Substructuring Method and Eigenfunction Representation for a Rolling Tyre Coupled to a Secondary Mechanical System

This paper deals with the simulation of a running, vibrating tyre coupled at its spindle to a secondary structure. First a generalized substructuring formulation is derived from the equation of continuum of the rolling tyre projected in the reference frame of the road. It results in the ability to express the coupling problem on the basis of the modal characteristics of the system with fixed interface. This simplified condition is then investigated further. Physical models of the tyre, such as membranes on springs, make it possible to extrapolate rolling conditions eigenfrequencies and mode shapes from quasistatic identifications. New results are provided concerning the direction along which resonances are observed at the spindle as a function of speed. In particular it is shown how the resultant of a mode ‘rotates’ when speed increases. Finally structural and physical models are used jointly for the simulation of the forces at the spindle of a tyre rolling over a small cleat. The input from the cleat is described using a ‘virtual profile’. This technique allows the contact area to be reduced to a single point and eigenvalues are then derived from the membrane analogy. It is found that the model allows for an accurate representation of experimental data at the speeds of interest.