Modeling Tripod-Tulip Using Hertzian Contact

[sbrenaman]

Hey guys, I have a few questions for you all. What sort of Hertzian (or other?) models are you using for Tripod-to-Tulip contact stress? I've got both Sphere-to-Sphere and Cylinder-to-Cylinder in a spreadsheet, but would really like to find Sphere-to-Cylinder which I believe to be a more accurate representation.

The 2 most significant factors of contact pressure are the diameter of the tripod ball's OD and the tulip housing ID. Increasing the diameter of the tulip housing by 0.010" can increase stress by 50%. But to increase the stress by 50% with tire grip, you'd have to increase grip by 333%.

What tripod-race diameters and tolerances are you guys using? I'd be interested to hear what the 7075 guys are using more specifically. I see from the formulas how you can have total destruction of a CV in 10 minutes with a horribly machined 7075 joint, but I can also see how you can last to nearly 10^7 cycles (about 10000 miles) with a well-machined 7075 joint.

It's also apparent from the formulas why people want to HT to RC45+ on a 4340 joint; the contact pressure is 50% higher with steel-on-steel contact (versus steel-on-aluminum).

Yeah, just some food for thought. I'd appreciate any info, thanks.

[sbrenaman]

Hey guys, I have a few questions for you all. What sort of Hertzian (or other?) models are you using for Tripod-to-Tulip contact stress? I've got both Sphere-to-Sphere and Cylinder-to-Cylinder in a spreadsheet, but would really like to find Sphere-to-Cylinder which I believe to be a more accurate representation.

The 2 most significant factors of contact pressure are the diameter of the tripod ball's OD and the tulip housing ID. Increasing the diameter of the tulip housing by 0.010" can increase stress by 50%. But to increase the stress by 50% with tire grip, you'd have to increase grip by 333%.

What tripod-race diameters and tolerances are you guys using? I'd be interested to hear what the 7075 guys are using more specifically. I see from the formulas how you can have total destruction of a CV in 10 minutes with a horribly machined 7075 joint, but I can also see how you can last to nearly 10^7 cycles (about 10000 miles) with a well-machined 7075 joint.

It's also apparent from the formulas why people want to HT to RC45+ on a 4340 joint; the contact pressure is 50% higher with steel-on-steel contact (versus steel-on-aluminum).

Yeah, just some food for thought. I'd appreciate any info, thanks.

[Mazur]

This shows how important it is to not machine to spec on the first cycle. It's just not worth it to try to save on machining time, and chances are people out there are not probing in their home location and tool offsets, and not taking enough care in doing it manually.

Best way is to cut the tulip undersized and increase your offsets a little at a time till you get a tight slip fit.

[thewoundedsoldier]

This might be a dumb question, but how are you accounting for the contact in the model? What little introduction to contact mechanics I have is all based on external-to-external contact between bodies. In the case of a tripod, though, you have an external-to-internal contact. I'm not experienced enough with it to write my own functions, if that is what you are doing.

As for the tolerances, last year we machined our 7075 tripod housings to about 0.001" oversize, then carefully sanded them down using a dremel until the contact was a snug slip-fit. They seemed to work fine all year long but there was slight galling that we only found once we took the car apart. I will post pictures shortly. We didn't even get high forces, either (no more than 0.6g vehicle acceleration, vehicle weight of 750# w/driver).

"Increasing the diameter of the tulip housing by 0.010" can increase stress by 50%."
Are you considering machining both the housing and the tripod races? Or is this comment referring to increasing the housing diameter without changing the size of the tripod itself? I'm a little confused. If it's the latter, shock forces will do much more damage than contact mechanics.

I'm really interested in how you created your model with the outside of one sphere in contact with the inside of another, or outside of a cylinder with the inside of another. I think that a sphere-to-flat plane model would be closer than either of those.

Nice post!

NOTE: the above numbers and tripod joint galling occured on the Formula-Hybrid@SJSU vehicle. I cannot speak for the FSAE team, though I know they made their housings from the exact same material.

