[JVN]

Originally Posted by JoelP

1. How do you calculate the minimum amount of torque needed to spin out the wheels to prevent the breakers from tripping?

This is dependant on lots of things, rather than explain it all here, I'm going to point you to a presentation I gave with my father last year in Atlanta, which spells it all out.
http://www.team229.org/resources/20/

Originally Posted by JoelP

1.a And how do you calculate the coefficient of friction of your wheels?

There is the simple answer, which will generate a lot of debate, and there is the more complicated answer.

The simple answer involves putting a piece of your traction material on a sample piece of FIRST carpet, and tilting this carpet until the traction material begins to slip. Measure the angle between the ramp and horizontal at the slip point. Take the tangent of this angle to calculate the coeff of friction between these two materials.

This is not TOTALLY true, because it is reliant on the laws of friction as dealing with perfect surfaces (we don't live in a perfect world). In real life, our wheels will interlock with the floor, and this will vary depending on weight loading and such. For a better estimation, calculate an approximate coefficient of friction for your entire drivetrain. This can be accomplished through the method sanddrag has outlined in the above post. (Though, I typically use a large linear-force scale, and not a bathroom scale.)

You can also just use benchmarks for your calculations. (i.e. if you search this forum, or ask those here, we can give you a good idea of what you're working with. For instance, skyway wheels measure in the 0.8 range.)

Originally Posted by JoelP

2. I've noticed in some other threads that a drivetrain efficiency of 81% was used. How was this efficiency calculated?

I typically use 81% as my base number when running calculations; I believe this is input as a default in some of the spreadsheets and whitepapers I have posted, because of this I think it is probably my fault that you're quoting it. 81% is a guestimate, rule-of-thumb, base value I use. I experimentally determined it many years ago during some of my drivetrain experiments on 229.

The type of systems I designed didn't vary too much from year to year (they all used similar gearboxes, with similar chain setups, with similar wheels, with similar frictional losses, manufactured in similar ways, with similar design methods) so because of all this similarity I continued to use that number. It was usually "in the ballpark" to what I really got, and so it proved to be a good design number.

This efficiency number varies a lot depending on your system. Some people use 90% efficiency per reduction stage as a bench-mark. I usually approximate 81% for the whole drive, and make it turn as smooth as I can, then call it a day. (For more on drivetrain efficiency, search this site. There are lots of methods people swear by.) My favorite method is to add some center-center distance in my gear meshing. This causes them to run a little sloppier, but a whole heck of a lot smoother. How much to use varies from person to person. I think I use .003".

Originally Posted by JoelP

3. Which maximum RPM value of the motor is used to calculate the maximum output speed of the transmission, the free load, average load, max efficiency, or max power?

Well, we know the motor won't run at the free-speed. This is the "perfect-world, no losses" speed of the robot. But there is no such thing as a zero-friction bearing (if you have one, patent it and never work again).

Once again, because I have learned to use some "close enough" approximations in my drivetrain design, rather than do detailed comprehensive modelling of the entire system, I use an 80% of free-speed value. This has always served me well. Again, this value was experimentally determined a million years ago when I wasn't so lazy or complacent with my gearbox design.

If you calculate for 80% of your free-speed, you'll probably be in the right place. You can do your own calculations for this if you have a robot similar to the one you are designing. Hand calculate how fast it SHOULD be going (based on free-speed), then experimentally measure how fast it really goes. Compare these two to get your % value.

The non-lazy approach:
Figure out how much parasitic loss is in your system. Experimentally measure the frictional load which will act on the motor during running. Use this value to calculate the load on the motor, and use the speed-torque curves to then calculate the robot speed.

Something to remember:
Motors vary, motor speed varies, and an approximation is probably going to get you close enough.

Originally Posted by JoelP

4. I know the efficiency of the transmission applies to the maximum RPM, but does it also apply to the maximum torque?

These two are related. When the motor is running at 0 load, it runs at max speed. If there is some load applied to the motor, it will run at less than max speed. When you are talking about torque applied to the floor, remember that the motor will also need to exert torque to overcome the load caused by friction, BEFORE it ever exerts anything on the floor.

Originally Posted by JoelP

5. What are the pros and cons of using direct drive and using chain reductions?

Someone once told me that the chain reductions on my drivetrain account for 80% of my total efficiency loss. While this may be an exageration, it is a valid point. Chain will decrease your efficiency.

However, it also provides an easy means to transmit torque across distance, and it allows for an easy (and forgiving) last reduction. I would rather have a chain break, than a gear or shaft.

If you direct drive, you will need to use a shaft which can handle the torque, which probably means more weight. You will also need additional gear reduction to compensate for your lack of chain reduction (more weight).

There are people who swear by both methods. I swear by chain reductions.
(Along with non-driven wheel axles, but that is another debate for another time.)

Search Chief, and you will likely find more pros/cons for each side.

Originally Posted by JoelP

6. I know that by using smaller wheels, I don't need as much reduction, but what are the other pro's and cons of larger and smaller wheels? Specifically 4" and 6" wheels?

Smaller wheels can be further out towards the outside of your robot. (i.e. the center of a 6" wheels MUST be 3" from the envelope of your robot, but a 4" wheel only needs to be 2" from the envelope of your robot.) This means that if used correctly, smaller wheels will result in a larger footprint, and increased robot stability.

Larger wheels can climb over obstacles better. Larger wheels make it easier to increase robot ground clearance.

Some people believe larger wheels increase robot traction, but I still haven't seen any logical reason why this is true. I'm not convinced.

I like small wheels - lighter, more stability, lighter, lighter.

Originally Posted by JoelP

7. I've made my own spreadsheet over the past few days to calculate things such as max rpm, max torque, and total reduction at various stages of reduction through the transmission, as well as Pitch diameter, center to center distances, total weight, and final speed and torque. Can you direct me to another spreadsheet made by someone more experienced to check mine against?

This is GREAT. I'm glad you've taken this step.
Here is mine: http://www.chiefdelphi.com/media/papers/1469
Which has seen a lot of use. I am still overdue for an update. Hopefully before kickoff this year.

Also,
http://www.usfirst.org/robotics/2006/cmp_conference.htm
If you're going to be in Atlanta this year, on Thursday at 12-12:45 Ken Patton and Paul Copioli are giong to be giving a drivetrain presentation. This is a must-see thing. Ken & Paul have both taught me INCREDIBLE amounts about drivetrain, and they're both "experts".

Good Luck, and welcome to the wonderful world of robot drivetrain design.

There is a lot of good stuff on Chief you can read to help you along the way. I am mostly "self-taught", simply by reading posts from guys like Ken Patton, Paul Copioli, Andy Baker, Joe Johnson, and others.
Feel free to ask questions, and you will certainly get help.

-JV

PS - Why would I do my real work, when I can spend 30 minutes posting about drivetrains? Yeah, I'm a sucker for gears.