Hi

Trying to calculate the rate of my anti-roll bars for some weird mathematically analysis that I don't quite understand yet (but intend to eventually).

Anyone know the METRIC equation for roll bar stiffness in Nm/deg twist based on effective length, effective arm length, ID and OD (or OD and wall thickness), and modulus of rigidity.

Also, can someone roughly confirm that G for steel is about 80GPa, and doesn't vary [much] with alloy and heat treatment? I'm pretty sure that's right, but not 100%. Would go and look it all up, but the relevant books aren't here at the moment.

Can find equations for lb/in (i.e. linear movement of arms, not degree twist), and I know the equation for roll stiffness taking vehicle track and ARB Motion ratios into account, but not an isolated bar. Thanks in advance.

I have to pass on the equation, not one I've come across, but I can say I'm using G as 79.3 GPa for steel. No idea on how it varies though.

I would have thought any metric equation would be in SI, so the answer it would give you would be in Nm/rad, so you'd need to multiply the final answer accordingly. If you do come across it though, would you mind sharing it?

Of course.

Nm/rad is fine, but as radian is a silly unit that nobody actually uses in real life I'd prefer degrees. For me radians is more of a theoretical unit, not something very useful.

Wiki to the rescue, I think

http://en.wikipedia.org/wiki/Torsion_%28mechanics%29

Can that not be rearranged so that

Nm/Rad = (D^4-d^4)RG/L
s
And therefore Nm/Deg = (180(D^4-d^4)RG) / (L*pi)?
where D=OD, d=ID, R=arm length, G=Modulus of Rigidity, L=length

Actually, no. As the result is in Nm, which is a torque, the arm length shouldn't come into it.

Quote from tristancliffe :

Wiki to the rescue, I think

http://en.wikipedia.org/wiki/Torsion_%28mechanics%29

Can that not be rearranged so that

Nm/Rad = (D^4-d^4)RG/L

Where does this 'R' come from?

If you remove it, then the units are Nm. Radians are dimensionless, so the units agree.

Quote :

And therefore Nm/Deg = (180(D^4-d^4)RG) / (L*pi)?
where D=OD, d=ID, R=arm length, G=Modulus of Rigidity, L=length

Actually, no. As the result is in Nm, which is a torque, the arm length shouldn't come into it.

You're forgetting that the conversion factor between radians and degrees has units.

I'll have a proper look through my data books when I get home.

The R was the radius (or arm length), but I realised that, being a torque, the length doesn't come into it. If I wanted to know the perpendicular force I'd need R (although myabe not where I put it ).

As for radians to degrees there are no extra units - the conversion is surely just 180/pi, which makes it work based on dim. analysis.

Anyway, I'm pretty happy with the results. I need a larger 25mm (1") rear bar, and a front bar between the 19mm and 25mm ones I have no, which can be acheived with running the 25mm one and using the blade adjuster Softer rear bar could be overcome by using slightly higher than ideal spring rates, or something along those lines I suppose. I'll just have to use the blades.

Hmm...I'm not sure I agree with your equations.

Using that Wikipedia link...

phi = TL/JG
T/phi = JG/L

T/phi = pi*G*(ro^4-ri^4)/2L

or, in terms of diameters,

T/phi = pi*G*(Do^4-Di^4)/32L

If you want 'phi' in degrees rather than radians,

T/phi = pi^2*G*(Do^4-Di^4)/5760L

Ah, yes, of course. R is the radius, so that's doubled for diameter, which comes out as 2^4 = 16. Where does the 2L come from? Surely the bar can be considered to be held at one end and twisted from the other, thus L is the total bar length, rather than half of it?

If it's meant to be 2L, then I can see where the 32, and therefore the 5760 comes from.

Is the second pi (that forms pi^2) from J = pi(R^4-r^4)?

This is such elementary (well, A-level) mechanics that I should really know it, but it's surprising how quickly it leaves the brain without more frequent usage!!

P.S. I was secretly hoping you'd see this thread Stewart, as you seem to know rather a lot more than me about these things Fancy joining a crappy club racing team as Official Consultant I already offered the position to Bob, but he ignored it! To be fair I was asking him to drive miles and miles to model our car numerically, which is asking a lot to be honest...

Quote from tristancliffe :

Ah, yes, of course. R is the radius, so that's doubled for diameter, which comes out as 2^4 = 16. Where does the 2L come from? Surely the bar can be considered to be held at one end and twisted from the other, thus L is the total bar length, rather than half of it?

The '2' came from the equation for J on that Wiki page. I just added it to the denominator rather than write pi/2 on the numerator.

Quote :

Is the second pi (that forms pi^2) from J = pi(R^4-r^4)?

Yes, that's right. The other comes from the radians -> degrees conversion.

Quote :

This is such elementary (well, A-level) mechanics that I should really know it, but it's surprising how quickly it leaves the brain without more frequent usage!!

Yes! It's been a while since I've used any of this myself! Moments of inertia usually end up confusing me...

Quote :

P.S. I was secretly hoping you'd see this thread Stewart, as you seem to know rather a lot more than me about these things Fancy joining a crappy club racing team as Official Consultant I already offered the position to Bob, but he ignored it! To be fair I was asking him to drive miles and miles to model our car numerically, which is asking a lot to be honest...

Hehe, this is the sort of subject which I really should know something about, but when it comes down to it, I usually realise that I don't I think I might have to pass too, I'm afraid, though I'm usually up for some technical discussion in this forum

So are we agreeing on Stewarts equation? I could add it into the ARB calculator in VHPA if that's the case.

Quote from tristancliffe :

I already offered the position to Bob, but he ignored it! To be fair I was asking him to drive miles and miles to model our car numerically, which is asking a lot to be honest...

Especially considering I don't have a car atm. Once that issue is solved, if you were nearer this end of the country, I'd be interested to take a look.

Just did this myself and I came up with the same result as Stewart. Luckily I didn't peek at this thread before or I would probably have given up in confusion trying to understand what Tristan had done.

Another thing you may want to look at is the bending of the arms that connect to the roll bar. These are often blade shaped so that you can adjust their bending stiffness by turning them (by changing the area moment of inertia).