Rear Torsion Bars

[dch1950 37 1 Cars]

Hi all,

I have some time on my hands while I wait for some spraying to dry off before I flat it. and I had a look at the ARB and torsion bar geometry (pulled out my Mechanics & Properties of Matter to refresh ageing brain). I also looked at the spring rate calculators that Pugtorque was playing with a while back. The flaw in the logic of using that formula is that the axis of the torsion bar and the axis of rotation must be one and the same and coincident. The PUG setup has the torsion bar rotating on an circular path with the ARB/arm shaft C/L as it's centre. Thus the ARB is the only bar acting as a true torsion unit. The two torsion bars do work together to restore/spring any wheel movement but their main restorative "spring" action seems to be that of bending/flexing a solid beam or rod along it's major axis and thus the spring constant coming into play is different (i.e. not a torsional restorative force). There may be some rotational movement of (a fixed point on) the cicumference of the torsion bar but it is minute compared to the angular displacement of the whole supension arm when it's moving.

Thus it seems that the ARB which plays the roll of solid connecting axle (in principle anyway) is the real torsion bar in the set-up. I read ADI's article with some interest , though the operation of the torsion bars was passed over rather in preference to different respective diameters of ARBs and torsion bars and the selection of rear dampers.

The general rule of "the thicker it is the stiffer it is" (so to speak!) applying. You have to ask yourself how did they think this system up in the first place.

Interesting though.

regards

Dave.

[RossD 44]

I've always thought this and wondered about the effects it has on the suspension. I wonder if the rotational movement induced by the position of the torsion bars actually has the effect of 'softening' them - For example calculating the spring rates using the formula meant for a 'true' torsion bar will actually give a spring rate that is too high?

[dch1950 37 1 Cars]

Hi Ross,

I've been looking at this topic for quiet a while - inspired mainly by the fact that this summer I have been finishing off my beam refurbishment and having it all available to play with on the bench set me thinking.

Those calculators are for torsion bars operating as I stated. The 2 modulii (moduluses?) conerned are 1) Youngs modulus and 2) the shear modulus or modulus of rigidity. symbolically E and n respectively.

Typical values for steel show that E is approx 2.3 times n. The modulus of rigidity is the one used in the calculator(s) and thus calculated values will be too low.

The actual fomula is restorative Torque (spring rate) = Pi*n*R^4/2L

where R is bar radius, L=major axis length, n is shear modulus. What is interesting is the restorative torque acts over a much smaller lever length than the actual wheel atttahced to the arm i.e. 47mm and 255.5mm respectively but the offsetting of the torsion bar does give some mechanical advantage to the system as a whole.

Better stop now before everyone falls asleep.

regards

Dave

[RossD 44]

Haha, not at all, it's always interesting to get down to the proper detail of how things work. Those formulas take me back to my A-level Physics days!!

[welshpug 1,645]

we want pictures!

[dch1950 37 1 Cars]

Haha, not at all, it's always interesting to get down to the proper detail of how things work. Those formulas take me back to my A-level Physics days!!

Hi mate,

not a fellow physicist surely? (masonic type handshake proffered).

regards

Dave

PS Welshpug - pictures of ......?

D

[RossD 44]

Not these days no. Did A-Level Physics and then started a Mechanical Engineering degree, got bored, so changed to Computer Science instead!

[dch1950 37 1 Cars]

Not these days no. Did A-Level Physics and then started a Mechanical Engineering degree, got bored, so changed to Computer Science instead!

shame, I took Physics and then spent my working life writing/designing telemetry and C3 system software. I now wish I had done Mech Eng. as I seem to be spending most of my time on my PUG. Funny how things turn out.

best wishes

Dave

[Rob Thomson 6]

How much does the fixing at the trailing arm actually move along its arc? 10mm? How long's the bar... 1.2m? I don't think the non-rotational movement is very much in the grand scheme of things.

 

I wouldn't know where to begin with the maths these days. Eight years after finishing my (Civils) degree the only maths I ever do is working out the ocassional percentage. I once asked my father (who's proper clever) if he could work out the equivalent spring rate of a Peugeot torsion bar and he worked it out from first principles in about two minutes; truly humbling.

[Tom Fenton 1,536]

I'd agree with you Rob that over the length and also considering the cross section of the bar, the bending moment of the bar contributes very little to the spring rate.

[dch1950 37 1 Cars]

I'd agree with you Rob that over the length and also considering the cross section of the bar, the bending moment of the bar contributes very little to the spring rate.

It will actually deflect around 22mm over full suspension travel - try bending that yourself with one end in a vice - it doesn't take minimal force to do it.

Dave.

[wracing 19]

as you have a beam on the bench it may be interesting to measure the main axis's of rotation and grounding points ill fea it and see if the results are comparable with the various static analysis.

james

[dch1950 37 1 Cars]

as you have a beam on the bench it may be interesting to measure the main axis's of rotation and grounding points ill fea it and see if the results are comparable with the various static analysis.

james

What is interesting in the overall geometry is that the front torsion bar (drivers side) is 50mm on the other side of the fulcrum (the centre line of the arm shaft) and the nearside bar is 50mm the other side of the fulcrum point and is thus disadvantaged in term of applied leverage (torque). Also the driver side is obviously loaded more and one would imagine that different spring rates would apply to balance things up. This could explain the left/right nomenclature for the OE bars.

regards

Dave

[Tom Fenton 1,536]

it doesn't take minimal force to do it.

