Page 95 - Gear Technology Solutions

7.2 Four Cases of Ratios

In the case of an integer ratio for example 10x30, there will be three pinion
revolutions and one ring gear revolution until the cycle repeats [1]. This sce-
nario is graphically shown in the matrix in Figure 2. One gear revolution is
shown in the top row in blue, labeled “A”. The pinion revolutions are shown in
row “B” and “C”. The first pinion revolution is shown in green, the second revo-
lution in maroon and the third in yellow. After this sequence, the colors repeat.
For example, pinion tooth 1 will mesh strictly with the slots 1, 11 and 21 of the
gear. The second sequence of pinion revolutions in row “C” is merely a repeti-
tion of the first three pinion revolutions in row “B”. The pinion rotation blocks do
not shift because of the integer ratio.

Figure 2: Integer ratio 10x30

In the case of a ratio 12x30, which has a common denominator of 2 but is not
an integer ratio, pinion tooth 1 rolls with the gear slots 1, 13, 25, 7 and 19. It
takes two gear revolutions (= 5 pinion revolutions) until the cycle repeats (see
Figure 3). It could be speculated if the scenario shown in Figure 3 has ad-
vantages to the scenario in Figure 2. Nevertheless, in both cases, the pinion
teeth mesh in groups of gear slots. In Figure 2 there are three groups and in
Figure 3 these are five groups. Only meshing between the groups is possible
for the defined ratios.

Figure 3: Common denominator ratio 12x30

A hunting tooth relationship in gear pairs means that there is no common de-
nominator between the number of pinion and gear teeth. As a result, every
tooth of the pinion will mesh with every slot of the gear. After all teeth and slots

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