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.

[Mazur]

Our team is making 7075 tripod housings/spindles and have been contemplating if we should implement hardened steel sleeves on the contact portions.

Problem is I don't really know how to go about manufacturing them. I was thinking about milling them out of some billet, but that might be improbable due to chatter. Anyone have any bright ideas?

[Hector]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">I was thinking about milling them out of some billet, but that might be improbable due to chatter. </div></BLOCKQUOTE>

Why should chatter be an issue? IIRC the lobes have a 1 inch diameter. I think we used a 3/4 inch endmill which was plenty stiff and had no chatter.

[Drew Price]

You will want to consult Machinery's Handbook or similar about machining things that are very hard, or look into different ways of getting them to finished size, like having them hardened and then ground to finished size.

Drew

[Chapo]

Our outboard tripod housings are 7075-T651 with heat treated 4140 inserts for the contact areas, we roughed out the block, heat treated it, surface ground it for thickness, edm drilled the start holes and then wire cut the inserts out.

We have no wear issues and the car has been running for over 18 months.

[Mazur]

No EDM here. The only process that I can think of that I can realistically do is to mill a solid piece of steel that I could press into the 7075 housing and then mill out the steel center to the tulip dimension.

[Chapo]

That could work, but what shape will you use? Will it just be a liner (ours are about 1.5mm thick I believe) or will it be a bit bigger to make the machining easier?

[Thrainer]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by sbrenaman:
... 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). ...

... Food for thought:
S2InternalSphere: pmax = 84 ksi
S2ExternalSphere: pmax = 2635 ksi
S3Plate: pmax = 1666 ksi
... </div></BLOCKQUOTE>

Hi,

doesn't this tell you that the aluminium contact surface will deform plastically no matter what you do?
About the 0.001" clearance, my experience is that the rollers can be off by that much, so the tripod ends up getting stuck in the housing.

Thanks for the calculations and sharing them with us. I only had to convert them to MPa.

In my first year, I used cylindrical bores with a rather small clearance to the rollers. The same design was manufactured in aluminium (anodized) and steel (no aftertreatment). The steel housings wore just as fast as the aluminium ones. The plastic deformation caused the rollers to contact on their edges, get stuck in the housing, some needles broke and the retainer rings broke regularely. With regular grinding, the alu housings lasted a season.

In the second year, I took the plastic deformation into account and designed slightly non-cylindrical bores. Further, the bores were placed on a smaller circle, so that the rollers are running on the needles properly. The 7075-T6 housings were not anodized, the steel ones were nitrided. I don't know how well the later are working, because we were running the alu housings the entire season (without need for grinding).

In the third year, the non-cylindricity was increased, only alu housing were manufactured and the same parts were used for the entire season without maintenance (except for applying grease).

For the fourth year, I increased the non-cylindricity slightly and also added some clearance. The alu housings now have a form fit to the hub instead of using bolts. We'll see how well that works. The housing with 40 mm length will weigh roughly 120 g. I also designed the tripod center myself.

Regards,
Thomas
AMZ - ETH Zurich

[Mazur]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Chapo:
That could work, but what shape will you use? Will it just be a liner (ours are about 1.5mm thick I believe) or will it be a bit bigger to make the machining easier? </div></BLOCKQUOTE>

As long as it's press fitted properly, I don't see why machining would become more difficult if formed as a liner.

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Thrainer:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by sbrenaman:
... 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). ...

... Food for thought:
S2InternalSphere: pmax = 84 ksi
S2ExternalSphere: pmax = 2635 ksi
S3Plate: pmax = 1666 ksi
... </div></BLOCKQUOTE>

Hi,

doesn't this tell you that the aluminium contact surface will deform plastically no matter what you do?
About the 0.001" clearance, my experience is that the rollers can be off by that much, so the tripod ends up getting stuck in the housing.

Thanks for the calculations and sharing them with us. I only had to convert them to MPa.

In my first year, I used cylindrical bores with a rather small clearance to the rollers. The same design was manufactured in aluminium (anodized) and steel (no aftertreatment). The steel housings wore just as fast as the aluminium ones. The plastic deformation caused the rollers to contact on their edges, get stuck in the housing, some needles broke and the retainer rings broke regularely. With regular grinding, the alu housings lasted a season.

