Cylindrical Gears Calculator — Tooth Root Bending & Hertz Contact Stress (ISO 6336 / AGMA 2001)

Applied in full: the form and stress-correction factors YFa and YSa from the ISO 6336-3 §6.4–§6.6 root-fillet geometry, the helix factors Yβ and Zβ, the contact-ratio factors Yε and Zε including the partial-overlap blend, the single-pair tooth-contact factors ZB and ZD, the zone factor ZH, the size factors YX and ZX, the rim factor YB from your rim thickness, the lubricant, velocity and roughness factors ZL·ZV·ZR from your oil viscosity and flank roughness, the application factor KA, the dynamic factor KV by DIN 3990-1 Method C, the face-load factors KHβ and KFβ = KHβ^NF, and the life factors Y_NT and Z_NT. Simplified and stated as such everywhere: the transverse load factor KHα = KFα is a fixed 1.10 placeholder rather than the ISO 6336-1 §8.3.4 expression (which grows for lightly loaded meshes); KHβ follows the AGMA commercial-enclosed-unit form and does not vary with the ISO accuracy grade, though you can override it; the work-hardening factor ZW is held at 1.0, which is the conservative direction; the elasticity factor ZE assumes a steel pair, which overstates the contact stress by about 9 percent for the ductile-iron option; and the tool performs no scuffing check (ISO/TR 13989) and no pointed-tip check. Every one of these limits is printed in the PDF report and returned by the API.

Yes. Leave the rim thickness at zero for a solid disc and the rim factor YB stays at 1.0. Enter the rim thickness below the tooth root and the calculator computes the backup ratio mB = sR/hT and applies ISO 6336-3 §7: YB = 1 for mB at or above 1.2, and YB = 1.6·ln(2.242/mB) below it, which raises the root stress and lowers the bending safety factor by the same factor. Below mB 0.5 the standard gives no value, so the calculator refuses to rate the gear rather than extrapolating — that case needs an FEA of the rim and web.

The 2026-08-05 revision closed four gaps found by an internal audit, all in the conservative direction. The transverse load factor no longer steps down from 1.10 to 1.05 the moment a helix angle is entered (the step had the wrong sign — ISO 6336-1 makes this factor grow with the total contact ratio, not shrink). The permissible root stress now carries the ISO 6336-3 size factor YX, which falls above a 5 mm module. The permissible contact stress now carries the ISO 6336-2 lubricant, velocity and roughness factors ZL·ZV·ZR. And the size factor is now applied to the safety factor itself rather than only to the displayed allowable stress. For the shipped example the effect is about 4.6 percent on every safety factor; it is larger for big-module, rough-flank or slow-running gears. No design gets a better answer than it did before — that was verified across 16,800 configurations.

Tooth-root bending stress is evaluated to ISO 6336-3:2006 Method B (form factor YFa, stress-correction factor YSa, helix factor Yβ) and the contact (pitting) stress to ISO 6336-2:2006 Method B (Hertz formula with zone, elasticity, contact-ratio and single-pair-contact factors). The dynamic load factor KV uses the DIN 3990 / ISO 6336 simplified Method C closed-form, and the face-load distribution factor KHβ follows AGMA 2001-D04 (Shigley Eq. 14-30) for a commercial enclosed unit — so the ISO accuracy grade drives KV rather than KHβ, and you can override KHβ with your own ISO 6336-1 Method C value. The transverse load factor KHα = KFα is a fixed 1.10 placeholder rather than the full ISO 6336-1 §8.3.4 expression, which can be larger for a lightly loaded or coarse-quality mesh; the tool states this on every surface, including the PDF report. Profile shift geometry follows ISO 6336-1 / DIN 3960 / ISO 21771. The full method and every scope limit are shown in the generated PDF engineering report.

Profile shift (addendum modification) moves the tool radially when cutting a gear, increasing the tooth thickness at the root and reducing undercut risk for low tooth-count pinions. The coefficients x1 (pinion) and x2 (gear) shift the pitch point relative to the reference circle, which changes the operating centre distance and operating pressure angle. The calculator solves the involute equation by Newton iteration to find the exact operating pressure angle αtw, derives the operating centre distance a_w and checks the undercut limit x_min = (z_min − z)/z_min for each member.

ISO 6336 does NOT specify minimum safety factors — ISO 6336-1 leaves them to agreement between manufacturer and purchaser. This calculator adopts the DIN 3990-11 industrial-gearbox guide values SF_min = 1.4 for tooth-root bending and SH_min = 1.2 for Hertz contact (pitting), and the verdict is the conjunction of both checks: a design passes only when BOTH factors clear their own minimum, and the governing mode named on screen is the one with the smallest margin relative to its own minimum. For critical or high-cycle applications a licensed engineer should confirm the safety factors are appropriate for the specific duty cycle and consequences of failure.

Yes — the full helical-gear analysis is included: helix angle β up to 45°, transverse module mt = mn/cos β, base helix angle βb, the helical contact-ratio factor Zε (spur, partial-overlap and full-overlap branches per ISO 6336-2), helix factor Zβ, helix angle factor Yβ for bending, and overlap ratio εβ = b·sin β/(π·mn). Profile shift coefficients x1 and x2 are applied across the full involute geometry, load-factor and stress chains.

Yes. The application factor KA is a selectable input following the ISO 6336-6 / DIN 3990-1 guide table (driving × driven machine shock character, floored at 1.0; default 1.25). For finite-life rating, enter the required number of pinion load cycles N_L and the calculator applies the ISO 6336 life factors — Y_NT for tooth-root bending (referenced to 3×10⁶ cycles) and Z_NT for pitting — selected by the material's strength class. The slower wheel is rated for its own N_L/u cycles, and leaving N_L blank keeps the conservative continuous-duty (endurance) design used by default.

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