Page updated: 10/20/2001 08:33 AM
You think work gives you a headache, wait 'til you read this! Kerry takes the time to show you a couple of his software-modeled variations that his 1/4-elliptical suspension has endured. Get that thinkin' cap nice and tight!
The following text is meant to relay some off-road suspension ideas, theories and observations through the story of my YJ’s 3 link rear suspension – as well as some design details. This article does not provide all the details of a design ready to use on the street. While I know the design is sound, it should be considered for off-road use only. It does provide details you will need to design your own ¼ elliptic suspension. I feel I need to approach it this way for liability reasons – I am not resposible for how you build your rig. I will be happy to answer questions you may have, however, and give you more specifics if you ask for them – all in the spirit of off-roading. That said… I had previously experimented with several leaf-spring suspensions, but much of what I learned about how control arm geometry affects suspension performance was through the research and iterative development of this project. Thanks go to my local wheeling buddies for putting up with my jawing about it. Lee Wells was especially instrumental in providing good discussion and ideas for the project, despite being a Sparky. There are a few cartoon pictures of suspension geometries generated from 3D solid models, not to be confused with the .bmp art for diagrams. The models were used to analytically predict 3D motion and stresses, but are not always visually complete.
I had a lot of reservations about investing much into the setup and wanted to make all the modifications somewhat easily reversible in case I didn’t like the outcome. As a result, the “test vehicle” (a.k.a MostlyYJ) suspension is not at all optimized for a clean looking fabrication – just function and strength with the available materials. The front of the vehicle is a SOA, so its performance is predictable, well-established, but hopefully temporary.
From the beginning, it was clear there were a lot of conflicting opinions about what suspension would work off-road and still be stable on the street. It’s hard to get a consistent opinion about suspension performance from shops trying to sell parts, or someone who just bought them. Even a good honest answer doesn’t replace personal experience and experimentation. So the decision was made to slightly modify a well established existing design, and use inexpensive tractor link control arms in case changes were required.
An A-arm acts as the upper link in this 3 link setup. The A-arm pivots about an axis near the center of the jeep to allow vertical axle travel but acts as a truss to provide lateral stability. This way, no Panhard (track) bar is required, and there is less binding during axe articulation. It is connected to a hoop over the differential by a bushing and threaded rod to allow rotation. The lower two arms attach at the frame near the skid plate and to the outer ends of the axle.
Description of Individual Components
Lower Control Arms
The A-arm pivots on a pair of ¾” bolts running through the frame on an axis near the center of the jeep. The bolt holes are supported by 1” tubing welded into the frame for the required strength. Alignment was achieved by the following operations: First the hole locations were marked relative to the spring hangers and 1” holes drilled through both sides of the frame. With the t-case removed, a section of the 1” round tubing was pushed through the holes on either side across the width of the entire frame. The holes in the frame were “adjusted” until the tubing fit squarely and was parallel to the axle. The tubing was then tacked in place, cut directly from the frame, and the remaining supports welded permanently. This way the A-arm is guaranteed to rotate freely without binding.
The heaviest single piece in the setup, the cross-member, needs to be very strong. Because it is loaded in the center, there is a large bending moment in this section of framework, and at both ends. The diagram shows the approximate bending moment, M, applied to the member, modeled as a beam rigidly attached at either end.
The cross-member is also bolted into the skid plate to provide additional rigidity. The main section was constructed from 3x3x ¼” tubing, and was gusseted with 1” angle stock.
Limiting straps are required in three locations: one at each end and one in the center. Again on the theme of “keep it simple”, they are aircraft cabling from Tractor Supply held together with cable clamps. The center strap prevents the driveshaft from binding when the whole axle droops. The straps at each end prevent the axle from articulating far enough to reach the limit of shock travel.
