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Thread: Some interesting axle strength calculations

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    Some interesting axle strength calculations

    Some things to discuss...not sure how to interpret this actually.

    Heres what I've learned.

    Torsional yield strength of circular shafts is based on shear yield strength.

    http://www.engineeringtoolbox.com/to...fts-d_947.html (equation 4)

    Shear yield strength for all steels is about 0.6 of the yield tensile strength.

    http://en.wikipedia.org/wiki/Shear_strength

    If we choose 4340, there is an enormous variation in tensile strength depending on how its hardened. But lets say 180,000psi tensile yield strength.

    https://books.google.com/books?id=S0...%20psi&f=false

    So 0.6 of that means a shear yield strength of 108,000 psi

    I measured my 90 Daytona's axle shafts and they appear to be 1.037" diameter.

    So using the equation #4 linked above, we get a yield torque of 1972 ft/lbs. Thats the theoretical point a perfect shaft in perfect torsion will start to permanently deform, not break.

    The breaking point would be use the ultimate shear strength, which is about 0.75 ultimate tensile strength. So if we say UTS is 230000psi (should be close), that gives an USS of 172500, and a breaking torque of 3150 ft/lbs.

    In 1st gear an A568 has an overall ratio of about 11.5.

    http://www.thedodgegarage.com/trans_guide.html

    So if our theoretical launch is taking place with say at least 200ft lbs of torque at the flywheel, thats about 2300 ft lbs at the wheels. Split in two assuming equal traction. So 1150 ft/lbs per wheel.

    If you crazy racer guys are somehow getting near full engine power at launch and its more like 400 ft lbs, thats more like 4600 ft lbs. Split in two around 2300 ft lbs per wheel.

    No we throw in the reality of stress risers in our non-ideal splined axles/hub interfaces, and its starting to look like even very good 4340 axles + very high power launches are close enough to start breaking.

    If we downgrade to 1040 axles, which I'm guessing the stock ones are made of, the breaking strength goes down to about 2250 ft lbs, or about 40% less than the 4340.

    http://www.alloyusa.com/front-axle-shaft-kits.html

    2250ft/lbs times 2, and then divided by 11.5 is 391 ft lbs...and that before stress risers. I think there are plenty of TD's putting out that much torque. And thats the breaking torque, not the yield torque.

    Even if traction is definitely not 100%, during a controlled wheel-spin sub 2 second 60ft launch, I would imagine that the engine output is high enough to put out that much torque. Some 60ft to horsepower calculators could prove it as far as minimum required torque to launch so much weight 60 ft in so much time. Its got to be way up there for some of the nastier builds.

    Has anyone figured out how to make the axles bigger? I'm guessing there is some kind of knuckle upgrade to something with a bigger hub, but what about the splined ends in the diff?
    Last edited by acannell; 05-27-2015 at 10:49 AM. Reason: corrected arithmetic

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    Re: Some interesting axle strength calculations

    The shafts will always break at the root of the spline just before it goes into the CV joints center section. That's where the stress riser is from the spline, and from the joint with the CV. They should never break in the middle of the shaft.

    Your analysis above all look correct to me.

    It's one of the reasons many racing axle shafts are made with 300M. It's a modified 4340 with an UTS of 300kpsi.
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    Re: Some interesting axle strength calculations

    Quote Originally Posted by ShelGame View Post
    The shafts will always break at the root of the spline just before it goes into the CV joints center section. That's where the stress riser is from the spline, and from the joint with the CV. They should never break in the middle of the shaft.

    Your analysis above all look correct to me.

    It's one of the reasons many racing axle shafts are made with 300M. It's a modified 4340 with an UTS of 300kpsi.
    what surprises me is how close the ballpark breaking strengths are (not yield but actual ultimate breaking strength) and the torques our modified TD's might actually put out during a launch..

    and thats before the stress risers!

    and then throw in more torque going to one wheel...

    and perhaps some sort of shock loading effects (not sure how to even ballpark quantify those)

    do automatics multiply the torque at launch even more than the manuals?

    I suppose all this makes some sense. 1.037" diameter is pretty small.

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    Re: Some interesting axle strength calculations

    heres a science graph, as you can see, yield strength vs. shaft OD is extremely non-linear. An increase of OD by 33% increases yield strength by 133%.


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    Re: Some interesting axle strength calculations

    Re making axles...this article from fourwheeler (not exactly the pinnacle of truth..some of their equations are flat wrong) shows an axle shaft being machined on what appears to be a typical CNC mill with a 4th axis and an involute cutter.

    http://www.fourwheeler.com/how-to/tr...nder-pressure/



    Those sorts of cutters are described in detail here:

    http://www.mmsonline.com/articles/speeding-up-splines



    That would lower the axle prototype cost quite a bit...looks like the star of the show is the Coromill 172 insert holder.

    http://www.sandvik.coromant.com/en-u...s/default.aspx

    I cant seem to find online pricing, which is unusual for machine shop stuff..and not a good sign. But if its like other insert holders, I would expect it to set one back several hundred dollars for the holder and a set of inserts.

