Must a tire slip to generate force?

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Ciro Pabón
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Joined: 11 May 2005, 00:31

Re: Must a tire slip to generate force?

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Well, not only the suspension.

In the case of steering forces, you have a tyre twisted around the axis of steering. In the case of the longitudinal forces, the carcass also twists around the axis of propulsion. You don't need a suspension in a car for it to move.

I agree: most of what we see in this world are the electrons. For example, in soil mechanics small particles adhere to each other by electric forces. Same goes for the colours of the things we see: light interacts with the electrons. So, the tyres interact with the track by electric forces, true, altough we suppose all the time in friction theories that the "significant" force is the weight of the car.

If I can make a summary, that's what I've learnt about tribology (the theory of friction):

The first known theory of friction was written by Leonardo Da Vinci around 1450. He studied a lot of things about friction, including wear, bearing materials, plain bearings, lubrication systems, gears, screw-jacks, and rolling-element bearings. Almost two centuries before Amontons' Laws of Friction were introduced, he had discovered them. Unfortunately his writings were lost and unread for two centuries. After Leonardo, the first guy (and almost the last...) to explain friction was Amonton, around 1650. He rediscovered Leonardo's principles of:

- friction proportional to weight and
- friction independent of the area of contact

Coulomb, around 1750, introduced the idea of:

- kinetic friction independent of speed of displacement

These three laws can be summarized in this graph, which, unfortunately is most of what the majority of people learn about friction:

Some engineers never go beyond this graph. Sad. :(
Image

Then after another century, Reynolds (and a russian guy whose name I cannot remember) came up with an equation (unchanged since 1880 or so) of:

- friction in fluids proportional to sliding velocity and bulk viscosity and inversely proportional to thickness of film

A few years later Stribeck (not sure about the name) came up with the Stribeck curve that explains that when the film is very thin, Reynolds equation fails. He stated that:

- the area enlarges because the contact surface deforms elastically and the film, with a larger area, can support the weight.

Then, after 50 years (we're getting some speed here... ;)), Hardy, around 1920, came up with the idea of very thin films like this:

- asperities coming in contact, breaking and then reacting chemically with the lubricant, thus creating a tenacious layer of lubricant and small chips of material that supports the weight and prevents further wear (I swear I'm not making this up... :)).

Hardy findings about films inspired some people to try to understand what happens in dry friction. Finally, a few years later, a guy named (I think) Bowden came up with the concept of friction by adhesion. Another guy called Desangulier in Coulomb's time had the same idea but nobody heard him because of Aumonton 2nd law (friction independent of area), so people devoted to purely geometric explanations (interlocking of asperities). Bowden discovered that Miguel is right and that:

- friction is created by adhesion of solids because of electric charges. It might sound incredible, but asperities in solids deform above a critical shear strength, which depends on the adhesive forces of the two surfaces in contact. That adhesive force, the one that "crushes" the asperities, is created by electric charges.

Yes, I know, it sounds like science fiction, but I'm dead serious. The relationship with the load is not lineal but is:

F = L^2/3 (that is, friction is proportional to load elevated to two thirds)

The inconsistence with Aumonton's first law (friction proportional to load) is explained because the real contact area varies under load. Why nobody noticed in five centuries beats me.

Once electronic force microscopes were developed, around 1950, Bowden (and Desangulier) were vindicated, because measurements were precise enough to validate their theory. Thus, Miguel is right. That's most of what I know about friction. and you can stop reading now.

If someone is interested in visualize (that's what distinguishes engineers!) what's going on, please, come with me for a couple more paragraphs and imagine what happens if you become really tiny: your weight decreases as the cube of your height does (a person half as tall, half as wide and half as deep, weighs eight times less!), right? However, if you're half as tall, your surface is only one quarter of the original one. For example, let me tell the story about Gauss famous observation on the size of things.

