KEVOS® MAKEOS · Gears
Planetary Gear Set Design (Ratio, Assembly, Forces and Bending)
Does this planetary gear set assemble with equally spaced planets, what ratio and torque does it give, and are the sun teeth within their bending allowable?
Design check of a simple planetary gear set: planet teeth, ratio, output speed and torque for the chosen fixed member (as the planetary gear tool), the equal-spacing assembly condition and the planet adjacency (tip clearance) check, pitch diameters and centre distance, sun torque and the tangential force per planet with a load-sharing factor, the meshing speed relative to the carrier, the planet pin load and the Lewis bending stress on the sun teeth.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Sun teeth | Teeth on the sun gear. | |
| Ring teeth | Teeth on the internal ring gear. | |
| Number of planets | Number of planet gears. | |
| Arrangement | choice | Which member drives, which is held and which is the output. |
| Input speed | rpm | Speed of the input member. |
| Input torque | N·m | Torque on the input member. |
| Efficiency | % | Efficiency of the stage. |
| Module | mm | Module of all three gears. |
| Face width | mm | Face width of the sun mesh. |
| Load-sharing factor | Factor for uneven load sharing between planets (1 for a floating sun and perfect sharing; higher for rigid mounting). | |
| Lewis form factor (sun) | Lewis form factor for the sun teeth. | |
| Tooth finish | choice | Manufacturing quality, which sets the velocity factor. |
| Allowable bending stress | MPa | Allowable bending stress of the sun material (your design value). |
Method and formulas
- Planet teeth z_p = (z_r − z_s) ÷ 2; ratio 1 + z_r ÷ z_s (ring fixed), 1 + z_s ÷ z_r (sun fixed), −z_r ÷ z_s (carrier fixed) (as the planetary gear tool).
- Equal spacing needs (z_s + z_r) ÷ n_p to be a whole number; neighbouring planets clear if (z_s + z_p) sin(π ÷ n_p) > z_p + 2.
- Sun torque from the torque split T_s : T_r : T_c = 1 : z_r ÷ z_s : (1 + z_r ÷ z_s); tangential force per planet F_t = 2T_s ÷ (d_s n_p) × K_s; planet pin load ≈ 2F_t.
- Lewis σ = K_v F_t ÷ (b m Y) with the velocity factor from the pitch-line speed relative to the carrier.
- Example: 24/72 teeth with 3 planets give 4:1; each planet carries 798.61 N and the sun bending stress is 97.985 MPa.
Limitations
- Lewis method for a first sizing; full ratings use ISO 6336 with the planetary load factors.
- Standard (unshifted) gears with planets of equal size.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Lay out a planetary stage for a gearmotor or winch
- Check tooth counts for equal planet spacing
- Find the planet bearing load
Who it is for
- Design engineers
- Maintenance engineers
- Power transmission engineers
What you get
- Planet teeth, ratio, speeds and torque
- Assembly and adjacency checks
- Tooth force per planet, pin load and sun bending stress
Interpreting the result
- More planets cut the load per tooth but need better load sharing (a floating sun or flexible pins).
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2211, 2122–2160. Topic reference; no source tables or recommended settings are reproduced.
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Open the Planetary Gear Set Design (Ratio, Assembly, Forces and Bending) calculator
