Calculating Wheel Size

[phrontist]

How do you optimize wheel diameter for a given set of motors? What variables effect optimal wheel diameter?

My thoughts:

It seems that in a perfect world, the larger the wheel, the better the bot. But because of friction and such, you want to minimize gearing. At what point does a larger wheel cause problems? Is there any other reason not to get the largest possible wheels (other then minimizing gearing)?

Bonus: What about width?!

[Arefin Bari]

one reason i would be against larger wheel is if you have a lot of friction you will and four wheels on the bot... you will have a lot of problem turning... as for example, the pnematic kop wheels that FIRST gave us... a lot of team have used it and had a lot of problem with it...

[Ryan F.]

I actually think that if you'd look at it, many of the more sucessfull teams have used smaller wheels on their robots. With a larger or wider wheel you sacrifice manuverability. Also when you start getting into some very large wheels, you'll have much more of a tipping issue. The robots I've seen that used wheels almost wheelchair sized all seemed to not be able to stand upright. You could probably help to compensate for this if you mounted the wheels high on the robot, but then that complicates your design.

[Greg Needel]

Other things to think about with wheels


With wider wheels you have a larger surface area touching the ground thus more friction force. They also take up more space on your robot

what I normally do is choose the wheels last this is because when you choose your gearing for optimal performance (either toque or speed, even in a 2 speed gearbox) then choose the wheels to determine your final max speed. See most people don’t think about the fact that if you put larger wheels on your bot, you will go faster without any gear change....

Now the catch with this line of thinking is that the wheel dilatometer also deals with the transfer of power a larger wheel takes more torque to get going as it also pulls more amps.

There is a lot to think about when choosing wheels and I for the most part make it my last decision when designing a driver train so I can optimize more.


Note: in the 2002 season we brought different size wheels to competition so we had options

[ChrisH]

Originally Posted by phrontist

How do you optimize wheel diameter for a given set of motors? What variables effect optimal wheel diameter?

1) Decide how fast you want or need to go.
2) Decide how much pushing force you need.
3) Decide which of the above is more important
4) Decide how much power you have available.
5) Remember that Power = Torque X Rotational Speed
6) Remember that your motors are happiest running about 75% of free speed.
7) Think about what factors other than flat ground robot performance influence your choice? (stair climbing etc.)
8) Now you can pick a wheel size.
8) Design your drive train so that your motors are running about 75% of free speed at the speed or torque output you desire. (If it winds up going too fast you can always limit the output in software, but you can't add power that way)

Note that you are at step 8 before you even think about wheel size.

Define the operational requirements FIRST. Check the power availability before you start designing. If you need 2000W to accomplish a task in a certain time and you only have 1000W of motor available, it just ain't going to happen. You need to either double the time or find more power.

To illustrate some different paths, let us look at two very different but highly successful robots from this year, 330 and 254/60.

The 254/60 robots were designed to be very fast and manouverable and dominate the floor. They used small wheels (4" dia as I recall). Since they weren't planning to climb the platform, they could use small wheels. The small wheels mean they have to turn faster to achieve the same robot speed as a larger wheel. But they also mean less gear reduction which results in more power to the ground, because every stage of gear reduction costs you power. The smaller wheels also give a larger wheel base which gives more stability.

330 decided to play the game differently. Our goal was to dominate the bar. We felt that this strategy fit better with our team's personality and abilities than all out domination of the floor. To do that we wanted to be on the platform at the end of autonomous. While 15 seconds is not a long period of time, it was more than adequate for the task. So we designed our robot to go about 7 ft/sec, turn and climb the platform. The wheel size was chosen to facilitate that. We used 6in wheels with a ramp in the front to get us on the lip of the platform and 12" pnuematic tires in the back to finish the job.

330 used a simple tank style drive train that just used two drill motors with the stock tranny's and mounts and a simple pnuematic shifting system. 254/60 used four motors (chips and drills) with custom gear boxes.

All the robots discussed above made it to their respective division elemination rounds in Atlanta on their own merits. I was not present in the design discussions for teams 254 and 60, but I was for 330. But I do know both 254 and 60 pretty well. We have been friends for years and often sit and chew the fat at competitions and other events. WE ALL USE THE ABOVE METHODS for figuring out drive trains. I can't say it enough. Figure out you requirements first, then figure out how to accomplish them.