Gauss teacher told the class (in primary school, according to legend) that the Universe could grow slowly to one million times its actual size and nobody would notice. Gauss answered that it was not true, because all the picture frames would fall from the walls. Their weight would increase to the cube, but the area of the strings holding the pictures would increase to the square and they would not be resistant enough to hold the pictures to the walls. Incidentally, that's why ants and spiders have such thin legs and elephants have sturdy ones, but I digress.

So, if you're a really small asperity, you have a very large surface compared with your weight. If your ten thousand times (2^13) smaller than a person (around 0.2 mm), your weight/surface relationship is 10.000 times larger (I think). Persons are taller than wider: this means that electric charges migrate to the pointy parts (by electromagnetic laws: that's why lightning rods are pointy). Like this:

Small clay particle with positive electric charges in the pointy parts
Image

Thus, any point in a microscopic asperity of the tyre (charged positively) adheres to the sides of the microscopic asperities of the track (charged negatively). Its weight is ridiculously small compared with the surface, thus the electric forces are immense compared with gravitational forces at these scales. Tyres adhere to asphalt by electricity. QED.

Finally, in the last ten years friction has been explained by quantum theory. In the improbable case that someone is interested in "The Master Equation" of friction, there you go: http://www.sbfisica.org.br/bjp/files/v27_214.pdf

Friction Quantum Theory Master Equation. If someone can explain it in simple terms, be my guest!
Image

As usual, sorry for going OOT and sorry for the length of the post, but I've been tempted to write it a thousand times. That's the same "lesson" I give in class when I explain the plasticity of clays originated in electric forces. Man, I love this forum... perhaps someone will read al this voluntarily! On the other hand, my poor students have no choice. :D
Ciro

Shredcheddar
Shredcheddar
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Joined: 22 Jan 2009, 06:16

Re: Must a tire slip to generate force?

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Ciro... great post as usual!

This is interesting, Ciro. The only time I've been taught about friction is in high school, and I'm a third-year mechanical engineering student at a very good engineering university! All I was ever told was that friction forces are proportional to load, introducing the coefficient of friction, and then that static and kinetic friction are different. That's it. It's the assumption we've used so far in problems involving friction. I understand the practical reasons behind that, but I think it's important that it's explored more so at least the level of our ignorance is exposed. That's certainly important when making engineering decisions.

So I felt quite challenged and later enlightened when I read about how tires generate force. I remember having a strong reaction when I first read that tires do not obey the linear coefficient-of-friction equation. So now reading that friction is a power function of load, and that contact area is a function of load is all very exciting! I do not feel as if I am completely replacing the things I thought I knew; I see it as refinement. For example, I learned the importance of load versus contact area when I was considering adhesion as another mechanism for tire force generation (why should it just apply to tires?).

It will bother me if I know the explanation goes deeper but I accept an ignorant understanding of it. So maybe I'll have some thoughts on this once I've read through your post a couple more times and take a look at the master friction equation.

Thanks again for the challenging post. :)

Jersey Tom
Jersey Tom
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Joined: 29 May 2006, 20:49
Location: Huntersville, NC

Re: Must a tire slip to generate force?

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Rubber "friction" doesn't quite work the same way as "normal" friction. The interaction between a viscoelastic material against an asphalt surface, is considerably different than a wooden block on an inclined plane. I have never got to the point of electric charges... but bear in mind that when a tire footprint meets the ground there are (loosely) conventional micro-scale friction, there are compliance effects as the rubber deforms to the large asperities in the surface, and there's adhesion.

If you want to read up on this stuff, look up the work of Persson.
Grip is a four letter word. All opinions are my own and not those of current or previous employers.

Shredcheddar
Shredcheddar
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Joined: 22 Jan 2009, 06:16

Re: Must a tire slip to generate force?

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I certainly intend to read up on Persson's work. I've got a big list of things I want to learn and understand. Persson's been on there for a while. I just need to get around to it. Also, do you know of any sources of his work that I couldn't find from a Google search?

