A planar quasi-static constraint mode tyre model†

The fast-paced, iterative, vehicle design environment demands efficiency when simulating suspension loads. Towards that end, a computationally efficient, linear, planar, quasi-static tyre model is developed in this work that accurately predicts a tyre's lower frequency, reasonably large amplitude, nonlinear stiffness relationship. The axisymmetric, circumferentially isotropic, stiffness equation is discretised into segments, then parameterised by a single stiffness parameter and two shape parameters. The tyre's deformed shape is independent of the overall tyre stiffness and the forces acting on the tyre. Constraint modes capture enveloping and bridging properties and a recursive method yields the set of active constraints at the tyre–road interface. The nonlinear stiffness of a tyre is captured by enforcing unidirectional geometric boundary conditions. The model parameters are identified semi-empirically; simulated cleat test loads match experiments within 7% including nonlinear stiffness when simulating a flat plate test and a discontinuous stiffness when simulating a cleat test.