Axel Diameter: Is smaller really better?

[gpraceman]

But hey -- shouldn't this friction stuff be discussed under the Racing Science category?

It is more than a little hard to discuss car construction without discussing the underlying science. I had intended that one forum would be for the theory and the other for the application. Maybe it would be better to just combine the two forums? But then I'm getting off topic myself...

What the heck, I went ahead and combined the two forums.

[MaxV]

In response to Stan's post on rolling friction, my understanding (from referring to a text book) is that rolling fricting has the same formula:

friction = mass x frictionalcoefficent.

The other factors mentioned (wheel compression, etc) do have some effect, but are not friction per se.

[Stan Pope]

I am really starting to think that all the stuff I am doing to the inside of hubs is all wrong. We have tried threading and also using a dremel engraver to hollow out the inside leaving only about 1/16 of an inch on either end.

These are neither wrong nor always useless. If your hub work results in smoother, more uniform surfaces rubbing (and if they retain lubrication), then you have improved the performance. Sometimes uniformity is easier to achieve in a small area than in a large area. I'm not sure if it is easier in the interior of a hub, however!

[Stan Pope]

In response to Stan's post on rolling friction, my understanding (from referring to a text book) is that rolling fricting has the same formula:

friction = mass x frictionalcoefficent.

The other factors mentioned (wheel compression, etc) do have some effect, but are not friction per se.

Expand on this a bit, please. Are you saying that the frictional coefficient is the same for rolling friction as for sliding friction between the same surfaces?

I ask because the relative motions of the two surfaces are totally different. For rolling friction there is no lateral (parallel) motion between them.

Help!!!

[TDean]

Forget what I said about you guys making this scientific discussion on friction easy for knotheads like me to comprehend.

As near as I can discern, the bottom line is: friction=bad, and there's a lot less that you can do about it than was once believed. Polish the axles, smooth the tread, true the hubs and OD, give attention to where wheel rubs against car and axle head -- and you're good to go... right? I mean AFTER ensuring the alignment is perfect...

Then there's that whole gravity-thing and the weight placement debate (yeah, I know -- depends on the track shape)...

[Stan Pope]

In response to Stan's post on rolling friction, my understanding (from referring to a text book) is that rolling fricting has the same formula:

friction = mass x frictionalcoefficent.

The other factors mentioned (wheel compression, etc) do have some effect, but are not friction per se.

Expand on this a bit, please. Are you saying that the frictional coefficient is the same for rolling friction as for sliding friction between the same surfaces?

I ask because the relative motions of the two surfaces are totally different. For rolling friction there is no lateral (parallel) motion between them.

Help!!!

Okay ... going back to the textbooks ... We just needed to read a bit deeper into them.

Yes, rolling friction and sliding friction have the same kind of formula. The coefficients of friction are quite different and derive from different physical properties. Hardness, smoothness and diameter are mentioned sources for rolling friction

Both coefficients are defined in the same manner... force to move (maintain uniform linear motion) divided by weight (normal force between objects). This accounts for the similarity of the formula.

[Jewel]

Axle Diameter is a controllable design variable and it would be nice to feel secure when making choices about how and why you might or might not machine your axle.

Rolling friction between the tread and track seems different than the friction between the hub and the body, because the hub and body are constantly sliding past one another.

There is a constant sliding friction between the fixed axle and the ID of the wheel. Changing the diameter of the axle seems to change the two cricular tangents that come together. I still don't know if a change in these tangents effects the friction? It seems that it may not matter, however Hugh made a claim on his website that smaller is better and is offering materials for sale. He may have empirical data that backs up his claim.

[MaxV]

Hugh's axles are between one and two thousandths smaller in diameter than standard axles. After preparing the standard axles (filing, sanding, polishing), they will be reduced a few thousandths as well. So there really isn't that much difference.

The key to remember is that reducing the surface area involved with friction simply causes the force to be focused on a smaller area. It doesn't make the force any smaller. To reduce friction (assuming the same mass), the coefficient of friction must be reduced. This can be done by lubrication or modification to the surface (polishing, coating, etc.).

[PwEngineer]

Hi all,

The Sensitivity of Wheel Friction to Axle and Tread Friction Coefficients article at http://www.worldforchrist.org/races/car ... m#critical includes the wheel bore radius, r and the wheel tread radius, R.

Wheel Drag (Dw)= Axle Friction + Tread Friction = nFr/R + 2u(F/2+w)

n is the sliding friction coef. u is the rolling friction coef.
F the supported weight, w the weight of the wheel.

Note axle friction depends on the ratio of r to R because of the geometry of the bore and tread. The distance traveled in one trip across the bore (its circumference) is 2pir, but it is 2piR across the tread. The ratio is r/R, representing the "leverage" of a wheel as compared to a skid.