[sbrenaman]

Read Section 3-19 in Shigley's 8th Ed, or whatever section is Contact Stress in your Edition.
but, here is a quote from Section 3-19 Shigley's:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">For a plan surface, use D=infinity. For an internal surface, the diameter is expressed as a negative quantity. </div></BLOCKQUOTE>

I am using Sphere-to-InternalSphere, and a Cylinder-to-InternalCylinder (with contact length "a" as a wild guess BTW)as defined in (Eq 3-68) the S2S contact problem.

My comment about increasing race size was with regard to increasing the tulip's tripod cylindrical bore race diameter without increasing the tripod size.

Regarding "shock forces", how do you define those and quantify what shock forces are? Your tire is always going to be the limiting factor assuming the rotating unsprung masses are negligible.

Re: your comment about sphere-to-flat plate. You're correct that S2Plate is a better approximation than S2S. However, define "better." Food for thought:
S2InternalSphere: pmax = 84 ksi
S2ExternalSphere: pmax = 2635 ksi
S3Plate: pmax = 1666 ksi

I would love to see pictures of this galling, along with your surface finish callouts, instantaneous rear swingarm lengths halfshaft lengths, and specific alloy/heat treat of 7075 Aluminum.

[Hector]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Regarding "shock forces", how do you define those and quantify what shock forces are? Your tire is always going to be the limiting factor assuming the rotating unsprung masses are negligible. </div></BLOCKQUOTE>
I was given the opportunity to talk with a GM drivetrain engineer at the 2010 Michigan event. They ran a test on a Camaro with large chrome rims in which they did clutch drops on regular asphalt and on simulation ice. Even though tire grip was different by an order of magnitude, drivetrain stress only dropped by 20%. This indicates that tire grip may actually be less important than shock loading for peak stress analysis. For cyclical stress I'd stick with maximum tire grip.

Take this with a grain of salt, as the Camaro's rotating mass is much larger than that of an FSAE car, but it should at least provide an idea of shock loading.

My team never had a good experience with 7075 Tripods. They were machined and hard coat anodized very carefully to insure a close fit with almost no slop, but failed catastrophically after about 10 minutes of run time. Granted, we tend to be a higher-powered team and we were seeing acceleration right around 1g during this particular testing run. We've gone the custom 4340 tulip route since then, and have achieved results that are as light as a bolted aluminum housing but can handle much higher contract stresses. You have to replace the entire shaft if the housing fails, but we haven't seen that issue yet.

[thewoundedsoldier]

Really interesting with the calculations. I don't have Shigley's book, so I'll have to take your word for it. I've never even solved out a contact stress problem so take everything I say with a grain of salt.

The best I can do for ya are these yuppy pictures with my measly iPhone camera:

h t t p : / / s649 . photobucket . c o m / albums / uu217 / FormulaHybridSJSU /

As you can see from the top view, the galling really isn't that bad and the serviceability of the part is not really affected. When you run your finger over the galling, you can only feel the slight rise in the leading edge of where the tripod makes contact (and by 'slight' rise, I mean you can BARELY feel it). There is galling on both sides, which is interesting and indicates that the shock forces ARE what cause the galling (if it was tire force, only the acceleration side would experience it). There was no specific surface call out--it's very difficult to polish inside of something like this. The housing is 7075 not hardened with any treatment (hint hint).

I would say the only way to try and quantify shock forces is to use conservation of kinetic energy. Even that is crappy. Most engineers in practice just use a multiplication factor based on assumptions.

[Mazur]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content"> The housing is 7075 not hardened with any treatment (hint hint).
</div></BLOCKQUOTE>

Are you implying 7075-O will perform better over 7075-T6?

[Drew Price]

That doesn't look like galling, that's total surface failure.

My immediate thought was also "Where do you even get 7075-O???", LOL.


So... who says the housing has to be one piece all made from the same material?


Drew

[thewoundedsoldier]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">So... who says the housing has to be one piece all made from the same material? </div></BLOCKQUOTE>

Time!

The raw material was T6. We didn't do anything to it post-machining. I've had guys on my team pick up 6061-T0 from our local metal supplier--it's like plastic.

The pictures look worse than what is really there, partly because the cv grease got ground into the contact surface. I'm sure such a stain would be on any joint, taken from any car. The actual damage is much less. Still scary., given that we never really went fast.