ISO 6336 vs AGMA 2001-D04: Por que a Mesma Engrenagem Retorna Fatores de Segurança Diferentes

A Comparação que Todo Engenheiro Faz e Nunca Confia Integralmente

Considere um par de engrenagens. Um determinado torque. Faça o cálculo conforme a ISO 6336-2:2019. Em seguida, aplique a geometria e o carregamento idênticos conforme a ANSI/AGMA 2001-D04. Os fatores de segurança não coincidem. Não apenas aproximadamente — a diferença pode atingir dois dígitos percentuais, em qualquer direção, dependendo do elemento do par que está sendo verificado e, em alguns projetos, uma norma pode indicar aprovação enquanto a outra indica reprovação.

A reação usual é tratar isso como um erro: uma consulta incorreta em uma tabela, uma conversão de unidades não realizada ou um grau de qualidade interpretado de forma equivocada. Na maioria das vezes, não é nada disso. As duas normas são sistemas de classificação desenvolvidos de forma independente, construídos a partir de diferentes populações de ensaios de referência, diferentes vidas de referência, diferentes modelos de carga dinâmica e diferentes convenções quanto à localização na malha de engrenamento onde se considera que ocorre a tensão “crítica”. Um cálculo executado corretamente conforme a ISO e um cálculo executado corretamente conforme a AGMA, para a mesma engrenagem, não devem necessariamente convergir. São dois sistemas de medição distintos aplicados ao mesmo componente físico.

Este artigo não procura reconciliar os dois métodos em um único número. Ele identifica os pontos específicos e quantificáveis em que eles divergem, quantifica cada um deles e, em seguida, dimensiona um par de engrenagens real — o mesmo par de engrenagens cilíndricas de dentes retos apresentado em Resistência ao Pitting conforme a ISO 6336: O Guia Completo do Cálculo de $S_H$ — conforme as duas normas, lado a lado. Nos casos em que um valor não pôde ser verificado independentemente no texto primário da norma, isso é declarado explicitamente, em vez de ser apresentado como um fato.

Declaração do contexto normativo para este artigo: ISO 6336-2:2019, Método B, engrenagens cilíndricas externas de dentes retos, lubrificadas a óleo | ANSI/AGMA 2001-D04, Fatores Fundamentais de Classificação e Métodos de Cálculo para Dentes de Engrenagens Cilíndricas de Dentes Retos e Helicoidais. A AGMA 2101-D04 é a edição métrica da mesma norma; as fórmulas de tensão e de vida abaixo são apresentadas na forma SI, e o único subpasso empírico que pôde ser verificado independentemente apenas em unidades imperiais (as constantes de alinhamento de $K_m$) é identificado no ponto em que ocorre.

O que “A Mesma Engrenagem” Realmente Significa — e Onde Essa Equivalência Deixa de Ser Válida

A geometria e o torque aplicado são transferidos entre as normas sem ambiguidade: $m_n$, $z_1$, $z_2$, $\beta$, $b$, $T_1$, $n_1$ representam a mesma grandeza física em ambos os documentos. Tudo o que vem depois da geometria, porém, não.

“Aço cementado, qualidade MQ” (ISO) e “aço cementado e endurecido, Grau 2” (AGMA) descrevem materiais metalurgicamente próximos — ambos especificam faixas de dureza superficial, requisitos de limpeza do núcleo e controles de profundidade de camada — mas não constituem o mesmo objeto normativo. Eles derivam de diferentes engrenagens de ensaio de referência, diferentes populações estatísticas e, em pelo menos uma dimensão que é mais relevante do que qualquer um dos coeficientes individuais: um ponto diferente da curva S-N é definido como a resistência nominal do material.

Todos os artigos sobre a ISO 6336 neste site têm repetido uma regra: todos os fatores de um cálculo devem pertencer ao mesmo objeto de contexto normativo, e esse contexto deve ser declarado antes da primeira equação. Este artigo acrescenta o corolário que decorre diretamente dessa regra — os fatores ISO e AGMA são dois objetos de contexto normativo distintos que, por coincidência, utilizam letras gregas e romanas visualmente semelhantes. $Z_E$ e $C_p$ calculam a mesma grandeza física associada à conformidade elástica; $S_H$ representa algo estruturalmente semelhante em ambas; porém, no momento em que um número de uma cadeia de cálculo é substituído na outra, o resultado deixa de pertencer a qualquer uma das duas normas. O cálculo não sinalizará isso como inválido.

