The physics of wheel studs - please educate me (1 Viewer)

[kcjaz]

I'm considering 1/2" wheel spacers to resolve a tire clearance issue. This requires extended wheel studs. This has got me over thinking how the wheel studs and lug nuts prevent the wheel from slipping against the axle hub.

What I think is going on is that the tension in the studs caused my torqueing the lug nuts forces the wheel fland against the axle hub with enough force that the friction between the wheel flange and the axle hub prevents any relative slippage between the two.

Or, do the studs just resist the shear force trying to snap them off during acceleration and braking?

If shear resistance is important, what happens when you add a 1/2" spacer into the equation? Is there now a bending moment created?

 

[SipLife]

My understanding is that the wheel studs when tightened act as a clamping force holding the wheel to the hub. The greater your clamping force, the greater the force required for the wheel to slip on the hub due to the friction between the two. Therefore in ideal situations there will not be a bending load on the stud.

As the vehicle is in motion the stress on the stud won’t change unless the the vertical component of the force applied on the wheel becomes greater than the clamping force on the wheel. If this occurs the wheel stud can have a bending moment or shear.

By adding a wheel spacer or longer wheel studs you are changing nothing related to the physics of holding the wheel to the hub.

Failure often seems to happen due to a lack of sufficient clamping force, too much clamping force, or purchasing cheap spacers that introduce flexing into the equation.

Full Disclaimer: I am a sophomore aspiring ME major and am not a PE. These are just my thoughts. Do your own verification.

 

[kcjaz]

My understanding is that the wheel studs when tightened act as a clamping force holding the wheel to the hub. The greater your clamping force, the greater the force required for the wheel to slip on the hub due to the friction between the two. Therefore in ideal situations there will not be a bending load on the stud.

As the vehicle is in motion the stress on the stud won’t change unless the the vertical component of the force applied on the wheel becomes greater than the clamping force on the wheel. If this occurs the wheel stud can have a bending moment or shear.

By adding a wheel spacer or longer wheel studs you are changing nothing related to the physics of holding the wheel to the hub.

Failure often seems to happen due to a lack of sufficient clamping force, too much clamping force, or purchasing cheap spacers that introduce flexing into the equation.

Full Disclaimer: I am a sophomore aspiring ME major and am not a PE. These are just my thoughts. Do your own verification.

I think you are correct. I believe one could actually calculate the frictional force resulting from the clamping pressure and compare it to torque transmitted through the axle to the wheel.

oh, and I am a PE but I got a C in machine design and that was a long time ago.

 

[04UZJ100]

What about wheel spacers that have supplemental studs? Do they increase bearing wear due to shifting the vertical force outward?

 

[bloc]

The biggest issue with spacers that don’t introduce their own studs is reduced thread engagement with the lug nut. If you run quality extended studs you’ve mitigated this problem.

 

[bloc]

What about wheel spacers that have supplemental studs? Do they increase bearing wear due to shifting the vertical force outward?

Yes.

The extent varies a lot though, obviously. A half inch spacer won’t present a substantial difference. 4” total offset between spacers and wheel? Different ballgame.

Also the location matters. On the rear due to the length of the axle shaft even a large shift in tire position won’t change much about the way the forces are applied to the bearing. On the front.. again, different ballgame. Less of an linear upward force and more of a twisting upward force. I’m too tired from work to recall the specific terminology.

 

[doru]

If the friction force is what matters then a simple interference interface would make a better design that flat surfaces that can get slippery fluids on them.
I'm not a ME but my thinking is that the studs/bolts act on shearing when resisting acceleration and breaking.
AFAIK you should have at least 5 full turns on both the spacer and wheel bolts. Material is important as you do not want to lose tension in the bolts because of spacer deformation under load.
I always buy high quality spacers and bolts, and keep them at the minimum thickness that I need. I never buy spacers that eliminate the centering ring.

 

[TimCFJ40]

A few thoughts:
When the lug nuts are torqued the lug studs stretch slightly, which provides the clamping force.
With proper clamping force, the friction between the wheel and the hub face is what carries the load, not the lug studs.
If clamping force is lost, the lug studs carry the vehicle in a shear stress on the stud. This won't last long. Usually the steel stud starts to wallow out the hole in the aluminum rim, and hopefully you notice something isn't right before you have one of your wheels pass you on the interstate and the truck becomes a tricycle.

With longer studs and a spacer sandwiched in the middle, a few things change:
Your studs stretch a little more due to the longer section in tension. Maybe this is ok, but..
1) You introduce two potential sliding surfaces in the clamping system
2) You have a longer lever arm on the lug nuts if clamping force is lost

To me this all adds up to:
1) under ideal conditions, a spacer sandwiched under the wheel with longer studs should be ok
2) there is a greater likelihood of an issue due to a more complex joint with multiple sliding surfaces, more fastener stretch, etc.