 

Compared to the twisting torque required to twist the bar through its arc of movement it does.

[Rippthrough 98]

What is interesting in the overall geometry is that the front torsion bar (drivers side) is 50mm on the other side of the fulcrum (the centre line of the arm shaft) and the nearside bar is 50mm the other side of the fulcrum point and is thus disadvantaged in term of applied leverage (torque).

 

Doesn't make a difference, 50mm is 50mm when it comes to torque from an axis of rotation, no matter which side it's on.

The bars are handed from the factory because they are pre-stressed during tempering to avoid sag.

[dch1950 37 1 Cars]

Doesn't make a difference, 50mm is 50mm when it comes to torque from an axis of rotation, no matter which side it's on.

The bars are handed from the factory because they are pre-stressed during tempering to avoid sag.

What sag is that - is one (unloaded) side heavier than the other. Or do you mean that because of the permanent weight in the drivers side (when driven anyway) that the driver side bar is subject to a greater static load and will over time fail to return to it's unloaded position - the so called metal memory. I have also raised this point about identifying the bars before

(a note on the painted rings) - they don't come out of the furnace (and presumably are allowed to cool down) with paint rings on them so is there another method of identification (for the lad painting the rings on them!). Just a thought.

regards

Dave

[dch1950 37 1 Cars]

Compared to the twisting torque required to twist the bar through its arc of movement it does.

Hi Tom,

the lever length difference is 5 to one though and that must make a difference for a given applied force at the stub axle end.

regards

Dave

[Rippthrough 98]

What sag is that - is one (unloaded) side heavier than the other. Or do you mean that because of the permanent weight in the drivers side (when driven anyway) that the driver side bar is subject to a greater static load and will over time fail to return to it's unloaded position - the so called metal memory. I have also raised this point about identifying the bars before

(a note on the painted rings) - they don't come out of the furnace (and presumably are allowed to cool down) with paint rings on them so is there another method of identification (for the lad painting the rings on them!). Just a thought.

regards

Dave

 

Yep, same as with springs, unless they're prestressed during the tempering process then they will eventually sag a little as there's always some residual stresses.

[Cameron 16]

I think you're half right here but getting a little carried away with it.

 

True you might not be able to bend the end of the TB 22mm, but given suitable leverage (i.e that of the trailing arm) it's very easy to bend it that amount. As Tom F says it would be far more difficult to apply the same amount of twist.

 

Anyway, the reason I say you're half right is that a proportion of the spring rate is made up of bending the bar, but the majority of it is twisting.

[Goliath 94]

I see what you are saying and have wondered this myself in the past. Mainly because the first beam I ever lowered was on my mk1 clio. They have a setup that I would expect, the two torsion bars are half the length of the beam and meet in the middle on the pivot point, in my eyes that is what I would expect as they are solely working by twisting movement and not being stressed in any other dimension.

[dch1950 37 1 Cars]

I think you're half right here but getting a little carried away with it.

 

True you might not be able to bend the end of the TB 22mm, but given suitable leverage (i.e that of the trailing arm) it's very easy to bend it that amount. As Tom F says it would be far more difficult to apply the same amount of twist.

 

Anyway, the reason I say you're half right is that a proportion of the spring rate is made up of bending the bar, but the majority of it is twisting.

Hi Cameron,

my point about the bar in the vice was that the bending element can't be dismissed

It's the weird PUG set which is throwing me - say compared to VW Beetle torsion bars.

It's a visualisation thing. I understand about pre stressing the bars for static load (of the body shell etc) but why does it seem to be different (for each) bar - i.e. 2 different part numbers from PUG

Dave

PS I knew I'd had to much glucose yesterday!)

D

[Tom Fenton 1,536]

My very rough and ready calcs suggest 90% of the spring force is down to the twist of the bar, against 10% down to the bending of it. This was assuming a number of things including torsion bar length being guessed as 1.2m as I don't have a size to hand.

[dch1950 37 1 Cars]

My very rough and ready calcs suggest 90% of the spring force is down to the twist of the bar, against 10% down to the bending of it. This was assuming a number of things including torsion bar length being guessed as 1.2m as I don't have a size to hand.

Cheers Tom,

I definitely had too much glucose yesterday. Just for info the bar is 992mm long.

I still don't see why they are different part no's though.

regards

Dave

[Tom Fenton 1,536]

That alters it quite a lot, more like 97% twist 3% bend, the bending calculation uses L^3 so the change in length makes quite a big difference. Having said all that they still are rough and ready. But it proves that the torsion is the major player, and especially when considering the increase in rate with outer diameter increase, its not worth worrying about too much.

[dch1950 37 1 Cars]

That alters it quite a lot, more like 97% twist 3% bend, the bending calculation uses L^3 so the change in length makes quite a big difference. Having said all that they still are rough and ready. But it proves that the torsion is the major player, and especially when considering the increase in rate with outer diameter increase, its not worth worrying about too much.

Hi Tom,

yes, the mistake I made was mixing units - twas ever thus.

Regards

Dave