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I would like to design a single stage planetary gearbox using standard gears.

There appears to be three primary conditions to ensure the geometry of the gears will fit - correct center distance, placement of planet gears around the sun, ensuring adjacent planet gears do not interfere.

A number of the conditions depend on whether the planet gears are evenly placed around the sun or unevenly placed around the sun. What does this actually mean? Using a ring gear of 100 teeth, three planet gears of 40 teeth, and a sun gear of 20 teeth - would the planet carrier physically position the planet gears 120 degrees apart, or would two planets be positioned 33 teeth apart and one 34 teeth apart, without causing interference of the ring, planet, or sun gears?

What is a good reference for planetary gear design?

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As long as the number of teeth of the sun plus ring gear divided by the number of planet gears is an integer, they will be equally spaced (120 deg for 3 planets). This is more about timing the points of highest and lowest tooth contact of the planet gears. When they're equally spaced the planet-sun meshes will all be hitting the highest tooth loads at the same time. These forces will balance out, minimizing vibration.

Think about 3 load vectors 120 degrees apart all pointing to the same point. The loading of gears is cyclical, so think about all 3 loads having the same sine function for intensity. If they're all in phase, they will always cancel out at the point of intersection. If they're out of phase, you'll always have one vector contributing more magnitude than the others, inducing vibration in your system. Excess vibration is bad.

AGMA 6123 is a helpful standard.

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