ISO 6336 Spur-Gear Rating Suite

Screen a parallel-axis involute spur-gear pair for contact-pitting or tooth-root bending capacity.

Engineering screening tool—verify inputs and results independently. Use at your own risk.

How to use

Select Contact capacity for pitting/contact screening or Tooth-root capacity for bending screening.
Enter integer tooth counts z₁ and z₂ (12–399), profile shifts x₁ and x₂ (0–0.5), normal module mₙ in mm, pressure angle α in degrees, face width b in mm, and positive elastic moduli E₁ and E₂ in GPa.
Enter the mode-specific material stress limit and independently established combined allowable/load factors. These factors must represent the actual material, life, safety, quality, alignment, lubrication, roughness, and duty.
Select Calculate. Select Reset to restore the worked example and Contact capacity mode.
Read governing tangential force and pinion torque first; use the geometry and factor metrics to diagnose the result. Correct red errors and do not ignore the working-angle warning.
Do not use this screen for helical/bevel/worm gears, internal gears, plastic gears, micropitting, scuffing, thermal balance, dynamics, tooth modifications, rim/web effects, or safety certification. Complete a current standard-compliant rating and design review.

Worked example

1. Select Contact capacity. Enter z₁=15, z₂=71, x₁=0.5, x₂=0.418, mₙ=7 mm, α=20°, b=44 mm, E₁=E₂=206 GPa, σHlim=1200 MPa, Kσ,H=0.92, and KH=1.6. 2. Calculate. Expected outputs are approximately Ft,H=11.174 kN, Tmax,1=598.31 N·m, αw=22.87°, a=306.98 mm, and εα=1.480. 3. For Tooth-root capacity with σFlim=300 MPa, Kσ,F=1.3, and KF=1.6, expected outputs are Ft,F1=22.869 kN, Ft,F2=22.366 kN, Ft,governing=22.366 kN, and pinion Tmax,1=1224.44 N·m from the pinion limit Ft,F1. These are mode-specific screening capacities under the entered combined factors, not a complete gear-set approval.

Equations used

Angles are evaluated in radians internally. Input lengths are converted from mm to m for force and torque equations; stresses are converted from MPa to Pa; elastic moduli are converted from GPa to Pa.

d₁=mₙz₁; d₂=mₙz₂; db,j=dj cos α; da,j=dj+2mₙ(1+xj)

q=2(x₁+x₂)tan(α)/(z₁+z₂)+tan(α)−α; αw=55200q³−8613q²+632.663q+12.308 [deg]

a=(d₁+d₂)cos(α)/(2cos(αw)); dw,j=2zj a/(z₁+z₂)

εα={0.5[√(da,1²−db,1²)+√(da,2²−db,2²)]−a sin αw}/(πmₙ cos α)

Contact capacity:

ZH=√[2/(cos²α tan αw)]; ZE=√{[1/(0.455/E₁+0.455/E₂)]/(2π)}; Zε=√[(4−εα)/3]

σHP=σHlimKσ,H; Ft,H=[σHP/(KH ZH ZE Zε)]²[u/(u+1)]bd₁; u=max(z₂/z₁,z₁/z₂)

Tooth-root capacity: YFa,j and YSa,j are piecewise-linear tooth-count/profile-shift interpolations over 12≤z<400 and 0≤x≤0.5.

Yε=0.25+0.75/εα; σFP=σFlimKσ,F; Ft,Fj=σFlim b mₙ Kσ,F/(YFa,j YSa,j Yε KF)

Contact: Tmax,1=Ft,H dw,1/2

Tooth root: Tmax,1=Ft,F1 dw,1/2; Ft,governing=min(Ft,F1,Ft,F2)

Equation intermediates: q is the dimensionless involute target used by the working-angle polynomial; u is the dimensionless absolute gear ratio (always at least 1); E′ is the reduced elastic modulus in Pa; ZH is the dimensionless contact-zone geometry factor; ZE is the elastic coefficient in √Pa; Zε is the dimensionless contact-ratio factor; YFa,j is the dimensionless tooth form factor for member j from the tooth-count/profile-shift interpolation; YSa,j is the dimensionless root stress-correction factor for member j from the same interpolation domain; Yε is the dimensionless bending contact-ratio factor; σHP is the permissible contact stress in Pa; and σFP is the permissible tooth-root stress in Pa.

Definitions and signs: z is positive tooth count; x is nonnegative profile shift; E is Young’s modulus; mₙ is normal module; α and αw are reference and working pressure angles; b is positive face width; d, db, da, and dw are reference, base, tip, and working diameters; εα is dimensionless transverse contact ratio; σHlim and σFlim are positive material stress limits; Kσ,H and Kσ,F are positive combined permissible-stress multipliers; KH is the positive square-root contact load multiplier; KF is the positive bending load multiplier; Ft is a positive transmitted tangential-force magnitude; Tmax,1 is positive pinion torque magnitude.

Theory and method

This calculator implements a compact spur-gear screening path aligned with ISO 6336-2 surface durability and ISO 6336-3 tooth-root strength concepts. It combines involute geometry with empirical geometry/stress factors. The entered combined factors intentionally remain user responsibilities: contact allowable factors may include life, lubricant, speed, roughness, work-hardening, size, and safety terms; bending allowable factors may include reference-test, life, notch sensitivity, roughness, size, and safety terms. Load factors account for application, dynamics, transverse distribution, and face distribution.

Assumptions are external parallel-axis involute spur gears, zero helix angle, positive nonnegative profile shifts in the tabulated domain, steady tangential loading, full usable face width, and independently valid material/factor inputs. The working-angle polynomial is documented only for 0.014904≤q≤0.053751; outside that interval the calculator warns rather than silently certifying the result. Tooth counts at 400 and above are excluded because the underlying interpolation endpoint does not provide a reliable second profile-shift branch.

References: ISO 6336-1, calculation principles and general influence factors; ISO 6336-2, surface durability (pitting); ISO 6336-3, tooth bending strength. Use the current editions and licensed standard text for a final rating.

Continue in TriboSolver to refine contact, load-sharing, material, and lubrication assumptions when the workflow needs numerical simulation or an independent check.