Handling of 2-axle and 3-axle Trucks
For my final project in my Vehicle Dynamics class in my first semester of my masters degree, I was in a group where we had to look at the ride and handling of 2 and 3 axles trucks. I did the handling portion of the projects. To evaluate the handling the bicycle model was used.
I began the problem by drawing out the bicycle model with the center of rotation then the labeled the tires velocities. The tires velocity will be at a right angle to the line connecting the center of the contact patch to the center of ration. For the front wheel which is used to steer it is the same effect but it will have a steering angle then a slip angle, the angle between the Y axis and the velocity (Beta) makes the right angle with the center of rotation. Beta plus the slip angle will give the steering angle. The second step I did was draw out the free body diagram for truck with the the forces Fx Fy and M about the tire. The forces will point in the direction of the tire. This free body diagram is what was used to start the differential equation in order to solve for the EOMs.
Bicycle Model of 3-axle truck during turning
Free Body Diagram of 3-axle truck during turning
Taking the forces from the free body diagram and setting them into a sum of the forces and moments in each direction. This will be a result in a second order differential equation with the velocity and yaw being the main components of it. In order to set up the differential equation there needs to be a substitution for the slip angle alpha. This substitution gives the velocity in terms of velocity in the X and Y direction as well as the yaw rate. Taking all of this it can be simplified down to solving for the acceleration in the y direction (Vydot), and the yaw acceleration (psidot). The Vydot deals with the forces in the X and Y direction while the Psi_dot deals with the moments created. From this problem I put the equations into matrix form with all terms groups by vy and r. then