ISO and AGMA: a controlled comparison

Running two standards is easy. Comparing them meaningfully requires more care: keep the physical pair unchanged, record what each method assumes, and separate differences in calculated stress from differences in permissible material strength.

Neither method is a universal ground truth for the other. This chapter compares the implemented methods, including their current defaults and limits, rather than claiming equivalence of the standards in every application.

Start with the same physical problem

The reference is the pair of Quick start:

Input	Value
Teeth	22 / 40, external spur
Normal module and pressure angle	2.5 mm, 20°
Face width	34 mm on both members
Profile shifts	0 / 0
Pinion speed and power	1450 rpm, 40 kW
Required life	10,000 h
Application/overload input	1.3
Accuracy	ISO class 6; AGMA quality estimated by the package
Material elastic properties	206,000 MPa, Poisson ratio 0.3

Both methods therefore start with the same nominal tangential force, approximately 9579 N. Both use an elasticity coefficient of approximately 189.812 \(\sqrt{\mathrm{MPa}}\). Agreement on these quantities is a useful first check, not a guarantee of equal final stress.

Similar roles do not imply identical factors

Physical role	ISO implementation	AGMA implementation	What to watch
External overload	\(K_A\)	\(K_o\)	Same supplied application-factor field in this package
Internal dynamics	\(K_v\), methods B/C or measured	\(K_v\), annex A quality/speed relation	Different methods; identical symbols do not make values interchangeable
Face load distribution	\(K_{H\beta}\), \(K_{F\beta}\)	\(K_m\)	Different empirical treatment and required inputs
Transverse sharing	\(K_{H\alpha}\), \(K_{F\alpha}\) and geometry factors	Sharing within geometry factors	Avoid double counting by importing factors from the other method
Contact geometry	\(Z_HZ_\varepsilon Z_\beta\), \(Z_B/Z_D\)	\(I\)	Different grouping, contact evaluation and overlap treatment
Root geometry	\(Y_FY_S\) and related factors	\(J\) and related factors	Critical-section construction differs
Thin rim	\(Y_B\)	\(K_B\)	Applicability and fallback assumptions must be checked
Material resistance	\(\sigma_{Hlim}\), \(\sigma_{Flim}\) and ISO adjustments	\(s_{ac}\), \(s_{at}\) and AGMA adjustments	No automatic equivalence of the stress numbers

For spur gears the normal and transverse modules coincide. For helicals the ISO bending expression uses \(m_n\), while this AGMA implementation uses \(m_t\) together with its own geometry factor. Substituting just one of those quantities would create a hybrid method, not a comparison.

Results for the reference pair

Quantity	ISO	AGMA
Dynamic factor	1.0284	1.1239
Contact face-distribution factor	1.0869	1.1931
Contact stress, pinion (MPa)	1492.2	1845.6
Contact stress, wheel (MPa)	1424.3	1845.6
Root stress, pinion (MPa)	456.9	509.3
Root stress, wheel (MPa)	438.2	462.1

AGMA returns a common contact stress with member-specific allowable stresses when material data are supplied. ISO additionally reports different applied member stresses through \(Z_B\) and \(Z_D\). The repeated AGMA value in the table is intentional, not an omitted wheel calculation.

Power varies; geometry and speed remain fixed. All applicable factors are recalculated at every point. This is a comparison of ratings, not an experimental validation or a ranking of accuracy.

The AGMA contact result is about 24% above the ISO pinion result for this case. The dynamic and face-distribution factors contribute, but they do not explain the entire difference: contact geometry and sharing are also grouped and evaluated differently. Do not generalize that percentage to other tooth counts, shifts, overlaps or accuracy classes.

The nominal Hertz peak at C is about 1334 MPa, with no rating load amplification. It is a third reference state, not a decisive arbiter between the two rated values. To compare a FEM solution, match load, position, material and load-sharing assumptions first; see Contact mechanics: from force to surface fatigue and Contact analysis.

Why the safety-factor comparison is deliberately incomplete

The reference material supplies ISO contact and bending limits, giving ISO pinion factors of approximately \(S_H=0.85\) and \(S_F=1.76\). It does not supply independently established AGMA \(s_{ac}\) and \(s_{at}\). AGMA safety-factor fields are therefore None.

Copying the ISO values into the AGMA fields would produce numbers but not a scientifically justified comparison. A proper capacity comparison needs material stress numbers with traceable quality, heat treatment, reference life and reliability for each method. The same alloy name and hardness alone are insufficient evidence of that equivalence.

Reproduce the comparison

Continue the quick-start definitions:

from gearbox.standards import iso6336, agma2101

iso_contact = iso6336.calculate_pitting(transmission)
agma_contact = agma2101.calculate_pitting(transmission)
iso_root = iso6336.calculate_bending(transmission)
agma_root = agma2101.calculate_bending(transmission)

print(iso_contact.contact_stress_pinion, agma_contact.contact_stress)
print(iso_root.tooth_root_stress_pinion, agma_root.bending_stress_pinion)
assert agma_contact.safety_factor_pinion is None  # AGMA material stress numbers were not supplied

docs/figures/contact_theory_figures.py regenerates the power sweep and prints the underlying results. For a report, also record package version, input models, quality assumptions, supported methods and applicable limitations; a screenshot of a curve is not a reproducible specification.

Choosing a method

Use the standard required by your contractual or regulatory context. Use the other as a diagnostic cross-check, not to select whichever safety factor is larger. Where results diverge substantially, inspect the common load first, then dynamics, distribution, geometry and finally material resistance. That order turns disagreement into an engineering question you can investigate.