Wire gauge vs. current

[AdamHeard]

this isn't for FIRST robotics, so I can't just look at the wire guide there and see what is required.

It's for a 3lb robot with a strict weight limit, so I want to use the smallest possible gauge I can without trying to pull more current when all the motors are at stall than the wire can handle.

My battery is two 7.4V Lipoly with 1.0 Ah and a discharge rate of 20-30 C.

The sum of the stall torques of the three motors is 27 Amps.

So, what gauge should I use for the initial wiring? And how do I determine what to use for the smaller loads within the robot.....

I've looked at charts online, but they seem way off based on what I've seen in FIRST and the fact that each battery has 14 AWG wire on it already.

[Richard Wallace]

I'd make the decision based on resistance. 10 AWG wire is 0.001 Ohms per foot. 12 AWG is 0.0016 Ohms per foot. 14 AWG is 0.0025 Ohms per foot.

If you limit your motor currents to 25% of stall (3 x 27 / 0.25 ~= 20A) then a 10 AWG circuit will drop 0.02 Volts per foot, and dissipate 0.4 Watts per foot. By similar math the same circuit wired with 12 AWG would drop 0.032 Volts per foot and dissipate 0.64 Watts per foot; using 14 AWG you'd get 0.05 Volts per foot drop and 1 Watt per foot dissipation.

You need to assess how much voltage drop and dissipation is acceptable, and also how much overload (beyond 20 Amperes) is expected.

[edit]Sorry I mis-read the stall current information. Divide all my voltage drops by three, and dissipations by nine. Jim's recommendations below are good. I agree it would be nice to hear from Al, too.[/edit]

[MrForbes]

rule of thumb I use for car wiring is that a #10 wire should be protected by a 30 amp fuse, a #12 with a 20 amp, #14 with a 15 amp, etc. It sounds like you are going to need about a 30 amp main fuse/breaker to keep from popping it at full stall (if you can actually get the robot into such a situation), so maybe a #10 wire for the main power would be appropriate. Wiring for the individual motors would probably be #16 with a 10 amp fuse/breaker for each, and you could go smaller on the power feed wiring for the controller.

Hopefully Al will chime in too

(edit: Richard, he said the SUM of the three motors is 27 amps, not 27 amps each)

[EricVanWyk]

I like to use this chart

http://www.powerstream.com/Wire_Size.htm

[MrForbes]

I guess I'm pretty conservative...

[dtengineering]

Originally Posted by squirrel

I guess I'm pretty conservative...

A) Not really... for 10ga wire they suggest limiting it to 15A for power transmission, and only go up to 55A when describing it as unbundled and for a short length. Since your estimate is for car wiring... which runs through insulated areas and for longer lengths, I'd say your estimates actually match up pretty well.

B) It's not like being conservative with wire diameter and load is a bad thing! Especially when wiring a car or a house. Igniting a 3lb robot is quite different from igniting a 3000lb Buick!

Adam,

For this application, however, I would also consider looking at where the "bottleneck" in the system is going to come. What will happen to the voltage of the LiPo's at their maximum rated draw? Their internal resistance at full draw may drop your voltage down too low for your microcontroller to keep running. Likewise you may find the LiPo's start to heat up... and you really do not want to overheat LiPo's. Although I don't have first hand experience with overheating them, I understand they are both expensive to replace, and somewhat combustible when abused.

What will happen to the motors? Keep in mind that if you use a 10ga wire to deliver current to your motor, that current still has to "fit" through a much smaller wire inside the motor that is wrapped tightly on all sides by other small wires carrying the same amount of current and giving off the same amount of heat. This can often be sustained while the motor is turning (due to the dynamic convection cooling of air moving over the coils) but at stall, or even low RPMs, small motors can let out their magic smoke fairly quickly.

An example is the FP motor in the KOP. Although it's stall is rated something like 55A, I find they smoke if you run them for more than a few seconds at anything above about 10A (okay, maybe 15 or 20... but I'm being conservative, too). Keep in mind that just because a motor has a rated "stall current" does not mean that the motor can handle being stalled (or close to stalled) for more than a second or two.

Practially you may need a wire diameter capable of carrying much less than 27A, as the motors may act as a fuse and go up in smoke long before the wire (which is likely larger diameter than the motor wires and has air on all sides to cool it) does... which isn't really a good thing.

On the other hand, the narrower you make the wire, the higher the voltage loss in the wire, and the less power reaching your wheels. That is a performance trade off, not a safety trade off, and one only you can decide.

