# Coefficients of Friction

I’m in the process of designing a 2 speed transmission for team 1155 the Sciborgs. One thing I need in order to design a transmission with adequate torque and for other calculations is the coefficient of friction of the wheels. However, we unfortunately do not have the resources to purchase different sets of wheels and experimentally determine the coefficient of friction.

So I’ve come to ask assistance from the chiefdelphi community. Since contact area is independent of the coefficient of static friction, wheel size and number shouldn’t matter correct?

What is the coefficient of friction for a 130lb robot (I hope they don’t raise the weight limit next year.) on standard FIRST carpet (I hope they don’t change that either.) with normal kit skyway wheels?
with Colson wheels?
with IFI traction wheels (roughtop/wedgetop)?
with polyurethane wheels (any specific durometer)?

Perhaps this can be turned into a sticky for other teams to reference if a good amount of data is collected?

Thanks for any help!!

With 1.125" wide wedgetop, 4 wheels contacting the ground, we obtained a COF of about 1.1 by using a cheap bathroom scale and pushing against a wall at full force on carpet quite similar but not identical. For Skyway beadlocks (8x2) turned down flat, we obtained approximately .9 from what I can remember, but that was with a (approximately) 90lb robot. The colson wheels have a lower COF than the wedgetop tread.

Width does have something to do with it on carpet. I saw teams with .75" wide wedgetop tread get pushed around. But I don’t think you need to go to 2" wide to get more traction. I’d say 1.25" is about the absolute max you need to go with wedgetop. There is a region where more width will give you more traction but there is a point where all more width does is take up more space.

Here is something on calculating coefficient, just find the 2nd reply

Edit:Sanddrag beat me to posting so no need for the link.

From experience though, the IFI Traction Treads, roughtop/wedgetop are the way to go if you want traction. IFI did some math and found out Wedgetop has a coefficient of friction of 1.2 and the roughtop has a coefficient of friction of 1.3.

Skyways - ~0.8
Colsons - ~1.0-1.2
Roughtop/Wedgetop - ~1.2-1.4

Those are the benchmarks I use.
JV

Friction force does not increase with a larger surface contact. The reasoning behind that is due to the force in between the surface and the wheel, in this case the robot weight. A larger area between the wheel and the carpet would create a larger source of frictional forces, but it reduces the pressure between them. The same force dissipated over a larger area with the same coefficient of friction is equivalent to a smaller area with less sources of friction forces.

Basically since your robot weight is a constant and your CG is basically the same with both smaller and larger wheels, your traction actually does not change based on wheel width, assuming the same traction material on narrow and wide wheels.

That’s what simple physics tells you, I know. But I have a feeling the interlocking action both on a macroscopic and microscopic scale between tread and carpet is anything but simple. Why do drag racing cars use such wide tires in the back?

Paul Copioli touched on that very question here.

<edit>There is a benefit to going wider in the form of slower wear on the tread surface. Perhaps not too useful for a one-regional team, but the long haulers might use that to their advantage.</edit>

Don’t worry about the weight. It has no effect on the coefficient of friction. It DOES, however, effect the force from friction. Force of friction = Coef of Friction * Normal Force. The weight is what we would call the “Normal” Force. At least, it is on a flat surface. (The normal force is really perpendicular to the surface you are thinking about, so a robot on a ramp has a force down based on weight, and a portion of that weight as a normal force.)

I just looked that over - if I confussed anyone… I’m sorry. I should look for a picture to explain that.

But I think your question has been answered. If you want to test the coef of friction of materials, let us know - I know there are several simple test rigs you could use. (But be careful… there is Static Friction, Dynamic Friction, Rolling Friction, and others, etc… make sure you learn the difference and check for the right one.)

I was only worried about that because the larger weight limit would create a larger normal force with the same coeff. of friction which would result in a larger frictional force than I had designed the transmission for.

What is your particular worry about having more frictional force? If it has to do with turning, using a six wheel drive should work with any coeff.

For example, if my robot was in a pushing match with another robot but unable to move it, the transmission would need to put out enough torque to cause the wheels to spin before the fuses blew. If the weight limit was increased, creating a larger frictional force which would have to be overcome by a transmission that wasn’t designed to put out that much torque.

Of course this could be easily fixed by changing the gearing in the transmission, but I’m not looking forward to making changes and testing a new transmission in the constrained conditions of the 6 week build period, especially when my team doesn’t have the resources to quickly create parts for a new transmission.

I think you might be asking the wrong question. Instead, it seems like you want to know “What’s the maximum torque I can expect to have to transmit to the wheels?” - am I correct?

If so, the amount of frictional force the wheel can see is important, but if we assume the wheel is never going to slide - like a gear on a rack - then it becomes a question of how much torque you can generate with your motor(s), and considering your gear ratios. This simplifies the problem, and makes knowing the wheel configuration irrelevant.

If I’m wrong - I frequently am - please also remember to think about shock loads, which can be easily 2 to 4 times the regular load. Then a factor of safety, at least 2. Then remember to de-rate all the components that are not perfect shapes - for example, a hole or keyway in a shaft has a known and calculable effect upon it’s strength and load capacity.

Another thing to consider would be to make a “fuse” - a part that will be the first to break, if necessary, but is easy to replace in a big hurry*, and of which you have plenty of spares. Like a shaft with a purpose-cut weakening groove.

Sounds like a very interesting project, good luck.

Don

*5 minutes is far too long. Ask Team 11 about their experience at Monty Madness, where they changed out a broken shaft that was about 30 minutes inside their robot in an absolutely amazing 7 minutes (I timed it). Unfortunately, the match started after 5 minutes, and so they couldn’t get onto the field in time.

