Planetary Gears — validation & limitations

What it calculates

Engineering estimate — this tool uses an accepted simplified model rather than one citable governing standard. Use it for preliminary sizing and verify the final design against manufacturer data or a qualified engineer.

• Gear ratio for 3K-I (ring fixed) and 3K-II (sun fixed), plus a Wolfrom option that is an explicitly badged single-stage STAND-IN, not a Wolfrom rating
• Read-only kinematic table covering all six input/output/fixed permutations, including the carrier-fixed reversal
• ISO 6336-2 contact (pitting) stress for sun-planet (external) and ring-planet (internal) meshes with ZH, ZE, Zε, Zβ factors
• Planet load sharing with a K_gamma mesh load factor (ISO 6336-1 symbol, industry guide values) (3–6 planets)
• Output RPM, torque and power for the three core arrangements (ring-, sun- and carrier-fixed) at an assumed stage efficiency, alongside a six-row ratio table for every permutation
• All three assembly conditions carried into the headline verdict: the mesh condition z_r = z_s + 2·z_p and actual planet interference as hard failures, equal spacing (z_s + z_r)/n and tip clearance as warnings
• Tooth-root bending estimate (Lewis-based, with the per-mesh load factors K_A·K_V·K_Fβ·K_Fα) for the sun and the planet, with the planet derated for fully reversed idler loading — flagged as an estimate, not the ISO 6336-3 rating
• Planet-pin diameter sizing (Shigley cantilever method) against a fixed 200 MPa allowable — a sizing rule, not a pass/fail check, and no shear or fatigue check is made
• Efficiency and power-loss map from an assumed per-mesh efficiency (η_total = η_mesh²), swept over input power, with a cooling-threshold rule of thumb

Standards this tool applies

• ISO 6336 — ISO 6336-2 contact stress on the sun-planet and ring-planet meshes with load sharing. SCOPE: a screening calculation, not a full ISO 6336 rating — K_A and K_V are fixed and K_Hβ = K_Hα = 1.00 (a face-load factor is physically ≥ 1, so 1.00 is a lower bound), and S_H is taken against the raw σ_H,lim rather than the permissible σ_HG. At the default geometry the combined shortfall is about 17 %: treat S_H as an UPPER bound and verify a marginal design against a full rating.

Validation evidence — independent reference cases (2)

Each case runs the tool's engine on a worked example whose values come from a published source or a hand derivation from the cited equations, and an automated regression test asserts the engine against those values within the stated tolerance. "Conservative" means the engine is known to sit on the safe side of the reference and the test asserts that side. Sources are cited; their text is not reproduced.

• Kinematic ratio and carrier-output efficiency

  Conservative

  Source: Willis equation (Mueller, Epicyclic Drive Trains, 1982, ch. 2; Shigley ch. 13); Mueller efficiency of a simple planetary train; Niemann/Winter Maschinenelemente Bd. II mesh-loss estimate

  Inputs: zs 20, zp 30, zr 80, 3 planets, m 2, 1500 rpm, 10 kW, 3K-I, mu 0.04

  Quantity	Reference value	Engine	Tolerance
  ratio / output speed	5.000 / 300 rpm	—	1e-12 relative
  efficiency	98.955 % (Niemann internal-mesh sign)	98.7063 %	1e-6 vs hand; engine <= 98.955 %
  output torque	314.21 N·m	—	1e-6 relative

  Conservative simplification: The engine adds the mesh-loss term for the internal ring-planet mesh instead of subtracting it, so efficiency reads about 0.25 points below the Niemann internal-mesh value.

  tests/golden/REF-planetary-efficiency.golden.test.ts

• Tooth-root Lewis bending check with load factors

  Conservative

  Source: Budynas & Nisbett, Shigley's Mechanical Engineering Design, 9th-11th ed., Sec. 14-1, Eq. 14-3 (SI) and Table 14-2; hand derivation

  Inputs: F_planet 1000 N, b 20 mm, m 2 mm, zs 20, zp 30, allowable 300 MPa, K_SP 1.5, K_RP 1.3

  Quantity	Reference value	Tolerance
  sun root stress (K-factored) / safety factor	129.75 MPa / 2.3122	1e-6 relative
  planet root stress / safety factor (governs)	114.78 MPa / 1.8297	1e-6 relative
  unfactored Lewis stress sun / planet vs Shigley 20-degree Y	86.50 / 76.52 MPa vs bounds 77.64 / 69.64 MPa	engine >= Shigley 20-degree value

  Conservative simplification: The engine uses the 14.5-degree full-depth Lewis form factor as a stand-in for 20-degree teeth and a 0.70 reversed-bending derate on the planet, so unfactored root stress reads about 10–11 % above the Shigley 20-degree value for the sun and the planet.

  tests/golden/REF-planetary-root-lewis.golden.test.ts

Limitations

Conservative simplifications

• Kinematic ratio and carrier-output efficiency — The engine adds the mesh-loss term for the internal ring-planet mesh instead of subtracting it, so efficiency reads about 0.25 points below the Niemann internal-mesh value.
• Tooth-root Lewis bending check with load factors — The engine uses the 14.5-degree full-depth Lewis form factor as a stand-in for 20-degree teeth and a 0.70 reversed-bending derate on the planet, so unfactored root stress reads about 10–11 % above the Shigley 20-degree value for the sun and the planet.

Not checked by this tool

• Ring-gear tooth root and ring rim strength — The internal ring teeth are not rated; rate them to ISO 6336-3 with the rim-thickness factor
• ISO 6336-3 tooth-root rating (form and stress-correction factors) — The root check is a Lewis estimate; rate the sun-planet pair in /gears
• ISO 6336-2 life, lubricant, roughness and size factors on the contact allowable — The contact safety factor uses the raw endurance limit; apply the ISO 6336-2 factors for a full rating
• Planet bearing life — Size the planet bearings for the planet force with /bearings
• Carrier deflection and the real load sharing between planets — Load sharing uses a guide factor per planet count; confirm with measured or FE data
• Scuffing and micropitting — Not rated; ISO/TS 6336-20/21/22
• Gearbox thermal rating (bearing, seal and churning losses) — Efficiency is mesh-only; check the heat balance with the gearbox maker's data