Construction and verification of tire grip state based on combined-slip theory

Abstract: In order to obtain accurate estimation of the tire gripping state, a model on the interaction between the tire and the ground playing a key role in the driving stability and the security of vehicles was studied in this paper. Adopting the Brush Model of tire and considering the contact differences between the longitudinal slip and the lateral slip considered, an improved Brush Model of tire based on the compound slip theory was proposed for modeling the tire gripping state. The Brush Model is an important method to predict the force between the tire and the ground, and in this simplified tire model, the contact state between the tire and the road can be divided into the adhesion area and the slip area. The forces in the adhesion area come from the static friction between the tread of rigid carcass and the road, and the forces in the slip area come from the sliding friction between the tread and the road. The innovation of this article is to distinguish the friction types between the adhesion section and the slip section, and the friction coefficients between the longitudinal and the lateral. The tire's ability to grip is the critical factor of driving, braking, steering and other performances of the vehicle, which comes from the horizontal friction between the tire and the ground. Various active control technologies have been developed to improve the drivability and applied to the active safety system of commercial vehicles. Some experts have raised the protection function of the limit manipulation cases, which was applied into the active manipulation controller. The ratio of the horizontal force and the vertical force was defined as the adhesion coefficient to analyze vehicle adhesion state in some papers. However, it only reflected the change of tire gripping, but the sliding state (the dangerous degree of tire slipping) could not be predicted due to the less accurate model or the complex parameter structure. The state of tire gripping was determined by the horizontal adhesive force, the slipping force and the maximum rolling friction coefficient. In order to obtain standardized expression for gripping state, a simple cubic equation was derived by defining the composite sliding coefficient and a series of constant terms, and the interaction of the parameters on gripping state in the model was discussed, together with the relationship between the velocity and the maximum rolling friction coefficient. In the end, the proposed model was validated by repeating three "Double Lane Change" tests, the equipment in which consisted of speed sensor (DEWE-VGPS- HS), fiber optic gyroscope (iVRU-C167), car centroid test platform (JT-16), steering angle tester (SFA-A-2004S), multifunction meter (TESTO 480) and data acquisition system (DEWE-43), and speed, acceleration, steering angle and displacement were measured. The test results showed that in the steering periods 1.8-2, 3.2-3.4, 4.4- 4.6 s, the gripping states were 0.54, 0.79 and 0.39, respectively, and the limit error values were 4%, 5.4% and 5.2%, respectively, compared with the analytical values, while in the straight driving, the limit error of gripping state was less than 2%, which indicates that this analytical model obtains the higher accuracy under the conditions of the lower gripping state or straight driving and provides a new way for the estimation of tire gripping state. The research gives some guiding principles for the study of vehicle handling and stability.