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

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

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

(OP)
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.

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

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

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

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

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.

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

I dont think wheel studs see shear forces.  

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

FYI

This issue is being addressed on Automotive Suspension Forum.

Michael

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

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.

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

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

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

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

Quote:

"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!

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

"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

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

         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.

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

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

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

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

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

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

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.

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

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! smile

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

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

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

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

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

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: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips Fora.
 

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

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

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

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.

 

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

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

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

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.




 

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

So for a racing wheel with drive pegs and a centre lock hub the pegs are just for radial location and all the forces are reacted through friction?

If that's the case then you should only need three pegs seeing as the clamping force is coming from the nut. Most cars have 6 pegs - is this just redundency or a (poor?) assumption that they're transmitting the torque?

I have seen drive pegs ratchet back and forth and lock the wheel on. I assume this is probably due to insufficient tightening torque due to poor air pressure in the wheel guns.

Ben

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

"a (poor?) assumption that they're transmitting the torque/"

The folks with early VW sometimes go to great lengths to augment their cranks' 4 dowels with stouter gland nuts permitting greater torque, then to 8 snugly fitting line reamed dowels as used in pre-914 4 cylindrical Porsceae. Racers then go to 8 plus a wedge fit (Gene Berg) or even to a proper crank flange (SCAT).

flywheel attachment history in pictures.
early British (MGT?)
http://www.mgcars.org.uk/mgtd/Pictures/Reports/tm_crankshaft.jpg

Jaguar XKE
http://www.limora.com/clickable/gross/Bilder/2608.gif

Chevrolet 1955 265 CID V8 or 1968 450 HP 454 CID V8
http://images.1aauto.com/CLF/1ACLF00024.jpg
(yes there is one dowel to ensure consistent positioning, but some crankshafts come with that hole empty)

Chrysler 426 Hemi
http://stores.casselent.com/catalog/130-10231_thumb.jpg

lexus V8 flywheel?
http://www.thor-racing.co.uk/images/1UZ-FE-to-r154_Flywheel.jpg

Civic SI/ del sol flywheel
http://www.slowboyracing.com/sbs/images/T/ACT%20600105%20Flywheel-01.jpg

If there's enough clamping force to keep the dowels or bolts from any real torqueage loading, there's enough.  If not, there's not, and the situation gets real bad real quick.

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

A pure guess - but they could be using 6 pins as insurance if the tire man doesn't torque the nut quite enough during a tire change. Plus, if the pins were line tight with the holes it would be more difficult to install the wheel. (And you have to deal with heat expansion - hot hubs and cold wheels)

A third possibility is that with only 3 pins the tire man might have to rotate the wheel 120° to hit a pin - but that doesn't prevent one from having only 3 pins but 6 holes in the wheel!? In reality the first person to do this probably figured that if the road going car needs 5 studs the race car will need at least that!

ISZ

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

My FSAE outboard suspension design used a single aluminum center lock nut (torqued to just 60 ft-lbs) and was hub centered (I don't like using a bolt pattern to center anything).  We included four 1/4" dowels to prevent the wheel from freewheeling on the hub, should someone forget to torque it, allowing the car to be stopped and preventing excessive hub/wheel damage.  We used four dowels purely because most of the available conventional wheels use four studs/nuts and it would allow us to adapt the hub to these wheels if custom wheels were not available.  No issues were found with the design but the dowels haven't been tested yet.  FSAE cars don't have to make timed pit stops so this did not figure into the design.

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

"My FSAE outboard suspension design used a single aluminum center lock nut (torqued to just 60 ft-lbs)"

what size thread is the center lock nut?

Dan T

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

It was about 1"-1.25" fine thread, from memory.  We used a similar approach to the napkin calcs above with our anticipated wheel loads.  Keep in mind this is a 500lb asphalt racecar (low safety factor) with a short design life.  Using the above approach gives ~1600 lbs to break the static friction on each wheel hub and our design bump load was 3.5g (or about 500lbs per wheel).  We didn't want to torque the nut down more than required as the threads were aluminum and could gall (they were anodized to help prevent this though).

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