Analytical model of tire rolling resistance based on elastic hysteresis theory

Abstract: With the situation of the global power shortage and the increasing demand for the fuel, it becomes an important subject for the tire researchers to reduce energy consumption of tire and improve tire's energy efficiency. In the field of the interaction mechanism between the tire and the road, a calculation model of the energy consumption of the tire is very meaningful, and it is restricted by multiple conditions, such as the tire temperature, the material properties and the friction conditions. The tire's friction force develops from the contact region. In the process of tire rolling, the forces generate periodical stress spectrum whose frequency lies on the tire's rolling velocity. The periodical stress causes energy loss according to the size and the material property of the tire. The parameter identification of the proposed model in this paper could be carried out through specific experiments, which possessed the variation characteristics for the vertical loading and velocity of the tire through the horizontal motion of the sine guide rail and the load of the guide rod, and the equipment consisted of guide pulley, guide rod, sine guide rail, tire and supporting structure. The brush model assumes that the slide rate develops from the relative displacement of the tread between the wheel hub and the road. The tread is supposed to be elastic brush adhered to the stiff wheel hub. The wheel hub can neither stretch nor shrink, yet deformations may occur in every small elastic brush. Using the brush model to simplify the interaction relationship between the tires and the ground, the contact patch is divided into two parts: the first is loading part which ranges from the starting contact point to the central of the contact region, and the elastic force fits the loading curve of tire's compound restoring force; the second is unloading part which ranges from the central of the contact region to the end contact point, and the elastic force fits the unloading curve of tire's compound restoring force. The analytical model of tire rolling resistance can be obtained by the integral within the two contact parts for the loading curve function and unloading curve function, which is the main innovation of this paper. In the end, by defining the velocity and the load as the test variables, the effectiveness of the proposed analytical model was verified by the experiments of the rolling resistance measurement in accordance with the standard of ISO 28580. The results showed that the rolling resistance of the tire increased with the increasing of speed (10-120 km/h) and vertical load (6-25 kN); and change trend of the test result was consistent with that of the analytical value under the same condition. The new model of rolling resistance proposed in this paper is helpful to structure optimization of the tire.