Development of planar rigid-elastic coupling tyre model with analytical multi-stiffness sidewall

In this study, combining the membrane feature with inflation pressure and the structural deformation caused by sidewall curvature, rigid-elastic coupling tyre model with analytical multi-stiffness sidewall is proposed for a heavy-loaded radial tyre with a large section ratio. The membrane pre-tension of sidewall arc resulting from inflation pressure is investigated. By means of virtual work principle, the structural deformation of sidewall curved arc resulting from the arc curvature, including stretching, bending and shearing deformation is derived. The structural stiffness caused by the sidewall curvature and membrane pre-tension caused by the inflation pressure are combined for the multi-stiffness sidewall model. The influence of the sidewall structural and geometrical parameters on the sidewall multi-stiffness, modal resonant frequency and transfer function is researched and discussed. The non-linear characteristic of sidewall multi-stiffness with respect to the sidewall radial deformation is investigated. Experimental and theoretical results show that: (1) the multi-stiffness of sidewall can characterise the membrane-tension stiffness caused by inflation pressure and the structural stiffness led by the sidewall curvature and material properties; (2) the different multi-stiffnesses of upper and lower sidewall arcs results from the different interval angles; (3) the multi-stiffness of sidewall is non-linear to the radial sidewall deformation. Taking the flexible deformation of tyre carcass and the analytical multi-stiffness of tyre sidewall into consideration, rigid-elastic coupling tyre model with multi-stiffness sidewall is suitable for the heavy-loaded radial tyre with a large section ratio or tyres under impulsive loading and large deformation.