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Old 9 Apr 2016, 00:48 (Ref:3631327)   #1
sambeeb
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rear twist beam motion ratios

Hi,

In trying to work out my F:R wheel rates in my FWD er, I'm stuck on how to calculate the motion ratio of a twist beam rear end.
The things that I find difficult to get my head around are the fact that the left and right wheels are always coupled to a certain extent, and difficulty in figuring where to measure trailing arm pivots from.
Regarding the permanently partially coupled left and right wheels (through the twist beam) I'm guessing that I can never think in terms of one wheels motion ratio - one wheels is always dependant on the other yeah? I'm thinking I'd need to calculate the whole axle at once with the piggy back RARB disconnected, but then also reconnnceted at the soft, medium and hard settings to get the full picture. And I'd have to repeat all that again if I ever changed rear springs.

Regarding finding the pivot to measure from, you have the pivot mounted to the chassis, but the trailing arms of the axle don't actually pivot from there, they pivot from the common twist/torsion beam itself don't they? I'm sure there'd be some theoretical coupling point between the chassis pivot and the twist beam that should be a reference point but I just can't find any info.

any help greatly appreciated
sam
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Old 9 Apr 2016, 10:40 (Ref:3631431)   #2
snailpace85
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The twist beam won't have a huge effect on where the trailing arms pivot because the bending stiffness of the trailing arms is pretty high. Just think of the twist beam as an anti-roll bar that can't be disconnected and think in terms of both rear wheels moving together. Measuring the wheel hub centre, spring mounting point and the trailing arm pivot point leads to the usual relationship between spring rate and wheel rate.

I don't know if you're going to the extent of calculating anti-roll bar rates but the twist beam itself is a little tricky to get right. It has an open section and you can look up the torsional stiffness for that in standard text books. The problem is that the end effects where the twist beam joins the trailing arms mean that the formulas will underestimate the real anti-roll stiffness.

Hope that's some help,

Scott
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Old 9 Apr 2016, 14:13 (Ref:3631474)   #3
sambeeb
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it just seems way more complex the more I think about it. For example a one wheel bump would be a combination of the spring stiffness but also the torsional force that goes through the twist beam. But a two wheel bump will be the pair of springs together, but no additional stiffness coming from the beam. You get the feeling that when cornering or when hitting a one wheel bump that the wheel rate comes from some degree of both springs + beam + RARB with the trailing arm pivoting from the trailing arms attachment to the twist beam. But a two wheel bump/launch compression will come from both springs only and pivot more from the whole rear ends pivot at the chassis mounting point because the compression loading is the same for both wheels. See what I mean - it seems as though its pivot point would vary depending upon what the car is doing, like a variable motion ratio, and its going to be inherently way stiffer in ride than in roll.
And my head really starts to hurt when you think about what might be happening when it lifts an inside rear.
When you guys work out wheel rates for normal Mac strut or double wishbone rear corners, do you do so with the bar disconnected or connected?
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Old 10 Apr 2016, 19:12 (Ref:3631745)   #4
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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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Old 11 Apr 2016, 05:37 (Ref:3631812)   #5
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Well thanks for the reply. It both gives me a sense of relief in having some confirmation that these twist beam rear ends are in fact complex beasts, but also shows me that I'm way out of my depth when it comes to the proper engineering side of looking at it.
Perhaps I should give a bit of back ground as to why I'm looking at the rear end. The car I have is a vw polo 9n3 gti 1.8t. I use it in street registered class hillclimbs. Following mark Ortiz and dick shine advice on these rear ends I have lowered it as far as practical to get the COG and roll centre as low as possible. I have added a 20mm RARB set on hard to get the car to lift its inside rear - the reasoning being that this is just about the only way to get good traction out of the open diff front end when going up hills. Of course I still have problems getting the power down though. So I was wondering if my rear springs weren't too soft. Yes it will currently lift the inside rear but I think it is doing so because I have added the most 'retail' torsional stiffness to the twist beam that I can. But when it does this though, the whole rear is then supported on virtually a standard spring rate on the outside rear. I'm worried this will be inducing an outside rear 'squat' that will try to lift the inside front. So I want to run stiffer rear springs to try to help with the above scenario and also help with a bit of 'anti-squat' on launch and when powering up straight uphill sections - I can reduce the RARB stiffness to compensate on roll if I have too.
So I guess what I'm wondering is 1. is my reasoning in the ballpark/worth a shot 2. that's why I was asking about motion ratio's so that I can take a punt at a better rear spring rate.
MY front has 150lb springs and 22mm FARB on hardest of 2 settings, rears are 130lb springs with 20mm RARB on hardest of 3 settings. The car weighs 1100kg with a 65/35 f:r weight spilt in event trim.
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Old 17 Apr 2016, 21:05 (Ref:3634184)   #6
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This thread peaked my interest after recognising the question from one of Mark Ortiz's newsletters so I thought I should register and chime in.
First of do you have a link to the regulations? It would be interesting to see what's allowed in regards to chassis modifications. I would definitely try harder rear springs and a softer RARB as an ARB will increase lateral load transfer and lift on the inside rear, you should be able to achieve a higher degree of roll resistance before you start to lift the inside rear with stiffer springs over an ARB. From reading your discussion with Mark it would be beneficial to increase rear roll resistance on the rear so you can use a softer front ARB that should decrease front lateral load transfer, increasing front cornering force but also keep the front from rolling to much as it sounds like you are in some real need of more camber.