All of the above assumes you have a 1/2" spacer that can maintain the center hubcentric interface with the wheel. If you just put a plate in between without a hubcentric feature, the potential for a slightly offcenter wheel as well as not having the secondary benefit of the hub supporting the rim if the joint lost some tension would amplify any issues in the system.

Is your clearance issue such that you couldn't get away with a 1" hubcentric spacer with integrated lug studs?

Finally, DEFINITELY avoid the cast aluminum, one size fits all $15 spacers at autozone, but I'll give you the benefit of the doubt that you would do better than that.

 

[grinchy]

I would suggest solving this problem with rims in the offset you require.

I ran spacers (1"), bolt on/studded, and never really felt good about it, though they were completely fine in function. Rims in the correct offset were a better long term solution.

As to the original question, the axial bolt clamp force of 5 14mm fasteners is immense, somewhere around 10550 lbs per stud (, using this calculator., in non metric units)

 

[Sandroad]

Does the fact the base of the lug nut fits tightly into the lug hole in the wheel have any role in transferring torque from the hub to the wheel?

 

[kcjaz]

I would suggest solving this problem with rims in the offset you require.

I ran spacers (1"), bolt on/studded, and never really felt good about it, though they were completely fine in function. Rims in the correct offset were a better long term solution.

As to the original question, the axial bolt clamp force of 5 14mm fasteners is immense, somewhere around 10550 lbs per stud (, using this calculator., in non metric units)

View attachment 3312868

I Googles at lunch and found this:

6.6: Disc Friction

Friction in common disc-shaped mechanisms. Calculating moment based on friction for such discs.

eng.libretexts.org

If yoyu read through it, it derives an equation for the rotational moment that can be between two discs (i.e. a hub and a wheel) based on the contact area and clamping force. The equation that is closest to our hub/wheel situation is:

where,

As @grinchy points out, the clamping force of 5 studs/nuts is a lot (50,000 lbs). Plugging in some ruff dimensions for Ro and Ri and a WAG for the coeficent of friction (Ri- 2.2", Ro = 3.7" u=0.2), I get a pretty big number for M (30,000 ftlb). Now the actual contact area for a real hub and wheel is not the full annulus as there is usually a raised area for each lug hole. So call it 1/3 of the contact area which means I only get 10,000 ftlbs of moment resiatance. M just needs to be bigger than the actual torque applied at the wheel. Max torque for a 200 is 700 NM (500 ftlb) at the engine which is 125 ftlb at each wheel. I would guess that hard braking is actually the worst case. I haven't thought about how to caluate that but I don't think it matters as there is an order of magnitude difference here. This tell me that clamping force and friction is the only thing needed to hold the wheel to the hub. The studs do not need to provide any shear resistance to keep the wheel from slipping on the hub.

Or my math is wrong....

 

[kcjaz]

A few thoughts:
When the lug nuts are torqued the lug studs stretch slightly, which provides the clamping force.
With proper clamping force, the friction between the wheel and the hub face is what carries the load, not the lug studs.
If clamping force is lost, the lug studs carry the vehicle in a shear stress on the stud. This won't last long. Usually the steel stud starts to wallow out the hole in the aluminum rim, and hopefully you notice something isn't right before you have one of your wheels pass you on the interstate and the truck becomes a tricycle.

With longer studs and a spacer sandwiched in the middle, a few things change:
Your studs stretch a little more due to the longer section in tension. Maybe this is ok, but..
1) You introduce two potential sliding surfaces in the clamping system
2) You have a longer lever arm on the lug nuts if clamping force is lost

To me this all adds up to:
1) under ideal conditions, a spacer sandwiched under the wheel with longer studs should be ok
2) there is a greater likelihood of an issue due to a more complex joint with multiple sliding surfaces, more fastener stretch, etc.

All of the above assumes you have a 1/2" spacer that can maintain the center hubcentric interface with the wheel. If you just put a plate in between without a hubcentric feature, the potential for a slightly offcenter wheel as well as not having the secondary benefit of the hub supporting the rim if the joint lost some tension would amplify any issues in the system.

Is your clearance issue such that you couldn't get away with a 1" hubcentric spacer with integrated lug studs?

Finally, DEFINITELY avoid the cast aluminum, one size fits all $15 spacers at autozone, but I'll give you the benefit of the doubt that you would do better than that.

Great reply! I agree with all you say. I would not consider a non-hub centric spacer. The 1/2" spacers I have test fit are hub centric Bora spacers, not the Autozone, Darwin Award special. A 1" spacer with integral studs would likely fix my KDSS issue but then cause an issue on the back side. If I can find a 1" spacer to try, I could test that. I think though, the difference between two types of spacers really comes down to which set of non-ideal things relative to just having the right offset wheel you want to live with.