If the car used skids instead of wheels the friction force would be 4nF instead of 4nFr/R.

Note, this expression doesn't mention axles. The question should be, are narrower bores better. Then we can show from theory that axle friction is reduced in proportion to the bore radius. They just aren't practical to make! Of course, you can't have narrow bores without thinner axles.

Also, if you used sewing pin axles (I have!) there is more force concentrated over the contact area which might dislodge more lubricating powder or grind it into the plastic. Both increase friction.

Moment of inertia is also increased by the difference between the bore radius and the axle radius squared times the mass of the wheel. This is why you want the bore and axle to be close in radius, but have enough room so your dry lube doesn't lock up the interface.

Lastly, a narrow axle may bend or bounce undesirably, affecting wheel alignment, etc..

Also, strictly speaking, the standard sliding friction model D = nF is NOT a physical law like F = ma. It is subject to any number of refinements (like this one), but is generally useful. In fact, many materials do not follow this form. Friction in Oilly lubes and "non-Newtonian" fluids do depend on viscosity, area of contact, etc.. But for dry lubes, the general form of the equation holds.

Also, it is possible to have so much perpendicular force that the bore or wheel is deformed. Then D = nF will not model the situation well. This is not likely unless you have thin treads and soft plastic.

So, I conclude in general, given the same "polish", smaller axle diameter is better only when the wheel bore diameter is also smaller and retains its "polish".

[Stan Pope]

Note, this expression doesn't mention axles. The question should be, are narrower bores better.

I think that question was a given in the discussion.

Also, if you used sewing pin axles (I have!) there is more force concentrated over the contact area which might dislodge more lubricating powder or grind it into the plastic. Both increase friction.

For open class cars, where the bushing prohibition is often absent, concentric brass tubing inside the wheel bore reduces the ID to a nice match to the sewing pin.

Moment of inertia is also increased by the difference between the bore radius and the axle radius squared times the mass of the wheel.

Help! I'm having trouble visualizing the causes for this one.

[Jewel]

Tread friction?

I have understood that the relative motion of where the tread meets the road is zero. If you look at a point on the treads surface it follows the path of a Cycloid, it rises and falls in a arching like motion. If the tread does not slip than there is no rubbing type friction in the plane of the track. The top of the tread is moving two times the velocity of the car, so air friction may be an issue at the top of the car tread?

The friction interaction between the tread and track I have thought is more like stiction. You want to avoid the mechanical loss of sliding in rolling motion, and any hooking or following of would grain or groves that prevent good tracking.

[PwEngineer]

For Tread Friction see http://www.worldforchrist.org/races/cars/why/fdrag.htm. "Stiction" is short for sticky friction - I don't believe it's a "first-class" tribology (science of friction) term. This kind is properly called "rolling friction" as Stan pointed out a few messages back.

By your posts, Jewel, you seem to know a lot more than you give yourself credit for. Keep it up.

Stan, I think most physics texts call the concept (if not theorem) something like Inertia Translation. It's the answer to the question what's the difference in moment of inertia taken at the center of rotation vs. when rotating at an edge (or some point in between). From the point of view of the contact point, the wheel is spinning about the contact point for a very short time.

[Stan Pope]

Stan, I think most physics texts call the concept (if not theorem) something like Inertia Translation. It's the answer to the question what's the difference in moment of inertia taken at the center of rotation vs. when rotating at an edge (or some point in between). From the point of view of the contact point, the wheel is spinning about the contact point for a very short time.

Checkpoint: In a more extreme case, a "hula hoop" swinging about a hoe handle?

If so, when does this happen on a real PW car?

[PwEngineer]

It actually happens all the time. As I said, "From the point of view of the contact point, the wheel is spinning about the contact point for a very short time."

The most notible time it happens in PW racing is when you spin the wheels sometimes they vibrate or buzz. That indicates the wheel is "orbiting" the axle like your hoola hoop. It starts when the axle stops sliding on the wheel bore and develops traction. I once derived the sufficient conditions for this and determined it is very unlikely that it could happen with the wheels loaded down by the car body. It would be more likely with a thin axle and large bore. Normally, if it happens at all, it would be on a very lightly loaded wheel - like a front wheel on a car with rear weighting. A wheel that orbits will have increased moment of inertia and could have all kinds of stability effects - drift, bobbing, etc..

The remedy is a good lube.

I got a chance to check a book and it is a theorem, but I can't remember the correct name now.

[Jewel]

Excellent points being made here. From the physics it seems like a larger axle diameter is better to help the wheel rotate about its true axis. In terms of grading and selecting where to put your components it may be advisable to put the larger axel diameter, or perhaps more precisely, the tighter fitting axle hub combination on the front wheel. If you encounter buzzing in a spinning wheel; experiment with more lubrication to observe the effects.

Very good, another detail of the design is understood.