Spiral bevel gears carry the final reduction in turboprop engines, helicopter tail drives, mill drives and marine transmissions, and their teeth most often fail first at the root fillet, where a bending fatigue crack initiates and eventually separates a tooth. Sizing a new pair therefore reduces to a single question: is the calculated root stress below the allowable one? Three documents answer that question in current practice — ISO 10300-3, AGMA 2003-B97, and the HB/Z 89 series that the Ministry of Aviation Industry of China issued in 1985 as a modified derivative of ISO and that Chinese aero-engine practice still applies. All three descend from the Lewis cantilever beam model, all three end in the same inequality, and yet for one and the same gear pair they return root stresses that differ by more than a factor of three, and safety factors whose ranking reverses as tooth count changes.
The disagreement visible in the literature is not random, but it is unusually easy to misread. Studies of the ISO tooth form factor have focused on the convergence of its iterative construction. Direct comparisons of ISO and AGMA have found ISO above AGMA when the load is placed at the tooth tip and nearly equal results at single-pair contact, while finite element checks have variously described AGMA as conservative, ISO as overestimating and AGMA as underestimating the maximum root stress. Comparisons of computed safety factors have reached opposite conclusions for the same two standards, and a HB–ISO comparison attributed the whole stress gap to the dynamic factor alone. Each of these results is correct at the point of the calculation chain it probes; none of them characterises the standards globally.
That chain has five links: the acceptance criterion and its reliability target, the reference section and load point, the stress equation, the correction-factor inventory, and the numerical evaluation of each factor. The sections below take the links in order and then quantify their combined effect on a representative gear pair, on a seven-gear sweep, and on the sensitivity of the result to tooth count, module, spiral angle, pressure angle, face width and speed.
Two acceptance criteria and three reliability targets
All three standards accept a design either by comparing stresses, σF ≤ σFP, or by comparing a computed safety factor with a required minimum, SF ≥ SF min. The second form conceals a difference in bookkeeping. HB and ISO 10300 prescribe a minimum safety factor directly; AGMA 2003 has no minimum-safety-factor concept and instead places a reliability factor YZ in the denominator of the allowable stress, so that a more demanding reliability target lowers the allowable rather than raising the required margin. The numeric targets are collected in Table 1.
| Standard | Criterion | Reliability class (failure probability) | Value |
|---|---|---|---|
| HB | SF ≥ SF min | ≤ 1 % | 1.00 |
| ≤ 0.1 % | 1.25 | ||
| ISO 10300 | SF ≥ SF min | general / higher / high | 1.30 |
| AGMA 2003 | YZ in allowable | ≤ 50 % | 0.70 |
| ≤ 10 % | 0.85 | ||
| ≤ 1 % | 1.00 | ||
| ≤ 0.1 % | 1.25 | ||
| ≤ 0.01 % | 1.50 |
At the 0.1 % failure probability level, HB asks for SF min = 1.25, AGMA applies YZ = 1.25 and ISO applies 1.30, so the three documents are numerically close once the different placement of the factor is accounted for. HB offers only two reliability classes and therefore little room to trade margin against weight, whereas AGMA spans five classes and is the only one of the three that lets a designer buy reliability explicitly for a commercial or an aerospace duty.
Reference geometry, dangerous section and load point
HB and ISO 10300 transform the bevel gear into a virtual cylindrical gear at the mid-face: outer-end data are converted to the mid-face, a virtual spur gear is defined there with the corresponding transverse module, virtual tooth counts and overlap ratios, and the 30° tangent construction is drawn in the normal section of that virtual tooth. The tangent fixes the critical section, from which the chordal tooth thickness SFn and the bending moment arm hFa at the tooth tip follow; the load is applied at the tip, at the load angle αFan.
