Friction, traction, torque - oh my...

[Gui Cavalcanti]

After a week of robot camp, a couple of months searching around FIRST sites, and a few weeks at competitions, I still haven't found anyone who can link this all together for me: what is the link between friction, traction, and torque?

First off, torque. Motors have a neat, pretty little 4-line chart saying "if my motor is moving at this rpm it's generating this torque which is so and so efficient pulling this much current at 12 volts". I understand the individual bits and pieces of it, and how they all connect, but what I don't understand is how you use it. Do you calculate the torque of your machine and then gear to that? Do you calculate the speed of your machine and then gear to that? How do you get to "peak torque" on a robot?

Related to that is how on earth do you link torque to moving your robot? Granted, the little 4-line charts mentioned earlier will tell you your torque at certain conditions, and I assume you scale up torque through gearing and mechanical advantage systems (arms, etc). However, how is torque related to moving your drive train and your available pushing power? Where do friction and traction fit into these calculations?

On the note of friction and traction - I've heard a lot of teams pulling the "f = uN" stunt recently. That doesn't work. Tell me if this logic is correct - carpet is not a surface. It's a conglomeration of threads strung together, and so you can't accurately test any sort of friction. Also, if you have things like file cards (which have next to no traction on any other surface) they dig into the threads and latch on, and don't really count as traction...

Now, static friction I can see coming into account from a wheel turning. However, how do you calculate this on a robot? Do you disengage your motors and pull your robot across a carpet on a spring scale?

Any answers to these questions would be greatly appreciated, as well as the random comment of "hey, that question has nothing to do with it, what are you talking about?"

Thanks!

[sanddrag]

Somebody's signature says "Build first, ask questions later" I completely agree with this. Sure you could calculate all that stuff and come up with the winning combination but why bother. Just make something that looks right and it will probably work fine. If not, modify it. More speed, bigger tires. More torque, smaller tires. More traction, wider tires. It's far easier to just make it and fix problems rather than calculate it all first. There are real-world factors and problems that no amount of calculations could ever forsee.

I hate calculations.

Hope this helped but I know it probably didn't.

[evulish]

To see how much friction our bot had, we did exactly what you said. We had two guys stand on the carpet and small pulley system and a spring scale to yank the robot. Not _exact_ results but it gives you the basic idea whether your robot is going to do much moving.

[Ian W.]

actually, on the traction idea, smaller (As in thinner) tires are better, i think. when i lived upstate, my dad always put snow tires on in the winter. they were much thinner than the regular tires. this might not be true on carpet though, following gui's line of thought on how the carpet really isn't a surface...

[Matt Attallah]

Originally posted by Ian W.
actually, on the traction idea, smaller (As in thinner) tires are better, i think. when i lived upstate, my dad always put snow tires on in the winter. they were much thinner than the regular tires. this might not be true on carpet though, following gui's line of thought on how the carpet really isn't a surface...

That's thanks to the weight of the car. Smaller tires-allowed more force on a smaller surface area = better grabbing, thanks to crushing the snow below = allowed snow tires a good, hard non-slippery surface to grab on to. I'm assuming that he had some chains on thoes wheels too? This same concept applys to tha' chains! (I think this theory is right, but can't guarantee it! )

And the carpet....That is a different story. I would have to agree w/ Gui, and say it isn't a surface. I think of it as really tough sand. It is constantly moving, thanks to it being made up of tons of tiny fibers! For this, the more surface area you have, the better you are! (The more you have your robot weight spread out and less force that 1 fiber has to take and no bending back!! like in most Jeep off-roading, or any off-roading for that fact, have huge tires.) And That is where you get traction from. Your robot pushing off these little fibers and propelling it's self. Torque is how much "pushing power" you have in your robot, but you loose speed to gain torque. And friction. With out this, we all would be stuck. (no pun intended) That is what enables our wheels/tanks to drive on this ground. With out any traction, it won't move! (literally)

I know i probaly made you more confused. If you have some Q's, just e-mail me. Redwingvksm@msn.com

[Ian W.]

lol, no chains (it wasn't that far north). but i do see how the two situations are completely different.

[evulish]

For better traction, my team sawed grooves into the tires to give it better traction. The results were visible. We just taped 3 hack-saw blades together and clamped down the tire and sawed away. (We being I...heh...I got the fun job of doing it on 8 tires )

[Gary Dillard]

I just caught your post - If you can wait a little while I'll clean up the whole answer and put it here. Anyone who saw the national finals is aware of the power, speed, traction, etc. of our little robot - thanks to 4 years of development of the drive train. Gary Jones - our drive train "Guru" - and I have been slowly putting together a paper that explains this and we would like to share it with the FIRST community. It's very detailed, based on theory, test data (including the pull test platform at nationals last year), and competition results that correlate pretty well. I guess your question was what I needed to get off TDC and actually finish it.

A few teasers till then:

It's all about power, not torque.
If you stall the motors before you slip the treads, you WILL burn them out.
Minimize friction losses in the drive train to minimize power loss.
The best traction we found is VERY expensive, but second best is pretty close and pretty cheap.
Believe it or not, f really does = uN (more or less) and carpet is indeed a surface.

