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Engineers and physicists are fond of saying ‘As a first approximation….’ before launching into a simplified calculation that’ll probably get things good enough (within 10 to 20% with a bit of luck). You’re quite right though. The real motion of the axle won’t quite go through the pivots on roll.
But using the dreaded ‘as a first approximation’ we can assume that the pivots act as perfect pivots which means that they are completely free in rotation but perfectly stiff against normal movement. This has the effect of forcing the pivoting to occur at those points. The twist beam is relatively flexible in torsion so the torsion moments about an axis parallel to the beam will put a bending moment into the trailing arms that won’t bend them very much simply because they are so much stiffer. There will be a bending moment in the twist beam about an axis along the length of the car. The twist beam is quite stiff in this direction. That could deform the trailing arms a little but the twist beam’s length does mean it is relatively flexible in bending just not as flexible as it is in torsion. Therefore you can reasonably assume, up to a point, that the twist beam simply has an anti-roll effect with the suspension otherwise acting as a pair of independent trailing arms pivoting about the bushed pivots.
There is an issue that the behaviour of open sections in torsion doesn’t perfectly comply with standard stress analysis formulas due to the stiffening effect at the ends where the twist beam is attached. That means that any calculations are likely to underestimate the roll stiffness of the suspension. You might be able to search the internet to find academic papers on the subject which might give you an estimate of this effect. If you’ve got experience and access to Finite Element Analysis (FEA) facilities that would be the easiest way to calculate more accurately. That contrasts with traditional circular section anti-roll bars which are reasonably easy to calculate by hand. I don’t know how familiar you are with beam bending and torsion hand calculations but a popular book with engineers here in the UK is Roark’s ‘Formulas for Stress and Strain’ and contains the relevant information.
I’ll leave this post here as I’m sure there must be a word limit but I’ll do more posts in the next few days for you on the role and limitations of calculations in motorsport and the motor industry generally (my background) and say something about the limitations of my first approximation assumptions above which turn out to be quite large really and become larger as you stiffen the suspension for motorsport. At that point what you said in your posts becomes more relevant and it isn’t completely straightforward.
Hope that makes some sort of sense,
Scott
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