The Structural Map

Sixteen rows. Only the elastic coefficient starts from the same formula with the same physical derivation — and even that one does not land on the same number once each standard’s own tabulated material constants are substituted in (see below). The safety-factor row agrees only in the abstract: both standards define $S_H$ as a stress ratio rather than a load ratio, but the terms populating that ratio are computed by none of the same rules. Everything else either uses a different reference basis, a different functional form, or exists in one standard and not the other.

Why even the one shared formula gives two numbers. $Z_E$ and $C_p$ are the same Hertzian elastic-compliance expression, $\sqrt{1/\left[\pi\left((1-\nu_1^2)/E_1+(1-\nu_2^2)/E_2\right)\right]}$, in both standards. For steel against steel, ISO 6336-2:2019’s own tabulated constant is $Z_E=189.8\ \sqrt{\text{N/mm}^2}$ — reproducible from $E=206{,}000$ MPa, $\nu=0.3$. AGMA’s tabulated constant for the same material pair is $C_p=2{,}300\ \sqrt{\text{psi}} \approx 191\ \sqrt{\text{N/mm}^2}$ — reproducible from $E\approx30\times10^6$ psi ($\approx206{,}800$ MPa), the same $\nu=0.3$. Poisson’s ratio matches exactly; the assumed steel modulus differs by roughly 0.4%, and that alone is enough to separate $189.8$ from $191$. Nothing here is a mistake in either standard — it is two independent reference tables rounding the same physical constant slightly differently — but it means that even the single row of this table with an identical formula does not hand two engineers the identical number to start from.

Root Cause 1: The Reference Life Is Not the Same Number of Cycles

This is one of the most reliably quantifiable sources of divergence — both standards state their reference cycle count in plain language, so unlike most of the causes below, this one requires no inference — and it is almost never stated plainly in either standard’s own text.

ISO 6336-5:2016 defines $\sigma_{H\lim}$ — the tabulated allowable contact stress — at the reference endurance $N_{ref} = 5\times10^7$ cycles. $Z_{NT} = 1.0$ at exactly that point.

ANSI/AGMA 2001-D04 states directly, in clause 16, that its tabulated allowable stress numbers $s_{ac}$ and $s_{at}$ assume a unity overload factor, ten million load cycles applied in a single direction, and 99 percent reliability. $Z_N = 1.0$ at $N = 10^7$ cycles — one-fifth of the ISO reference point.

Two consequences follow, and both are easy to miss:

First, the two “1.0” baselines are not the same fatigue condition. A material rated at $\sigma_{H\lim}$ (ISO) represents its capacity at $5\times10^7$ cycles; the AGMA $s_{ac}$ value for a nominally similar material represents capacity at $10^7$ cycles — a factor of five in absolute cycle count, roughly $0.7$ of a decade on the log-$N$ axis the S-N curve is actually drawn against. Reading the two raw table numbers as directly comparable material properties, before either life factor is even applied, treats two points on the same fatigue curve, seven-tenths of a decade apart, as though they were the same point.

Second, the shape of the life-factor curve past its own reference point differs by material class in each standard, and by design intent. ISO’s $Z_{NT}$ (documented in the $S_H$ walkthrough) is piecewise: static/low-cycle, limited-life, reference, and long-life regimes, with case-hardened and nitrided steel explicitly dropping below 1.0 beyond $N_{ref}$ because — per ISO’s own position — these materials have no true endurance limit. AGMA’s $Z_N$ and $Y_N$ are continuous power-law curve fits, $Z_N = \alpha N^{-\beta}$, drawn from a family of curves selected by material class and hardness band, with the standard’s own figure explicitly marking a shaded judgment zone — spanning, among other regions, the long-life range this article’s worked example operates in ($N \geq 5\times10^7$). Inside that zone, the standard names seven separate considerations bearing on which curve to pick — among them lubrication regime, the failure criterion adopted, required smoothness of operation, pitch-line velocity, and material cleanliness, ductility, and residual stress — a list of engineering judgment calls, not a lookup table. ISO’s long-life treatment is more prescriptive about which curve applies to which material; AGMA is explicit that, past its own reference point, the curve choice is partly the engineer’s to make.

