K&C Testing Tips
How to Measure Roll Centers
Roll centers and corresponding virtual swing arm geometry are important properties of a suspension which can be measured on the K&C rig. Though there is much folklore surrounding “roll centers,” we endeavor here to describe the two different ways to make this measurement on the K&C rig: kinematic and force-based.
In the kinematic approach, geometric motion of the wheel relative to the chassis is measured in a vertical bounce test. The rate of change of camber with respect to wheel travel gives us the virtual swing arm length. Lateral motion of the tire contact in bounce (scrub motion) gives us the virtual swing arm angle. These values are then used to determine instant center positions and kinematic roll center height and lateral offset. Further, the kinematic roll center height of an individual corner is reported by projecting from the geometric tire contact point to the centerline of the vehicle. Note that the roll center height and virtual swing arm geometry are calculated based on wheel motion, without measurement of actual suspension hard points. This method only works with an independent suspension.
In the force-based approach, lateral force is applied at the tire contact and the change in vertical force is measured. This change in vertical force with lateral force is commonly referred to as jacking force. The slope of this jacking force curve gives an angle that is analogous to the virtual swing arm angle. This force-based angle we call the force anti-roll angle. By projecting from the tire center of pressure to the centerline of the vehicle along this angle, we are able to determine a force-based roll center height at each corner of the car. This method works with any suspension type.
So, which method is correct? That depends on your application. If you are trying to correlate a kinematic model of the suspension, you should look at the kinematic roll center heights. These should be close to rigid body kinematics, but often vary due to vertical force compliance effects. If you want to better understand the behavior of the car on-road or on-track, the force-based roll center height is more appropriate. This is because the car responds to forces and knows nothing of the kinematic geometry you or its designer have built into it. It only knows the forces resultant from that geometry.
Do the two methods give the same answer? Generally, the force-based and kinematic roll center heights are similar, but not the same. The trend is for the force-based roll center height to be lower than the kinematic. This is understandable because in most K&C tests there is a large compliant member in the system, namely the tire. Compression of the tire with jacking force will tend to reduce the measured jacking force, leading to a lower anti-roll angle and a lower force-based roll center height. In addition, for cars with a lot of static camber and/or a lot camber gain, there can be significant differences between the geometric tire contact point and the tire center of pressure. This will lead to different “roll center” heights because we are projecting from a different tire contact point. The kinematic method uses the geometric tire contact point while the force-based uses the measured center of pressure position of the tire.
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