A DOT approved extended SS brake line was run from the stock position on the frame to the hoop. At full flex I still have plenty of line left – almost too much.
|Shocks are triangulated above the axle to a second cross-member in front of the gas tank. More 2x2x 3/16” tubing was used for simplicity, but this was probably overkill. This puts the shocks at enough of an angle that the rear damping is reduced somewhat. The first set of shocks tried were RS9000’s and I noticed I wanted to set the valving one notch higher than previous suspensions. After I bent those and readjusted the hoop location to prevent future problems, I used a set of Doesch Tech shocks. They are a little better valved – having a more progressive rate and offered a better ride, but were a little softer in some circumstances than I would like. However, without in-cab controls, the RS9000s always seemed to “need” an adjustment.|
The passenger side cable was disconnected from the body mount position to allow more droop. A passenger side cable was used on the driver side for the extra length.
I had to move the fuel lines for the shock mount cross-member. This could be avoided if the shock mounts were tied into the stock cross-member, rather than making a new one.
I cut up a set of offending 4” custom National leaf packs for the task. One end was trapped with a 5/8” bolt in a section of 3x3x ¼” box tube and attached to the stock spring hanger on the frame. Drilling the springs is a PITA, since the material is so hard. The other end was retained on the rear of the axle with a YJ shackle. Any springs could be modified for the task, but it’s important to consider the original design of the springs when determining how many leafs to use. The original 4” rear packs were 13 leaf, with several of them being very short and used only for supporting heavy loads. The ¼ elliptic packs use 9 leafs each and sit flat at ride height. A good source for springs might be Grand Wagoneers. The picture above shows the suspension slightly flexed upward. Ride height can be adjusted by changing the shackle length or changing the frame stop point (at right on pic). The frame in this area should be reinforced to handle the extra loading.
Description of the suspension in 2D, as viewed from the side.
The mounting points on the frame and control arm lengths were modified to allow the axle to rotate the pinion up as it drooped. The plan was to keep to the same CV driveshaft, and the rotation was designed to allow the driveshaft angle to remain near zero at the pinion across the full range of axle droop.
To accomplish this, the upper arm was made longer than the lower two arms. This forces the top of the axle to travel across a flatter arc than the bottom, thereby introducing rotation. The arms were mounted such that the CV was positioned between them and the pinion would point in that direction throughout axle travel. The magenta bar represents the pinion vector (angle) from the differential – aimed at the CV location.
Rear end lift -- So-called “anti-squat”
For the above reasons, this particular system tended to act very much like a set of constant radius arms under straight line acceleration – not yet considering flex. The assumed length is found using the instantaneous pivot point for the axle rotation during droop (average bar). The bar is assumed to have negligible deflection, so how hard the rear axle will be forced downward under acceleration can be roughly estimated by calculating the resultant forces of a torque applied to a simple beam.
The idea is that the rear plants downward solidly as torque is applied, and tire traction may be improved in lower traction conditions. While the average bar may be different, the majority of (control arm constrained) off-road rear suspensions will follow this trend to varying extents, including TJs. The actual lifting force seen at the rear of the vehicle is affected by wheelbase and can be estimated by the following equation:
|EQUATION: F(lift)= [Mt/(WB*L*cos(b))] * [1+ L*sin(b)/Rt]* [WB – L* cos(b)]|
As a vehicle climbs at a steep angle, weight is transferred to the rear axle, but a lower percentage of the total axle loading is applied normally (90deg) to the springs.
As the vehicle pitch increases, so does the angle of the average bar relative to ground. This begins to aim the resultant force on the frame less parallel to gravity, such that the weight of the rig resists anti-squat less. The normal force applied to the springs decreases as the CG (center of gravity) of the vehicle approaches the breakover point and more weight is transferred directly to the control arms. Conversely, higher torque must be applied to the rear axle to climb the steeper angle, thereby increasing anti-squat. These factors are additive and tend to make the rear of the vehicle lift relative to the axle well before the breakover point.
As you might assume, if the control arms started at a lower angle to begin with, the jeep would have to be on a steeper incline to feel the same magnitude of the effect. Essentially, if there were less anti-squat, the effect should be reduced – something I would like to investigate further on future iterations.
