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This is a simple guide based on my experience with gears. I've had gears that have cracked apart, worn down, and mashed down their teeth. I believe the key to using gears without damaging them is to control your torque and speed, and use the appropriate gears for the given situation.
Worm gears are bad for high torque.
1) The friction causes wear on the gear teeth. You will notice a gray powder after operating the gear set for a while. The excessive friction grinds the teeth and wears them down.
2) The worm gear is forced axially (i.e. in-line with the axle the worm gear is on) into its supports. What happens is the worm gear is pushed into whatever is restraining it from sliding off the axle it's on. If the torque is high enough, the restraining surface (usually a Technic brick with a hole) will be eroded, or ground into "dust".
3) Excessive heat can build up and melt the plastic. I haven't experienced this, but I've heard that if a worm gear is operated for a long time with enough torque, it can cause a melt down.
So what is the best application for a worm gear?
For low torque applications, it should be okay. If you have to use it for high torque applications, don't operate it very long. If you have to use them extensively, do it in short time intervals, or short "bursts", and take breaks to let things cool down. But you'll still have the friction and the gears will erode.
I used worm gears in the gear trains for the winches on my crawler crane. This was a bad application because I operated the winches for a very long time (more than 15 minutes) and the gears began to erode.
Because of the high friction involved, worm gears are very inefficient.
Normally, when meshing two spur gears, the involute (curved surface) of the gear teeth reduces (or theoretically elimitates) sliding between the surfaces of the meshing teeth. Therefore you have negligible friction.
With worm gears, the surface of the helical teeth slide against the radial teeth of the spur gear (24-toothed, 40-toothed, etc.). This sliding causes a lot of friction.
General note on gears and friction:
What's the best and most efficient way to gear down a motor? I think using the regular spur gears (i.e. 8, 16, 24, or 40 toothed) with the fewest gear sets is the best way. This means using combinations of the 8 and 40 toothed gears. However, I'm partial to using combinations of 8 and 24 toothed gears, just because the 40 toothed gear is too large.
You can compare the efficiency in using different combinations:
- three sets of 8 and 24 toothed gears makes a gear train with a 1:27 reduction.
High speed gears are bad in high torque.
When gearing down a normal motor (i.e. a regular, non-geared 9V or an old 4.5V), the first few reducing gear sets nearest to the motor axle will slowly erode. You will notice the gray dust after operating the motor for a while.
Again, on my crawler crane I noticed the gray dust on the first few reducing gear sets at the output axle of the motor. The gear teeth were noticeably worn down.
So how should I use gears in high torque?
Similar to using the worm gear, do it only in short bursts and avoid prolonged operation.
Another good option is to use the new geared 9V motors. Not only does this eliminate having to use normal Technic gears to reduce the speed, but it is more efficient. The gear reduction that is built into the motor seems to operate with much less friction and therefore more efficiency than an equivalent gear reduction set built out of normal Technic gears (e.g. 8 and 24 toothed gears).
So what exactly is high torque?
When gearing down a normal non-geared motor, a gear ratio (output of gear train to output of motor) of 1:243 or greater creates high torque. Well, you also have to load the gear train to actually see the high torques. You have to use it in an application where the motor is strained or even stalled.
The above picture is the gear train (1:1080 ratio) from the crawler tracks of my crawler crane. The 40 toothed gear was the driving gear connected to the tracks. You can imagine that moving the whole crane put a very high load on the gear train. This was definitely the case as the motor nearly stalled.
The 24 toothed gear that is being driven by the black worm gear broke, but I'll get to gear breakage later. You'll notice extra axles connecting the 3 24-toothed gears. This was done later to help distribute the torque and prevent gear breakage.
Gear breakage
* 24 toothed gears: I've broken them (the old-style ones) at a ratio of 1:648. This gear train was driven with one 4.5v motor.
Note on pictures: On the gear on the right, notice that the center axle support has been badly warped, causing the axle to slip out of the gear. The gear now has an oval shape. Also notice a small crack that has developed between the teeth at the bottom. This was an older gear, as you will note the yellowing.
* 8 toothed gears:
- For ungeared motors, I wouldn't use them at ratios 1:500 or greater (driven by one motor).
- For geared 9v motors, I've broken them at a ratio 1:40.5 (driven by one motor).

* 12 toothed bevel gears (the one-sided bevel): These gears are relatively weak. I've broken them at a ratio of 1:27 (driven by two geared 9v motors). If driven by one geared 9v motor, I estimate breakage to occur at a ratio of 1:54.
Note on pictures: On the gear on the right, notice that some of the teeth have been mashed down. This was caused by meshing with another 12 toothed bevel gear, which received similar damage, at high torque.

General Note On Above: It's difficult to provide a guide to recommended maximum torque per gear size. Therefore I've simply stated the conditions in which each gear failed. Gears of the same size will vary in strength such that one set of gears may fail in a given situation, whereas another set may hold up. Also, it's difficult to account for power losses in a gear train so the torque could vary between different constructions (i.e. gear train #1 produces greater torque than gear train #2 at the same reduction ratio just because they're set up differently).
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