# Friction losses between spur gears: less teeth are better than many teeth?

In my project, a little Nema11 stepper motor turns for max +/-90° an handle. When the windings of the motor are not energized, the handle can be manually rotated by a human operator.

The load is not big: the stepper offers max 19 N x cm of torque and the max load in the handle is around 3 Kg. The gear ratio is around 1 to 4. My goal is to reduce as much as I can the bad feeling of "clunkyness" and friction/resistance added by the gears when rotating the handle by hand.

What is the better? An "high" number of small teeth, or a small number of "big" ones? (I.e. a small m value versus a big m value, while keeping the pitch diameter the same.)

From an intuitive point of view, I could think that many small teeth have more probability to stay in close contact, increasing friction. While few "big" teeth stay more "away" one from the other. But I could be wrong...

I've read somewhere that efficiency of spur gears is substantially independent from the value of the modulus. It is strongly related to the value of the pressure angle α instead.

Is this true? It seems that I can simply choose almost the value m that I like more to build the gears (in acetal/Delrin).

• I word reword your question a little bit. What you asking about is fine pitch vs coarse pitch (in other words small or large gear teeth). Because the actual number of teeth on your gears is determined by the gear pitch, the diameter of the gears, and the gear ratios you need. You needn't mention number of gear teeth at all in your question. May 2, 2021 at 18:55
• "From an intuitive point of view, I could think that many small teeth have more probability to stay in close contact, increasing friction. While few "big" teeth stay more "away" one from the other. But I could be wrong..." I think it might actually be the opposite. With proper tooth geometry, a consistent contact area size is maintained through the rotation so I do not believe that coarse vs fine pitch gears have a difference (or big difference) in friction or positioning resolution. Finer pitch strips and skips more easily and requires better tolerances. May 2, 2021 at 18:58
• What would be the purpose of the green gear? Anyway you dont really want to use gears with less than 12 teeth. As they need to be modified significantly for them to work. May 2, 2021 at 19:24
• @SolarMike yeah but because it has less than 12 teeth it needs to have undercuts so its also a weak ooint in the design. Also a tip: Polyoxymetylene gears work better when their counterpart is nylon. May 2, 2021 at 19:39
• @DKNguyen The problem is that with a small number of teeth, the "ideal geometry" is impossible, because the tooth before or after the driving tooth would overlap part of the gear wheel profile. You are right that fine teeth are more fragile, but (as usual with engineering) the "best" number of teeth is a trade-off of different factors. May 2, 2021 at 21:47

If your gear is manufactured reasonably accurately your tooth spacing will be pretty consistent. As for the gaps between mating teeth, this is called backlash and has almost zero effect on friction. If you're more concerned with position than power (and losses due to friction) finer pitch/module gears will have less backlash due to the scaling of the tooth geometry.

As others have pointed out your use of a green idler gear is not a good idea. The best way to minimize friction is have as similar a number of teeth on each mating gear as possible. You said you want a 4:1 reduction, I would suggest two 2:1 stages. Friction is mostly due to the sliding action between gear teeth, this occurs whenever they're contacting beyond the working pitch diameter when the teeth are in pure rolling motion. To minimize sliding velocity you need as similar gear radii as possible and as low a pressure angle as possible (14.5 degrees is an older standard angle that should still be available). Sliding velocity and friction are functions of the sine of the pressure angle.

• Hi, unfortunately I have some dimensional constraints on my project. The distance from the pinion and the driven gear is fixed, and I cannot use two 2:1 stages because the mechanism has to be as thin as possible... : ( Anyway, I read somewhere that 20° is the optimal pressure angle for the teeth... I will investigate further about the value you propose. May 3, 2021 at 19:58

IMHO, "the bad feeling of "clunkyness" and friction/resistance added by the gears when rotating the handle by hand" is not influenced by the number of teeth (provided that you are using gears with more than 17 involute teeth).

The involute design results in teeth rolling (and therefore minimises the friction sliding of the teeth), so theoretically there should be no - or very little friction. So it shouldn't really matter whether you have many or few teeth.

If the spacing between the teeth is large, (i.e. if at the pitch circle the gap between two teeth is much larger that the tooth's thickness), then you might have a slightly different behaviour. The reason is that with many teeth, you will have more impacts.

In any case the "clunkyness" you are describing is probably a matter of other factors. More specifically:

• alignment of teeth
• proper distancing
• Teeth condition or manufacturing

Usually, the first two account for most of the friction losses, so its useful to putting some time in to think and make sure that the gear mesh together in the most optimal way.

• Thanks for you observations. I have 15 teeth on the pinion, IIRC... : ( So I think that I must increment the modulus a little. This can be a problem because I never used so small milling bits (i.e. 1 mm of diameter or less) on my CNC machine. May 3, 2021 at 20:03