One of the theoretical disadvantages to this lifting is that the CG is raised. It might only be a couple inches, but the front end may lift easier than an equivalent jeep with less anti-squat. Another disadvantage is the potential for rear hop on loose terrain as 1) the front end encounters greater resistance (i.e. ledges) and 2) the rear traction is inconsistent (i.e. ledges and slippery terrain). Hop could be aggravated in part by the reaction force of anti-squat on the frame. Its lifting effect at high pitch angles aims away from the direction of travel and off the rock face. It is suspected this is the primary cause of TJ hop. As the rear end lifts, it approaches a point of maximum droop due to shock length, driveshaft limits, or binding due to Panhard bar limitations. The energy otherwise used to lift will be quickly transferred to the wheels causing a loss of traction and/or hop.
This is why in some cases you may see a 2” lifted TJ with 32” tires easily climb a steep rock face that bigger rigs can’t seem to conquer without wheelhop and throttle, if at all. The “average bar” angle will be much lower as will the torque required at the axle. Less anti-squat is the result – and the suspension is nowhere near binding.
Back to the 3 dimensional world…
Like the majority of ¼-elliptic suspensions on the trail, the first version of the test vehicle steered the rear axle as it flexed. Because the lower control arms were mounted to the frame rails, they pulled the axle forward (along an arc) as the wheel drooped and pushed it backward under compression. The net result is the axle rotates under the jeep to produce steering.
Pictures of flex-steer: Note the rear wheels are aimed toward the compressed side.
This can be an annoyance when driving over an obstacle since the rear end may move several inches off the expected line depending on how hard the suspension flexes. I found this can both help and hinder rock crawling, but is predictable enough to accommodate in driving style.
The problem we began to notice was on steep rock climbs, particularly where the passenger rear wheel contacted an approaching ledge before the driver side wheel. With the driver side wheel already flexed downward, as torque is applied the natural motion of the axle is to walk forward until 1) the ledge is found or 2)the limit of wheel travel is found or 3) the pucker factor becomes too great for the driver.
Picture of flex-steer on a moderately steep hill and the above described ledge type.
This effect is responsible for the permanent wrinkling of at least two seat covers. When the driver-side wheel walks forward to contact the ledge, there is more resistance encountered – i.e. now the rear axle is facing the ledge squarely and cannot simply articulate over. Forces due to anti-squat are applied at each side and are unequal because control arm angles are different during axle articulation. Added to flex-steer, the result is the vehicle is rolled to the passenger side rather than forced up and over the obstacle. You could think of it as TJ tire pick on steroids. Of course, this is the extreme case, but it was the deciding factor in eliminating flex-steer -- off-camber situations could get ugly fast.
I found my jeep had the same squirrelly peculiarities as pictured above and certain local obstacles had become impassible to MostlyYJ. It bothered me enough that I filled my acetylene tank, and strong consideration was given back to SOA.
One way to significantly reduce flex-steer is to triangulate the two outer (lower) control arms closer to the center of the vehicle. This is because as one wheel droops the control arm tries to follow a circular path that coincides with a more vertically planar path where the bracket attaches to the axle.
For the purpose of discussion, flex-steer is described as how far the drooped wheel moves fore to aft. The first version was calculated to have a maximum of 6.5” of flex-steer at the drooped rear wheel, compared to a TJ with about 2.6”, but at about half max droop. The triangulated lower arms reduced steering effects to 0.6” with no loss of wheel travel. If a TJ track bar, shocks and driveshaft could be removed to allow more droop for comparison in 3D simulation, the flex-steer would be extreme (but physically impractical).
|About 7" Droop||About 12" Droop|
|Typical 1/4 elliptic||2.3||6.5|
|Triangulated 1/4 elliptic||0.1||0.6|
Flex with very little rear-steer
It would be possible to further reduce flex-steer by replacing the lower control arms with a lower A-arm turned 180deg from the upper arm. However, control arms are much easier to replace and repair on the trail and both lead a perilous existence. The drawback is that a cross-member is required behind the skid plate for mounting, and the forces acting on it can be very high. The cross-member is not visible in the model above, but acts as part of the frame and is assumed to be rigid.
