Page 96 - Gear Technology Solutions

have been rolling with each other, the cycle repeats. The cycle repetition hap-
pens after the gear performs a number of revolutions, equal to the number of
pinion teeth. This is of course also true if the pinion performs a number of revo-
lutions equal to the number of gear teeth. The number of revolutions to
achieve “one tooth hunting sequence” is independent from the fact if the num-
ber of teeth are prime numbers or if simply both tooth counts have no common
denominator, which basically means that none of the two tooth counts has to
be a prime number. For example, the ratio 21x22 has no prime number, but by
not having a common denominator it will achieve hunting tooth condition.

Figure 4: Hunting tooth ratio 11x30

In Figure 4 it is graphically demonstrated how revolution by revolution of the
pinion the green, maroon and yellow blocks shift from row to row. It requires
the pinion revolutions in rows “B” to “L” until one hunting tooth sequence is fin-
ished. Row “M” has the identical phase relationship as row “B” and therefore
presents the first repetition

The shifting of the pinion revolution blocks from row to row in Figure 4 allows,
in each pinion revolution, each pinion tooth to mesh with a different gear slot.
However, in one revolution each pinion tooth can only mesh with one particular
gear slot. In order to cover all gear slots, the pinion has to rotate for each gear
slot once which is then called the hunting tooth number of rotations.

A graphic representation of the hunting tooth meshing sequence based on a
co-prime ratio is shown in Figure 5. The pinion has again 11 teeth and the
gear has now 31 teeth. Just like in Figure 4, eleven gear revolutions are re-
quired until the meshing sequence of row “B” repeats in row “M” with the same
tooth combinations. This visual experiment proves that having a co-prime ratio
leads to the same result as if only one of the two tooth counts is a prime num-
ber.

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