Documentation/Modules/Planetary Gear Set

Planetary Gear Set

Sun, planet and ring sizing for target ratio

Standards catalog

Validation: indicative · Method band: formula

Open calculator

Indicative method: Indicative closed-form or numerical model

Assumptions

  • Linear elastic material behavior unless noted otherwise.
  • User is responsible for load combinations and load factors per the selected design code.
  • Design standard (US/EU/ISO) sets unit defaults and screening check labels — not a full code worksheet.

Limitations

  • Professional screening / indicative workspace — does not replace a licensed PE or official code compliance review.
  • Where specialized evaluators are not implemented, checks map solver outputs to catalog templates for orientation only.

Engineering checks

CheckINDUSEUISO
Actual ratio vs targetimplemented———

Planetary Gear Set (planetary-gears)

Purpose

Size planetary (epicyclic) gear trains by selecting sun, planet, and ring tooth counts for a target ratio while checking assembly, planet spacing, and approximate strength balance. Used for compact high-ratio reducers and automatic transmissions.

Physics & theory

A basic planetary set has sun gear , planet gears , and ring gear with carrier . Fundamental speed relation: for internal ring mesh. Gear ratio depends on which element is held fixed.

Tooth count constraint: for equally spaced planets. At least two planets require integer. Planet–ring and planet–sun meshes share load; planet bearing load and equal spacing are design constraints.

Governing equations

Numerical method

Integer tooth search for target ratio within bounds. Validates assembly condition and planet spacing. Approximate torque sharing assigns equal planet load; strength screening uses per-planet tangential force vs allowable.

Inputs

ParameterDescription
Target ratioDesired speed reduction
numPlanetsNumber of planet gears
Min/max tooth countsSearch bounds
module, faceWidthGear geometry
power, speedOperating conditions

Outputs

  • Sun, planet, ring tooth counts, actual ratio, ratio error, assembly validity, approximate planet load.

Design codes & checks

  • Indicative: Actual ratio vs target, assembly constraint check

Assumptions & limitations

  • Single-stage planetary; no compound or multi-stage trains.
  • Full ISO 6336 planet load sharing factors not applied.
  • Planet carrier stiffness and pin bearing loads simplified.
  • Helical planets require additional axial load analysis.

References

  1. Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, 11th ed., Ch. 13.
  2. Müller, H. W. Epicyclic Drive Trains. Wayne State University Press.
  3. ISO 6336 series (planet gear load sharing context).
  4. AGMA 6123-B06. Design Manual for Enclosed Epicyclic Gear Drives.
  5. PhyCalcPro verification benchmarks in src/data/verification/ where available for this module.
  6. Beer, F. P., et al. Mechanics of Materials, 8th ed. McGraw-Hill — foundational stress and deformation theory.
Maintainer note: Planetary tooth count sizing.