Cylindrical Gears — validation & limitations

What it calculates

• ISO 6336-3 Method B tooth-root bending stress — form factor YF and stress-correction factor YS from the root-fillet geometry at the outer point of single-pair contact, helix factor Yβ, size factor YX and the rim-thickness factor YB from an optional rim-thickness input — enter it for a thin-rim or web gear and the backup-ratio penalty is applied
• ISO 6336 Hertzian contact stress with zone factor ZH, elasticity factor ZE, contact-ratio factor Zε and helix factor Zβ, including single-pair tooth-contact factors ZB/ZD for spur and partial-overlap helical gears; the permissible flank stress carries the size factor ZX and the lubricant, velocity and roughness factors ZL·ZV·ZR from your oil viscosity and flank roughness
• DIN 3990-1 Method C dynamic load factor KV across quality grades Q6–Q12 (DIN 3962 / DIN 3990 Method C K1 values; the mapping to ISO 1328 grades is not verified), AGMA 2001-D04 / Shigley Eq. 14-30 face-load distribution factor KHβ (commercial enclosed unit, uncrowned, symmetrically mounted — the accuracy grade drives KV, not KHβ), and bending face-load factor KFβ = KHβ^NF per ISO 6336-1
• Application factor KA as a selectable input (ISO 6336-1 Annex B / DIN 3990-1 guide table) and finite-life rating via the ISO 6336 life factors Y_NT (bending) and Z_NT (contact) — enter a required number of load cycles, or leave it for the conservative continuous-duty (endurance) design
• Profile shift analysis to ISO 6336 / DIN 3960: operating centre distance, operating pressure angle and transverse contact ratio εα computed from the involute function
• Sensitivity (tornado) analysis — contact safety factor SH vs ±20% variation in module, face width, power and pinion tooth count

Standards this tool applies

• ISO 6336 — ISO 6336 rating of spur & helical gear pairs — σH, σF, SH, SF, with the ISO 6336-2/-3 stress and life factors. Two of the Part 1 load factors are NOT ISO 6336: K_Hβ follows the AGMA/Shigley commercial-enclosed-unit form (an ISO 6336-1 Method B/C value can be supplied to override it), and K_Hα is a fixed 1.10 rather than the §8.3.4 Method B expression.

Related standards — reference only, not implemented

• AGMA 2101reference only — ISO 6336 contact and bending stress for spur & helical gear pairs, with a Shigley-form (AGMA-style) face-load distribution factor Km as K_Hβ. No AGMA 2101 rating is computed.

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.

• Flank (pitting) safety factor SH through the ISO 6336-2 Method B chain

  Agrees

  Source: ISO 6336-1/-2:2006 Method B (σH0, ZH, ZE, Zε, ZB/ZD, ZL, ZV, ZR) with DIN 3990-1:1987 Method C dynamic factor KV and KHα guide value 1.1

  Inputs: spur mn 4, z1 20, z2 50, b 40 mm, x 0, 30 kW at 1450 rpm, grade 7, KA 1.0, KHβ 1.20, σHlim 1500 MPa, Rz 4 µm, ISO VG 100

  Quantity	Reference value	Tolerance
  Dynamic factor KV	1.161515	2e-4 relative
  Flank stress σH,B (pinion)	816.522 MPa	2e-4 relative
  Permissible stress σHG	1396.2367 MPa	2e-4 relative
  Flank safety factor SH (pinion governs)	1.709981	2e-4 relative

  tests/golden/REF-gears-contact-pitting.golden.test.ts

• Tooth-root bending safety factors SF1 / SF2 vs ISO 6336-3 Method B

  Conservative

  Source: ISO 6336-3:2006 Method B (σF = σF0·KA·KV·KFβ·KFα, YF/YS at outer single-pair contact) with ISO 6336-1:2006 load factors

  Inputs: spur mn 4, z1 20, z2 50, b 40 mm, x 0, 30 kW at 1450 rpm, grade 7, KA 1.0, KHβ 1.20, σFlim 500 MPa

  Quantity	Reference value	Engine	Tolerance
  SF1 (pinion)	7.693818 (tool fillet 0.38·mn); 6.719842 (0.20·mn)	6.7194	2e-4 relative to the 0.20·mn value; one-sided (engine <= reference) to the 0.38·mn value
  SF2 (wheel)	8.152738 (tool fillet 0.38·mn); 7.001262 (0.20·mn)	7.0008	2e-4 relative to the 0.20·mn value; one-sided (engine <= reference) to the 0.38·mn value
  KFβ	1.153646	—	1e-6 relative
  Pinion YF·YS (Method B, 0.20·mn)	3.270440	—	1e-5 relative

  Conservative simplification: The engine is ISO 6336-3 Method B with the smallest standard hob fillet (0.20·mn) assumed, because the tool radius is not an input; on this case that reads about 13 % below the value for the common 0.38·mn hob.

  tests/golden/REF-gears-root-bending.golden.test.ts

Limitations

Conservative simplifications

• Tooth-root bending safety factors SF1 / SF2 vs ISO 6336-3 Method B — The engine is ISO 6336-3 Method B with the smallest standard hob fillet (0.20·mn) assumed, because the tool radius is not an input; on this case that reads about 13 % below the value for the common 0.38·mn hob.

Not checked by this tool

• Scuffing load capacity (ISO/TS 6336-20/21) — Only a screening indicator is shown; rate scuffing to ISO/TS 6336-20/21 for high-speed or high-load meshes
• Micropitting (ISO/TS 6336-22) and tooth flank fracture (ISO/TS 6336-4) — Not rated; check case-hardened, highly loaded flanks with ISO/TS 6336-22, and large case-carburised gears with ISO/TS 6336-4, or ask the gear maker
• Static / peak-torque tooth strength (ISO 6336 static rating) — Only the endurance (fatigue) rating is computed; check start-up, stall and shock peak torque against the static root and flank strength (ISO 6336-2/-3 with the static life factors ZNT / YNT)
• Tooth tip thickness (pointed tooth) at large profile shift — Verify the tip thickness (at least 0.2 x module) from the gear geometry when x is large
• Transverse load factor K_Halpha by ISO 6336-1 Method B — A fixed value is used; lightly loaded or low-accuracy meshes may need a larger factor
• Gear body: hub, web and bore / keyway strength — Check the shaft-hub connection with /keys or /pressfit and the web on the gear drawing
• Gearbox thermal rating (heat balance of the housing) — The oil temperature shown is a rule of thumb; use the gearbox maker's thermal rating
• Shaft and bearing sizing for the mesh forces — Size them with /shaft and /bearings