Maximizing the Effective Quasi-Usage Rate for 4WIMD-EVs Under Combined-Slip Conditions

Since the coupling of tire forces, the single longitudinal or lateral vehicle analysis method cannot adequately characterize the vehicle stability, especially the large tire slip ratio under the combined-slip conditions reduces the effective usage rate of tire force, which will increase the risk of vehicle instability. Thus, the effective quasi-usage rate of tire force based on the Monte Carlo method is proposed to solve the constraint of tire slip ratio that can maximize the quasi-usage rate. Firstly, the effective quasi-usage rate
$P_{e\!f\!f}$
is proposed, which is a better comprehensive evaluation standard for vehicle stability and tire force usage rate under the combined-slip conditions by employing the Monte Carlo method and
$\beta -\dot{\beta }-V_{x}$
phase space; Further, the trend of
$P_{e\!f\!f}$
with tire slip ratio is divided into 3 characteristic points and 2 variation stages, the constraint of tire slip ratio is defined by analyzing the characteristics of tire force at different points and stages; Then, the neural network is used to train the data set of constraint to generate the dynamic constraint model, and the objective function of model predictive control strategy considering the constraint of tire slip ratio is established to verify the controller under the combined-slip conditions. The acceleration and deceleration-in-turn are conducted by 4WIMD-EVs on the Hardware-In-the-Loop (HIL) simulation platform. The results show that when the tire slip ratio is controlled under the dynamic constraint proposed in this article, the vehicle has stronger stability and c.g. acceleration, which also proves the effectiveness of the proposed effective quasi-usage rate.