All teams will eventually have to repair or diagnose a motor problem. It may seem a bit daunting at first—like this is something you're not really supposed to be doing because it doesn't open with a standard allen wrench—but really it's OK. And if this troubleshooting is being done on a motor that's broken anyway, there's probably even less to worry about.
First, find a small Phillips-head screwdriver that fits the motor screws, either via a VEX seller or just at the hardware store (bring a motor along to the store to make sure it's the right size).
Second, get 1 or 2 tissues or paper towels. The gears inside the motor are greasy, so one paper towel is for putting down the gears while you're working, and the other is to clean your hands, because they will get greasy too. When taking out the motor screws, put all 4 of them in one, deliberate location; you'll be thankful later when you need to put things back together.
Both sides of the motor can be unscrewed, and there are gears to replace or inspect on both sides! This diagram is a little overly technical,1) but it shows all the parts involved:
Unscrew the side of the motor that the shaft goes through (the black side of the motor); this is where one finds the gears that control how fast the motor can go (or conversely, how much torque is has/how strong it is). VEX motors come from the factory with “torque” (also referred to as “normal speed”) gears installed, and high-speed gears in a little plastic packet. At some point every team will end up with a big bag of mixed normal-speed and high-speed gears and someone is going to have to figure out what's what. So here's a little primer:
The motor uses a pair of gears for each speed level and they mesh together, one nested on top of the other as in the somewhat-hokey picture at left. So if the stem of the gear on the left gets fatter, then the base of the gear on the right must get smaller to all still fit into the motor casing. Returning to the image above, torque (or normal speed) gears have the thin-stemmed grooved gear, and high-speed motors have the fat stem. If these gears get all mixed together, someone will just have to go through them one at a time and figure out what's big & what's small and make piles (set out one paper towel for each type ahead of time). This process requires paying a bit of attention for the gear with the barrel-shaped stem (right-hand gear in the image at left), as the difference between the 2 types is very slight. Holding them up to each other base-to-base can help figure out which is which.
Once the motor is opened up, take out these 2 gears and take a very close look at them, especially the gear with the grooved stem, as this is the one that usually has the problem. Look at it under good lighting, compare it against a new gear if one is available, and make sure to rotate it all around. Often-times there will be a groove running around the stem like a ring that has been cut there by its partner gear. Next, look at the gear stem-end-on and look at the teeth on the stem from this angle. Sometimes this viewpoint it can be seen that they are a bit junky or worn down. Last, look at all the teeth on the big round part of this gear and the barrel-gear. If the motor sounds odd but you can't see anything wrong with the gear, close your eyes and run your fingers up & down the grooved stem; sometimes your fingers can tell you what your eyes cannot.
If *any* of these things look bad, and spare gears are available, replace the damaged gear and THROW THE BAD GEAR IN THE TRASH NOW to make sure it never goes back into a motor by accident. If the team does not have any spare gears, ordering the VEX motor refurb kit ($5) is probably the next step.
If everything looks fine on this shaft-side of the motor, put everything back in, and screw the black plastic cap back on. If any of those little tiny motor screws seem like they're starting to get stripped, TRHOW THEM IN THE TRASH NOW. Every VEX motor comes with a bunch of extra screws, so there's no need to penny-pinch; trying to get a stripped screw out of a critical motor in an emergency—or, really, ever—is something to avoid.
So, there is another side to this whole thing, and this is where many gear problems seem to occur; this author's Team 1666 Nothing But Net flywheel had repeated problems with the gears on this side. Same instructions as above: get a workspace set up with the motor-screw-sized screwdriver and some tissues or paper towels, and take the green cap off of the back of the motor.
This end also has 2 gears, shown in the image at right. If a team is in need of replacement versions of these, they only come in the motor refurb kit linked above, unfortunately, and there's only 1 of each gear in the kit. So often the entire $5 kit must be purchased just to get 1 of these gears.
When there are problems with gears on this side of things, most often it's on the “stick gear” (the one with the long skinny stem), and in extreme cases it will look lie the photo at left,2) with a serious groove cut into the stem by its neighboring gear.
Another problem that occurs, though less often, is a broken or missing tooth from the big round part of the one of these gears. That is Not Good. Replace immediately; stop driving the robot if you start to hear a clicking sound in the motor.
Same advice for the green-cap end as above: inspect each gear in good light from every angle—stem-on, from the side, the teeth, and rotate it all the way around. On the stick gear, close your eyes and run your fingers down the stem of the gear; sometimes this will reveal that the stem gears are just a bit chewed up, even if nothing is visually wrong. If the gears feel chewed up or rough, it's time for a replacement.
Sometimes on a suspect gear there will be a ring of gunk, but nothing that seems actually broken or damaged; this is a more ambiguous situation with no clear smoking gun. If there is an extra gear hanging around that's better than the one with the gunk, replacing it is the most useful thing to do. Don't throw away the gear with the gunk; since nothing is obviously wrong, it may come in handy in a pinch some day in the future, since extras of these gears can only be found in the $5 refurb kit.
Again, if it is a damaged or broken gear that needs replacing, take the damaged gear and THROW IT IN THE TRASH RIGHT NOW. This is the sure-fire way of not getting it mixed up with a functional part that goes back into someone's robot someday. (Do you detect a pattern here?)
This happens frequently. All the removable gears on both ends show no obvious signs of wear, and the teeth are all in good shape. For additional troubleshooting, the next thing to do is (with the green cap end still opened up) put a shaft with a wheel on it into the motor and turn the wheel by hand and see what the green-cap-end gears are doing. Do they turn evenly and consistently or do they wobble? Do they stay connected to the teeny gear that's being driven by the actual DC motor, or do they move together and apart as the wheel is turned (indicating a shaft mis-alignment)? (This process requires a few people to hold the various parts in place and turn the wheel.)
And sometimes it's never clear exactly where the problem is, but when that wheel is cranked, the motor still makes that clicking sound. At this point, one may conclude that a) there is indeed something broken, b) its exact location is not known, and c) in the end it doesn't matter, because the motor is a goner.
If the motor is headed for the graveyard, take it apart and salvage whatever gears inside still look good. Especially those gears on the green-cap side; they're hard to come by, and it's easy to end up with a crisis if a motor that is attached to the robot needs replacement gears and none are available. Having some of these back-side gears on hand could save a team a week of waiting for the refurb kit to come in the mail.
Alternately, if some of the gears need to be trashed, but replacement ones are not on hand, tape the green cap back onto the motor with blue tape and write “missing stick gear” (or whatever's appropriate) on the tape with a Sharpie. Having a mostly-complete motor on hand is better than throwing it away. Someday it can be reassembled as a Frankenstein motor with some parts from here, some from there; your note to yourself on the blue tape will save you figuring it out again sometime in the future…