[Tom Fairchild]

On the note of friction and traction - I've heard a lot of teams pulling the "f = uN" stunt recently. That doesn't work. Tell me if this logic is correct - carpet is not a surface. It's a conglomeration of threads strung together, and so you can't accurately test any sort of friction. Also, if you have things like file cards (which have next to no traction on any other surface) they dig into the threads and latch on, and don't really count as traction...

Carpet is indeed a surface but F=uN is not the correct equation for dealing with rolling friction. Take drag racers, for example. In a physics lecture, they will explain to you that if you have a box of uniform substance that has more surface area on one side and less on another, it will take it the same time to slide down a hill on either side. Why do drag racers have big tires then? Surface area does matter when it comes to wheels.

~Tom Fairchild~

P.S. Carpet is a surface but things like the file cards just have very high u's. If you experiment with it, you can get fairly consistant static friction and kenetic friction measurements. Once again though, that doesn't work for rolling friction.

[Lloyd Burns]

Friction, Traction, & Torque

Friction comes in many forms: static, sliding, and rollling are but a few. Sometimes we call an energy loss 'friction' rather tham explain exactly what it is, because the loss acts just like a friction. Remember that friction is a human construct to make it easier to explain Nature - it probably doesn't work that way at all. The 1940's cartoon joke about "aerodynamically, a bee cannot fly - but the bees never read the book, and they just go on flying" really says that the jokester's aerodynamics are woefully inadequate for the study of bee flight.

Static friction is sometimes thought of as the microscopic mountains of roughness on one surface fitting into the microscopic valleys of roughness on another surface, locking the two together. Often we get more friction by roughing up the surfaces - but not for the shiny surface of leather belts turning smooth drive pulleys on lathes and other factory machines in the days when electric motors were really costly (the days of the steam engine in Dean's 'house').

Sliding friction could be envisioned as the two surfaces bouncing along, the peaks of their microscopic mountains banging into one another as the peaks of the moving surfaces fly over the valleys. We could then evision putting something (like oil) between the surfaces to float the surfaces away from one another to lower the friction.

Static friction, by definition only occuring when the one surface does not move relative to the other, is often more than the friction when the same surfaces slide (move past each other). A rolling wheel's point of contact is stationary on the winter road, until the brakes siezes it, and prevents turning: then it slides over the road. A bookcase, pushed to one side by little brother to re-arrange the furniture, resists movement (static friction with the floor is high). Little brother's shoes slip on the floor: the friction he can muster is not equal to the friction between the case and the floor. Big Brothe comes along, and with the extra weight on his shoes helping F=uN to make more friction, his shoes do not slip (static). The bookcase resists (static), then with a bit of a bang, starts to slide (!). Big brother now doesn't need to push as hard to keep the case sliding.

Rolling friction is a funny kind of friction: It is due to a bike wheel of a railway wheel having to become flat under the load it carries. Since it would be round if it carried no load (bike on a rack), this means it had to change shape (deform). The energy to change shape had to come from somewhere. It is easy to calculate the energy loss if you conjure it as a friction; hard, if you try to examine the dynamic plastic deformation of the rail wheel.

Torque is a force acting in a circle, or turning, often within a shaft. A given amount of torque is constant whether it exerts a large force tangentially, close to the centre of rotation, or a small force farther out. (T = F(tangential) x radius) Hold a weight at the end of your arm, and think of the arm being 'torqued' around your shoulder. The weight is pulled down, at right angles to your arm's length, that is, tangential to the circle your hand goes in around your shoulder. More weight requires more pull from your muscles; different muscles if somebody tries to lift the weight and you resist. If you notice, this example uses forces (gravity, muscles) which are not torques, but because their lines of action do not not go through the pivot point (shoulder) they generate torques to 'spin' the arm one way or the other. A motor continuously generates a tangential pull around the armature, a short distance away from the axis of the armature's (rotor's) turning: what you'd observe in the shaft is a turning force, a torque.

If you turn a shaft with the torque, and put a wheel on the shaft, and the wheel has friction with a surface, the torque of the shaft will turn the wheel (or not) and a force of the wheel pushing the surface (and vice versa) will be observed. A small diameter wheel exerts a large force at its circumference, a larger wheel (or gear) exerts a smaller force as the radius increases. (F = T / radius)

Traction depends on the friction between the surfaces. The push depends on the torque delivered to the levers that push the one surface past the other. If your robot has adequate static friction, and adequate torque, it will move in the desired direction. If it has insuffienct friction with the floor, it will slide.

-=-=-=-=-=-=-=-=-=-=-=-=

BTW, on a macroscopic level, sand is a surface (try jumping of a cliff onto a beach) and so is the carpet. Each can be examined microscopically or treated as a surface.

