Anti-roll / sway bar design book / reference?

[Daox]

I am looking for a book or information on sway bar design. I've been doing a bit of searching and found a few people recommend Carrol Smith's Tune to Win. Ironically, I think I own just about every book he wrote but that one. However, I was wondering if anyone has any other references or books of note.

[Gasoline Fumes]

Can you really fill a book with anti-roll bar info? They're fairly simple. Both Grassroots Motorsports and Sport Compact Car have had good suspension articles over the years. GRM has some of their articles online.

[gone-ot]

+1 on the Carroll Smith book.

[Daox]

Thanks guys. I'll check out grassroots online stuff. Tune to win isn't just about swaybars. It's about suspension setup and design for race cars. Carroll's other books have been great, so I'll probably add it to my collection anyways.

[Daox]

The main reason for looking for this info is to design an anti-sway solution (not necessarily a bar) for the 2014+ Mitsubishi Mirage. As some of you know, Darin and I also run Mirageforum.com. The Mirage is known to soak up bumps really well with its soft suspension. However, along with that soft suspension comes quite a bit of body roll. The solution would be a rear sway bar (the front is already equipped). Ultra Racing does make a rear sway bar, but it is kinda pricey at over $200 delivered. The buyers of this bar LOVE what it does for the car. They say it totally transforms it and makes it so much more enjoyable to drive. So, I've made it a fun side project of trying to figure out another cheaper solution.

My first attempt was made via a suggestion from an Autospeed article on sway bars. Julian suggested that brackets that clamp around the rear torsion beam, increasing its resistance to twisting, would act similarly to adding a rear sway bar.

So, I designed some and had them made up. The idea is you could add as many clamps as you want to get the sway stiffness you like. I loved this idea as it would be cheap and adjustable.

Clamp design. These clamp tight, not loose.



Example of two clamps on the rear torsion beam.



I was able to borrow a local Mirage owner's car to do the testing (she actually made the clamps for me at the shop she works at).




However, in testing, these made no noticeable effect! I was a bit surprised as the Autospeed article mentioned quite a noticeable difference. So, I went back to the drawing board for a 2nd design like any good engineer!





I came up with the idea of shoving a piece of angle iron up into the torsion beam, and using u-bolt clamps to hold it there. This beam was thick, thicker than the rear beam itself (3/16" vs 1/8"). However, no matter how many u-bolt clamps we put on it, it still made no noticeable difference!

At this point I gave up on the project for the time being. I decided I need to learn a bit more about sway bar design before making another attempt. So, if you have any suggestions, I'm all ears.

[Occasionally6]

To address the OP, How to MakeYour Car Handle by Fred Puhn has a few pages on Anti Roll Bar (ARB) design. Included is a figure with a mathematical formula for calculating the spring rate of a "conventional", 'U' shaped, ARB with the bar supported in bearing blocks. The suggested material is 4130 or 4340.

Before you rush out to find a copy - it's old but a bit of a standard; I have seen copies in libraries from local to college - an ARB of that configuration can be modelled as a shaft in torsion and two cantilever beams. The fixed ends of the cantilevers are at the ends of the shaft in torsion.

For a shaft in torsion with circular cross section, the angular deflection is given by:
Theta = (T*L)/(G*J)
Where Theta is the angular deflection in radians along the length, L, of the shaft.
T is the torque on the shaft. In this case, the perpendicular distance from the shaft to a line joining the free ends of the cantilevers, multiplied by the force on the end of one of the cantilevers.
G is the shear modulus of the shaft material. For a steel alloy, about 77 000 MPa.
J is the polar moment of inertia of the shaft. For a circular cross section:
J = pi * (D^4)/32

The deflection at the end of each cantilever beam is given by:
d = [F*(L^3)]/(3*E*I)
Where F is the normal (perpendicular) force on the end of the beam.
L is the length of the beam. Note this is a different 'L' to the shaft 'L'.
E is Young's Modulus of the beam material. For steel, about 200 000 MPa.
I is the second moment of area about the neutral axis. For a circular cross section:
I = pi * (D^4)/64

The use of consistent units is necessary. With MPa (= N/mm^2), use Newtons (N) and millimeters (mm).

