FEM CONSTRAINT

[spedtoe169]

I'm trying to figure out how to constrain a wheel model. I'm only analyzing the wheel center of a 3-piece wheel. It is in NO WAY in contact with the tire. I want to know how I should constrain the hub face and the studs. I realize that the nuts on the studs will be torqued and there will be a compressive load at the lug holes. But I want to know, is a torque about the wheel axis transmitted soley between the hub and the wheel hub face? Or do the studs take some of this load as well.

Thanks!

John

 

[jetmaker]

spedtoe169,

The worst case senario would be to have the wheel studs taking out all the torque. This is conservative but very reasonable when looking at ultimate load conditions as the friction forces between wheel and axle hub are likely going to be exceeded.

To model this problem as accurately as possible, I would look at a simple contact problem in which the wheel hub is in contact with the axle hub, resisting only inward loads. The studs would then handle any outward loading through tension. Furthermore, the stids would carry all shear loads due to vehicle weight and torque.

Hope this gives you a start.

jetmaker

 

[spedtoe169]

Yes thank you, that is an excellent start. I think you are exactly correct but I'm not sure about and shear loads due to vehicle weight and vertical loading due to weight transfer. As it will be a hubcetric wheel, the center hole should take these loads instead of the studs. I think the studs would still take any torques about the axis of the wheel.

Does this seem right?

You answered my main question about whether the friction between the wheel and hub would be exceeded.

How should I go about calculating the compressive load due to the torque in the nuts?

 

[analyzer]

The compressive load is the negative of stud tension.

 

[EnglishMuffin]

For a correctly preloaded bolted joint, the additional load seen by the bolts when the joint is loaded in a direction normal to the joint should be minimal. It depends on the relative stiffness of the bolt and the mating structure at the joint. The same would be true in the case of torque - the additional stress seen by the studs, which would likely be a bending load if anything, would depend solely on the torsional deflection occuring between the wheel and hub at the bolt pitch circle, which should be minimal if the friction developed at the hub is high enough - it really requires a drawing, so that one could figure out if the friction is high enough. I can't believe that it would be acceptable to have any movement at that point during acceleration in any case. The wheel/hub relative deflection due to torsion could be calculated of course, by FEA if necessary.

 

[jetmaker]

spedtoe169,

I am not sure what a hubcetric wheel is, but to determine whether the shearing loads are taken by the studs or hub is simply a matter of tolerance. All the vehicles I've own have had large clearances between the wheel centerline and the axle hub. Also, they all used beveled nuts which nest into the holes in the wheel. So, the wheel load is transfered into the nuts and then through the studs. So the wheel never really contacts the studs directly. If this is the configuration you have, it looks like the load passes through the studs first.

Analyzer calls it correctly. Calculate the preload in each bolt based on nut/stud torque. If the idea is to add this preload into the analysis, apply it concentric to each stud over a small diameter about the stud hole in the wheel.

Have fun... and a good weekend.

jetmaker

 

[EnglishMuffin]

On a normal wheel, whether or not the studs carry much shear in normal service is not simply a matter of tolerance, but depends largely on the friction developed between the hub and the wheel during bolt preload. In a crash condition or a severe impact it might be another matter. But I guess we need to know what a hubcentric wheel is.

 

[analyzer]

When it comes to wheels for Trucks, Trailers, and Buses, there are two types of wheels and loads on studs depends on type of wheel.

1. Hub Piloted Wheels (spedtoe169 calls this hubcetric)
A single cone lock nut is used on each bolt, for single or dual wheels. Wheels for this type system have straight through stud holes without a spherical chamfer. In this design shear loads are taken by the hub.

2. Stud Piloted Wheels
Wheels of this type have a spherical countersink on each stud hole. In this design shear loads are taken by the studs.

In both designs studs will see tensile loads due to nut torque, etc loads.

 

[spedtoe169]

This might sound like a rookie question, but how do you calculate the tensile force based on the torque applied to the fastener?

 

[jetmaker]

EnglishMuffin,

Question for you... would you typically account for friction during ultimate loading??? What about for fatigue loading???

The policy at the company I work for is that friction is neglected for ultimate loads as the applied loads are often thought to exceed the static friction capability of a joint. I would agree that if the surface finish of the mating parts was sufficiently rough, and the preload high, it would be a reasonable assumption to consider friction effects.


spedtoe169,

There are many ways to calculate the preload on a bolt due to friction. One accepted method is detailed in MIL-S-8879(c). Shigley also specifies a method for calculating it.