Neither approach is more rigorous than the other. They are simply not the same function of $N$, anchored at different points.

Root Cause 2: Two Different Physical Models Hide Behind the Same Symbol $K_v$

ISO 6336-1:2019’s dynamic factor model (documented in the $S_H$ walkthrough) requires pitch-line velocity, an ISO 1328-1 accuracy grade or measured base-pitch deviation $f_{pb}$, and — critically — a resonance ratio $N = n_1/n_{E1}$ relating the operating speed to the gear pair’s own natural mesh frequency. It is a physically-grounded transmission-error excitation model.

AGMA 2001-D04 Clause 8 (verified directly against the standard text and cross-checked against the worked examples in Budynas & Nisbett, Shigley’s Mechanical Engineering Design) computes $K_v$ from a purely empirical curve fit against a transmission accuracy level number $A_v$ (range 6–12, lower is more accurate):

$$K_v = \left(\frac{A + \sqrt{200,v}}{A}\right)^{B}, \qquad B = 0.25(12 – A_v)^{2/3}, \qquad A = 50 + 56(1-B)$$

with $v$ in m/s. This curve is fitted to empirical gear-noise and failure data across accuracy classes. It contains no resonance term. AGMA’s own commentary in Clause 8.2 is explicit about this: $K_v$ “does not apply to resonance,” and gear-pair, gear-blank, and system resonance are each called out as conditions the factor does not cover and that require separate dynamic analysis.

The practical result: for the same gear at the same pitch-line velocity, comparing an ISO quality grade to an AGMA $A_v$ number as if the labels transfer directly produces two structurally different $K_v$ values, because the underlying physical models are different, not because one grade table is more conservative than the other. There is no certified numerical equivalence between ISO 1328 quality grades and AGMA transmission accuracy levels $A_v$ — practitioners commonly carry the grade number across (treating, say, ISO Quality 7 as $A_v = 7$) as a working approximation, and that is the assumption used in the worked example below. It should be understood as exactly that: a practical approximation, not a normative crosswalk.

Root Cause 3: AGMA Rates One Stress Point. ISO Rates Two.

This is one of the least obvious structural gaps in the pitting-resistance chain, and it is rarely stated outright.

ISO 6336-2:2019 computes separate determinant contact stresses for pinion and wheel, $\sigma_{H1}$ and $\sigma_{H2}$, through the factors $Z_B$ (pinion) and $Z_D$ (wheel). These shift the stress calculation from the pitch point to the inner point of single-tooth contact (IPSTC) — and because the pinion and wheel geometries differ, that point, and therefore the stress, is not identical for both members.

AGMA 2001-D04’s fundamental formula computes a single contact stress number $s_c$:

$$s_c = C_p\sqrt{W_t,K_o,K_v,K_s,\frac{K_m}{d_P,F},\frac{C_f}{I}}$$

where $d_P$ is always the pinion’s operating pitch diameter and $I$ is a single geometry factor for the pair, derived — per AGMA 908-B89 — from the curvature radii at the pitch point with a gear-ratio correction $m_G/(m_G+1)$, not from a per-member single-pair-contact shift. Physically this is defensible: Hertzian contact pressure is a mutual quantity, equal in magnitude on both flanks at any given instant of contact, by Newton’s third law. What it does not capture is ISO’s refinement that the pinion and wheel reach their own worst-case point — the single-tooth-contact point — at different locations along the line of action, because their addendum contact ratios differ. AGMA’s allowable side then diverges between members (different $s_{ac}$, $Z_N$, $C_H$ for pinion vs. wheel), but the applied stress side does not distinguish them. ISO’s applied stress diverges between members as well as the allowable side.

The consequence shows up directly in the worked example below: AGMA and ISO do not just disagree on the magnitude of $S_H$ for a given member — they disagree on how much of that number’s variation comes from the load side versus the material side, because they’ve drawn the boundary between those two categories in different places.

