Integrated Vehicle Dynamics and Control
by Wuwei Chen, Hansong Xiao, Qidong Wang, Linfeng Zhao, Maofei Zhu
3Longitudinal Vehicle Dynamics and Control
3.1 Longitudinal Vehicle Dynamics Equations
3.1.1 Longitudinal Force Analysis
The dynamics problems along the x-axis in a vehicle coordinate system are called the longitudinal dynamics problems. The characteristics of vehicle acceleration and deceleration are the main research topics, and these two states of motion correspond to, respectively, the traction and braking of the vehicle.
3.1.1.1 Traction
In the case of traction, the force on a car pointing to the positive direction of the x-axis is the longitudinal force produced by the interaction between the driving wheels and the road, which is represented by Fx.
When the tyre is on a high adhesion road, the longitudinal force Fx is equal to the force of traction Ft.
where Tt is the torque transmitted to the driving wheels, Te is the engine torque, ig is the transmission ratio, i0 is the main gear ratio, ηt is the driveline efficiency, and r0 is the driving wheel radius.
When a tyre is running on a poor adhesion road, the longitudinal force Fx is equal to the tyre longitudinal force, which is actually provided by the ground. It can be calculated through the tyre longitudinal force and slip ratio curve, or through tyre models when the tyre motion status is given. The longitudinal slip ratio has a linear relationship with the tyre longitudinal force when the ratio is small; ...
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