In the second year, I took the plastic deformation into account and designed slightly non-cylindrical bores. Further, the bores were placed on a smaller circle, so that the rollers are running on the needles properly. The 7075-T6 housings were not anodized, the steel ones were nitrided. I don't know how well the later are working, because we were running the alu housings the entire season (without need for grinding).

In the third year, the non-cylindricity was increased, only alu housing were manufactured and the same parts were used for the entire season without maintenance (except for applying grease).

For the fourth year, I increased the non-cylindricity slightly and also added some clearance. The alu housings now have a form fit to the hub instead of using bolts. We'll see how well that works. The housing with 40 mm length will weigh roughly 120 g. I also designed the tripod center myself.

Regards,
Thomas
AMZ - ETH Zurich </div></BLOCKQUOTE>

Excuse my ignorance, but what exactly do you mean by making the bores non-cylindrical? Are you basically making the walls more square?

If that's correct, then what you're basically achieving is allowing for plastic deformation to occur, but not enough to allow contact with the outer edges of the roller, thereby getting "stuck".

Am I on the right track here?

[Chapo]

Richard,

WRT making the bores non cylindrical; the tripod roller is a section of sphere, from what I understand most teams make their housings by boring three cylindrical holes 120 degrees apart on the same (correct) PCD. A considerable amount of this space (everything past the end of the tripod roller) is not used, so what can be done is to no longer make the bore cylindrical, but truncated it to make the whole assembly smaller. It makes machining harder, but improves packaging and reduces weight.

Thats why I was asking the question about the liner, press fitting some steel in the truncated shape would come with considerable manufacturing difficulties to get the shape correct. I was thinking you might need to make the steel component a little larger to get the part to an easy to manufacture shape.

[JasperC]

Actually I think Richard's interpretation is the right one. The way I interprete it, Thomas increased the radius of the bores, causing the roller/housing contact to be concentrated to a very small area upon installation. This very small area would then deform until the bore radius matches the roller radius, and at that point you just hope no more plastic deformation will occur due to the larger contact area and strain hardening of the surface material. I must say it's quite a smart idea.

I would say you'll need some iterations to get the "non-cylindricity" right, as it's nearly impossible to correctly model the deformation & hardening of the surface. It would be really nice to have someone working on the same part for 4 years in a row... http://fsae.com/groupee_common/emoticons/icon_smile.gif

Thomas, don't you end up with a lot of play in your tripod housings, after the plastic deformation has occurred? Which would of course increase shock loads.


In the past two years, we've had 7075 housings with a ceramic coating. Last year this proved to be insufficient as we had some nasty pitting in the housings after about 1000km of testing. One problem with these coatings is you don't know very accurately how thick it will be, so you can't manufacture them to very tight tolerances. I think the bore diameter was about 0.05mm larger than the roller diameter.

I must add though that the pitting only occurred in one housing AND that we may have been driving around with a chain that was a bit too loose, which is of course a nightmare for shock loads. So maybe it wasn't really a design error that caused the pitting, but poor servicing.

Either way, very interesting topic about a very interesting part to design. http://fsae.com/groupee_common/emoticons/icon_smile.gif

Cheers,
Jasper Coosemans
Chief Drivetrain 2009-2010
DUT Racing Team

[Thrainer]

Richard and Jasper are correct about the contact surface, but also Matthew is right about the bore design. I got the overall diameter of the housing down to 63 mm and can still use a 10 mm cutter.

The "big secret" is getting rid of the idea that the two contact circles must share the same center point. I have increased the diameter to over 28 mm (the rollers are 25.4 mm). I must admit I didn't do the math like Scott, just designed what I thought might work and then let the testing speak for itself.

Actually, the first design with non-cylindrical bores was already ten times better than the cylindrical bores and reduced our need for replacement tripods to zero.

We haven't had problems with freeplay and I wouldn't say the clearance is significantly larger after testing. Since I like the axles to move axially without getting caught, the housings will have about 0.1 mm clearance this year. We'll see if that causes unknown problems. But since I've used a first-year housing with lots of freeplay for dynamic testing of two carbon driveshafts, I don't expect any failures from moderate clearance.

I don't think anodizing or a coating is a good solution, because they are thin and brittle. They cannot prevent plastic deformation because the stress maximum is below the surface (Scott should be able to tell us at which depth), which causes pitting and breaks up the coating.

Regards,
Thomas