Root Cause 4: The Hardness Ratio Factor Doesn’t Depend on the Same Things

ISO’s $Z_W$ (work-hardening factor, documented in the $S_H$ walkthrough) is a function of wheel Brinell hardness alone — $Z_W = 1.2 – (HB-130)/1700$ over the applicable range, per the 2006-edition clause 13.2.1.2 form; the walkthrough already flags that the 2019 edition’s constants for the 300–400 HB band were not independently re-verified there — and applies only when the pinion is surface-hardened and the wheel is through-hardened. Edition question aside, the structural point holds regardless of which edition’s constants are used: the factor carries no gear-ratio dependence.

AGMA’s $C_H$ (Clause 14) has two separate formula branches, verified directly against the primary standard text:

Through-hardened pinion and wheel ($1.2 \le HB_P/HB_G \le 1.7$): $$C_H = 1.0 + A(m_G – 1.0), \qquad A = 8.98\times10^{-3}\frac{HB_P}{HB_G} – 8.29\times10^{-3}$$

Surface-hardened pinion, through-hardened wheel (pinion $\ge 48$ HRC, wheel 180–400 HB): $$C_H = 1.0 + B(450 – HB_G), \qquad B = 0.00075,e^{-0.0112 f_P}$$

where $f_P$ is pinion surface finish in microinches $R_a$.

The first branch — the one covering the more common through-hardened/through-hardened pairing — is explicitly gear-ratio-dependent through $m_G$. ISO’s $Z_W$ never is. Two gear pairs with identical wheel hardness but different gear ratios receive the same $Z_W$ under ISO and different $C_H$ under AGMA. Neither factor is wrong; they encode different empirical relationships derived from different test populations, and a design near the ratio boundaries of either formula’s validity range will show measurably different sensitivity to gear ratio depending on which standard is governing.

Root Cause 5: Explicit Knobs vs. Implicit Judgment

AGMA 2001-D04 provides an explicit reliability factor $K_R$ (Clause 18), log-linear in $\ln(1-R)$, letting the engineer dial the target reliability directly — $K_R = 1.0$ at the standard’s own 99% baseline, rising to 1.50 at $R=0.9999$, falling to 0.70 at $R=0.50$. It also provides an explicit temperature factor $K_T$ (Clause 19), unity for oil or gear-blank temperatures up to 250°F (≈121°C), greater than unity above that point.

ISO 6336-2:2019’s $S_H$ chain contains no explicit temperature factor — the eighteen-factor inventory established in the $S_H$ walkthrough has no $K_T$-equivalent term. Thermal effects enter only implicitly, through the temperature-dependence of the operating oil viscosity used to derive $Z_L$. There is no reliability factor either: ISO leaves the required safety margin, $S_{H,\min}$, to be specified by the application standard, the purchase contract, or engineering judgement — the standard supplies the calculation method, not the acceptance criterion.

This is a genuine methodological difference, not a computational one. Two engineers rating the same elevated-temperature application, one under each standard, are not applying two versions of the same correction — one of them is applying an explicit multiplier the other standard’s $S_H$ formula has no place for.

Root Cause 6: Do the Material Tables Even Agree?

This is the point in the comparison where the honest answer is partially verified, and it is stated that way deliberately rather than smoothed over.

Case-hardened / carburized steel — well-corroborated agreement. ISO 6336-5’s $\sigma_{H\lim}$ for case-hardened steel (Eh, MQ quality) is 1,500–1,650 MPa, per the range already published on this site. AGMA’s carburized-and-hardened Grade 2 $s_{ac} = 225{,}000$ psi converts to $1{,}551$ MPa — and that exact figure, in both units, is independently reproduced in a second published source (a bevel-gear rating comparison citing the same AGMA carburized Grade 2 value; AGMA’s bevel and cylindrical standards draw on the same underlying material stress-number tables). That figure sits comfortably inside the ISO band. For the dominant premium gear material — carburized case-hardened steel — the two standards’ raw material data are close.