 

[Sandroad]

I Googles at lunch and found this:

6.6: Disc Friction

Friction in common disc-shaped mechanisms. Calculating moment based on friction for such discs.

eng.libretexts.org

If yoyu read through it, it derives an equation for the rotational moment that can be between two discs (i.e. a hub and a wheel) based on the contact area and clamping force. The equation that is closest to our hub/wheel situation is:
View attachment 3313066

where,
View attachment 3313069

As @grinchy points out, the clamping force of 5 studs/nuts is a lot (50,000 lbs). Plugging in some ruff dimensions for Ro and Ri and a WAG for the coeficent of friction (Ri- 2.2", Ro = 3.7" u=0.2), I get a pretty big number for M (30,000 ftlb). Now the actual contact area for a real hub and wheel is not the full annulus as there is usually a raised area for each lug hole. So call it 1/3 of the contact area which means I only get 10,000 ftlbs of moment resiatance. M just needs to be bigger than the actual torque applied at the wheel. Max torque for a 200 is 700 NM (500 ftlb) at the engine which is 125 ftlb at each wheel. I would guess that hard braking is actually the worst case. I haven't thought about how to caluate that but I don't think it matters as there is an order of magnitude difference here. This tell me that clamping force and friction is the only thing needed to hold the wheel to the hub. The studs do not need to provide any shear resistance to keep the wheel from slipping on the hub.

Or my math is wrong....

There is torque multiplication at the transmission, t-case, and differential, plus it's possible to have different torque at each wheel due to traction control action.

 

[kcjaz]

There is torque multiplication at the transmission, t-case, and differential, plus it's possible to have different torque at each wheel due to traction control action.

Good catch. 500x3.909x3.33/4=1627ftlb. Could be higher at any wheel as you say. Still a lot of margin compared to 10000.

 

[Fisher23]

Yes the bora centric spacer will work fine. Obviously wheel offset is better.

 

[bloc]

Does the fact the base of the lug nut fits tightly into the lug hole in the wheel have any role in transferring torque from the hub to the wheel?

My gut is telling me that is to make up for not having a cone at each lug to index the wheel correctly, meaning every lug is in the dead center of the hole. All lugs tightened when perfectly straight.

Plus even with the washer we still don’t want the lug hole to be any larger than necessary.

 

[Jeriel Guerrero]

start with a free body diagram

 

[Fisher23]

Does the fact the base of the lug nut fits tightly into the lug hole in the wheel have any role in transferring torque from the hub to the wheel?

No, the lug hole just avoids sheering.

The wheels are hub centric and that is what holds the wheel centered vs the cone on lug nuts.

The torque on the lug nuts is what transfers the torque. Increasing the length of the stud does increase the chance of sheering, but in this case it's minimal.

 

[TimCFJ40]

Great reply! I agree with all you say. I would not consider a non-hub centric spacer. The 1/2" spacers I have test fit are hub centric Bora spacers, not the Autozone, Darwin Award special. A 1" spacer with integral studs would likely fix my KDSS issue but then cause an issue on the back side. If I can find a 1" spacer to try, I could test that. I think though, the difference between two types of spacers really comes down to which set of non-ideal things relative to just having the right offset wheel you want to live with.

It seems like folks are getting away with more offset than our more conservative +25 is optimal thinking might suggest. If you're talking about KDSS clearance, etc then I would assume you're talking about tires bigger than 34s, so maybe the 1" spacer isn't too much. What is your wheel offset now that you are adding +2" spacers to? I at one point ran 2" spacers on mine with the stock wheels(installed by the previous owner), netting +10mm offset, and it honestly didn't have any issues on the outside, but that was with a relatively narrow 275/70R18 tire.

I think with the Bora hubcentric 1/2" spacers and high quality longer studs you're stacking the potential deck as much in your favor as possible, but IMO there is still some risk. The good news with the 1/2" spacer is you could easily check lug torque every time you stop somewhere for a while until you get comfortable with it... Bolt on spacers you can't so easily check the torque, but I've run them on several vehicles for tens of thousands of miles with no issues.

 

[Karbon]

In general, shear is not carried through threaded features as a structural load path. There are too many tolerances that come into play to make to make that path reliable. The shear capacity of threaded features is much lower, with higher stress concentrations in the root of the thread. Then there is diametric tolerance on the holes in the wheel and on the threaded studs, combined with positional tolerance of the holes and studs. When looking at the stack up, especially when considering mass-production methods and manufacturer variances once non-OE parts are introduced, there would be no way to evenly distribute a shear load through the studs. More than likely one stud would have to take the entirety of the load, and I think intuitively we can see that one stud is not capable of that.