The two‐dimensional contact pressure distribution of a running radial tire under load is a fundamental property of the tire structure. The two‐dimensional contact pressure distribution in the static case and the one‐dimensional contact pressure distribution in the dynamic case were previously analyzed for a spring bedded ring model consisting of a composite belt ring and a spring system for the sidewall and the tread rubber. In this paper, a Voigt‐type viscoelastic spring system is assumed for the sidewall and the tread rubber. We analyzed the dynamic deformation of the belt ring in a steady state, and obtained the two‐dimensional dynamic contact pressure distribution at speeds up to approximately 60 km/h. The predicted contact pressure distribution for a model with appropriate values for the damping coefficient of each constituent rubber is shown to be in good agreement with experimental results. It is a characteristic feature that increasing velocity yields an increase in the pressure at the leading edge of the crown centerline in the contact area and at the trailing edge of the shoulder line.
The contact pressure distribution and the rolling resistance of a running radial tire under load are fundamental properties of the tire construction, important to the steering performance of automobiles, as is well known. Many theoretical and experimental studies have been previously published on these tire properties. However, the relationships between tire performances in service and tire structural properties have not been clarified sufficiently due to analytical and experimental difficulties. In this paper, establishing a spring support ring model made of a composite belt ring and a Voigt type viscoelastic spring system of the sidewall and the tread rubber, we analyze the one‐dimensional contact pressure distribution of a running tire at speeds of up to 60 km/h. The predicted distribution of the contact pressure under appropriate values of damping coefficients of rubber is shown to be in good agreement with experimental results. It is confirmed by this study that increasing velocity causes the pressure to rise at the leading edge of the contact patch, accompanied by the lowered pressure at the trailing edge, and further a slight movement of the contact area in the forward direction.
The contact deformation of a radial tire with a camber angle, has been an important problem closely related to the cornering characteristics of radial tires. The analysis of this problem has been considered to be so difficult mathematically in describing the asymmetric deformation of a radial tire contacting with the roadway, that few papers have been published. In this paper, we present an analytical approach to this problem by using a spring bedded ring model consisting of sidewall spring systems in the radial, the lateral, and the circumferential directions and a spring bed of the tread rubber, together with a ring strip of the composite belt. Analytical solutions for each belt deformation in the contact and the contact‐free regions are connected by appropriate boundary conditions at both ends. Galerkin's method is used for solving the additional deflection function defined in the contact region. This function plays an important role in determining the contact pressure distribution. Numerical calculations and experiments are conducted for a radial tire of 175SR14. Good agreement between the predicted and the measured results was obtained for two dimensional contact pressure distribution and the camber thrust characterized by the camber angle.
The spring characteristics of a radial tire loaded on a crossbar put on a roadway was analyzed with a spring bedded ring model. Nonlinear radial and tangential spring effects of the sidewall and large deformation of the tread were considered. The tread curvature in the cross section was found to be the most important structural factor for elucidating the enveloping properties of a radial tire in contact with a crossbar. Experimental verifications of the spring effect and the tread deformation of a radial tire were in good agreement with the theoretical predictions.