Through-hardened steel — not independently verified to the same standard. AGMA’s through-hardened $s_{ac}$ formula, verified directly against primary standard text and cross-checked against Shigley’s independent reproduction, gives for Grade 2 steel: $$s_{ac} = 349,HB + 34{,}300 \text{ psi}$$ At 300 HB: $s_{ac} = 139{,}000$ psi $= 958.3$ MPa. The $\sigma_{H\lim}$ value used for the through-hardened wheel in the original ISO worked example (≈600 MPa) was itself stated there as an approximate illustrative figure rather than a value read directly from the ISO 6336-5 curve. This specific comparison — AGMA’s formula-derived through-hardened figure against a precise ISO 6336-5 table lookup at the same hardness — has not been independently verified here and should be checked directly against ISO 6336-5:2016 before being treated as a normative conclusion. It is flagged rather than asserted, consistent with the standing rule on this site that unverifiable claims are declared, not presented as fact.

The Shared Pitfall: $S_H$ Is a Stress Ratio in Both Standards

This is not a divergence between the standards — it is a mistake available in both of them, worth stating precisely because it compounds with everything above.

Contact stress scales with the square root of load in both models (Hertzian contact theory is shared physics, not a normative choice). ISO defines $S_H = \sigma_{HP}/\sigma_H$, a stress ratio. AGMA defines $S_H = \dfrac{s_{ac}Z_NC_H/(K_TK_R)}{s_c}$, also a stress ratio — not a load ratio, in either standard. Comparing $S_H$ directly against a bending safety factor ($S_F$ or ISO’s $S_F$), which is linear with load, without squaring $S_H$ first, misidentifies which failure mode is closer to the design boundary. Budynas & Nisbett state this caution explicitly in their AGMA treatment: compare $S_F$ against $S_H^2$ (or $S_H^3$ for crowned, point-contact gears), never $S_F$ against $S_H$ directly. The same correction applies to ISO’s $S_H$ for exactly the same physical reason. This has nothing to do with which standard is governing — it is a property of Hertzian contact stress itself, and it is worth stating here because a design compared incorrectly this way can appear to have its threat concentrated in the wrong failure mode, under either standard.

Same Gear, Two Verdicts

The gear pair is the one already published on this site: $m_n = 2.5$ mm, $z_1=20$, $z_2=40$, $\beta=0°$, $\alpha_n=20°$, $x_1=x_2=0$, $b=25$ mm, $T_1 = 80$ N·m, $n_1 = 1{,}500$ rpm. Pinion: case-hardened Eh, MQ/Grade 2 quality. Wheel: through-hardened steel, 300 HB, Grade 2. ISO Quality grade 7. $K_A = 1.25$. Design life $N_L = 10^8$ cycles.

ISO 6336-2:2019 result (from the published walkthrough)

ANSI/AGMA 2001-D04 result (computed here for the identical gear and load)

Assumptions made explicit: $A_v = 7$ (numerically mirrors ISO Quality 7 — not a certified crosswalk, see Root Cause 2); $K_o = 1.25$ (assumed numerically equal to $K_A$); $K_s = 1.0$, $C_f = 1.0$ (AGMA’s own recommended defaults absent detailed data); straddle-mounted, uncrowned teeth, commercial-enclosed-gear-unit alignment class for $K_m$ — for this last group, $A$, $B$, $C$ in $C_{ma}$ and the constant in $C_{pf}$ are only independently verified here in their imperial-unit form, so $F$ and $d_P$ are converted to inches for that specific sub-step before feeding the resulting dimensionless $K_m$ back into the SI stress formula below; pinion surface finish $f_P = 16\ \mu\text{in } R_a$ for $C_H$, chosen as the finest of the three curves AGMA tabulates in Figure 3, representing a ground case-hardened flank; stress-cycle curve $Z_N = 1.4488,N^{-0.023}$ applied to both members (the through-hardened curve, validated against a published AGMA worked example; its use for the case-hardened pinion here is an approximation pending direct verification against the standard’s full $Z_N$ figure); Grade 2 material documentation level assumed for both members, for consistency with the “MQ” assumption on the ISO side.

$$K_v = \left(\frac{65.06+\sqrt{200(3.93)}}{65.06}\right)^{0.731} = 1.30 \qquad I = \frac{\cos20°\sin20°}{2}\cdot\frac{2}{3} = 0.1071 \qquad K_m = C_{mf} = 1.167$$

$$s_c = 191\sqrt{3200(1.25)(1.30)(1.0)\cdot\frac{1.167}{50\times25}\cdot\frac{1.0}{0.1071}} = 1{,}286\text{ MPa}$$

This is a single shared value — AGMA’s fundamental formula does not compute $\sigma_{H1}$ and $\sigma_{H2}$ separately the way ISO does (Root Cause 3).