In this post: http://www.chiefdelphi.com/forums/sh...34&postcount=4 Dave Lavery says that 254 has figured out something important. This is part of it. 60 has it figured out too, they just don't get as much credit.

ChrisH

[Billfred]

...wouldn't having smaller wheels also allow more fun with appendages, since you
a) wouldn't have as many gears (which have weight, not to mention take power and drain your batteries somewhat), and
b) wouldn't have as much wheel (which has weight)?

But I'm definitely bookmarking that post. Thanks, Chris!

[Travis Covington]

Originally Posted by Greg Needel

With wider wheels you have a larger surface area touching the ground thus more friction force.

This is not 100% true.

Frictional force is independent upon wheel width theoretically. 'Friction' or traction does not increase with a wider wheel since friction = µ · N. The weight of the robot is distributed to a larger area, thus decreasing the frictional force per unit area, and keeping the total friction essentially the same. This does not take into account the deflection of the carpet, or any tire that 'digs' into it.

If you relate this to the automotive industry, in most cases wider tires do have more traction, but this has little to do with contact patch width (as most wider tires, of the same OD, with the same tire pressure, have the same contact patch as the thin tires). Cars, for example, desire wider tires primarily because of composition, as well as temperature, side wall deflection, pressure allowances etc. It is not as simple as the commercial "wider is better" Wider tires of the same compound do not have more traction, but will usually have stiffer sidewalls which inherently have less roll and give better handling characteristics.

For a robot, in some cases wider is better, but not always in regards to friction (unless there is some sort of protruding element that goes into the carpet, in which case it gets really complicated and testing is the best way to determine what width is desired using a given material). A wider tire (using belting as a traction material) in most cases will wear better. It has less pressure per unit area as the same belting on a smaller width wheel, and as such, also has a larger total area decreasing the frequency of belt replacements.

Again, you must remember that some belting has an optimal deflection at which its friction coefficient is the highest. You have to take this into account as well when talking about wheel width, especially if the belting is deflecting or protruding into the carpet fibers.

In 2002, team 60 had one of the most powerful and "grippiest" robots on the field. But they only had ~1" wide wheels. How is that? They lifted the 2 goals and used that weight to increase the wheels friction by increasing the normal force the robot put on its wheels.

Just remember that "wider isn't always better".

[Holtzman]

Contrary to popular belief, size does matter.

Both large and small wheels have there benifit. Large wheels are able to roll well over bumps, stairs, ledges and so on. On the other side, as a robots wheels increase in size, its wheel base decreases in size making it very unstable. We saw countless examples of robots this past season that had the 12' skyways. (props to team 69's unique expanding chassis design to counter act this problem)
Small wheels do not roll well over obstacles, but in a year like 2002 for example, where there were no field features, there is no need for large wheels, and you can use something smaller. Smaller wheels are also lighter, and anyone who saw 1114's robot can attest to our weight problem.

We at 1114 used a 3 3/4 inch wheel in our strafing design to minimize space while also minimizing the amount of reduction needed in the gear box.

So, in my opinion, unless theres some field features that require a large wheel, go small, there's no detectable difference in traction between a large wheel and a small wheel and there are real advantages to small wheels.

[Adam Y.]

If you relate this to the automotive industry, in most cases wider tires do have more traction, but this has little to do with contact patch width (as most wider tires, of the same OD, with the same tire pressure, have the same contact patch as the thin tires). Cars, for example, desire wider tires primarily because of composition, as well as temperature, side wall deflection, pressure allowances etc. It is not as simple as the commercial "wider is better" Wider tires of the same compound do not have more traction, but will usually have stiffer sidewalls which inherently have less roll and give better handling characteristics.

Actually your wrong. In very special cases wider tires will actually help traction. Race cars are one example of such a creation. Their tires are wider than an average cars. This is designed so that as the car races through the track the tires start to become gummy. This actually causes the tire to stick to the track.

[Travis Covington]

Originally Posted by Adam Y.

