Gears and Gear Trains flashcards

$N_1{n}_1=N_2{n}_2$: teeth times rpm is equal on both gears. An 18-tooth pinion at 1,200 rpm drives a 54-tooth gear at 400 rpm. The bigger gear always turns slower.

Each external mesh reverses direction. Odd number of meshes: output turns opposite the input. Even number: same direction. An internal (ring) mesh does not reverse.

It sits between driver and driven gear, reversing the output direction so it matches the input and bridging a gap. Its tooth count cancels out, so it does not change the overall speed ratio.

Gears on a shared shaft turn at the same rpm and direction. Multiply the stage ratios (driven/driver for each mesh): $i=\frac{N_2}{N_1}\times \frac{N_4}{N_3}$. Two 3:1 stages give 9:1.

$T_{out}=\eta i{T}_{in}$: torque rises by the ratio i as speed falls, times efficiency η. A 5:1 reducer at 90% with 6 N·m in gives 27 N·m. Power never increases.

$i=\frac{N_{wheel}}{\text{starts}}$. A 3-start worm driving a 60-tooth wheel gives 20:1. Worm sets give big reductions, are often self-locking, and connect shafts crossing at right angles.

Spur and helical: parallel shafts. Bevel: intersecting shafts, usually 90°. Worm and wheel: crossed, non-intersecting shafts. Rack and pinion: converts rotation to straight-line motion.

Rack moves $s=\pi d$ per turn (pinion pitch diameter d). Module $m=\frac{d}{N}$ in mm per tooth; mating gears need the same module. Center distance $a=\frac{d_1+d_2}{2}$.