Bevel & Worm 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.

• contact stress after ISO 10300-2:2014 (Method B1, AGMA 2003 load factors) on the virtual cylindrical gear (Tregold construction) with bevel factor ZK = 0.85
• ISO 6336-3 root bending stress via virtual tooth numbers — YFa and YSa fitted to the standard's tabulated curves
• AGMA 2003-B97 load factors: overload factor Ko, dynamic factor Kv (quality-grade-dependent), mounting factor Km
• Tangential, radial and axial tooth force components at the mean pitch circle, including spiral-angle correction
• Worm gear efficiency and self-locking detection (γ < ρ condition indicative; cf. DIN 3996 / ISO/TS 14521)
• Heat generation from friction losses — critical for worm drives with low efficiency

Standards this tool applies

• ISO 10300 — ISO 10300-2:2014 Method B contact stress and ISO 6336-3 root stress on the virtual cylindrical gear; SH, SF, tooth forces, efficiency and heat generation for bevel and worm drives.

Validation evidence — independent reference cases (3)

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.

• Straight-bevel tooth forces at the mean radius

  Agrees

  Source: Shigley's Mechanical Engineering Design (Budynas & Nisbett), 9th ed., §13-15, Eq. 13-38 and Example 13-8

  Inputs: z1 15, z2 45, mean radius 1.293 in (dm1 65.684 mm), phi 20 deg, 5 hp at 600 rpm, 90 deg shaft angle

  Quantity	Reference value	Tolerance
  Tangential force Wt	1806.85 N (406 lbf)	1e-6 vs hand; 0.5 % vs printed
  Radial force Wr	623.89 N (140 lbf)	1e-6 vs hand; 0.5 % vs printed
  Axial force Wa	207.96 N (46.7 lbf)	1e-6 vs hand; 0.5 % vs printed

  tests/golden/REF-bevel-forces.golden.test.ts

• Bevel root stress sigma_F and root safety factor

  Agrees

  Source: ISO 6336-3:2006 §6.2 Method B (30 deg tangent, tip load); ISO 10300-1 §5 virtual teeth; Shigley 10th ed. Eq. 14-27/28 and 15-13; AGMA 2003

  Inputs: z1 18, z2 54, m 4 mm, b 40 mm, 15 kW at 1450 rpm, grade 7, 42CrMo4; plus cases z 20/40, 30/90, 14/42

  Quantity	Reference value	Tolerance
  sigma_F, case 1 (zv 18.97)	125.61 MPa	1e-5 relative
  sigma_F, case 2 (zv 22.36)	210.84 MPa	1e-5 relative
  sigma_F, case 4 (zv 14.76)	217.96 MPa	1e-5 relative
  YFa·YSa at zv 18.97	4.3925	1e-5 relative

  tests/golden/REF-bevel-root-stress.golden.test.ts

• Worm drive forward mesh efficiency and its 50 % verdict gate

  Agrees

  Source: Shigley's Mechanical Engineering Design (Budynas & Nisbett), 9th ed., §13-17, Eq. 13-46; DIN 3975 lead-angle geometry

  Inputs: phi_n 20 deg, f 0.05, z2 40, m 4 mm, 0.3 kW at 1450 rpm; (z1, q) = (2,10), (1,10), (1,20)

  Quantity	Reference value	Tolerance
  Efficiency A (z1 2, q 10)	78.15 %	1e-9 relative
  Efficiency B (z1 1, q 10)	64.92 %	1e-9 relative
  Efficiency C (z1 1, q 20)	48.32 % (not SAFE)	1e-9 relative
  Lead angle A	11.3099 deg	1e-9 relative

  tests/golden/REF-bevel-worm-efficiency.golden.test.ts

Limitations

Not checked by this tool

• Bevel-gear scuffing (ISO/TS 10300-20) — Not assessed; check high-speed or heavily loaded bevel sets to ISO/TS 10300-20 or with the gear maker
• Finite-life and reliability factors on the bevel allowables — Allowables are nominal endurance values; apply the ISO 10300-2/-3 life factors for a finite-life rating
• Tooth contact pattern under load (mounting deflection, crowning) — K_m uses the AGMA mounting factor only; confirm the pattern with a loaded-contact test or the gear maker
• Worm-wheel pitting by the DIN 3996 / ISO/TS 14521 mean contact stress — The worm contact stress is a single-point Hertz estimate; verify with DIN 3996 / ISO/TS 14521
• Worm temperature safety (DIN 3996 / ISO/TS 14521) — The thermal row is an estimate outside the verdict; verify the oil temperature with the gearbox maker's thermal rating
• Worm-shaft deflection between its bearings — DIN 3996 deflection safety; model the worm shaft in /shaft
• Shaft bearings for the gear forces (including the axial thrust) — The forces are reported; size the bearings with /bearings