# The formula for the optimum helix angle

### An optimum helix angle makes plan­e­tary gears better and more compact. Much more compact.

In a plan­e­tary gear — or epicyclic gearing — at least two, or often more, plan­e­tary gear wheels run in a ring gear. All planets are connected to one another via the “sun,” a central gear wheel. This compact arrange­ment trans­mits torques in appli­ca­tions where there is little space avail­able. With the right design tricks, you can get a lot more out of plan­e­tary gears.

Stefan Fischer develops plan­e­tary gears for indus­trial drive tech­nology at ebm-papst in Lauf. (Photo: ebm-papst)

An impor­tant starting point is the helix angle β on the gear­wheels. If the wheels are straight toothed, it is tech­ni­cally diffi­cult to always have a tooth meshing when there are high trans­mis­sion ratios. This means that the trans­mis­sion vibrates, is loud and wears faster. There­fore, it is good to design the teeth at an angle and achieve an overlap ratio. Although this is tech­ni­cally chal­lenging, it is rewarded with a smooth oper­a­tion with low noise and low wear.

The overlap ratio εβ can be tinkered with. With some of our trans­mis­sions, we have opti­mized the helix angle β with a seem­ingly para­dox­ical result: although our sun only has three teeth, every planet has 2.049 teeth meshing at all times, i.e. on three planets, this is a total of 6.147 teeth.

In addi­tion to even quieter oper­a­tion, we achieve one thing above all else: compact­ness. This means that we can manage with fewer trans­mis­sion stages one after the other. For a reduc­tion ratio of 17 : 1, we need just one gear stage instead of the usual two; for a reduc­tion ratio of 204 : 1, two stages suffice instead of three — always one stage less than usual. This greatly reduces the overall length of the trans­mis­sion.

The overlap ratio is an impor­tant factor for plan­e­tary gears. Although the sun (a) only has three teeth, there are always 2.049 teeth meshing simul­ta­ne­ously on each of the three planets (b). The opti­mally selected helix angle β makes this possible.