    You could actually do the 4th axis with an indexer or manual table, since it doesnt rotate during the cut.

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    Re: Some interesting axle strength calculations

    Quote Originally Posted by acannell View Post
    w
    do automatics multiply the torque at launch even more than the manuals?
    Yes, they do! The torque multiplication is proportional to the speed difference, minus the efficiency (just like a gear ratio). Theoretically, if you are brake torquing, the torque is infinite! In reality, it just dumps a ton of heat into the tranny fluid while brake torquing as the converter slips. But, the torque output can be 3-4 times the gear ratio in 1st gear as the car initially starts to move.

    You also need to take into account what the tires can hold. If the tires will not hold the torque against the pavement, they will spin and the torque seen at the axle shaft will be much lower.
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    Re: Some interesting axle strength calculations

    Quote Originally Posted by ShelGame View Post
    Yes, they do! The torque multiplication is proportional to the speed difference, minus the efficiency (just like a gear ratio). Theoretically, if you are brake torquing, the torque is infinite! In reality, it just dumps a ton of heat into the tranny fluid while brake torquing as the converter slips. But, the torque output can be 3-4 times the gear ratio in 1st gear as the car initially starts to move.
    Wow that puts things in definite breaking territory then even with 4340 shafts!

    You also need to take into account what the tires can hold. If the tires will not hold the torque against the pavement, they will spin and the torque seen at the axle shaft will be much lower.
    What do you think engine output is during a full slicks burnout? I would think a high power, sub 2 second launch would be at least as much power as that plus quite a bit more. In other words, even a zero traction situation can present a high load to the engine and therefore transmit torque through the axles. Or are burnouts done at much lower power levels?

    So do automatics break axles more than manuals?

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    Re: Some interesting axle strength calculations

    Quote Originally Posted by acannell View Post

    So do automatics break axles more than manuals?
    FYI- The Reliant comes out of the hole at 27 pounds of boost, 1.6 short times and is running the same 87 Shelby Z Daytona axles, never broke one.

    Dumb luck perhaps?


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    Re: Some interesting axle strength calculations

    I see more people break axles from wheel hop then those who are running slicks without wheel hop involved

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    Re: Some interesting axle strength calculations

    Quote Originally Posted by bgbmxer View Post
    I see more people break axles from wheel hop then those who are running slicks without wheel hop involved
    What he said. Wheel hop kills axle shafts.
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    Re: Some interesting axle strength calculations

    Quote Originally Posted by mopar-tech View Post
    FYI- The Reliant comes out of the hole at 27 pounds of boost, 1.6 short times and is running the same 87 Shelby Z Daytona axles, never broke one.

    Dumb luck perhaps?

    I think theres something that the calculations I did (simplified torsion breaking strengths) arent taking into account. At 27psi how much torque do you think is at the crank? 200ft lbs at least right?

    If we say 200ft lbs, and then assume twice the ratio of an A568 1st gear because the automatic multiplies via torque converter, thats 200 * 11.5 * 2 = 4600 ft lbs. Assuming even traction (it is the Reliant after all), thats 2300 ft lbs to each axle. If we say 1040 steel @ 140ksi ultimate tensile strength (so 84ksi ultimate shear strength), and 1.037" OD, the ultimate breaking torque is 1534 ft lbs. So the shaft should be breaking every time, easily, and by a wide margin (almost 800ft lbs beyond breaking point).

    So something in the calcs isnt right....especially if you consider that at 27psi there was probably more like 300 or 400 ft lbs of torque available. And maybe the torque converter output is 3 times higher than an A568 1st gear at 0 rpm.

    If I imagine the axle shaft from the daytona, bare with no cv joints. Lets say I put it in pillow bearings and attach a 1 foot lever on it. Then I park the front of the daytona on the end of the lever to put about 1500 ft lbs on it. Its hard to imagine the shaft tearing apart....that doesnt pass the smell test. Not exactly scientific but still ....

    I think I could rig up an axle breaking rig and test one of our stock axles. I have a small load cell that could measure the force and I should be able to make the rest of the rig using mostly junkyard parts like a wheel bearing, axle, and a side gear, with things arranged to let the wheel bearing side rotate while the side gear side is locked. Use the load cell to measure force at some distance like a foot.

    That should give us an absolute best case axle strength, since it wouldnt take into account radial loads, bending, or shock loads. So things could only get weaker in real use.

    Is there something about torque converters which, along with multiplying the torque very high at low rpms, also has some ceiling to that torque multiplication? I.e. yeah its 4 to 1 at near 0 output rpm but its not going to transmit more than 1000 ft lbs even if the input torque is 400 ft lbs?

