Formula for number of bolts/bolt-holes required on a wheel

[sprashanth]

How do you determine the optimum number of bolt holes or bolts required on an automotive wheel (like the wheels of cars or trucks), when you only have data on the tyre size, the corresponding wheel size and the load rating for the wheel? And for instance, why is it that tractor wheels have usually 6 or 8 bolt holes - while those for buses have 10 or 12 bolt holes?

I'm guessing this involves calculating of Tensile and Shear stresses on the bolts based on the wheel load, but what are the exact formulae I need to use in this regard & what are the types of forces to be considered? Is it due to tyre friction or cornering effect? Can someone help me out on this, since I haven't really worked on this type of problem before.

 

[GregLocock]

It's a good question, but I only know a bad answer.

The life of a wheelnut is not easy, and over the years the design of wheels and wheelstuds has converged on the sizes, and numbers, you see in use today.




Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[dgallup]

If cost is your over riding concern, 3 was enough for Renault. Lose 1 & it fails almost instantly so it's not a popular solution. I don't even like 4 although it is widely used. Knockoffs only use one but they were banned. Somehow my motorcycle still gets away with one & a spring clip on it's single sided swing arm.

 

[NickE]

I dont think wheel studs see shear forces.

 

[dadof275103]

FYI

This issue is being addressed on Automotive Suspension Forum.

Michael

 

[thundair]

It makes a difference if you are hub centric or lug centric.
For my use I like the centering of the wheel to be hub center and I machine a step to engage a concentric pocket in the wheel.
I noticed a lot of late model stuff is hub center. You can tell lug center stuff, it has the tapered lug nuts.

Cheers

I don't know anything but the people that do.

 

[NickE]

thundair,

I dont know of a modern wheel/hub that actually transfers load through the wheel center. This has been discussed heavily here.

The friction btw the hub face and its mating area with the wheel is the mechanism that transfers the load. The tension produced by the studs is what creates the normal force to produce the friction.

I napkin'd the calcs once, I'll see if I can find it.

nick

 

[NickE]

Found it, How'd I do Greg? (I dont generally do this kind of math.)

"The center section of the hub does not support any loading when the lugs are properly and completely torqued. The lugs see clampload in excess of (see below).

The tension in a bolt is given by:

F=T/Kd :: where F==Tensile force; T==torque; K==factor (0.2); d==diameter

So for an M12 torqued to 70ft-lbs:

F=840_in-lbs / .2*(.472_in) = 8898_lbf per lug. At 5 lugs thats 44,491_lbf pulling the wheel in contact with the hub.

Now the loading of the wheel is transfered to the hub on the frictional interface btw the wheel and hub. The following is how to solve for the force required to break that static friction.

f=u(s)*N:: where: f==frictional force required to break static friction; u(s)==Static coefficient of friction; N==normal force (or clamping force)

f=0.45*44,490= 20,000_lbf

So in order to cause the wheel to move in relation to the hub would require ~20,000_lbs of force to act on the wheel independantly of the hub. "

Nick
I love materials science!

 

[IceStationZebra]

"I dont know of a modern wheel/hub that actually transfers load through the wheel center."

Many off-road applications are hub-centric, including tractors. I have had problems with axles that were stud-centric. The wheels are stiff enough that if the studs are not perfectly centered with the holes they will eventually loosen up.

ISZ

 

[FoMoCoMoFo]

Locating ? Load carrying

I think some of the lug pattern changes in modern
cars and light trucks are designed solely to give the oem an
advantage in wheel sales.

 

[GregLocock]

That calculation looks about right

0.45 is a tad high for mu though, I'd have used 0.15 which is greasy steel on steel. That would drop the load to 60 kN.

A wheel only sees forces that high during events like square edge pothole, which are designed to rip the suspension apart.

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[IceStationZebra]

FoMoCoMoFo - I see your point. In theory the hub pilots do not carry any load, it is all transferred through clamp load. In practice this is difficult to guarantee 100% since off-road vehicles can see some very high shock loads on a regular basis, there is usually no suspension besides the tires, and the wheels are very stiff. And once the wheel starts to move things will deteriorate until someone retorques the lugs. A pilot hub can serve as a belt and suspenders approach.

ISZ

 

[tbuelna]

Since the wheel studs are not a shear fit, they must be capable of applying enough (plus a suitable MoS) clamping force to carry any load the wheel experiences solely through friction at the wheel/hub interface. Any relative motion between the two surfaces, however small, will result in fretting/galling.

