Question

Design a power transmission mechanism with gears that converts 360 RPM to 2 RPM. The output gear must have the same rotational direction as the driving gear. In your design, you need to include at least two shafts with stacked gears.

Answer 1

The easiest way to convert 360 rpm in 2rpm while maintaining the same rotational direction is by using a three shaft system with 4 gears as shown below (Not in scale).

The speed relation between the gear 1 and 4 is:

Sr = Sr1* Sr2

Where Sr1 is the speed relation between the gear 1 and 2, while Sr2 is the speed relation between gear 3 and 4. These relations can be represented by their number of teeth as follows:

Sr1 = N2/N1 and Sr2 = N4/N3

Thus:

N2 * N4 Sr = N1 N3

Also, Sr can be calculated by:

Where n is the rotational speed, thus:

Sr = 360rpm/2rpm = 180

Knowing that the diametric pitch Dp= Np / Pd, where Np is the number of teeth and Pd is the pitch diameter:

We start by establishing a diametric pitch of 16 for the first reduction, and a pitch diameter of 0,5”for the gear #1. Thus the pitch diameter is:

Np1 = 16 * 0,5 = 8 Teeth

We may also establish a pitch diameter of 8”, but the diametric pitch must remain the same. Thus:

Pd2 = 20*8 = 160 teeth

Knowing this, the speed relation is:

Sr1= 160/8= 20

The speed relation between D3 and d4 must be:

Sr2=Sr/Sr1= 180/20= 9

We may use the same model of gear of the gear 1 for the gear 3, thus

Pd1 = Pd3 = 0,5”; Dp1 = Dp3 = 16 and N1 = N3 =8teeth

Thus:

Sr_N2* N4 **N1* N3 = 180 = 160 * N4 = 8 = 2,5 * N4

N4 = 180/2,5 = 72 teeth

Since Dp4=Dp3= 16.

The Pitch diameter must be:

Dp4 = 72/16 = 4,5”

Resuming the Pitch Diameters:

D1 = 0,5”

D2 = 8”

D3 = 0,5”

D4 = 4,5”

The distance between centers is:

D1 + D2 0,5 +8 C1 = -= 4,25

D3 + D4 0,5 + 4,5 C2 = -= 2,5"