The comparison

Both standards agree on the qualitative verdict at $S_{H,\min}=1.0$: the pinion passes, the wheel does not. They disagree sharply on the margin. Under ISO, the pinion carries 34.4% more capacity than required; under AGMA, only 14.4% more — a pinion design that looks comfortably safe under one standard and marginal under the other. Under ISO, the wheel is deficient by 37.1% ($S_H=0.629$); under AGMA, by 21.4% ($S_H=0.786$) — a 25% relative difference in how severe the same shortfall appears. Set the required $S_{H,\min}$ anywhere in the window between those two numbers — not an exotic choice; ISO 6336-2:2019 itself permits $S_{H,\min}$ below 1.0 for some large-module, low-hardness industrial gears, as the $S_H$ walkthrough documents — and this exact wheel, on this exact gear pair, fails under ISO and passes under AGMA. That is not a hypothetical extrapolation; it falls directly out of the two numbers already computed above. Notice, too, that the direction reverses between members: AGMA is more conservative than ISO for the pinion and less conservative for the wheel, on the same gear pair, in the same calculation. There is no single “AGMA runs hotter” or “ISO runs colder” rule to extract from this. The divergence is member-specific and factor-specific, which is exactly what the structural map above predicts and exactly why a blanket correction factor between the two standards does not exist.

So Which One Is Right?

Neither. That question assumes the two standards are estimating the same underlying quantity with different error, like two thermometers reading the same room. They are not. They are two different, internally self-consistent rating conventions — different reference test populations, different reference lives, different treatment of resonance, reliability, and temperature — that happen to converge on a broadly similar physical picture of gear tooth pitting without agreeing on where to draw most of the intermediate boundaries.

The engineering answer is procedural, not numerical: use the standard the application, the customer contract, or the governing regulation specifies. Run its full factor chain, from geometry through to the reported $S_H$, without borrowing a single coefficient from the other standard’s tables — the normative context rule from the first article on this site applies here without modification. If a design must be shown compliant to both — common in export or dual-market equipment — run both chains completely and independently, and report both results as what they are: two separate certifications, not two measurements of one number.

Qevork implements ISO 6336-2:2019 and ANSI/AGMA 2001-D04 as fully isolated normative context objects. Coefficients, life-factor curves, and safety-factor definitions are never shared or interpolated across standards, and every AGMA comparative report states explicitly which factor tables, quality-grade assumptions, and material grade level were used — the same assumptions this article had to declare by hand. Entre na lista de acesso antecipado para ser notificado no lançamento.

Entre na lista de acesso antecipado

Referências normativas:

• ISO 6336-1:2019 — Princípios básicos, introdução e fatores gerais de influência
• ISO 6336-2:2019 — Calculation of surface durability (pitting)
• ISO 6336-5:2016 — Resistência e qualidade dos materiais
• ANSI/AGMA 2001-D04 — Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth
• ANSI/AGMA 2101-D04 — Metric edition of ANSI/AGMA 2001-D04
• AGMA 908-B89 — Geometry Factors for Determining the Pitting Resistance and Bending Strength for Spur, Helical and Herringbone Gear Teeth
• Budynas, R. G. & Nisbett, J. K., Shigley’s Mechanical Engineering Design, 8th ed., Ch. 14 — used here to cross-verify AGMA 2001-D04 formula application and worked-example arithmetic

Tags: ISO 6336, AGMA 2001-D04, S_H, safety factor, pitting, dynamic factor, stress cycle factor, hardness ratio factor, spur gears, cylindrical gears