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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers. This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr., Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by e-mail to: firstname.lastname@example.org. Readers are invited to subscribe to this newsletter by e-mail. Just e-mail me and request to be added to the list.
ROLL AXIS FOR LIVE-REAR-AXLE ROAD/HILLCLIMB CAR
I've been reading your column in Racecar Engineering for several years now and I'm gradually increasing my knowledge of the dynamics of a suspension system, slowly but surely.
One thing I haven't been able to find much about anywhere is front roll centre height on a car with live axle rear suspension and independent front. The car in question uses a panhard rod and 4 parallel leading links to locate the axle. With the current wheel / tyre combination the centre of the diff /roll centre height is approx. 11.9 inches. The front suspension is double wishbone, and I have complete freedom to do whatever I want with the front geometry.
Most things I been told, or read, suggest that the front roll centre should be close to the ground, but surely on a car with a live axle rear this will cause a steep inclination of the roll axis.
The weight of the car is around 2100lbs, distributed approx. 49/51% F/R, car is front engined.
Can you offer any advice as to a suitable starting point from which to base my design?
The car is to be used for hillclimb and sprints, but will still be a road legal car so ground clearance is an issue (otherwise I'd be using a Woblink at the rear).
It is true that the roll axis will be steeply inclined if the front roll center is low and the rear roll center is high, and this is indeed the norm in cars with independent front suspension and beam axle rear suspension. It is usual to make up for the low front roll center by adding front roll resistance with an anti-roll bar.
In a car with close to equal front and rear weight distribution, and equal tires sizes front and rear, we will need close to equal total lateral load transfer front and rear. That implies somewhat less total roll resistance in the rear suspension than the front, because at the rear there is a substantial portion of the load transfer that does not act through the suspension. I am referring to the unsprung component of the load transfer, the portion that comes from the mass of the axle exerting a centrifugal inertia force at a height above the ground. There is also an unsprung load transfer at the
front, but it is much smaller because there is much less unsprung mass, and even the unsprung mass that is there partially acts as sprung mass for purposes of lateral load transfer, because it moves laterally with the sprung mass in roll.
In addition to the unsprung load transfer, there are three other components to load transfer: elastic, geometric, and frictional. All of these result from the action of the suspension, and may be said to act through the suspension.
The elastic component comes from the anti-roll moment generated by the springs and anti-roll bars. The geometric component comes from the anti-roll moment generated by the rigid members of the suspension: the links, uprights, and axles. The frictional component comes from all the frictional forces in the suspension system. Frictional forces include the mostly unintentional ones in the springs and pivots, and the mostly intentional ones in the dampers.
Cars with independent front suspension and beam axle rear suspension generally have small geometric components and large elastic components in the front load transfer, and large geometric components and small elastic components in the rear load transfer.
Independent suspensions cannot work well when they have large amounts of geometric roll resistance (i.e. a high roll center or large amounts of lateral anti). If we build an independent suspension that way, it will jack up when cornering. The reason for this is that geometric roll resistance in independent suspension consists of linkage forces that try to extend the suspension of the outside wheel (net upward jacking force at the outside wheel) and compress the suspension of the inside wheel (net downward jacking force at the inside wheel). The outside wheel carries the greater load, so the outside tire has more grip and generates greater lateral force. When the lateral force is greater, the jacking force is greater. Thus, the upward jacking force generally will exceed the downward jacking force, and the net jacking force for the wheel pair will be upward.
To avoid this, the roll center of an independent suspension system must be low. There is no hard limit, but as a general rule anything above four inches is too high, and two or three is more prudent, because the anti-roll generally increases as the suspension extends, and we know that the car will sometimes be going over crests.
We also need to design our suspension so that we do not get any large camber changes. With independent suspension, we cannot reduce camber change in roll without increasing it in ride, so the best we can do is avoid any huge amount of change in either ride or roll.
To get good camber properties and an appropriate amount of geometric anti-roll in a front suspension for a car with a beam axle rear end, I generally recommend a front view instant center between 55 and 85 inches from the wheel horizontally, and between five and ten percent of that distance above the ground. Make the control arms as long as possible, consistent with packaging and bump steer constraints, with the front view projected upper control arm around 2/3 the length of the lower one.
At the rear, there is no need to have the Panhard bar at axle height. If we are dealing with an existing rear suspension, and we don't want to change it, we can make the car work reasonably well with any Panhard bar height by choosing appropriate spring and anti-roll bar rates.
However, there is a case for having the Panhard bar as low as ground clearance and mounting constraints will permit, particularly for a road car or a road racing car, and accepting the need to increase the elastic roll resistance accordingly. The primary reason this strategy works is that it reduces torque roll and torque wedge: body roll and wheel load change due to driveshaft torque reacting through the suspension. With a live axle, driveshaft torque rolls the sprung mass to the right, unloads the right rear and left front tires, and correspondingly adds load to the left rear and right front tires. In oval track terminology, driveshaft torque adds wedge to to the chassis. In my application of the terminology, it wedges the car for left turns, and de-wedges it for right turns. That makes the car looser (adds oversteer) exiting right turns, and tightens the car (adds understeer) exiting left turns. It also makes the right rear tire spin prematurely under power if the differential does not lock, or makes the car try to turn right if the diff is locked.
