Abstract
At the beginning of this chapter, the simplifying assumptions to formulate a simple, yet significant, vehicle model are listed. Then the kinematics of the vehicle as a whole is described in detail, followed by the kinematics of each wheel with tire. The next step is the formulation of the constitutive (tire) equations and of the global equilibrium equations. A lot of work is devoted to the load transfers, which requires an in depth suspension analysis. This leads to the definition of the suspension and vehicle internal coordinates, of the no-roll centers and no-roll axis, for both independent and dependent suspensions. The case of three-axle vehicles is also considered. In the end, the vehicle model for handling and performance is formulated in a synthetic, yet precise way. A general description of the mechanics of differential mechanisms, either open or limited slip is included.
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Notes
- 1.
The reason is that df=cosψdx 0+sinψdy 0 is not an exact differential since there does not exist a differentiable function f(x 0,y 0,ψ).
- 2.
But not on the tire slips.
- 3.
At first it may look paradoxical, but it is not. Actually it is common practice in engineering. Just take the most classical cantilever beam, of length l with a concentrated load F at its end. Strictly speaking, the bending moment at the fixed end is not exactly equal to Fl, since the beam deflection takes the force a little closer to the wall. But this effect is usually neglected.
- 4.
A more precise definition of roll angle is given in Sect. 9.2.
- 5.
The symbol \(\hat{\phi}\) (instead of just ϕ) is used to stress that this is not the roll angle under operating conditions.
- 6.
This is true only if the left and right suspensions have perfectly symmetric behavior. For instance, the so-called contractive suspensions do not behave the same way and, therefore, a pure rolling moment also yields some vertical displacement.
- 7.
Just consider that, since ω h >ω s , both M s and \(\hat{\omega}_{s}\) are negative and hence their product is positive, meaning input power for the differential mechanism inside the housing. Consistently, \(M_{f}\hat{\omega}_{f} <0\), which is an output power for the differential mechanism.
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Guiggiani, M. (2014). Vehicle Model for Handling and Performance. In: The Science of Vehicle Dynamics. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8533-4_3
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DOI: https://doi.org/10.1007/978-94-017-8533-4_3
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