WHEEL LIFTOFF MODELING AND BIFURCATION ANALYSIS FOR THE ROLL DYNAMICS OF A FULL VEHICLE NON LINEAR MODEL

Abstract

It is desirable that a vehicle be stable at higher speeds and steering angles. A vehicle can undergo maneuver induced stability failure through yaw and roll instability. Vehicle rollover is considered as the most severe problem faced because it involve the fatal head injuries and the risk of death increases when a vehicle undergo stability failure through rollover. Generally vehicle wheel liftoff condition is considered as an end to roll dynamics when designing a controller to solve vehicle rollover problem but there is a possibility that after wheel liftoff, depending upon the value of lateral acceleration’ the vehicle may return back to the again make contact with the surface of the road. Many control systems have been developed based on the pre-liftoff roll model to prevent vehicle rollover problem. In order to prevent the vehicle from rollover a better control system can be designed depending upon the vehicle roll model after wheel liftoff. It is therefore necessary to first develop a post wheel liftoff roll model of the vehicle. The vehicle roll model gets the value of the lateral acceleration as an input from the nonlinear full vehicle model. In order to solve this issue a non-linear model for the vehicle is developed. The model includes vehicle handling model. Tire forces are developed on the tire-road contact point of the vehicle. There are many tire formulas which include magic tire formula, Fiala tire model, Dug off tire formula and Calspan tire model. Both Magic tire formula and Calspan tire formula were used to calculate the tire forces. Individual tire slip angle and longitudinal slip was the input to the tire formula to calculate the lateral and longitudinal forces respectively. A non-linear full vehicle model was developed and validated with commercial software Carsim. After the successful validation of the vehicle different states and variables a roll model of the vehicle was made for vehicle for post lift off condition. The wheel lift off model was used to get the behavior of the vehicle when due to high lateral acceleration at advance speeds and steering angle the adjacent wheels of the vehicle loses its contact with the surface of the earth. The phase portraits were drawn for the roll states of the vehicle model after and before wheel lift off. Analytical and technical stability was discussed with reference to wheel lift off and rollover 10 problem. Rollover thresholds were found to limit the stable and unstable region. Rollover threshold in term of the control parameter lateral acceleration were found.