If we add elastic roll resistance at both ends of the car, we reduce torque roll but not torque wedge. If we increase the rear elastic roll resistance, leaving the front end unchanged, we reduce both torque roll and torque wedge. However, we can only do this if we reduce the rear geometric roll resistance.
For this reason, the fastest live-axle road racing cars place the rear roll center as low as packaging constraints allow, and use rear anti-roll bars.
To some extent, we can compensate for torque wedge. We can set the car up with less than 50% static diagonal (RF+LR) percentage, use somewhat stiffer springs on the right side than on the left, and use a bit more anti-dive in the right front suspension than at the left front. If we apply these crutches in a suitable combination, we can get reasonably good behavior in right and left turns, and under power and braking. However, we can get away with applying these crutches in smaller measure, or get better car behavior without them, if there is less torque wedge to begin with.
The questioner mentions the WOB link (from Watt-Olley-Bastow) suspension. This refers to a mechanism that approximates straight-line motion for small displacements. It consists of a rocker and two links, like a Watt linkage. It differs from a Watt linkage in having the pivot on the rocker outside the attachment points for the links, rather than between them, with both links extending in the same direction away from the rocker, rather than opposite directions. It can produce approximately straight-line motion at the pivot if the links have unequal length, in the correct proportion to each other. It provides a way to get a low roll center when the only frame members we have available to anchor to run above the axle. It has the disadvantage that the link loads tend to be very high. We are still unable to get a roll center lower than the lowest part of the mechanism.
With a Mumford linkage, it is possible to get a roll center somewhat below the lowest part of the mechanism. In fact, it is possible to get a roll center dramatically lower, except that then the roll center then moves up and down a great deal as the suspension moves. A Mumford linkage has two rockers and three links.
It is possible to make a Watt linkage approximate the behavior of a Mumford linkage. We can put the rocker under the differential, lying flat, and at an angle when seen from above. We run the links upward toward the frame from the rocker. The roll center is approximately at the height where the two link centerlines intersect in front or rear view. Careful detail design is necessary to avoid running the rod ends on the links out of travel.
ROLL AXIS OF THE AXLE
I have read about how to find a rear axle's axis of rotation in roll. On a triangulated four-link system, for example, you find the intersection of the lower link centerlines (usually ahead of the axle and above the links), then find the intersection of the upper link centerlines (usually behind the axle and above the lower link intersection), and then connect those two points with a line. The axle moves about this line in roll. The point where this line intercepts the rear axle plane is the rear roll center.
It would seem obvious that the inclination of this line must determine the rear axle's roll steer properties also. If the axis slopes down toward the front, that would seem to imply roll understeer. Yet when I apply the suspension geometry program on my computer to such a layout, it tells me the system has roll oversteer. Am I crazy? Can the computer be wrong?
Note that the axis the questioner is referring to here is different from the roll axis of the car as a whole, which was the subject of the previous discussion. This is the axis about which the axle rotates with respect to the sprung mass.
Yes, the computer can be wrong, and I have seen similarly anomalous outputs from suspension geometry programs regarding bump steer and roll steer properties in independent systems.
For example, consider the case of a front independent suspension with the steering rack ahead of the axle line. If you raise the rack, leaving all else unchanged, you know that the wheels will toe out more, or toe in less, in bump as a result of this change. It always works this way, for intuitively obvious reasons. Yet I have had the same computer program the questioner says he's using tell me the opposite. I am leaving the name of the program out of the discussion, as the person who sells it is a friend of mine. But I will definitely say that having a computer is no substitute for understanding things with your own brain, and that computer outputs definitely can be wrong. (The computer can also be right when you think it's wrong. The computer is not infallible, nor are the people who write the programs, nor are you, nor am I. We all do the best we can.)
Returning to the triangulated four-bar, yes it generally does have roll understeer, despite the up-at-the-front slope of the lower control arms in side view. The unloaded or inside wheel moves rearward in roll, and the outside or loaded wheel moves forward. This is due to the arms' in-at-the-front angularity in plan view, combined with the lateral motion at their rear ends in roll, which results from their being well below the roll center.
If the lower arms were parallel with the vehicle centerline in plan view, and sloped up at the front in side view, then the system would have roll oversteer. It would also have a rear axle roll axis sloping upward toward the front, not downward. The axis would pass through the upper arm intersection, as
before, and it would be parallel to the lower arms in side view, since they are parallel to each other, meaning they have no intersection, or, to be slightly incorrect, an intersection at an infinite distance.