Gussets were required at each end and in the center of the steel ¼” 3x3 tubing used for its construction. To add additional rigidity, it was bolted into a reinforced flat skid plate. The plate and drivetrain can be removed without disturbing the cross-member or suspension – barely.
The effect on trail performance was a marked improvement on loose climbs as well as off-camber, high wheel travel rocky, accents. The same obsacles no longer rolled the jeep to the right and the decision was made to not return to SOA. Fortunately, it was just in time for our spring-2001 trip to Moab and Phoenix.
While virtually eliminating the flex-steer significantly improved stability on climbs, it did not eliminate the anti-squat force balance described previously. At some point, the test rig will reach a steep enough incline that there is little normal force acting on the springs. Because high torque is still required to climb, the reaction force from the driveshaft at the axle tends to pitch the vehicle to the right – there is little resistance from the mass of the vehicle at this point and the rear springs are very soft.
|Suspected torque-flex effect. Similar results observed here on an SOA YJ but with less rear travel|
It is reasonable to surmise that adding a sway bar would significantly reduce this condition, but it would also reduce wheel travel appreciably. The frequency at which this torque-over becomes a problem may be less than that of high wheel travel obstacles, and might be further reduced by increasing wheelbase and control arm length. Additionally, the vehicle is still at the mercy of what little flex-steer remains. The effect would only be found at much steeper angles, however, and may be impractical to eliminate completely.
Certainly the effects of torque-over and flex-steer are additive and can be difficult to visually differentiate unless one effect is particularly strong. It is also clear there are other considerations that need to be given to suspension design that are not covered here – this is only meant to relay some ideas, concepts and theories generated between beers and spreadsheets in our spare time. One such effect would be the spring rate balance between the front and rear. The first version ¼ elliptic setup had similar flex-steer as the lifted TJ model within the first 7” or so of droop. Obviously the first setup has more total steer at its maximum droop. The first version also has a stiffer front end (SOA) compared to the TJ coils. The rear rates, however, are fairly similar. The net result is that most of the flex was seen in the rear suspension on the test vehicle, and was more evenly distributed on the TJ. The second version had fewer leaves in the front spring packs, in addition to control arm changes. The rates were softened to a personally acceptable level, but as expected, the springs were too weak and bent after little use. I hope to convert the front to coils and control arms of some undetermined flavor this winter for better front to rear balance.
As a comparison, lifting a TJ increases the control arm angles so anti-squat and flex-steer are also increased. Many people won’t notice the effect this has on vehicle performance - they either started with a big lift and tires or the obstacles they try do not readily produce it. Combined with increased tire size (read: torque to axle) , these factors, I believe are the primary causes of “tire-pick” and hop in a TJ – of course removing the rear sway bar will only make it worse. Personal experience and opinion is that these effects really don’t start getting bad until the lift is 3” and tire size is 35”+ ; or the lift is 4”+ and the tire size is 33”+. Lots of mass on the back end of the jeep will only serve to make matters worse by imbalancing it on a steep incline. I would like to model a long arm kit in a TJ and see how these effects are improved in the design – next time I see one I’ll crawl under it with measuring tape…
At this point I’m considering stretching the wheelbase to around 100”, lengthening the control arms in the process, and adding room for an auto tranny (just in case). The control arm mounting points will be changed to reduce anti-squat, but at this point it is unclear if it should be eliminated altogether. The result should be improved stability on steeper ascents with less torque-over and rear lift under throttle, and no loss of wheel travel. Fortunately, there are a couple people copying this design and making these mods so we should have some idea in the near future. Of course, increasing wheelbase is nothing new to rock crawling, but being a jeep geek means I have to think I know why I’m doing something.