As GregLocock noted, a safe value to use for Mu with dry-metal-on-dry-metal (but not greasy)is 0.15. If there is any grease or oil present you may potentially achieve boundary conditions. So you should use a much lower Mu of around 0.06 to be safe.

I would disagree with what others said about the center pilot though. It's not there to carry loads. It's only purpose is to locate the wheel at installation.

Good luck.

 

[IceStationZebra]

In a past job I tested two different forklift axles on an off-road test course. The goal was >110k cycles at 2g vertical. The machines were approx 31-34,000 lbs. with the only real difference between the wheel mounting was one piloted off of the hub and the other off of the studs. The axle with stud piloted wheels had continuous problems loosing wheels despite our best efforts.

My last employeer, which makes warehouse forklifts, previously used stud piloted wheels but switched to hub piloted in desperation over loosening wheels. They tried different approaches but none of them worked until they switched to hub centered.

My current employeer is experiencing a problem with loosening wheels on one product. They suggest checking the lug nuts every 10hrs! I haven't been privey to the details yet, but I suspect my old friend is back!

I agree that friction should be enough, but that can be tough to guarentee in my field. Many times both surfaces get thick coats of paint, well intentioned mechanics applying anti-sieze compound, almost non-existant use of torque wrenches, etc. etc. My fellow test engineers have a saying - Just because it fits on ProE doesn't mean it works in the lab (or the real world)!

ISZ

 

[GregLocock]

That's an ugly test - I like it!

Do you see any wear or fretting on the hub or the centre hole?

Checking whellnut torque every 10 hours is OK so long as you use a torque wrench, there was a spate of wheel stud failures in the UK because the weekly maintenance check on ambulances meant every wheelnut got 'tweaked up' every week.



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[patprimmer]

Old 5 stud VWs were only retained by the stud. They set the standard for off road racing for many years with OEM type hubs and wheel studs. They rarely failed, and then only if they were not tightened correctly.

Regards

eng-tips, by professional engineers for professional engineers
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[IceStationZebra]

I have not noticed any significant fretting. Since the wheel never moves significantly there is no wear.

I will also note that on the stud centered wheels we rarely noticed any movement or fastener loosening until there was permanent damage. We put on witness marks, checked the torque every 6-8hrs., etc. Once they started to move things deteriorated very quickly. On one machine the inattentive driver actually sawed the planetary housing off of the axle before he noticed anything was wrong!

ISZ

 

[tbuelna]

IceStationZebra,

Lug nuts (or any threaded fastener that is not self-locking) will tend to maintain its preload, and thus not loosen, if there is some elasticity in the installed joint. This can be achieved by lengthening the stud or by making the compressive spring rate of the clamped components lower. Having more elasticity in a joint will make it less likely for the fastener to lose the preload-induced thread friction that keeps it locked.

The fastener preload can be affected by thermal expansion mismatch in the clamped components, or by dynamic load variation due to vibration. If the preload strain in the fastener is very small (ie: a very rigid structure), it only takes a very small deflection in the joint to relieve the preload and allow the fastener to back off.

Good luck.

 

[IceStationZebra]

Most OEM's in the off-road industry buy their axles from a supplier and rarely have any say in the design, short of specifying turn angles and maybe custom attachment points. The major players like CAT or Deere even buy most of their small-mid volume axles.

And as far as a rigid structure goes, most of the wheels are cut from a piece of flat steel. So fastener selection is usually very important.

ISZ

 

[Tmoose]

Can't speak for the off-road industry, but.........

When I bought snow tires from Sears last fall they stamped the invoice with a disclaimer saying I would have to come back within a few hundred miles to have my alloy wheel lugs re-torqued. I pointed out they had mistaken the stock 1996 Accord hub caps for alloy wheels, so I did not have to come back. Typical steel car wheels I've seen have contours around each lug hole, with the actual hub contact surfaces offset a good bit, reminding me of a stout belleville washer.

http://www.finishlinewheels.com/prodimg/STL63730U.jpg

here's a shot showing a steel 60s Studebaker wheel.
Stud centered, with re-entrant contours apparently designed before the days of FEA

http://i210.photobucket.com/albums/bb222/gordintrochu/64Daytona/CrackedRim.jpg

Worked with some brother engineers, sons of the family business was making very popular handsome forged alloy wheels for tractor trailer type trucks. Flat uniform wheel centers. Lug loosening was a problem, requiring frequent maintenance.