AGMA 2003 keeps the outer-end parameters and works with them directly, and replaces the 30° tangent by a parabola inscribed in the tooth: the auxiliary angle is solved iteratively from the parabolic beam condition instead of being constructed geometrically, and the load is placed at the worst point of the profile rather than at the tip. The parabolic section is the more accurate representation of the fillet, so AGMA’s chordal thickness and moment arm differ slightly from those of the other two standards, and the difference propagates into the tooth form factor and the stress correction factor rather than into a separate term.
The two routes also differ in cost. The mid-face virtual-gear conversion carries more bookkeeping — transverse and normal modules, virtual tooth numbers, transverse, overlap and total contact ratios, cutter radius and mean cone distance — and is the more instructive of the two when a designer needs to know which geometric quantity drives the stress. The parabolic construction is shorter and yields a cleaner critical-section geometry.
The three stress equations
HB writes the calculated stress as a basic value multiplied by three load factors, and the allowable stress as the fatigue limit reduced by a minimum safety factor and multiplied by three correction factors:
$$\sigma_F=\sigma_{F0}\,K_A K_v K_{F\beta},\qquad \sigma_{F0}=Y_{Fa}Y_{sa}Y_{\varepsilon}Y_{\gamma}Y_i Y_{LC}Y_b\,\frac{F_{mt}}{b\,m_{mn}}$$
$$\sigma_{FP}=Y_{\theta}Y_X Y_{ST}\,\frac{\sigma_{F\lim}}{S_{F\min}}$$
ISO 10300 adds a transverse load-sharing factor to the load side and splits the allowable side into five factors:
$$\sigma_F=\sigma_{F0}\,K_A K_v K_{F\beta}K_{F\alpha},\qquad \sigma_{F0}=Y_{Fa}Y_{sa}Y_{\varepsilon}Y_{BS}Y_{LS}\,\frac{F_{mt}}{b\,m_{mn}}$$
$$\sigma_{FP}=\sigma_{F\lim}Y_{ST}Y_{NT}Y_{\delta relT}Y_{RrelT}Y_X$$
AGMA 2003 is written around the torque rather than the tangential force, uses the outer transverse diameter de1 and outer transverse module met, and concentrates most of the geometry in a single factor:
$$\sigma_F=\frac{2000\,T_1 K_A K_v Y_X K_{F\beta}}{b\,d_{e1}m_{et}Y_{\beta}Y_J}$$
$$\sigma_{FP}=\frac{\sigma_{F\lim}Y_{NT}}{S_F K_{\theta}Y_Z}$$
Here Fmt is the tangential force at the reference circle of the virtual gear, b the face width, mmn the mid-face normal module, σFlim the bending fatigue limit and T1 the pinion torque. Two structural differences matter beyond the algebra. First, the AGMA size factor YX sits in the numerator of the calculated stress while the HB and ISO size factors sit in the allowable, so its physical meaning is inverted between the documents. Second, the test-gear stress correction factor is a fixed “reasonable value” in both HB and ISO — 1.775 and 2 respectively — which by itself puts ISO’s allowable above HB’s by about 13 % for the same fatigue limit.
Factor inventory: eight, thirteen and fourteen coefficients
Counting the factors that actually enter Eqs. (1)–(6), AGMA defines eight, HB thirteen and ISO fourteen, and the way they are grouped explains most of the practical difference between the documents (Table 2).
| Influence group | HB | ISO 10300 | AGMA 2003 |
|---|---|---|---|
| Load | KA, Kv, KFβ | KA, Kv, KFβ, KFα | KA, Kv, KFβ |
| Geometry | YFa, Ysa, Yε, Yi, Yγ, YLC, Yb, YST, YX | YFa, Ysa, Yε, YBS, YLS, YST, YX | YJ, Yβ, YX |
| Material | — | YδrelT | — |
| Tooth surface condition | — | YRrelT | — |
| Service conditions | Yθ | YNT | YNT, Kθ |
Two features stand out. AGMA replaces the entire geometry block of HB and ISO — tooth form, stress correction, load sharing, contact-line length, overlap and longitudinal curvature — by the single geometric factor YJ, which is tabulated against tooth number, spiral angle and pressure angle for a given cutter geometry. Conversely, ISO is the only document that separates material notch sensitivity and root surface roughness from the geometry, and the only one that resolves the transverse distribution of load between meshing teeth through KFα and YLS.
