Planetary gearboxes are used in numerous industries for many reasons. In particular, they are favored for their high torque density, making them ideal for heavy-duty applications, often in low-speed machines. Their compact size is another advantage, along with the distribution of the load between the planet gears.
The primary components of a planetary gearbox are the ring gear (1), the planet gears (2), the planet carrier, which holds the planets together (3), and the sun gear in the middle (4). Of these components, only the ring gear, the planet carrier, and the sun gear can be used as input or output for a planetary gearbox stage. There can be multiple inputs but only one output from a stage.
Figure 1: Planetary Gearbox Components
For a simple planetary gearbox like the one shown in Figure 1, there are a total of nine possible combinations of inputs and outputs. There are more complex planetary gearboxes that contain more than one set of planets, but this article will focus on simple planetary stages.
Figure 2 shows the nine possible configurations of a simple planetary gearbox stage. The gearbox stages are shown as cross-sections, with the grey rectangles representing the ring, the yellow rectangles immediately next to them representing the planets, the black prongs representing the planet carrier, and the central rectangle representing the sun.
Figure 2: Nine possible configurations of a simple planetary gearbox
In Configurations 1 and 2, the ring is held fixed. In Configurations 3 and 4, the sun is held fixed. In Configurations 5 and 6, the planet carrier is held fixed. In Configurations 1–4, the rotational direction of the output is the same as that of the input. In Configurations 5 and 6, the rotational direction of the output is opposite to that of the input. In Configurations 7–9, there are multiple inputs and one output.
The output of each configuration can be calculated using the equation shown in Figure 3, where RPMr = the RPM of the ring; Zr = the number of teeth in the ring; RPMpc = the RPM of the planet carrier; Zs = the number of teeth in the sun gear; and RPMs = the RPM of the sun gear.
Figure 3: Equation relating inputs to output with formulas for each configuration
If you know the inputs, you can use this formula to calculate the output for each configuration. These equations will work regardless of the number of planets in a planetary gear stage.
The gearmesh frequency calculation of a planetary gearbox may differ from what you are used to. Because the centers of the planets rotate around the center of the other components, the gearmesh frequency cannot be calculated directly as the RPM times the number of teeth of one of the components unless the planet carrier is held fixed. Instead, use the difference between the RPM of the component and that of the planet carrier.
If you take the ring, for example, use the difference between the RPM of the ring and that of the planet carrier, times the number of teeth of the ring.
This is because the rotation differs so sharply from that of a normal gear. If you follow the teeth of a planet as the planet rotates around the sun, you will see an epicyclic pattern. For this reason, planetary gears are sometimes referred to as epicyclic gears.
Figure 4: An epicyclic pattern
To calculate defect frequencies for the bearings supporting the planet gears, the differential RPM between the outer and inner ring must be used. This is because one of the rings on the bearing rotates with the planet RPM, while the other rotates with the planet carrier RPM.
Figure 5: A bearing supporting a planet gear
