Solid rear axle motion ratio's

[damir130]

Hi everyone, congratulations on the high level of the discussions that have been going on here for the past few years. I've been reading and learning as much as I can, but there is one problem where I hope someone can provide some insights..

I am preparing a classic toyota for classic car races here in Europe. I have read a lot about basic setup procedures regarding initial spring, arb and damping rates. However most of these procedures seem focussed on A-arm or McPherson suspensions and no mention is made of the old solid axle type setups. Question that I am trying to tackle are:

Is it correct that a solid axle's motion ratios vary between one wheel bump (vertical rotation around other sides contact patch), two wheel bump (motion ratio == 1) and roll?

I'm having special difficulties visualising what happens during body roll. Do I consider the rear axle fixed and move the chassis around the spring base (attachment of springs to body), do I do the usual and take the lower spring attachment point and reference it to the wheels?

The ARB is giving me similar issues.. its bolted to the rear axle and the ends are attached to the car. The opposite of the usual setup. The mounts on the axle are spaced really close together compared to the arm-mounts.

Any hints on how to model a solid axle rear end are more then welcome.

Thanks!

 

[BrianPetersen]

Yes, the motion ratio will be different between two-wheel bump and one-wheel bump. The spring and antiroll bar attachments at the axle are positioned inboard of the tire contact patches. If the left wheel goes up (say) 10mm then the left spring may go up (say) 9mm and the right spring may go up (say) 1mm.

The path that the axle moves relative to the body - assuming coil springs! - is determined not by the spring attachment points but rather by the way the linkage works. The various arms swing in radii that locate the axle. Don't forget that the instant-center of where the axle rotation is, also has an influence on weight transfer.

This is not a simple situation to analyze properly. Why not just look at what others are doing with that vehicle, start out with something similar, and test, test, test?

 

[damir130]

The problem is I am the only one running this particular car in Europe (that I know of). Its a 72 corolla with a 5-link rear end and coilovers. I could use some tried and tested English Ford Escort Mk1 settings, but then I have different- linkages, spring base, rear track, axle, spring/shock mounting points, corner weights etc.

I am not to concerned with the longitudinal positioning of the rear axle..yet. First I'd want to get the wheelrates in the ballpark so that I'm not chasing my own tail with springrate and linkage adjustments.

Surely someone must have a decent way of calculating wheelrates for solid rear axles?

 

[BrianPetersen]

In 1972, that car originally came with leaf springs, so presumably you are dealing with some sort of retrofit. Corollas had leaf spring rear ends up until the square body style came out around 1980. I presume by "5 links" you are dealing with two trailing links on each side and a panhard rod. Your effective roll center is at the height of the panhard rod pivots, and I sure hope that at nominal ride height, the panhard rod is horizontal (and as long as possible).

Are the coil spring perches directly on top of the axle, or are they on the arms? If they are on top of the axle, for jounce and rebound, just use the direct 1:1 motion. For body roll, use the ratio of the distance separating the spring perches to the distance separating the tire contact patches - that's how much the springs move relative to the tire contact patch (relative to the body).

Draw a diagram with the bodyshell straight, and again with it leaned over (say) 5 degrees. It's easier to see what's going on that way.

 

[damir130]

Thanks for taking the time to think along with me Brian. Appreciate it.

The corolla did indeed come with leaf springs, but has been converted using parts from a celica from the same era. Its similar to some factory setups of that age and the conversion was done a long time ago.

The setup is similar to an GP4 turreted escort and has coilover shocks attached directly to the axle. I did the calcs you described and come up with a motion ratio in roll that is around 85% of that in one wheel bump.

Question is...what to do with the ARB? Its attached to the rear axle. The "arms" are attached to the body and about 5 feet apart (as you would expect). The inboard mounts on the axle..the things actually producing leverage to the wheels, are just 1ft~1.5ft apart. Using the traditional approach their rate would be close to zilch.

Then I found this article:

http://www.circletrack.com/chassist...ring_rates_to_use_in_your_race_car/index.html

talking about spring base in terms similar to wheel rate. Add that to the strange ARB situation and I'm starting to think I'm missing something.. Should I be looking at the body seperate from the wheels in the roll rate equations?

 

[BrianPetersen]

If that antiroll bar is mounted as you describe, it is probably flexing as much as it is twisting, and the contribution to roll stiffness is probably nowhere near what the calculations would otherwise suggest. I'd consider either re-mounting it with the axle mounts further out or ditching it completely and substituting a different antiroll bar with more predictable characteristics ...