Yes, that is the question I ultimately wanted to answer, but I have all the information to do the calculations and come to that answer myself, except for the frictional force the transmission will have to overcome, which is why I needed the Coeff. of Friction of different wheels my team was considering.

If so, the amount of frictional force the wheel can see is important, but if we assume the wheel is never going to slide - like a gear on a rack - then it becomes a question of how much torque you can generate with your motor(s), and considering your gear ratios. This simplifies the problem, and makes knowing the wheel configuration irrelevant.

If I’m wrong - I frequently am - please also remember to think about shock loads, which can be easily 2 to 4 times the regular load. Then a factor of safety, at least 2. Then remember to de-rate all the components that are not perfect shapes - for example, a hole or keyway in a shaft has a known and calculable effect upon it’s strength and load capacity.

Another thing to consider would be to make a “fuse” - a part that will be the first to break, if necessary, but is easy to replace in a big hurry*, and of which you have plenty of spares. Like a shaft with a purpose-cut weakening groove.

Sounds like a very interesting project, good luck.

Don

*5 minutes is far too long. Ask Team 11 about their experience at Monty Madness, where they changed out a broken shaft that was about 30 minutes inside their robot in an absolutely amazing 7 minutes (I timed it). Unfortunately, the match started after 5 minutes, and so they couldn’t get onto the field in time.

Thanks, I’ll be sure to take those in to account. I’ve been told to design the transmission and drivetrain to be practically bulletproof.

This is absolutely right.
If the weight limit goes up, suddenly a transmission that would have drawn 30 amps/motor will now draw 60 amps per motor, and you’re in trouble.

So design a transmission that leaves you some breathing room…
I always try to leave some adjustability in the final sprocket reduction between the transmission and the wheel:

• If I find the robot is going too fast, I can increase this sprocket ratio, to slow it down.
• If I find the robot is going too slow, I can decrease this sprocket ratio to speed it up.
• If I see FIRST has increased the weight limit by 30 lbs, I can increase this sprocket ratio to bring the motor-load back down to acceptable levels.

This method would allow you to design your transmission, and just tweak your final chain/sprocket reduction when you see the game.

JV

Anyone know the coefficient of friction for that?
(on a standard 120lb robot of course)

I’m just curious.

Our team hopes to do a traction test over this summer with varying materials. We’ll post the results we get on here. Alot of what we test depends on the price of it and how difficult it is to attain, but these are some of the things I have in mind right now…

Standard Skyway Wheels (both 6" and 8" to settle the debate once and for all on whether bigger diameter wheels get better traction)
Pneumatic Skyway Wheels
Gum Rubber
Tread on Bottom of a Shoe
Anti-Slip Matting
Go-Kart or Mini-Bike Pneumatic Wheels
Colson Wheels

Some of these things we already have lying around, the others we’ll have to figure out. Any other suggestions are welcome, and it can be ANYTHING (if you didn’t gather that from the fact that we’re going to test a shoe).

Our team went through this a couple years ago when we were picking wheel types.

While it’s true that the coefficient of friction between two surfaces is based on what the materials are made from, there is still a macroscopic relationship that must be accounted for. There are tables of friction coefficients you can use as a start, but we have seen that things such as knobby tires of the same rubber compound will grip the carpet better. That’s more because the knobs deform the carpet, so there is no longer a purely tangential force acting on the carpet; the tire has become something like a gear.

But I think the big question is really what kind of forces to design for in your gearbox, and friction coefficients are only one part of it. You know what your maximum torque on the motor is, and you should have some idea what your desired top speed for the robot will be as well.
Looking at those, you also want to figure where in the drive train the transmission will be; if the transmission will be stepping down the motor speed, and will go straight to the drive wheel, then it will have to handle the full torque you expect the wheels to see. However if the 'box will step down to a mid-level, then you’re using chains and sprockets to step down the speed more, your max torque will not be as much at the gearbox. Remember also that the ultimate thing your transmitting from the motor to the wheel is power, which is RPM*Torque. Raise one, and you lower the other.

But I wouldn’t design for max torque, and add a little, I would design for max torque, and multiply by 5 or 10. I don’t know how many regionals your team will attend, or if you’ll be at nationals, but add up all the matches you’ll be in, plus practice matches, and practice time at home before it ships. Our team lost out winning the Philly regional because our drill motor transmission died in the finals. Very frustrating. But that was probably the robots 20th match, so it had a few miles on it. I can’t stress (no pun intended) that enough.

Hope this helps.

Ted

We’ve used the 8 inch (nominal) Skyway pneumatic wheels for a couple of years. The ones that are available with the 5/8 inch bore and keyway. They are a bit taller than 8 inches. We generally end up with more traction than we really need, at least on carpet. I’d prefer 6 inchers, but these are easy to work with and fairly inexpensive. They do tend to bounce around, though. We were using 4 CIMs and the kit gearboxes with about a 1:2 further reduction to the wheels.

Wait, I didn’t think coefficients of friction got above one. How do you get more frictional force than normal force?

The coefficient of friction can theoretically reach infinity (think Spiderman). The coefficient of friction can be calculated by taking your floor material and putting it on a ramp. Be able to change the angle of the ramp with respect to the floor. Place your item that you want to test on the ramp. Change the angle until the item starts to slip. Measure the angle. The coefficient of friction equals tan(angle). As you can see, any angle that can get higher than 45 degrees with have a coefficient of friction higher than 1.