3 and 4 link rear suspension questions

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Jer73
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Re: 3 and 4 link rear suspension questions

Post by Jer73 »

Brian P wrote:Your supports for your upper arm look quite far apart (at both ends). Have you calculated the tension force on that upper arm under maximum acceleration and calculated the stresses on the crossbar that the upper arm is secured to?
No I have not done an analysis of the possible forces on any of the links or mounting. So far I have been building it to what I think is husky enough. I have thought about making spacers that utilize 2 bolts per rod end to secure the upper link instead of just one bolt as I do fear that it will have issues with flexing the mounting bolt. The mounts for the upper link on both the chassis and axle have a 5 inch spread and will be using 3/4in grade 8 fine thread bolts. If you could walk me through or present an example of how I would go about doing an analysis that would be greatly appreciated Brian.
j-c-c wrote:Might be a little late in the game for your progress, but this link applies I believe, and is a respect build:

http://www.lateral-g.net/forums/showthread.php4?t=52748
Very nice build looks like quite a bit of $$$ in that one :mrgreen:
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Re: 3 and 4 link rear suspension questions

Post by Brian P »

Let's start with establishing how much pull force there could be on that upper link.

Engine torque output x transmission 1st gear ratio x torque converter multiplication (if automatic) x rear axle ratio / distance vertically between the lower and upper link attachment points on the axle.

Use consistent units and report back with what that number is.
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Re: 3 and 4 link rear suspension questions

Post by MadBill »

Don't forget that distributed between the upper arm and the lower ones there are also compressive loads created by the forward reaction from the tire thrust that is accelerating the vehicle. On the upper, this cancels out a significant % of the tensile torque reaction but on the lowers it is additive. 'Fortunately', there are normally two lowers to divvy it up...
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Re: 3 and 4 link rear suspension questions

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Lets say the peak engine out put is 350 lb ft, it is just a mild 306 small block ford, transmission first gear is 3.35, rear axle ratio is 4.11 distance between the upper and lower links at their farthest configuration would be 21 1/2 inches apart, upper link being 14 inches from axle center line and lower links being 7 1/2 inches from axle center line. The closest configuration would be 14 inches apart with the upper link being 8 inches from axle center line and the lower link being 6 inches from axle center line.

350lbft x 3.35 x 4.11 / (21.5in / 12) =
350lbft x 3.35 x 4.11 / 1.791ft =
1172.5 x 4.11 / 1.791ft =
4818.975 / 1.791 = 2690.661 ft lbs
At its farthest configuration

350lbft x 3.35 x 4.11 / (14in / 12) =
1172.5 x 4.11 / 1.666ft =
4818.975 / 1.666ft = 2892.542 ft lbs
At its closest configuration.
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Re: 3 and 4 link rear suspension questions

Post by Brian P »

Typo. 14" = 1.166 ft. The tension on the upper link is 4132 lbs. The forward thrust does offset some of this but it's erring on the safe side to disregard that.

So now you have 4132 lbs applied at the center of a "beam" (the pivot bolt for the upper link) which is 5 inches long and is the cross-section of a 3/4" bolt. The threads in that bolt don't help you but I am going to ASSume that you are not using a full-threaded bolt and that the most critical part of it through the rod-end is 3/4" diameter without threads on it.

The end reactions are 2066 lbs each and the moment is 2.5 x 2066 = 5165 in.lb. (Half the length of the beam x the magnitude of the end load)

The second moment of the area Ixx = 0.016 in^4 and the outer fiber is 0.375 inch from the centerline of the section

Stress = M y / I = 5165 x 0.375 / 0.016 = 121,000 psi

Ouch.

The side plates on either side of the rod end should be brought in as close as possible around the rod end so that the clamp bolt is as short as possible.
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Re: 3 and 4 link rear suspension questions

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Brian P wrote:Typo. 14" = 1.166 ft. The tension on the upper link is 4132 lbs. The forward thrust does offset some of this but it's erring on the safe side to disregard that.

So now you have 4132 lbs applied at the center of a "beam" (the pivot bolt for the upper link) which is 5 inches long and is the cross-section of a 3/4" bolt. The threads in that bolt don't help you but I am going to ASSume that you are not using a full-threaded bolt and that the most critical part of it through the rod-end is 3/4" diameter without threads on it.

The end reactions are 2066 lbs each and the moment is 2.5 x 2066 = 5165 in.lb. (Half the length of the beam x the magnitude of the end load)

The second moment of the area Ixx = 0.016 in^4 and the outer fiber is 0.375 inch from the centerline of the section

Stress = M y / I = 5165 x 0.375 / 0.016 = 121,000 psi

Ouch.

The side plates on either side of the rod end should be brought in as close as possible around the rod end so that the clamp bolt is as short as possible.
I did the math on the farthest configuration and got 78827.977 psi. Which is still a no go as that also exceeds the shear strength of the hardware being used.

I ASSumed that since some modifieds are running a similar suspension like this https://youtu.be/_5kc-qUrS6g I would be okay with the brackets and hardware. Dirt cars like modifieds don't usually see 100% traction they don't weigh 3200lbs either... :oops: I am going to need some time and coffee to see if I can work around what I have if not, it is time to break out the cut off wheel and start over. Or just hook up the 4 link bars and go from there. Again thank you for your input Brian this could have been a potentially hazardous oversight.
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Re: 3 and 4 link rear suspension questions

Post by MadBill »

When I was messing with 3 links a few years back, I found an on-line calculator for A-S %, loads in the links, etc. AIR, the tire thrust forces reduced the net single upper link tensile load to about the same as in the two lowers.
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Re: 3 and 4 link rear suspension questions

Post by Brian P »

It will help. Really what's needed is to treat the whole axle assembly as a supported beam in side view.