Don't confuse reality with human tricks to make things easier to work with. The physics of Aristotle asked why a thrown javelin keeps moving: they figured all motion that wasn't the object returning to its 'natural' place (where its nature demanded it should be) was "Violent" motion, which, by definition, required a force to continue. The javelin was not in "Natural" motion, so a force must exist to keep it going horizontally. They invented a force to keep it going (the air molecules, closing in around the end of the javelin, to avoid a vacuum [the 'void'] banged into the end of the javelin, propelling it forward. Following this idea, Boeing should make the aft end of their fuselages come not to a point, but a nice flat circle.

On the other hand, Newton and Gallileo saw that a moving object will remain moving in a straight line unless a force prevents this. They had to invent something to slow things, and turn things. They invented what we call friction. We use rubber tires for more of it, and oil for less of it. We use the friction idea because it works better than the violent motion option. Being pragmatists, we don't care if it's true, if it works.

Maybe you will create the next construct - maybe we'll all talk of demons grabbing things, and of oil offered as a sacrifice to make the demons go away.

Sorry this is so long, I hope it helps.

[Gary Dillard]

Lloyd, you did a pretty good job of summarizing the "rubber hitting the road" end of it - I was leaning toward the same description of friction; if I plagiarize any of your post in our paper I'll be sure to give you credit.

On another note, has anybody seen the teaching unit from FIRST Place on motor power? Goes through pretty good detail on correlation between torque, speed, efficiency, current, etc. Just curious - I wrote it and haven't gotten any feedback from anyone who has used it.

[Gui Cavalcanti]

Thanks to everyone that responded so far, I'm learning a lot (everything from rolling friction to why people's robots didn't work as they intended... ;-) )

Lloyd, can you walk through a physics problem combining all of these concepts into one? This is what I think it would look like:

First, find your place on the motor torque/efficiency/speed chart. Then, re-calculate the torque by multiplying it times the gear ratios in your drive train. Then, convert the radius of your wheel into whatever units of length your torque is in (ft-lbs, oz-in, n-m) and divide torque by the covnerted length. Now you have the torque of your wheel.

Now lets see if we can cheat with the units a little bit... you would then proceed to say (if you used the metric newton-meter) "For every meter I move, I can push with such and such newtons of force". You would then take that and subtract the losses to rolling friction, and would get a pretty good estimate of the pushing force of your robot.

To see if you can push another robot, you would take the force you have available for pushing and compare to either their "static" friction, if they are standing still and not pushing their motors, or you would do the same calculations for their drive train and compare the pushing forces - the robots would move in the direction of whoever has the greater pushing force, and the force of them moving in that direction would be equal to the difference of forces in their drive trains.

Yes, no, maybe?

I did take a year of physics, but right now I'm flying by ear.

[Dennis Hughes]

Gary, I look forward to your White Paper !!!! Question, What value of Mu did you use and how did you obtain it? I have always just taken a swag of what I figured our wheel mat'l to the carpet would be.
And a HELLO!!! from Kyle to you!!

Thx
Dennis

[Gary Dillard]

OK - time to spill the beans a little more.....

Dennis - we measured 1.7 with the green BrekoFlex belts - under load on the robot by pulling against a spring scale (the traction pit we brought to Disney); 200# pull with a 115# robot. The belts were slipping on the carpet since we had plenty of motor power. We measured the same on team 144's robot with the same belts at stall (they were underpowered). We had measured 1.8-1.9 by just dragging the belts across the carpet before we built the robot.
Here's the big surprise from the pit results: Second best was pneumatic tires! 2 teams (457 and 121) pulled 180# or a u of about 1.4.

Gui - for your physics problem you need to start at the other end.

Say, hypothetically, you wanted to push rolling goals full of balls and other robots around. You want to maximize your pushing power (we'll address speed later), and you can assume the other team is doing the same. Only 2 things impact whether you will push or be pushed: friction factor between you and the carpet, and downward force. Take the friction factor times your weight plus any downward force from lifting up on the goal, and thats the most you can push.

Now, ignoring internal drive train friction losses for a moment, the maximum pushing force times the wheel radius divided by the total gear ratio through to the motor equals the torque that the motor will see at any point after the belt or wheel starts slipping (if you have multiple motors, divide by the number of motors). That tells you where you are on the motor curve. In design it works the other way around; you pick the point on the motor curve where you want to operate (generally either max efficiency or max power) and determine your gear ratio from the same equation.

Nothing about speed yet, right? That's a fallout of your chosen design point and the losses in the system. If you have a higher gear ratio than necessary you will drive slower but push the same (remember, the pushing force is limited at the carpet, not by the motor) - the tread will slip first. The motor operating curve times the gear ratio times the wheel radius gives you the speed.

So why a 2 speed gearbox? We were (and usually are) current limited. We have one gear ratio for speed (under no load) and a different gear ratio for pushing. Actually it turned out this year with the Chips that we had plenty of power to run in high gear most of the time. Finding the optimimum gear ratios is a lot of field testing, but the method above gets you in the ballpark.

Ooops - lunch is over; gotta get back to work. Hope this helps. Stay tuned for the full version.

[EricS-Team180]

I've been looking forward to that white parper, too, Gary <crack the whip - crack the whip>

...could it be ready by MiM?
Eric