The importance of frame rigidity

Chassis (or really hub-to-hub) torsional rigidity is a term thrown around FSAE Design Event tents frequently. When I was doing the FSAE thing I knew it was important and that you didn't want a floppy frame, but really didn't know why. So, and I suspect a lot of folks do this too, I would BS in the design event about how it adds another spring to the system, makes the car hard to tune, etc.. without a real explanation.

Thought about this a bit last night after I woke up from an entirely too long nap, had a Red Bull-Vodka, and watched a bit of Police Academy and Blacula (and its 1973 sequel, Scream Blacula Scream). Here's the real deal, to the best as I can determine.

Two of the biggest and most common tools we have to adjust vehicle balance (understeer vs oversteer) are adjusting spring and anti-roll bar (ARB) rates. Really what we're trying to adjust roll stiffness distribution front to rear, and both the spring and ARB act as roll-resisting springs in parallel (they add) at both ends of the car. Generally we assume the frame to be a rigid member. See picture below.


Kwheel is the wheel rate, since we're technically interested in how much stiffness the spring is providing to the tire/ground and this is NOT equal to the actual spring rate. Anyway, more roll stiffness at the front relative to the rear -> more load transfer at the front relative to the rear -> front tires have less grip than rears -> understeer. The corollary is true, ie stiffer rear -> less rear grip -> oversteer. That's all well and good. The fact we're tuning relative stiffness and not absolute is a key point. You'll often hear the term Total Lateral Load Transfer Distribution (TLLTD) used to describe the ratio of front to rear load transfer in roll.

In reality, particularly in the FSAE class, the chassis ALSO acts as a torsion spring in series to the front and rear suspension. For simplicity's sake I'll assume the sprung mass is a point mass, connected by a front and rear chassis "spring" to their respective suspensions. See picture below.



Springs in series act like resistors in parallel. For example if I have a 10 ft-lb/deg spring in series with another 10 ft-lb/deg spring, the resultant springrate is 5 ft-lb/deg. Oh snap, serious implications. If you have a compliant front end of your frame (in this case from the CG to the front suspension mounts) you're effectively changing your roll stiffness distribution, TLLTD, and vehicle balance! If it's bad enough you can make a massive spring or ARB change on one axle and get almost no change in balance. Additionally it's not really good enough to look at global frame rigidity, it's better to have the stiffness distribution fairly equal between sections.

How stiff is stiff enough? Tough to say, really depends on how load sensitive your tires are and what your suspension rate is. The stiffer your suspension rates are the more rigid your frame has to be. For a relatively softly spring FSAE car a well-designed tube spaceframe chassis is perfectly fine, and you quickly hit a point of diminishing returns trying to go stiffer. For an absurdly stiffly sprung F1 car a carbon tub is mandatory. An order of magnitude higher than the highest axle roll stiffness might be a decent minimum target value.

I'll throw in now, another reason Solidworks' Weldment feature is awesome is you can VERY quickly drop all the geometry into a beam-element FEA study that automatically picks out all your element MOI's etc. And beam-element analysis is wicked fast. Bitchin'!

Now you know. And knowing is half the battle.

Or at least that's my theory on the whole thing.