It may be worth getting some second-hand springs and cutting a coil or two off since they have a higher spring rate that will get higher when they are cut shorter, by no means the best solution but I get the impression you don't have a massive budget for racing. it will also allow you to try progressively harder springs with the more coils cut off. With regards to increasing roll resistance on the rear, increasing the track width at the rear with spacers or a lower offset wheel will increase the amount of roll resistance that you could achieve before lifting the inside rear which is the limiting factor to roll resistance.

With regards to your worry about the inside front unweighting due to outside rear squat, this is a dynamic situation and the main effect of dynamic load transfer in the CG height and the track width/wheelbase, do not confuse suspension displacement for weight transfer; suspension displacement is the effect of weight transfer and not the cause. If anything the squatting of the rear would decrease load transfer since the CG would be lower.

A thought on corner weights, using shims under a spring would allow the corner weights to be adjusted, I imagine the front will be sensitive to static weight distribution on launch with an open diff.

If anything doesn't make sense I apologise, I have just finished a very long weekend at Castle Combe.
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Old 18 Apr 2016, 04:02 (Ref:3634278)   #7
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Thanks for the reply and no worries, it did make sense.
One of the things I'd been asking Mark Ortiz about in his newsletter was why I was getting power understeer in the fast stuff but not in the slow stuff. I was lifting the inside rear in hairpins which really helped the car rotate, lots of front end traction, brilliant, but no inside rear lift in faster stuff and figured that's why the car was pushing under power in the fast corners ie too much rear grip.
At the time I was thinking I needed to add more rear roll resistance but was pretty much maxed out on the rear bar. Ortiz had said that the bar was the bigger governor of how early/high the inside rear would go compared to springs so I couldn't understand which way to turn. In my mind adding more rear spring would add more rear roll resistance (I was worried way to much relative to the front) but probably do little more for lifting the inside rear. He advised to go stiffer on the rear bar. I was looking into boxing the rear beam when I had a light bulb moment...
it actually ended up having more to do with the intrusion of the ESP than anything else. Firstly I went to Yoko A050 R specs. This gave me the mechanical grip to be able to run with the brake modulated "diff" turned off. I'd been getting awful mid corner throttle cuts that would dump the power suddenly - the front end had been on line and gripping just fine anyway (but a sensor disagreed due to a slight amount of power wheel spin). Also when I had been getting this drama previously I was on softer compound fronts than rears. I think I was getting too much rear slip and in the high speed stuff when the ESP was all keyed up and ready to intrude (but wouldn't in the slow stuff) it was reading the situation as life threatening oversteer and braking this wheel and that and straightening the car up on me. So now that I have more grip that is consistent all round, I'm not getting that problem anymore.
Now my problem is more what you alluded to. I'm coming around to the idea that a bit of rear squat is not such a bad thing like you said. Ortiz seemed to say that too. I think the front is the drama now. I have nearly 5 degrees neg caster but only 3/4 degree neg camber (and hub geometry that tends to eat up that neg camber very quickly apparently). So in the tight stuff I'm still all good due to lots of caster induced corner camber, but in faster flowing stuff without much steering lock I simply don't have the camber. I recently did the Bathurst, Mt Panorama hillclimbs and some of the fast stuff across the top of the mountain between the walls got very hairy as the car wanted to push wide under power. I was just loosing so much time waiting on the throttle before I could plant it.