JT, I see you're a Colorado Buffalo. I go to Texas A&M University. So the Big 12 is getting some representation here. :)

Jersey Tom
Jersey Tom
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Joined: 29 May 2006, 20:49
Location: Huntersville, NC

Re: Must a tire slip to generate force?

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"Theory of rubber friction" I think is the one you want to be after.

But yea, Colorado '07, BS MechEng. Currently working on race projects at a major tire company. Wouldn't mind moving back out west though. Hell of a lot nicer weather.
Grip is a four letter word. All opinions are my own and not those of current or previous employers.

Shredcheddar
Shredcheddar
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Joined: 22 Jan 2009, 06:16

Re: Must a tire slip to generate force?

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Sounds like you're stuck in Akron, eh? :) I actually know the feeling. I moved to Michigan for the semester to co-op with Toyota... so it's safe to say I miss Texas a bit.

Ok, Googled a bit and found the title (referenced): "Theory of Rubber Friction and Contact Mechanics". Thanks for the hint.

riff_raff
riff_raff
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Joined: 24 Dec 2004, 10:18

Re: Must a tire slip to generate force?

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As some wise old racing engineer so eloquently explained it: "The brakes only stop the wheel. It's the tire that stops the car."

The tire does not generate braking, cornering, or accelerating forces. Those forces are generated by the engine, brakes, aerodynamic bodywork, and chassis inertias. The tires simply transmit those forces from the wheel to the pavement. The amount of traction force the tire can transmit without slipping is a function of the tire-tread-to-track-surface instantaneous traction coefficient times the normal force applied. If the tangential and axial shear forces at the tire contact point exceed the tractive force, then the tire will slip. This slippage will release energy which causes heating of the tire tread surface, and this temperature rise in the tire tread also changes the traction coefficient of the tire.

A tire that is not slipping or spinning will be able to transmit more force than a tire that is experiencing slippage. Once the tire's breakaway tractive force has been exceeded, the amount of force to keep the tire spinning is much reduced.

So, to answer your original question: No, a tire does not need to slip to generate force. Tires don't generate force, they transfer force. And a slipping tire will transfer less force than a tire that is not slipping.

As a courtesy, I won't bore you with the details of elastomer compounds and hysteresis effects.
"Q: How do you make a small fortune in racing?
A: Start with a large one!"

xpensive
xpensive
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Re: Must a tire slip to generate force?

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Now that we are into semantics, the slippage doesn't "release" energy, it generates it, as force times length of slippage. But that is not really through either, when energy cannot reproduced, only transformed.
"I spent most of my money on wine and women...I wasted the rest"

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Ciro Pabón
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Joined: 11 May 2005, 00:31

Re: Must a tire slip to generate force?

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I've posted some free references to Bo Persson in this forum, pretty elementary.

Why Tires Grip The Road: New Theory Reduces Testing

Non-contact friction

If you wish you can invest on the books and articles that are not free, but they're pretty heavy for an engineer, they're for a tribologist (friction scientific):

Sliding Friction: Physical Principles and Applications (NanoScience and Technology) U$158

Elastoplastic Contact between Randomly Rough Surfaces U$25

Theory of rubber friction and contact mechanics U$24

I did not want to confuse anybody with more posts, out of thread (sorry again) about the new discovery of non-contact friction, but the idea is that:

- Atoms act like a tiny dipole antenna which attracts atoms "clinging" to the opposite surface

There is no need for "true contact" of the kind Miguel mentioned (that is, interaction among electron clouds).
Image

Actually, I think that if you get the electrons to interact, you're fusing the objects instead of exterting friction forces. The kind of "charge displacement" or ionization of atoms that I mentioned in my previous post is enough to explain "classical friction".

Why do I call it classical? Because Mr. Person and Alexander Volokitin have proven this truly interesting point: under some circumstances, for example in nanorobots or nanomachines (I quote):
... van der Waals friction can be greatly enhanced (by up to a factor of ten million at a separation of 10 angstroms in comparison with the case of good conductors with clean surfaces) This increases the resonant electromagnetic force (which can be viewed as the tunneling of photons) between the objects, especially if they are made of the same material. The adsorbate atoms can be thought of as tiny antennas, one acting as an emitter and one as a receiver; when the two antennas are in tune the electromagnetic interaction between them will be greatly enhanced.
Wow.

