Problems
Problem 1.1 (MADRID)
Consider the drivetrain of a standard internal combustion engine vehicle. When accelerating from a stop in wet weather it is common for the wheels to slip due to a film of water between the wheels and the road. Develop a lumped parameter model of this system with the following assumptions,
the engine and transmission together can be simulated as a torque source,
the transmission and wheels are connected with a drive shaft of finite stiffness, and
each wheel has equal mass.
From this description please,
draw a one dimensional lumped parameter model (like the diagrams in problem granda), and
draw a linear graph of the lumped parameter model.
From this description we can draw the following lumped parameter model,
In this diagram we have the torque source mentioned in the problem connected to the wheels modeled as an inertia through the drive shaft modeled as a spring. We know the wheels have inertia because the problem mentions the wheels having mass. There is also a damper connecting the wheel inertia to ground. Furthermore, the inertia \(J\) and damping \(B\) should be multiplied by the number of driven wheels on the vehicle. Alternately, multiple inertias and dampers could be added to the lumped parameter model.
A damper is used here because the viscosity of the fluid film between the tires and the road causes viscous friction which is accurately modeled as a rotational damper. It should be noted that this system is only applicable at low vehicle velocity because the damper is connected to ground.
This lumped parameter model can be converted to the following linear graph,
Online Resources for Section 1.9
No online resources.