the effect of oil viscosity is predominant, the accuracy of the shear modulus calculation deteriorates when the shear modulus is estimated by assuming that the oil is perfectly elastic.

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