Actually your wrong. In very special cases wider tires will actually help traction. Race cars are one example of such a creation. Their tires are wider than an average cars. This is designed so that as the car races through the track the tires start to become gummy. This actually causes the tire to stick to the track.

I never disagreed with this statement. If you look closely, I noted temperature as a reason tires are chosen. Race car tires are usually very thin to maximize heat transfer. But like I said, the gummy nature of the tires is due to their soft composition. Completely opposite of this, a spike in temperature can actually decrease traction. So again, the wider tire (think greater overall surface area) can more quickly dissipate the temperature spike during hard braking or the accidental skid.

Also, the larger width increases the likely hood of the tire having contact with the road on uneven surfaces. The lack of a tread (on dry courses) also helps in this area. The soft rubber compound used in race car tires fills the nooks and crannies in the road surface. The wider the tire, the more nooks and crannies it fills, to a certain degree.

[Adam Y.]

I never disagreed with this statement. If you look closely, I noted temperature as a reason tires are chosen. Race car tires are usually very thin to maximize heat transfer. But like I said, the gummy nature of the tires is due to their soft composition. Completely opposite of this, a spike in temperature can actually decrease traction. So again, the wider tire (think greater overall surface area) can more quickly dissipate the temperature spike during hard braking or the accidental skid

Here is a question. Which is better for a robot? Wheels with a tread pattern or bald wheels. Just take last years game as an example.

[greencactus3]

it matters on the floor material too... just as in 'race' cases. you want tread to let the rubber get to the ground without hydroplaning if you have wet or very dusty ground.. but in very well conditioned tracks, (such as very smooth asphalt with sugar water sprinkled on) you want the slicks... as in our robots, too.. if its a very smooth plastic floor, no tread might give you more traction.. and then theres a matter of do you want that much traction? as in 4 wheel drive skid steering.. do you want to stick to that floor that much?
and then again, what material tires are you using? if its a soft gummy rubber, its definitly going to be different from say, abs tires..(works very well for drifting )

[Paul Copioli]

Pick the smallest wheel diameter the obstacles allow you to get away with. Smaller wheels allow for less gear ratio in the gearbox (to get the same speed/force characteristics). There are a few white papers on this. Ken Patton and I also did an FRC conference in Atlanta and we had some content on this very question.

With respect to wheel width, I have used 1/2", 1", and 1 1/2" for reasons other than traction (packaging, for the most part). We have used the same two tread types and our frictional force never changed between the wheel widths. For the most part, the coefficient of friction is not dependent on width of tires. For many other reasons tires on cars (or race cars) are wide, but coefficient of friction is not the primary. Drag race tires are really wide, why? The thickness of the tire walls is a major contributor, temperature rise is another. The other major contributor is torque transfer between the hub and the rubber part of the tire. In this case the tire pressure and the surface area are major contributors (as well as some other tricks) to decreasing the likelihood of the rubber separating from the hub.

For FIRST robots, the phenomena listed above just do not apply.

-Paul

[Andrew]

Thanks for the words of wisdom, Paul.

I have been an advocate that smaller is better in tires for the reasons you have listed (primarily efficiency). The question is not how large a tire can you choose but how small.

Limiting factors on minimum tire size include ground clearance and obstacle handling (bumps, etc). An additional factor in "smalling down" the tires is weight. If you use the minimum GR that you can get away with, you will have fewer gears.

Therefore, smaller, thinner tires give you less weight in the tire, less weight in the gears in the gear boxes, and less weight in the walls, spacers, and other gear box parts.

The issue of ground clearance can be solved with wheel diameter. But, it can also be solved by using a suspension. I'm surprised at how few teams have looked into suspensions. Although the suspension does add weight back into the equation, this can be traded off against the weight deleted in slimming down the gear boxes.

If you take 10 lbs out of your weight by going to a very small wheel and add back in 2 lbs in suspension parts, you are a net 8 lbs lighter for accomplishing the same task.

[Max Lobovsky]

How can suspension help with ground clearance? I understand how it helps handling bumps, but how does dampening vertical shock forces on your wheel give you greater ground clearance?