Engineering Notes About Planetary Gear Ratio
Compact Power Transfer
A planetary gear set is compact and strong. It uses a sun gear, planet gears, a carrier, and an internal ring gear. Several power paths are possible. One member can drive, one can react, and one can deliver output.
Speed Relationship
The calculator applies the Willis relationship. This relation compares sun, ring, and carrier speeds. It also checks the tooth geometry used by simple planetary sets. When the ring and sun tooth counts are known, each planet tooth count should equal half the difference. The value must be practical for manufacturing.
Design Applications
Use this tool when selecting a reduction stage. It is useful for gearboxes, robotics, winches, vehicle transmissions, indexing drives, and compact actuators. The result shows speed ratio, output speed, torque change, pitch consistency, and direction notes. It also estimates planet load sharing when you enter planet count and efficiency.
Member Selection
Planetary ratio can be confusing because the answer changes with the held member. For example, fixing the ring and driving the sun gives carrier reduction. Fixing the sun and driving the ring gives another carrier speed. Holding the carrier creates a reversing train between sun and ring. The general speed equation keeps each case consistent.
Tooth Checks
Good designs need more than a ratio. Tooth count choices should avoid tiny planets, poor clearances, and impossible mesh geometry. The ring count should exceed the sun count. The ring and sun difference should be divisible by two when identical planets are used. Many designs also prefer phasing checks, bearing checks, and strength calculations.
Efficiency And Torque
Efficiency matters. Real gear meshes lose power through sliding, rolling, bearings, seals, and lubricant churning. The calculator includes an efficiency field, so output torque is not overstated. It also displays ideal torque for comparison. Use conservative efficiency when the stage is small, loaded, or poorly lubricated.
Exporting Results
The example table gives common cases. You can change every value and export the result. The CSV file helps with spreadsheets. The PDF file gives a simple record for reports. Always confirm final gears with standards, material data, stress ratings, backlash targets, lubrication plans, and supplier limits before production. For early sizing, the calculator gives a clear starting point. It cannot replace detailed tooth stress analysis, thermal review, shaft deflection checks, or prototype testing under real loads.