29-01-2013, 02:52 PM
Vehicle Dynamics Theory
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The Roll Center
“Roll Center” is the most misunderstood term in vehicle dynamics. A fairly simple concept - how much lateral force applied at the tire contact patch is transformed into vertical force - has generated a remarkable number of myths. The “roll center” is a simple measure, derived from symmetric production car design, extrapolated to asymmetric racing cars, which overwhelmed the underlying reality. The vary name “roll center” implies much more than it delivers.
Tires generate forces which produce lateral and longitudinal acceleration. This process involves complex concepts ranging from molecular adhesion to the conformity of a soft tire to an irregular road surface. But the result is simple: a force in the plane of the road surface and a vertical force perpendicular to the road surface. The best analogy, due to tire author Paul Haney, involves a broom. If you hold the handle of the broom low it may glide over a washer lying on the ground. If you raise the handle it becomes harder to push but there is more vertical force pushing the bristles into the ground and more likely to dislodge that washer.
The reality of this analogy is the angle of the broom handle, not the height of the end. Cut the broom handle in half but maintain the angle and the effect is the same: the height of the end is irrelevant. “Roll center” is a measure of the height of the broom handle, not the angle. Reality is the angle snf the resulting forces.
The History
Most of vehicle dynamics theory was developed around production cars simply because there were many more production car engineers than racing engineers (and there still are). Production car suspensions are usually symmetric with the center of gravity near the centerline of the car.
Production cars are rarely subject to large lateral forces (outside of racing applications). Few drivers use more than 0.3g even in emergency situations. Consequently production car analysis is usually limited to low lateral forces. Under this assumption chassis roll and subsequent suspension movement can be ignored and the roll center is treated as a static point. Good vehicle dynamics texts, including Dixon and Gillespie, mention this.
The Kinematic Instant Center
Kinematic analysis gives us the four bar theory of movement which defines instant centers of motion. Applied to the double wishbone suspension four-bar theory establishes an instant center. The four bars are the two wishbones, the chassis, and the upright/hub/wheel/tire assembly. The upright/hub/wheel/tire assembly rotates about this instant center. This is a very useful concept because it explains camber change (for small displacements). We will later show it also explains jacking force. The instant center corresponds to the end of the broom handle in the earlier analogy.
The Kinematic Roll Center
The familiar roll center, shown in Illustration 1, is the intersection of lines drawn from the suspension instant centers to the tire contact patches. This is an application of 4-bar theory applied twice. The second application treats the theoretical lines from the kinematic instant centers to the tire contact patches as solid links. The other two links are the chassis (connecting the two instant centers) and the ground. The instant center of this mechanism gives the rotation point which minimizes tread change in reaction to chassis roll. This would be important if we were rolling the chassis in the shop where every bit of scrub would be expressed with the same screech you hear in car parks. But we are dealing with moving vehicles where tread change becomes a small toe change. The kinematic roll center is easily drawn (in two dimensions) and understood but analyzing the resulting movement is complex and leads to myths which are often wrong.