基于复合滑移理论的轮胎抓地状态建模与验证

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

为了精确地估计轮胎抓地状态，该文针对影响汽车行驶稳定性和安全性的轮胎和地面之间的相互作用模型进行了深入研究。采用轮胎刷子模型，同时考虑纵向滑移和侧向滑移情况，提出了改进的复合滑移轮胎刷子模型。利用抓地力和最大滚动摩擦系数确定轮胎抓地状态。通过定义复合滑移系数建立了一个关于抓地状态的一元三次方程式，讨论模型中参数对抓地状态的影响，为了提高模型适应性，同时考虑了速度与最大滚动摩擦系数的变化关系。选用225/60R18轮胎的某车型进行3次重复双移线试验，结果显示：在转向时间段内（1.8～2，3.2～3.4，4.4～4.6 s）抓地状态分别为0.54、0.79和0.39，与估计值极限误差分别为4%、5.4%和5.2%，而在直线行驶时测量值与估计值误差小于2%，说明此解析模型可为预测轮胎滑移状态提供一种新的方法。该文对汽车操纵稳定性的研究具有一定的指导意义。

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.