1998-11-16

Asymmetric Roll Centers 983085

The roll center is an important analysis tool for vehicle dynamics. But most analysis of the roll center is based on production cars, which usually have symmetric suspensions and a center of gravity near the centerline of the vehicle. Racing cars, particularly oval track stock cars, often have asymmetric suspensions and usually have a weight bias. For a car that is only going to turn left there is no reason for the left side front suspension to be anything like the right side. Oval track cars usually have as much weight on the inside as the rules allow.
Analytical tools adapted from the standard industry texts or production car use do not properly address asymmetric suspensions. This paper will analyze the asymmetric suspension and discuss the role of the roll center. It will begin with a theoretical analysis of the roll center and the underlying assumptions. It will show that the roll center is a clever device for calculating forces where you do not know how lateral force is distributed between the inside and outside tires.
The paper will include an analysis of the relationship between lateral movement of the roll center as a result of roll and vertical movement of the roll center as a result of bump movement. The paper will prove that a symmetric suspension which exhibits no lateral movement of the roll center as a result of chassis roll will also have a roll center which moves vertically with the center of gravity when the chassis exhibits vertical movement. This desirable property preserves the moment arm and contributes to stability. It also explains why lateral movement of the roll center, which is calculated by popular software programs, can be used as a design criteria.
This analysis will then be extended to asymmetric suspensions and will derive stability criteria for suspensions that do not have the roll center on the centerline of the car. Techniques will be developed which allow the designer to place the roll center wherever he wants and keep it near there as the vehicle moves.

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