To convert the angular deflection into linear deflection at the beam ends, multiply theta by the perpendicular distance from the shaft to a line joining the ends of the beams. The total deflection is the sum of the effect of the angular deflection and the two beam deflections. You can then relate the force on the bar ends to their deflection. How that relates to the wheel movement - and forces at the tire contact patches - will depend on the geometry of the installation.

If you want to use the Ultra Racing ARB as a reference for added roll stiffness, you have to take into account that the fixed ends of the cantilevers for it are under the spring seats, the shaft is unsupported and so is subject to bending as well as torsion. That means the cantilevers are also subject to torsion.

The total roll stiffness will also depend on the (progressive) spring rates, their location and, in the case of a twist beam rear suspension, the torsional and bending stiffness of the twist beam. These latter can be calculated in a similar way to the ARB above with some additional considerations due to the non-circular cross section. I can't cover that in a forum post so some study of the mechanics of materials is required. I, J, E, G and L are still relevant with I and J dependent on the shape of the twist beam.

It may be easier to measure, rather than calculate, the existing roll stiffness. You would need corner weight scales (two), possibly additional weight (friends/family of various weight?) and a floor jack to measure the weight on the tire contact patches with differential suspension travel across the rear wheels.

Tune to Win is useful for a basic understanding of vehicle dynamics. It does not cover the design of an ARB explicitly.

One thing that is covered are the effects of roll stiffness on vehicle handling. Two tire properties are relevant. The coefficient of friction of a tire rises and then falls as the camber angle with respect to the road moves from positive - leaning outboard at the top - to negative. The peak is with a slightly negative angle. The coefficient of friction of a tire also falls as the vertical load on it increases.

These two phenomena are illustrated in Tune to Win - at least in my edition of it - as two generic plots. Were they combined, using the common coefficient of friction axis, they would form a three dimensional map of tire performance data. Having this for the real tires you are using would be the basis for determining the effect of modifications to the suspension. Obtaining even basic data requires more work than is warranted but understanding what it looks like is useful.

If you increase roll stiffness at the rear you will alter the roll stiffness distribution, front to rear, the dynamic camber angles of the tires and where on the tire performance map are the tires - all four of them - for a given cornering speed, and so the handling balance. This may be good or bad depending on where you are starting from and where you end up. (You will likely increase oversteer.)

Given that you don't have tire data, you are reduced to empirical testing but, hopefully, doing so using as much information as you do have.

What I might try:

Remaking the clamps - the current ones don't match the shape of the twist beam and therefore don't limit the beam deflection.

Augment/replace the custom clamps with wooden blocks - diaphragms - made to fit precisely inside the twist beam. They would need to be wide enough - along the length of the twist beam - not to twist out of position. Hold them in place with the custom clamps or 'U' bolt clamps. It would help to size them so they extend slightly below the twist beam.

Conduct a junkyard search for a twist beam with a bar inside it of suitable size, like the silver one in the Autospeed article. Mount this bar inside the Mirage twist beam with split wooden blocks and external clamps. This would be my preferred option.

[slowmover]

Been recommending Puhn for a couple of decades. Everyone should have it in their library.

$200 isn’t that expensive, IMO. One needs to upsize the front bar if adding a rear, as a basic rule of thumb. Understeer trumps oversteer any day.

My Dodge pickup didn’t have rear bar. Both new ones came from Helwig and had to replace front bar links with improved. Truck could also use a rear Panhard Rod (instead of asking leaf spring mounts to counter body versus suspension force). Shocks had already been upgraded to entry level Bilstein.

Be systematic. No piece by piece changes.

Tradeoff is reduced rear wheel travel and ride is slightly degraded. But my rack & pinion IFS 2WD one ton is (literally) a slot car compared to live axle 4WD.

The change was made to better handle crosswinds with a loaded bed under cab-height bed topper, and counter forces from 35’ travel trailer. That it also marches up cloverleaf ramps with authority makes it impressive. I don’t launch hard enough to induce wheel tramp from Cummins torque, but testing there shows better transference.

Good luck.

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