Regards,

jetmaker

 

[EnglishMuffin]

analyzer:
Assume for the sake of argument that a conventional wheel is attached with five 1/2" studs each preloaded to 5000 lbf (a not unreasonable figure). Assuming a coefficient of friction of .2, it would take a transverse force of 5000 lbf before the bolts experienced any shear load whatsoever. And the studs would probably be subjected to bending loads as well as shear at that point.
In the case of hub piloted wheels, I thought the issue was whether the studs see shear loads due to torque, which again depends on friction.

 

[EnglishMuffin]

jetmaker : sorry - didn't see your post, was writing another one. Well, as I implied before, for determining the ultimate strength of the wheel/hub connection, you would of course have to rely on the studs. From a fatigue calculation standpoint, I would have thought that you would proceed as for any bolted connection, taking into account the reduction in stress range produced by the preload, and certainly not assuming that the wheel could slide transversely relative to the hub. But maybe in the automotive world, you have to do such calculations on the assumption that someone is going to drive long distances with loose wheel nuts. Maybe GregLocock can help us - I am sure he is reading this.

 

[analyzer]

EnglishMuffin
Stud piloted Wheels used to gouge/break due to shear and bending loads on them , the stud hole size was close to the stud size that is why the industry (large truck) is getting away from that design.
In the case of hub piloted wheels the stud hole is so much bigger than stud that it is not practical for the studs to take shear loads under NORMAL loading and proper torque.

 

[EnglishMuffin]

analyzer : Well - we seem to be saying much the same thing. The thing is, to what extent does one design for the case where the nuts are not properly tightened ? Years ago, some cars had LH thread wheel nuts on the driver's side (US). Rolls Royce was one example, but a number of US cars also did this. It was my understanding that this had something to do with the probability that loose nuts would unscrew. Obviously, you would not be able to develop any preload under these circumstances, but the fact that they thought about this seems to indicate that they were anticipating that drivers might travel significant distances with loose lug nuts.

 

[spedtoe169]

This is really helpful guys! Keep it up!

For the purposes of my analysis, I'm assuming that everything is torqued properly and won't come loose. The vehicle we're talking about weighs 2700lbs with driver and no fuel (it can carry about 14gal).

My company has no policies for anything of this sort. Part of my task is to develop such criteria.

 

[EnglishMuffin]

There is a book that might be of interest to you, often recommended on Eng-Tips, called "An Introduction to the Design and Behavior of Bolted Joints", by Bickford. In this book, you will find a discussion of preload, fatigue, slip resistant joints (which is what I have been alluding to), etc etc. I recommend it.

 

[electricpete]

I'm not sure if it addresses all the above but I see there is a lot of good stuff at

http://www.boltscience.com/pages/info.htm

 

[GregLocock]

There's an SAE standard for testing wheels, and I have seen the studs fail on a conventional car type wheel during those tests. The particular test is called grist mill (from memory), and simulates continuous hard cornering, so the studs are partly in tension. In general I believe the studs do not routinely take much of the vertical loads directly in shear, I think the vertical load is mostly reacted by the friction. However the wheelnuts do have a conical face, so there is definitely a load path into the stud.

Torques would be reacted by the same mixture of paths.

Incidentally typical peak shock loads at the wheel centre would be of the order of 3-5 times the wheel loading, on a car.

I have a feeling that you will need to model the hub and studs in order to investigate the propertion of the loads taken by the studs and by friction properly.

What I do know for sure is that the design of optimised steel wheels is quite tricky.

Cheers

Greg Locock

 

[EnglishMuffin]

There are of course gap elements or contact elements which one can use to model the joint, which most FEA codes have in one form or another, and the most sophisticated versions include friction. The only time I have tried to use the friction type, I wasn't able to get the solver to work (endless iterations etc). It wasn't a wheel analysis of course. But I guess it all depends on which analysis package one is using, some may work better than others, and there are various convergence factors and criteria that you have to get right, so maybe I gave up too easily.

 

[EnglishMuffin]

GregLocock: One point about your post: You say that the studs are partly in tension under hard cornering. If the nuts are properly torqued, the studs will be in tension all the time, whether cornering or not, and in fact the tensile stress in the studs should not increase appreciably even when cornering, assuming the preload is not exceeded, the actual increase depending on the relative stiffness of the stud and the joint interface, which should be a sizeable ratio. But under hard cornering, you (sort of) seem to be implying that the stud preload is sometimes exceeded, something that you would know much more about than I in view of your automotive background, although I would not have thought that cornering forces would ever be high enough for that.