Motion ratios for sway bars

[High Plains Mopars]

I'm working on formulas for rear suspension sway bars. I've got the rates for different sized bars figured out, but I've run into a situation where some of the bars mount differently, hence they will produce different motion ratios. My question is which dimension to use to calculate the motion ratio.

Some bars I have are frame hung and the arms mount on the axle housing in line with the springs. In this instance I use the same motion ratio for the springs and apply it to the sway bar rate to get the bar's wheel rate.

The other bars I have are axle hung bars, so they mount off the axle inboard of the springs, and their frame mounting point is also inboard of the springs, but in a differing position than where the axle mounts are at.

So the question is when determining the motion ratio on the axle hung bars, do I use their location where they mount to the axle housing or the location where they mount to the frame?

The difference between which location to use for the motion ratio can alter the wheel rate by around 45 pounds, which would be a significant amount on rear wheel rate.

[David Pozzi]

Found this:
"To calculate the Anti Roll Bar Rate at the wheel, we need to find the Motion Ratio of the Anti Roll Bar. If the
Anti Roll Bar moves 6.3mm and the wheel moves 10mm, then the Motion Ratio = 0.63.
The force at the wheel can now be calculated as follows -

Anti Roll Bar Rate (at wheel)
= Anti Roll Bar Rate (at suspension) x Motion Ratio2
= 8.16 x (0.632) = 3.2 kg/mm

For the rear suspension with a live axle, the Motion Ratio equals the distance between the roll bar links on the rear
axle divided by the Rear track width."

I don't think it matters if the bar is mounted to the axle, or chassis, just the width of the end links.
David

I think I'll move this to the tech section, you might get more help there.

[Norm Peterson]

You ought to be able to work with either the bar end rate and distance or the rate at the brackets on the central (torsional) section and the distance between those brackets, as long as you stick to a single frame of reference. What you can't do is "mix and match" the rate at the bar ends with the separation distance between the brackets.

IOW, I don't think it matters as far as the roll stiffness is concerned if you work with (say) the ends of a bar at 100 lb/in with those ends separated by 4' or its brackets on 3' centers and 100*(4/3)^2 = 177.8 lb/in that would be the rate at the bracket locations. You'd get the same wheel rate (64 lb/in @ 5' track) and roll resistance (2011 in-lb/°). What would be different is the actual loads applied to the chassis and their locations, so you might end up with slight structural differences as a consequence.

BTW, I'm assuming that the axle and its tubes and any local chassis structure that picks up the sta-bar loads are significantly more rigid than the bar. If the effective rate of everything else in the load path combined isn't at least 10 times the bar's "bracket rate", you won't actually see any more than about 60.5 lb/in at the wheels once it's built.


Norm