In principle, if we could change the radiation properties of the atoms of the tyre, we could get better tyres. How? We need a new Leonardo here... but I can imagine a thousand "science fiction" scenarios. Engineering of race cars and friction understanding is in his infancy, as I see it. :D

Riff_raff is right about the point that "macroscopic" slippage is not good if you lock your brakes, for example. However, I don't know how clear is the idea that you have to have micro-slippage (at the micro-texture level) for friction to develop. If a tyre were infinitely rigid, it would have no friction, or at least that's what I get from what I've read (unless I got everything totally wrong).

As another physicist, Brian Beckman, explains (and finally we got to something that a racer can use!):
``Driving by the seat of your pants'' means sensing the slight changes in cornering, braking, and acceleration forces that signal that one or more tires are about to slide. You can sense these change literally in your seat, but you can also feel changes in steering resistance and in the sounds the tires make. Generally, tires `squeak' when they are nearing the limit, `squeal' at the limit, and `squall' over the limit. I find tire sounds very informative and always listen to them while driving.
So, to confuse everybody: you need micro-slippage to get friction. That works at atomic level. Nonetheless, Riff_raff is right (he always is, AFAIK :)). Nor Riff_raff nor me can see this kind of slippage with our eyes: we say, being practical, that the tyre is NOT slipping.

A tyre works by twisting (for steering): that's the grip angle. Same goes for the longitudinal traction: the tyre has to deform at the micro-texture level.

Finally, in practical terms, you have to go over the macro-slippage limit to get the most of your tyres, that is, you want them to actually slipping in the macroscopic world, to the point of making them squeal. You do not want them to get to the point of making them squall. Something like the effect you want to cause on your spouse or girl/boyfriend... ;)

I don't know if someone is getting the point, but what the heck. It's a complicated answer because it's a complicated question. Perhaps JTom (as usual) can summarize it in his precise and concise style.
Ciro

Shredcheddar
Shredcheddar
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Joined: 22 Jan 2009, 06:16

Re: Must a tire slip to generate force?

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www.physics.hku.hk/~nanohk06/talks/Persson.pdf

Here is a quick slide presentation where Persson talks about adhesion and contact mechanics. Interesting and kept light due to the sub-par presentation method, but there are some good graphs in the presentation and I think it's a neat read as it just kind of overviews and introduces his theory.

riff_raff
riff_raff
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Joined: 24 Dec 2004, 10:18

Re: Must a tire slip to generate force?

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Ciro,

I read the article you linked, "Why tires slide". The gist of that article was that tires grip due to surface roughness between the tread and road surface. That principle is similar to any other type of sliding contact. The tiny surface irregularities, technically referred to as asperities, are literally bonded together at the microscopic level for an instant due to the high local contact stress, and then immediately sheared apart by the relative motion of the two surfaces. That strain energy loss is what creates rolling resistance. Of course, most losses in a rolling tire are due to hysteresis losses in the tire body, and not the tread/track contact.

You are correct in your statement that two infinitely rigid bodies in rolling contact would have no friction losses. The reason is that infinitely rigid bodies are not, by definition, capable of experiencing strain effects.

Nice discussion about the subject. I enjoyed it.
"Q: How do you make a small fortune in racing?
A: Start with a large one!"

Shredcheddar
Shredcheddar
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Joined: 22 Jan 2009, 06:16

Re: Must a tire slip to generate force?

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I agree with Riff Raff. Great contributions from everybody; I feel like my question was sufficiently answered, and that I've sufficiently justified that answer through your explanations and my own expanding understanding of the subject.

So thank you all. =D>

I've got another fundamental tyre-related question... but it's a bit off-topic (or OOT as Ciro puts it), so if you're interested, follow me over to another thread!