We have 4818 lbs applied at one end of the beam (the tire contacts).

If we assume 28" tall tires (a guess) then the lower links are 8" above ground and the top link is 14" above that. Imagine a teeter-totter with the pivot being the lower link, one end being the tire contact patch, the other end being the upper link.

The tension on the upper link taking the drive force into account with the links in the closest configuration is 4818 x (8 / 14) = 2753 lbs.

So it's about two-thirds of way too much, but it's still too much.

Bear in mind that the pivot of that teeter-totter - the lower links - has to handle (in compression) the total of the tire contact thrust AND the tension on the upper link, so that's 2753 + 4818 = 7571 lbs split (unequally) between the lower links. The split will be unequal because the upper link isn't in the middle, but it's close enough to the middle for this purpose - and the tire contact patch loads, which are the bulk of it, are split equally.

Going to a 4-link won't make this go away!

Making the side plates on either end of the relevant link-end joints closer together, e.g. so that the side plates immediately adjoin the rod-end itself, so that we are not dealing with 5 inch long bolts in bending, will fix this. But it requires a bunch of cutting and welding.

Installing a tubular solid bushing on either side of the rod-end, filling the gap out to the side plate, of significantly bigger diameter than the bolt itself, and with a good thick washer on the outside so that the clamping load gets distributed better, would help very substantially by no longer relying on just the bolt itself to handle the bending load. And this way you don't have to cut and re-weld everything.
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Re: 3 and 4 link rear suspension questions

Post by Brian P »

On looking at the photo again, it looks like the lower links have the side plates much closer together - those shouldn't be a problem. It's just the upper link that has them too far apart.

Go with the spacer idea to spread out the bending loads. It will let you fine-tune the amount of driveshaft torque cancellation by using different spacer lengths (so that you can move the link side to side).
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Re: 3 and 4 link rear suspension questions

Post by BillyShope »

I believe the best 3link was that originally designed for the Ramcharger High And Mighty C/A. Unfortunately, the timing was such that the design was never really utilized. The idea was a 4link configuration with the upper driver side link telescoping so that it was carrying a braking load only. The car was "thrown together" for the '59 NHRA Nationals with things being added as the car went through Inspection. Although equations were available for link angles, the angles were only estimated. The result was over compensation to the point that both passenger side tires bounced on the first hard launch. To appease the NHRA officials, a bolt was put through the telescoping link, where it remained for the rest of the car's existence. I went back to graduate school very shortly after the Nationals, so I never tried to get the car back to the original concept. I understand the car reset the C/A records numerous times, but I had no further contact with it. I just hated to see Billy Rassmussen, of Texas, displaced as the record holder.

As for braking with a 3link, I would point out that Jaguar, with its asymmetric 3link in the C-Type, won at Le Mans, where, I think you would agree, braking performance is greatly valued.
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Re: 3 and 4 link rear suspension questions

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BillyShope wrote: Wed Jun 27, 2018 9:36 am...As for braking with a 3link, I would point out that Jaguar, with its asymmetric 3link in the C-Type, won at Le Mans, where, I think you would agree, braking performance is greatly valued.
The C Jag used a laterally adjustable 3rd link I believe. Do we know how much offset they settled on, if any?
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Re: 3 and 4 link rear suspension questions

Post by BillyShope »

The C-Type used the asymmetric rear suspension to obtain equal rear tire loading on acceleration. As is often the case, I don't believe the engineer in charge was fully cognizant of the results. I have read that he did not realize that the braking would be affected and that, upon this being pointed out to him (after Le Mans), he regretted his use of the 3link. As Jaguar was in the process of changing to an IRS, all of this makes little difference, and, for that matter, I might be making some unwarranted assumptions.
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Re: 3 and 4 link rear suspension questions

Post by MadBill »

I'm itching to try your 'Traction Dyno' procedure on one or more cars with offset upper links, just because it's such a neat and simple exercise! The couple of cars I work on have symmetrically located upper links.. :(
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Re: 3 and 4 link rear suspension questions

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As you probably know, some engineers at Chevrolet worked with d'Alembert's Principle at the proving grounds. (This was for a very short time, as they were going to the static hydraulic loading as used now.) They simulated cornering loads by tethering a car to the side of a bus or other heavy vehicle. My idea of a "traction dyno" simply rotates their work ninety degrees. With a traction dyno, this silliness of testing suspension settings at the strip over a couple of seasons would be completely eliminated. The engine, in fact, would not be started. This concept causes some racers to go ballistic! I remember one saying, "I'm not gonna tie my race car to a tractor!"
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Re: 3 and 4 link rear suspension questions

Post by j-c-c »

Jer73 wrote: Sun Jan 29, 2017 10:10 pm Just an update for anybody interested, I have finished the rear suspension aside from the swaybar and have started on the roll cage.

IMG_20160911_171942[1].jpg
IMG_20170112_171157[1].jpg
IMG_20170126_172418[1].jpg
I'm sure you are way beyond the pics here, but with all the discussion/concern with loading on the upper 3/4" link 5" bolts, I noticed the pictured upper TR located approx 75% off center of the two upright brackets, the loading would also follow that offset I suspect, but the outside bracket is axle clamp restrained on a cantilever welded bracket. Seems slightly edgey for lack of a better word. Is that what you had as your final result?
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