This article is part of a series on the kinematic simulation and analysis of the Acura RSX suspension. To learn more, feel free to check my other posts:

Front Suspension

Rear Suspension

Full Vehicle

rsx front axle

Introduction

Suspension setup is much more than just changing springs and dampers. Modern multi-link suspensions are carefully designed to react handling loads in a desirable way. Springs and dampers are only one part of the equation.

Suspension links control how certain loads are transmitted from the tire to the chassis. The roll centre concept considers this when loads are reacted. This is especially important for lowered vehicles on aftermarket coil overs without a geometry correction kit.

The kinematic roll centre, although a virtual point in space, can be found via computer simulation. We use the suspension points from an Acura RSX to study how the kinematic roll centre responds to chassis movement.

Kinematic roll centre

The kinematic roll centre is a virtual point on the axle plane where cornering forces can be resolved into the suspended mass. This point simplifies a force analysis of the suspended mass to a simple rigid body dynamics problem.

Before we can discuss the kinematic roll centre, we need to define the front-view kinematic instant centre. The front-view kinematic instant centre is a virtual point on the axle plane the wheel assembly rotates about. For a MacPherson strut, the front-view kinematic instant centre is found at the intersection of:

  • the lower control arm plane defined by the two inboard attachment points and the outer ball joint
  • the upper strut plane defined by the upper strut attachment point and a normal vector defined by the strut
  • the axle plane defined by the contact patches and the wheel centres

By drawing a line from the tire contact patch to the front-view kinematic instant centre, we obtain the side force line of action. The intersection of this line for the left and right wheels is the kinematic roll centre. Force analysis of the suspended mass at the kinematic roll centre is possible because forces can be translated along its line of action per the Principle of Transmissibility.

It is important to note that we are using kinematic constructs to make assumptions about how forces are reacted into the suspended mass. It is for this reason we explicitly call this point the kinematic roll centre.

Parallel Wheel Travel

We begin the analysis by examining the kinematic roll centre in parallel wheel travel. This is a simulation of the front axle in heave where both wheels are displaced by the same amount in the same direction. This analysis preserves some convenient properties; there is symmetry along the XZ-plane and the roadway banking angle stays constant at zero.

The animation shows the front axle in heave with lines representing the line of action from the tire contact patch to their respective kinematic instant centres. You will notice a point at the intersection of the two lines. This is the kinematic roll centre. Two interesting observations arise from visual inspection:

  1. the kinematic roll centre height decreases and goes below the tire contact patches
  2. the kinematic instant centre for each corner flips sides near the end of its jounce travel

We can examine the kinematic roll centre height in more detail by quantifying its movement relative to the heave displacement. The graph below shows the kinematic roll centre height with respect to the contact patch vertical displacement.

parallel wheel travel roll centre height

The static kinematic roll centre height at factory ride height is quickly lost as the axle travels in bump. With just +31mm of bump displacement, the kinematic roll centre height crosses the ground plane. The reduction of the kinematic roll centre height in bump is consistent across the wheel travel range.

The kinematic instant centre flipping near the end of the suspension travel is noteworthy even if not directly related to the kinematic roll centre analysis. We already discussed kinematic wheel plane control and how the Acura RSX front suspension is designed from the factory. This is one explanation for its poor performance near the end of its bump travel. Suspension parameters are inter-related and this example highlights how parameters can affect each other.

Opposite Wheel Travel

Studying the axle in opposite wheel travel simulates the axle in roll. Both wheels are displaced the same amount but in opposite directions. This is considered a contrived motion because in reality the axle is free to move in both heave and roll. Despite this, it is still worth investigating due to the asymmetry created by the motion.

The animation shows the front axle in roll with lines representing the line of action from the tire contact patch to their respective kinematic instant centres. You can see how opposite wheel travel causes the kinematic roll centre to move laterally and vertically. In this scenario, the kinematic roll centre moves towards the contact patch of the wheel in rebound before going into the ground. The relationship between the kinematic roll centre height and the chassis roll angle is shown in the graph below:

opposite wheel travel roll centre height

The kinematic roll centre is highest above the ground when the roll angle is zero. The kinematic roll centre height decreases with roll angle regardless of direction. Beyond 3.5 degrees of roll, the kinematic roll centre passes through the contact patch of the wheel in rebound before going into the ground.

opposite wheel travel roll centre lateral migration

The kinematic roll centre lateral migration is worth looking at since it is an indicator of a kinematically induced asymmetry. You can observe the kinematic roll centre moving through the wheel contact patch by looking at the lateral migration when the kinematic roll centre is on the ground at 3.5 degrees of roll. The lateral migration will approximately be equal to the half track.

Final Comments

MacPherson strut suspensions are limited because they have no upper suspension link. The angle of the lower control arm plane defines the position of the kinematic instant centre which in turn controls the kinematic roll centre height. The Acura RSX has a kinematic roll centre that lowers into the ground with just over an inch of heave travel. The kinematic instant centre flip sides near the end of its jounce travel. This is why we see such poor kinematic wheel plane control in this region.

Installing a coil over kit can be a double-edged sword. These kits often lower the ride height and can cause the kinematic roll centre to go into the ground. Carefully selected spring rates can offset this, but will make the problem worse if tuned incorrectly. Modified lower ball joints raise the kinematic roll centre by relocating the lower control arm plane. However, not all geometry correction kits are created equal and must be placed under scrutiny; some do not provide meaningful correction. Ride height effectively locates the kinematic roll centre and can be used as another form of adjustment. The Acura RSX front suspension was clearly designed to operate within a fixed range of suspension travel. Staying within this range is just one way preserving the Acura RSX’s performance as intended by Honda.

Acknowledgements

I would like to acknowledge Ping Zhang at Formula Delta for sharing the suspension points used in this study.

References

  1. Dixon, John C. Tires, Suspension and Handling, Second Edition. Warrendale, PA: SAE International, 1996.
  2. Milliken, William F., and Douglas L. Milliken. Race car vehicle dynamics. Vol. 400. Warrendale: Society of Automotive Engineers, 1995.
  3. Blundell, Michael, and Damian Harty. Multibody systems approach to vehicle dynamics. Elsevier, 2004.