Calcualting Chain Requirements (25 v 35)

[gburlison]

Martin Sprocket and Gear has a variety of engineering data in their catalog.

http://www.martinsprocket.com/cat2001DL.htm

Section E details sprocket data and includes information on how to design a chain drive.

[Tristan Lall]

Unfortunately for those who would prefer a stringently mathematical approach to chain design, no such thing currently exists (in general form). One would need to understand a lot of stress/strain, materials, dynamics and vibration theory to be able to derive working equations for the general case of a chain drive. (And they would be ugly equations.) Engineering practice simplifies this, with tabulated approaches and approximate factors for safety, service class, operational lifetime, etc.. Multivariable calculus will not be very useful here, and to be honest, apart from simple concepts like torque and tension, the AP Physics course will probably be of little assistance.

The Tsubaki catalogue also has similar engineering data, which (I believe) was reprinted from Machinery's Handbook.

You also need to be aware that the published engineering data typically refers to equipment that will be required to withstand continuous operation for several million cycles, with lubrication as indicated, but which may not necessarily be subjected to heavy reversing loads (e.g. the momentum of the entire robot plus the thrust of the robot are going one way, and then your driver reverses the motors). Also, it typically assumes a properly-tensioned chain, and adequately parallel sprockets. Many FIRST robots don't meet these last two criteria very well, and chain life and efficiency will be reduced because of it.

On the other hand, a FIRST robot doesn't necessarily need to withstand 10 million cycles; often they'll only be expected to operate for a few hours (a few hundred thousand cycles, at most). So fatigue performance isn't something that we would worry about. In principle, we could exceed the working load, and still have an acceptable rate of failure due to fatigue, at the end of the design life.

But while that may be true, we don't really know enough about the system to be able to set safety factors with a high degree of accuracy. It can therefore be a little misguided to believe that this increase in working load is something which we can actually realize, because other factors may impose limits that are not immediately obvious. For this reason, I would tend to err on the side of caution, or otherwise, have a backup plan for dealing with failures.

That's from personal experience, especially with the 2003 robot. It was notorious for destroying chains—in fact, in the final match of the 2003 West Michigan Regional, which we won with 245 and 1140, we ended with only one of four wheels driving. It broke at least 13 #25 drive chains over that season. Of course, we erred in design decisions. We didn't have a proper tensioning system (the chains ran over hard guides), we chose sprockets which were too small (given a set torque, the stress on a chain around a sprocket increases as sprocket diameter decreases, because stress is proportional to force, and force is governed by F=T/r), and we had the most powerful drivetrain in FIRST that year, with over 2100 W (mechanical) available at the motor outputs (and perhaps 1800 W at the wheels).

You can save yourself a lot of unknowns by designing your drives to use an adjustable tensioner, or by using the formula for centre distance between sprockets (from Machinery's Handbook, 26^th edition):

Center Distance for a Given Chain Length.—When the distance between the driving and driven sprockets can be varied to suit the length of the chain, this center distance for a tight chain may be determined by the following formula, in which c = center-to-center distance in inches; L = chain length in pitches; P = pitch of chain [in inches]; N = number of teeth in large sprocket; n = number of teeth in small sprocket.

c=P/8*(2*L-N-n+sqrt((2*L-N-n)^2-0.810*(N-n)^2))

This formula is approximate, but the error is less than the variation in the length of the best chains. The length L in pitches should be an even number for a roller chain, so that the use of an offset connecting link will not be necessary.

Even if your sprockets are at the optimum centre distance, it's not a bad idea to have a place to put a tensioner, just in case you need to change something.

Ensure that you have enough chain wrapping around the driving and driven sprockets. Aim for 180° each, but under no circumstances use less than 135° (for a power transmission system; positioning drives can get away with less, under certain conditions).

In general, read through a few catalogues for chain products, and the appropriate section of Machinery's Handbook (or similar) to get a feel for what's out there.

Also, don't limit yourself to roller chain; belts and silent chain are worth investigating, if you can find a supplier who is willing to produce them cheaply for you.

Originally Posted by Andrew Blair

One important thing to note is that it doesn't matter how much torque your gearbox can output, but how much the chain is ever going to see. The force of friction multiplied by the radius of your wheel tells you the torque that that wheel can transfer and the maximum load (theoretically) that the chain will experience. Divide the torque by the radius of your sprocket, and you have the force the chain will experience. Multiply that by at least two or three to maintain a decent safety factor- perhaps more. Compare that to the breaking strength of the chain, and decide if you are too close you are to the rating, and need to bump up the size.

Just as a clarification; this is an example of using the static load times a safety factor to determine the load rating. It's a common practice, but because of the difficulty of choosing an accurate safety factor, it's important that the safety factor be conservatively large, in order to account for the dynamic loads on the chain. It doesn't directly account for a reversing (dynamic) load, which is rather difficult to predict, without a whole bunch of information about the angular momentum of the gearbox, the linear momentum of the robot, and the rate of change of the speed of the motors—here's where the calculus starts, if you're so inclined.

Also, you need to decide whether or not you wish to design for the maximum load that a robot can exert at wheel slip (like in Andrew's example), or the maximum load that the gearboxes can exert. The latter is only really applicable in a wheels-locked situation, such as if you have a rod jammed through the spokes of your wheel, while it attempts to drive. In practice, it's just not reasonable to design for this case, unless your drivetrain is sufficiently exposed that you anticipate this happening. And if that's the case, I'd suggest protecting your drivetrain against jamming with foreign objects, rather than increasing the size of your drive components.

[psquared89]

Thank you everyone for your responses. These were exactly what I was looking for, other threads became too much of a debate and less useful for practical information.

[DonRotolo]

One thing Tristan hints at but does not state explicitly: #25 chain, because the sprocket teeth are not as tall as #35, requires the tension to be just right to avoid slippage. This happened to us on our ball conveyer last season. #35 is a lot harder to get to slip, even when the chain is badly under-tensioned.

Don