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    Re: Some interesting axle strength calculations

    Quote Originally Posted by acannell View Post
    At 27psi how much torque do you think is at the crank? 200ft lbs at least right?
    A stock 2.5 turbo I "hi torque" exceeds that.


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    Re: Some interesting axle strength calculations

    Remember that while the wheels are spinning the torque seen by the axles is actually low as there is less resistance to the tires spinning once they are spinning (dynamic friction).

    The Reliant was VERY light. This reduces the resistance against the movement of the vehicle at launch and reduces the instantaneous torque load. That's what is going to break your axle. That's why shock loads such as wheel hop and dumping clutches breaks axles and auto's typically don't...they apply the torque in a softer manner.

    Think about this...if you have a big 1/2" drive impact and you adapt it down to a 1/4" drive extension and you want to break a bolt loose...if the bolt actually breaks loose, then you probably won't break the 1/4" extension, however, if the bolt stays put...I hope you have some PPE on because that extension is going to shatter like glass!

    Now...freewheel the impact and have the other side of the extension attached to a torque absorber (some sort of breaking device). Apply a load slowly and you will probably twist the extension like a candy cane before it breaks (depending on the toughness of the metal). Lock it up and again you will shatter it.

    Eliminate shock loading and a good majority of the breaking issues will probably go away.

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    Re: Some interesting axle strength calculations

    Quote Originally Posted by Reaper1 View Post
    The Reliant was VERY light.
    Oh? 2350 isn't that light, l-body territory.

    Getting it below 2000 lbs was the goal, not sure if its possible though.


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    Re: Some interesting axle strength calculations

    Quote Originally Posted by Reaper1 View Post
    Remember that while the wheels are spinning the torque seen by the axles is actually low as there is less resistance to the tires spinning once they are spinning (dynamic friction).

    The Reliant was VERY light. This reduces the resistance against the movement of the vehicle at launch and reduces the instantaneous torque load. That's what is going to break your axle. That's why shock loads such as wheel hop and dumping clutches breaks axles and auto's typically don't...they apply the torque in a softer manner.

    Think about this...if you have a big 1/2" drive impact and you adapt it down to a 1/4" drive extension and you want to break a bolt loose...if the bolt actually breaks loose, then you probably won't break the 1/4" extension, however, if the bolt stays put...I hope you have some PPE on because that extension is going to shatter like glass!

    Now...freewheel the impact and have the other side of the extension attached to a torque absorber (some sort of breaking device). Apply a load slowly and you will probably twist the extension like a candy cane before it breaks (depending on the toughness of the metal). Lock it up and again you will shatter it.

    Eliminate shock loading and a good majority of the breaking issues will probably go away.
    Elephant acknowledged.
    Most people are still doing very little about this. I will say it again, a carbon carbon clutch is a smarter investment than upgrading every single drivetrain component in succession of weakness.
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    Re: Some interesting axle strength calculations

    Quote Originally Posted by mopar-tech View Post
    Oh? 2350 isn't that light, l-body territory.

    Getting it below 2000 lbs was the goal, not sure if its possible though.
    Is that with you in it? My 4 door car K car, with triple core intercooler, steel fender flares, nitrous tank, roll bar, sway bars and heavy 15x10 steel autox wheels/275 rubber was way lighter. I'll have to look it up, but I think it weighed in at 2200.

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    Re: Some interesting axle strength calculations

    Quote Originally Posted by Pat View Post
    Is that with you in it?
    That is correct


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    Re: Some interesting axle strength calculations

    Quote Originally Posted by acannell View Post
    Wow that puts things in definite breaking territory then even with 4340 shafts!



    What do you think engine output is during a full slicks burnout? I would think a high power, sub 2 second launch would be at least as much power as that plus quite a bit more. In other words, even a zero traction situation can present a high load to the engine and therefore transmit torque through the axles. Or are burnouts done at much lower power levels?

    So do automatics break axles more than manuals?
    Technically, zero traction (literally) would mean there was NO load on the axle. The axle won't see any torque if there's nothing holding it on the other end (IE, the tire).

    Personally I get 1.8x 60' times with a 'low' power non-IC 2.5. I run 24.5" slicks, and I almost always get a little slip out of them. They never hold completely.
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    Re: Some interesting axle strength calculations

    Quote Originally Posted by ShelGame View Post
    Technically, zero traction (literally) would mean there was NO load on the axle. The axle won't see any torque if there's nothing holding it on the other end (IE, the tire).

    Personally I get 1.8x 60' times with a 'low' power non-IC 2.5. I run 24.5" slicks, and I almost always get a little slip out of them. They never hold completely.

    Any chance you know your mph at 60 foot? We could back-calculate a minimum axle torque using that.

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    Re: Some interesting axle strength calculations

    Reading some articles on driveshafts and found that Quarter Master rates their Ultimate Torsion driveshaft at 4100lbft. I think it's safe to say that we aren't going to exceed this.

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