external spur pair · reference geometry · no ISO rating

Spur-Gear Reference Geometry and Load Relation Worksheet

Calculate reference diameters, reference centre distance, ratio, angular speed, torque and tangential tooth load for one documented external spur-gear load case.

d = mzP = TωFₜ = 2T/d

Not an ISO 6336 stress or capacity calculator. No contact stress, tooth-root stress, material limit, safety factor, pitting life or acceptance decision is produced. ISO 6336 requires the applicable current parts, validated geometry, load spectrum, materials and many influence factors selected by an experienced gear designer.

Documented inputs and traceability

Controlled module m (mm)positive plain decimal; same transverse module for this spur pair

Pinion tooth count z₁positive integer; no interference conclusion is inferred

Gear tooth count z₂positive integer; external mating gear

Transmitted mechanical power P (kW)non-negative value at the pinion for the same load case

Pinion rotational speed n₁ (r/min)positive magnitude for the same load case

Calculation / model record ID

Gear-pair and drawing identifiers

Module source, method and revision

Tooth-count source and drawing revision

Axis arrangement and external-spur confirmation

Basic rack, pressure angle and profile-shift record

Operating centre distance, backlash and interference review

Power basis, load spectrum, duty and service-factor record

Speed source, direction and transient record

Materials, heat treatment, quality and manufacturing record

Lubrication, temperature, roughness and contact-pattern record

Licensed ISO 6336 parts, factors and rating record

Responsible gear engineer / reviewer

Review date

Notes and exclusionsOptional: losses, measurement uncertainty, profile modifications, overloads and omitted failure modes.

The pair is documented as parallel-axis external spur gears using the same controlled module; the entered tooth counts and module come from the cited drawings.
P and n₁ describe the same pinion load case; P is transmitted mechanical power at that shaft and no efficiency, overload, application or dynamic factor is added automatically.
a₀ is only the zero-shift reference-centre relation. Operating centre distance, profile shift, pressure angle, backlash, contact ratio, interference and contact pattern were reviewed separately.
No ISO 6336 stress, capacity, life, safety factor or acceptance verdict will be inferred from these reference and load relations.

Reference and load quantities

Reference diameters d₁ / d₂

—

Reference centre distance a₀

—

Tooth-count ratio u = z₂/z₁

—

Pinion angular speed ω₁

—

Transmitted pinion torque T₁

—

Nominal tangential tooth load Fₜ

—

Formula, units and classification

d₁ = m z₁; d₂ = m z₂ [mm]
a₀ = (d₁ + d₂)/2 [mm], reference-centre relation only
u = z₂/z₁ [1]
ω₁ = 2πn₁/60 [rad/s]
T₁ = 1000P/ω₁ [N·m], P in kW
Fₜ = 2000T₁/d₁ [N], d₁ in mm

Символ	Quantity and unit	Граница
m,z₁,z₂	controlled module in mm and integer tooth counts	not proof of standard module, compatibility, undercut or manufacturability
d₁,d₂	reference diameters, mm	not necessarily operating pitch or tip/root diameters
a₀	half-sum reference-centre relation, mm	not the approved operating centre distance when modifications apply
P,n₁	transmitted mechanical power, kW; pinion speed, r/min	same documented load case; no efficiency or service factor added
T₁,Fₜ	torque, N·m; nominal tangential load, N	not design tooth load, stress, capacity, bearing reaction or acceptance result

These are general geometry and mechanics relations, not ISO 6336 rating formulae. Exact ISO geometry, preferred module values, stress factors, permissible stresses and rating procedures require the applicable licensed current documents.

Removed unsafe rating claims

No invented ISO contact stress. The former code fixed Z_E=190 and Z_H=2.5, omitted the required geometry, material, load-distribution, dynamic and application factors, then called the result simplified ISO 6336.
No invented ISO tooth-root stress. A universal Y_F=2.5 cannot represent tooth form, stress correction, contact ratio, helix/load-distribution and other required terms.
No generic material limits or colour verdict. Hardness labels alone do not establish permissible pitting or bending stress; heat treatment, material quality, size, life, reliability and stress-cycle factors matter.
No tip diameter without a controlled tooth system. d_a=d+2m applies to a stated standard unshifted geometry, not every spur gear.
No truncated torque constant. The worksheet uses P=Tω and ω=2πn/60 directly rather than the rounded shortcut 9549P/n.
No hidden state. Defaults, presets, auto-calculation, clipboard output, generated FAQ HTML and external KaTeX were removed.

Source traceability

Claim	Классификация	Evidence
ISO 6336-1:2019 Edition 3 is current and confirmed in 2025; its public scope says the method is for experienced gear designers and does not assure an assembled drive.	Official ISO status and scope	ISO 6336-1:2019
ISO 6336-2:2019 Edition 3, corrected 2020-11, addresses surface durability and includes the influences that can be assessed quantitatively.	Official ISO status and scope	ISO 6336-2:2019
ISO 6336-3:2019 Edition 3, corrected 2020-11, specifies tooth-bending-strength calculation.	Official ISO status and scope	ISO 6336-3:2019
ISO 21771-1:2024 covers cylindrical involute-gear concepts and geometry; it is published but marked to be revised and has a replacement draft in development.	Official ISO status and scope	ISO 21771-1:2024
ISO 54:1996 Edition 2 specifies normal-module values and remains current after confirmation in 2022; this worksheet does not certify an entered value as a preferred ISO module.	Official ISO status and boundary	ISO 54:1996
For a documented standard external spur pair, KHK Table 4.1 gives d=zm and distinguishes standard from profile-shifted geometry.	Manufacturer technical reference	KHK gear dimensions
Rotational mechanical power is P=Tω.	MIT engineering tutorial	MIT motor torque/speed tutorial
Tangential tooth load is Fₜ=T/r=2T/D at the pitch/reference radius.	University mechanical-engineering material; page visually inspected	Fairfield ME312 Tooth Loads, p. 2

Accessed: 15 July 2026. No ISO clause/table-level stress implementation is claimed. Exact geometry and rating details remain NEEDS_LICENSED_SOURCE.

Reference check

For m=3 mm, z₁=20, z₂=80, P=15 kW and n₁=1500 r/min: d₁=60 mm, d₂=240 mm, a₀=150 mm, u=4, ω₁=157.079632679 rad/s, T₁=95.4929658551 N·m and Fₜ=3183.09886184 N.

Questions

Does this prove ISO 6336 capacity?

No. The worksheet deliberately produces no contact/root stress, permissible stress, safety factor, life or acceptance result.

Is a₀ the mounting centre distance?

Only for the documented zero-shift reference case when the relevant geometry conditions are satisfied. Use the controlled drawing and full geometry calculation for the operating distance.

Why is face width absent?

Face width is needed for stress rating, which this worksheet does not perform. Including it would suggest a capacity conclusion that the available inputs cannot support.