In the interest of preserving what little camber I have I run the car at a 'lower control arms level' ride height to keep the RC up, and run 50 profile 15's so the tyres aren't too camber sensitive. I have enough money for only two things 1. fit adjustable camber tops, or 2. fit bilstein B8's or koni yellows. Not both. I honestly don't know which - either better damping or just a bit more negative will give me the best gain. When I do either 1. or 2. ill be fitting slightly stiffer springs at the same time for a bit more camber control too.
With my rules I need to be on road legal tyres, suspension is free in terms of bolt on componentry but I can't modify the chassis. I can fit bolt on braces but not weld in ones without being classified up to type 2 or type 3.
So what do you think - better front damping with minimal neg camber, or more front camber on OEM sachs damping.
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Old 18 Apr 2016, 11:42 (Ref:3634373)   #8
pipcarder
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I believe that Mark wanted to achieve inside wheel lift in faster corners with an increase in rear bar. This may have been a better way of doing things since you compete in hill climbs where the start is very important and increasing rear spring rate would slightly increase rear weight transfer on launch from raising the CG height as the front extended over the rear compressing. However, for cornering the rear has reached 100% of its capability to resist roll when the inside has left the floor and so any further roll resistance would be on the front axle. This will adversely affect your camber since any compression that moves the lower arms past the point of being level will start to quickly diminish camber, also lower the roll centre and increase the roll couple exponentially, causing more roll and so forth. So increasing rear spring rate and decreasing the bar a little may still help your current problem. I have to say that driver aids interfering hadn't crossed my mind, that could have taken a long time to realise!

With regards to the pushing under power, from my limited experience running FWD race cars I have used toe out at the rear to help the car rotate more so the front wheels can have less steered angle and thus be able to provide more forward traction. I know it is common practice in "spec" championships where adjustments are limited, I don't know if the shims required are available for your car though, maybe something to look into?

It is difficult to decide between the two, first off what else do you use the car for? Do you have a significant other that is going to be annoyed about an uncomfortable car? if it is daily driven then camber plates may be good as they will allow you to reduce the camber for every day driving and put it back on for competitions. Out if the two damper choices I would personally go for the Koni since you already have them on the rear and I doubt the Bilsteins are adjustable? How much of an increase in spring rate are you going? Since this may dictate the need for stiffer dampers to control the stiffer springs, you really don't want to have underdamped front springs as this will reduce traction and front cornering force. Increasing you tyre pressure should help you get a larger footprint during cornering with insufficient camber, do you have or have access to a pyrometer? Another option would be to look into roll centre correction kits as this would reduce roll at the front geometrically and increase camber gain under roll. You would probably also need a bump steer correction kit as well since adjusting the lower arm position would also affect your bump steer. If you haven't read them there is a very good series of articles on Moto IQ called the ultimate guide to suspension and handling (link at the bottom) that has examples of adjusting roll centres and bump steer kits using rose joints. Since your lower arms use the bolt in ball joints it shouldn't be too much trouble to make something up or have a shop make it. You could also take the opportunity to increase the track width at the same time, this will reduce lateral load transfer giving an increase in cornering force.

http://www.motoiq.com/Tech/TheUltima...nHandling.aspx
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Old 18 Apr 2016, 12:36 (Ref:3634393)   #9
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sorry an edit on post #3. What I meant to say is that the twist beam is way stiffer in roll than in ride.
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