Planetary Gear Calculator — Ratio, Contact Stress & Load Sharing (ISO 6336-2)

Contact (pitting) stress is evaluated to ISO 6336-2:2019 using the ZH·ZE·Zε·Zβ surface-durability method, with KA = 1.25 and KV = 1.05 applied and the distribution factors KHβ and KHα held at 1.00, plus a K_gamma mesh load-sharing factor. Tooth-root bending is a badged Lewis ESTIMATE — there is no ISO 6336-3 rating. Kinematic ratios come from the Willis equation; AGMA 6123, the epicyclic design manual, is cited as background reading and is not an implemented rating basis. The governing standard, the three assembly checks, the methodology substitutions and every scope note are shown in the generated PDF report.

The ring-planet mesh is a concave-convex (internal) contact, which has lower curvature stress than the equivalent external pair at the same load. ISO 6336-2 handles this by replacing the (u+1)/u curvature term used for external gears with (u−1)/u for the internal mesh, and by computing the contact-ratio factor Zε from the internal tooth geometry. The calculator applies both formulae automatically based on the mesh type.

K_gamma (also written K_γ) is the mesh load factor that accounts for imperfect load sharing among the planet gears, caused by manufacturing tolerances such as pitch errors and carrier runout. Without it a 3-planet set would be assumed to carry exactly one-third of the total load per planet, which is optimistic. K_gamma raises the per-planet force above that ideal share: 1.10 for 3 planets, 1.25 for 4, 1.35 for 5, 1.45 for 6. Two honest caveats. First, ISO 6336-1 defines the symbol but does not tabulate it against planet count — these are published industry guide values, and 1.10 at three planets sits at the OPTIMISTIC (floating-sun) end, so treat it as a nominal allowance rather than a worst case; a rigidly mounted sun is usually taken nearer 1.2–1.3. Second, K_gamma/n falls monotonically across the range, so more planets always lower the per-planet force in this model — the tip-clearance check, not the load sharing, is what bounds the planet count.

Yes, for viewing. The kinematic table evaluates all six input/output/fixed permutations at once — including the carrier-fixed arrangement, which reverses the output shaft — and shows the ratio for each. The configurations you can SELECT for the stress calculation are 3K-I (ring fixed, sun input, carrier output) and 3K-II (sun fixed, ring input, carrier output); the carrier-fixed reversal is shown for comparison but is not a selectable stress case. A third selector option, Wolfrom, is offered but is a single-stage STAND-IN and NOT a Wolfrom rating: a real Wolfrom (3K) drive needs a SECOND ring gear, and its very high ratios come from two rings differing by one or two teeth. This tool models one ring, so within its own assembly rule the stand-in ratio tends to 2·z_p/z_s — at typical tooth counts it returns a ratio LOWER than the plain 3K-I value for the same gears. It is badged as illustrative in the tool; use 3K-I or 3K-II for a defensible number.

The governing, standards-cited check is surface durability (pitting) to ISO 6336-2. Tooth-root bending is reported as a Lewis ESTIMATE — sigma_F = F_t / (b · m · Y), with Y interpolated per member from the classic 14½° full-depth Lewis table, used as a deliberately conservative stand-in for 20° teeth (it runs about 10 % below the published 20° values, so the root stress comes out high) — and is clearly badged as such, because it is not the ISO 6336-3 rating. Both the sun and the planet are rated; the planet is an idler, loaded on one flank by the sun and the other by the ring, so its allowable carries the Shigley §14 fully-reversed factor of 0.70. The ring is an internal tooth, to which the Lewis external-tooth form does not apply, so it is not rated. Use the estimate to see which member is closest to its root limit, and a full ISO 6336-3 rating for final design.

The zone, elasticity and contact-ratio factors (Z_H, Z_E, Z_eps, Z_beta) are computed from your geometry. The LOAD factors are fixed rather than computed: K_A = 1.25, K_V = 1.05 and K_Hbeta = K_Halpha = 1.00. A face-load distribution factor is physically at least 1.0, so taking it as exactly 1.0 is a lower bound rather than a value, and the safety factor is also taken against the raw allowable contact stress sigma_H,lim rather than the full ISO 6336-2 permissible stress sigma_HG. Together these make the reported safety factor optimistic by roughly 15–20 % for a typical industrial set. The tool states this on the result and in the PDF report; treat a design near the 1.2 acceptance line as unverified until it has been through a full ISO 6336 rating.

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