Vehicle Shimmy Modeling With Pacejka’s Magic Formula and the Delayed Tire Model

Tian Mi, Gabor Stepan, Denes Takacs, and Nan Chen (January 23, 2020). "Vehicle Shimmy Modeling With Pacejka's Magic Formula and the Delayed Tire Model." ASME. J. Comput. Nonlinear Dynam. March 2020; 15(3): 031005. https://doi.org/10.1115/1.4045943

Shimmy is a self-excited vibration which can appear in various wheeled mechanisms such as trailers, motorcycles, bicycles, cars, landing gears of aircrafts, and even baby strollers or supermarket trolleys. Shimmy of cars is also known as vehicle shimmy or death wobble. The cause of shimmy is related to the dynamic characteristics of the tire-road contact and the overall system structure. It increases tire wear, deteriorates vehicle handling, and causes further instability problems of the whole vehicle.

In this paper, a 3 degree-of-freedom model of vehicle front wheels with dependent suspension is studied from the viewpoint of possible appearance of shimmy, and two tire models are compared. The two tire models have essentially different assumptions: Pacejka’s magic formula uses linearization in space along the tire-ground contact line where the tire points stick to the ground, while the delayed tire model uses linearization in time by considering small (but spatially nonlinear) lateral deformations of the tire in the contact region. The theoretical results show that the delayed tire model presents additional instabilities (i.e., shimmy) at low speeds, and especially at low damping values.

The investigation of this model is motivated by the occurrence of shimmy on some heavy vehicles and jeeps with worn front wheel suspension system, and the conclusions might be useful in the future study of shimmy in systems with independent suspensions of some electric vehicles.