Some gear drive design tips from an engineering point of view.
The 5.5Nm value as calculated above gives the torque on the motor shaft.
Divide that by the radius of the gear and you get and you get how much force goes through the drive, that’s what @Flyboy calculated.
The force going through the drive is can be used for gear life expectancy calculations. Basically the drive can fail in two ways:
- wear: this is almost exclusively decided by the surface hardness of the gear and the quality of lubrication
- chip a teeth from too weak material: if material is too weak to begin with, the first time it sees the big load, it snaps. Lets call the point it snaps at as max load.
- chip a teeth from fatigue: I’ll try to simplify stuff a bit. Your material would break at max load as defined above. With steels, if the given load is less than ~0.3x max load, you can apply the load and remove it infinite amount of times. Lets call this acceptable load. If you apply a bigger load than the acceptable load, every time you apply the load and then remove it (do a load cycle), your material gets weaker. Until after x amount of cycles, it will snap.
If you apply some mechanical engineering math, you can determine your acceptable load for each material that doesn’t weaken the material, no matter how many cycles you do.
Here you can find that math if you want to learn more and dive deeper:
The calculations there gave the results that the ~6Nm shaft torque was still under the acceptable load with a mod1 17t gear.
Whereas my ~11Nm shaft torque on my BN gear drives was above the acceptable load of the mod1 17t gear, and I snapped a teeth off of that gear after maybe ~2000km of very hard riding.
Basically to strengthen the gears you have 3 options: increase modulus but keep diameter (stronger teeth), and keep modulus but increase diameter (reduced forces acting between the gears), increase gear width (distribute the force over more material)
One more design constraint I’d like to throw in is related to wear. Higher teeth count means a single teeth carries the lead for fewer degrees each rotation. There’s a maximum advised amount of degrees that the teeth can carry the load before the angle of the load becomes suboptimal and starts wasting energy and creating lots of heat. For standard gear teeth profiles, this results in about 17T of minimum recommended teeth count such that the gear teeth only works at the optimal angles.
Regarding wear one last thing, its very good practice to have the number of teeth on the two gears relative primes, meaning their greatest common divisor is 1. I like to use 17T for the smallest pinion, as 17T is prime, so no matter the teeth count of the other gear, the relative primeness is satisfied. This makes sure that every teeth will come into contact with every teeth, making sure wear stays even over time.
Essentially gear drive design can be summed up by following these principles: determine your shaft torque; if possible keep smallest teeth 17t or more but relative prime to other, use as wide gears as reasonable, play with modulus to find what gives you strong enough gears that you stay below maybe 1/4" of the material limit. Then either decide reduction ratio by maximum allowed diameter, or calculate diameter by ideal reduction ratio.