Effect of Tire Repeated Root Modal on Tire Modelling with Experimental Modal

The effect of tire repeated root modal (RRM) on tire modeling with an experimental modal is studied. Firstly, a radial tire with radial and tangential RRMs is tested and analyzed. By multi-point exciting of the radial tire, a multiple reference frequency domain method based on a least squares (LMS PolyMAX) algorithm is used to identify modal parameters. Then, modal stability diagram (MSD), modal indication function (MIF) and modal assurance criteria (Auto-MAC) matrix are utilized to induce multiple inputs multiple outputs (MIMO) frequency response function (FRF) matrixes. The tests reveal that notable repeated roots exist in both radial and tangential response modes. Their modal frequencies and damping factors are approximately the same, the amplitudes of modal vectors are in the same order of magnitude, and the mode shapes are orthogonal. Based on the works mentioned, the method of trigonometric series modal shapes fitting is adopted, the effects of RRM model on tire modeling with a vertical experimental modal are discussed. The final results show that the effects of considering the RRM shapes are equivalent to the tire mode shapes depended on rotating the tire's different exciting points during tire modeling, and since considering the RRM, the tire mode shapes can be unified and fixed during tire modeling.