Load-side factors
Application factor KA. The three documents define KA identically as the external overload factor and, where their tables overlap, give identical values (Table 3). HB tabulates only the 2 × 2 corner of uniform and light shock on both sides of the mesh; ISO and AGMA extend the grid to moderate and heavy shock, reaching 2.25 and above, which is why the HB table is adequate for aero-engine drives and insufficient for a crusher or a mill.
| Driver characteristic | Uniform | Light shock | Moderate shock | Heavy shock |
|---|---|---|---|---|
| Uniform | 1.00 | 1.25 | 1.50 | 1.75 or higher |
| Light shock | 1.10 | 1.35 | 1.60 | 1.85 or higher |
| Moderate shock | 1.25 | 1.50 | 1.75 | 2.00 or higher |
| Heavy shock | 1.50 | 1.75 | 2.00 | 2.25 or higher |
Dynamic factor Kv. This is the largest single source of divergence. HB uses an empirical power law on the outer pitch-line velocity ve in m/s and an accuracy-grade index μ:
$$K_v=\left(\frac{14}{85-v_e}\right)^{\mu}$$
AGMA uses a two-parameter expression driven by the transmission accuracy grade QV and the outer pitch-line velocity vet:
$$K_v=\left(\frac{A_0}{A_0+200\,v_{et}}\right)^{-B_0},\qquad B_0=0.25\,(12-Q_V)^{0.667},\qquad A_0=50+56\,(1-B_0)$$
ISO abandons the single closed form altogether. It introduces a dimensionless reference speed N that locates the operating point relative to the main resonance of the mesh, and gives four separate branches — subcritical, main resonance, intermediate and supercritical — built from the single-mesh stiffness c′, the effective base pitch deviation fpeff, the virtual face width bv, the virtual tangential force Fvmt and seven empirical influence coefficients cv1…cv7. Internal excitation from mesh stiffness variation and induced mass therefore enters the ISO dynamic factor explicitly, while in HB and AGMA it enters only through the empirical accuracy index. A further trap is that the accuracy scales run in opposite directions: a lower HB grade denotes a more accurate gear, whereas a higher AGMA QV does.
Face load distribution factor KFβ. When the contact pattern along the face is not known in advance, HB and AGMA do not separate the contact and bending versions of this factor and tabulate KFβ against mounting arrangement and load state only (Table 4). ISO computes KFβ from the contact factor and a longitudinal curvature factor,
$$K_{F\beta}=\frac{K_{H\beta}}{K_{F0}},\qquad K_{F0}=0.211\left(\frac{r_c}{R_m}\right)^{0.279}\lg\sin\beta_m+0.789$$
where rc is the cutter radius, Rm the mean cone distance and βm the mean spiral angle. For a 35° spiral angle the curvature factor is close to 0.74, so ISO’s KFβ is roughly 1.35 times its own KHβ; combined with the larger constants of the ISO contact-factor expression, this makes ISO’s KFβ clearly the largest of the three.