It may make sense to hook up your 2 LiPo's in series, to get 14.4V, which should give you higher RPM on your motors, then gear the motors down (roughly by a factor of two) to get increased torque at a given current, while keeping your top speed the same. Of course the gearing adds weight, too, but it is just a thought. Cramming voltage down a wire (up to a point) is quite painless in terms of power loss, while current gives off heat... P=I(squared)R, after all. Motors will also tend to be more efficient at higher voltages as well. Perhaps you are already doing that, I couldn't tell from the post whether your batteries were in series or parallel.

So keep your wire runs as short as possible, do some practice driving, that will simulate what you expect from competition and feel the wires. If they are heating up, then they are too small. Oh... and feel the motors, too. Warm to the touch (in this application) isn't a problem... hot to the touch is.

Jason

[Al Skierkiewicz]

Adam,
Since the battery is not likely to produce the full 27 amps if all motors stall, it is unlikely that any one motor will draw more than 7 amps. If you keep the wiring short and a match is only a few minutes (using the chart linked above) you could use #22 for each of the motors without damage. I am guessing that your 3lb robot is not very big so the weight difference between a #22 and a #18 is not going to significantly change your weight budget. The #18 will supply more power to the motor and would be the better overall choice. As always, the electrical design is important. Keep the leads short and distribution to the motors should occur as close to the power input as possible. You do not specify that a fuse(s) are required but at least a main fuse should be considered to protect the battery.
You also did not specify if the batteries are in series or parallel so I am assuming they are in series. As such the maximum current from the pack is still only the single battery current spec, 30C x 1 amp=30 amps. This is in keeping with the #14 wire suppplied. Using the wire table again, notice that the specification is the chassis wiring column. #14 is good for 32 amps in that situation. All wire/current is rated by temperature rise in the wire and this table only lists open fram or chassis wiring. Other tables will list current or "ampacity" based on open or closed applications. The table lists the maximum amps for power based on the 700 CM/amp (circular mil or effective cross section of copper wire) rule. In general this computation is designed to give at least 80% of the input voltage at the load for a given length. None of these applies in a small wiring job. Even a foot of the #22 at 9 amps would only drop 0.14 volts. You may find some wire with a lightweight teflon insulation that could significantly reduce your weight allowing a #16 to be used at less weight (but more cost) than a PVC insulated #18.
If your battery packs will be wired in parallel (something I never think is a good idea without diode protection) than the #18 is the only choice. BTW #20 wire is difficult to find that is why I did not consider it in this discussion.
If our assumptions are incorrect or there are other rules to consider, just let us know.

[travis]

Sounds like you are working on a beetle weight fightin' robot, and I'll weave this tale in that light.

210W sounds high for 6oz of battery, or perhaps 1lb of motor. Kinda like my 85W computer speakers with 24ga wire going to them (and 40ga inside). I had a 60lb spinner in the old days that had a theoretical max current draw of 400A, mostly from a grossly oversized weapon motor. I would have had maybe 3 seconds of 160A before a battery fire started. An amp clamp never registered more than about 100A, and that was a transient from the weapon motor start up.

Breakers have no place in this sort of machine. Your typical cheapie low voltage beetle type motor is a heater that happenes to produce torque, they are a perfectly good fuse. Sizing a breaker below your motor burn out current can leave you vulnerable at key moments. Even the 500ms of a quick breaker is enough time to sustain major frame dammage, a more costly repair than a fried motor. Test drive with breakers, but remove them for the competition.

You might want to find out who actually made the cells in those batteries, they'll tell you the straigh dope on discahrge characteristics. I don't think you could expect 30C out of a Li poly, shorted with a silver crowbar. The A123 litium ion battereis (availible here http://www.battlepack.com/A123.asp ) are quoted by the manufacturer as sourcing 70A continous, which is semi terrifying.

The quick answer is to use the above referenced wire sizing guides. The long one is to start with a smaller than expected gauge, lock the motor shaft in a bench vise, and keep bumping up the gauge until the fires stop (safety glasses + ABC rated fire extinguisher on hand). This is a good time to break out the amp clamp and determine what the worst case loads are. Note the voltage depression as well. The extra cost of silicone wiring is always worth it.

In closing, I never went to a robot fight where fires were frowned upon. These things only need to work for 3 minutes, 30 seconds if the audience is lucky.

Travis