| Load state | Both gears simply supported | One gear simply supported | Neither simply supported |
|---|---|---|---|
| Both at full load | 1.00 | 1.00 | 1.00 |
| Both at light load | 1.05 | 1.10 | 1.25 |
| Test gear at theoretical full load | 1.20 | 1.32 | 1.50 |
Transverse load sharing factor KFα. ISO alone resolves how the total load is divided between the teeth in mesh at a given instant. The factor depends on the total overlap ratio εvγ, the pitch deviation fpt, the running-in allowance ya and the mesh stiffness cγ:
$$K_{F\alpha}=\varepsilon_{v\gamma}^{2}\left[0.9+\frac{0.4\,c_{\gamma}(f_{pt}-y_a)}{K_A K_v K_{H\beta}/b_v}\right],\qquad \varepsilon_{v\gamma}\le 2$$
$$K_{F\alpha}=0.9+\frac{0.4\sqrt{2(\varepsilon_{v\gamma}-1)}}{\varepsilon_{v\gamma}}\cdot\frac{c_{\gamma}(f_{pt}-y_a)}{K_A K_v K_{H\beta}/b_v},\qquad \varepsilon_{v\gamma}>2$$
Neither HB nor AGMA contains an equivalent term; in HB part of the effect is hidden in the load-sharing factor Yγ on the geometry side, and in AGMA it is absorbed into YJ.
Geometry-side factors
HB. The tooth form factor follows directly from the 30° tangent construction,
$$Y_{Fa}=\frac{6\,(h_{Fa}/m_{mn})\cos\alpha_{Fan}}{(S_{Fn}/m_{mn})^{2}\cos\alpha_n}$$
and the stress correction factor converts the nominal bending stress into a local fillet stress using the fillet radius of curvature ρf and the empirical constant H, equal to 0.18 for a 20° pressure angle:
$$Y_{sa}=H+\left(\frac{S_{Fn}}{h_{Fa}}\right)^{0.4}\left(\frac{S_{Fn}}{\rho_f}\right)^{0.2}$$
Four further factors describe how the load is shared and where it acts. The load-sharing factor, valid for total overlap ratios at or above 2, is
$$Y_{\gamma}=\left\{1+\left[1+2\left(1-\frac{4}{\varepsilon_{v\gamma}^{2}}\right)\right]^{1.5}\right\}^{-1}$$
while below εvγ = 2 it takes the value 1 and the inertia factor Yi = 2/εvγ takes over the penalty for running with fewer than two teeth in mesh. The load application factor Yε converts the tip-loaded tooth form and stress factors to the values at the actual point of load application, and depends only on the load application position εK: 0.17 + 0.83/εK for the pinion and 0.27 + 0.73/εK for the wheel. The longitudinal curvature factor is the reciprocal of the ISO curvature term,
$$Y_{LC}=\left[0.211\left(\frac{r_c}{R_m}\right)^{0.279}\log_{10}\sin\beta_m+0.789\right]^{-1}$$
and the root stress longitudinal distribution factor Yb, defined as the ratio of the maximum to the mean root stress, is built from the projected contact-line length over the effective face and the ratio of the load arm to the tip-to-critical-section distance; it therefore responds to spiral angle, pressure angle and face width. The size factor is 1 for outer modules up to 1.588 mm and 1.225 mt−0.25 above it, so it falls as the gear grows.
ISO 10300. The tooth form factor is again obtained from a 30° tangent, with the same definition but different starting values and iteration equations for the auxiliary angle. The stress correction factor, however, is a different function of the same two geometric quantities, with La = SFn/mmn and qs = SFn/(2ρf):
$$Y_{sa}=(1.2+0.13L_a)\,q_s^{\,1/(1.21+2.3/L_a)}$$
The load-sharing factor YLS plays the role of HB’s Yγ but is derived from the contact-line length and the peak load in the tip, mid-face and root contact ellipses, with the peak load falling off as a parabola whose exponent is 3.0 for a non-crowned tooth and 1.5 for a crowned one. It becomes unstable when the overlap ratio is very small. The helix angle factor YBS expresses the non-uniform distribution of root stress across the face through the developed face width and the projection of the mid-face contact trace, and the overlap factor is bounded below:
$$Y_{\varepsilon}=\max\left(0.25+\frac{0.75}{\varepsilon_{v\alpha}}-\varepsilon_{v\beta}\left(\frac{0.75}{\varepsilon_{v\alpha}}-0.375\right),\ 0.625\right)$$
so that it equals 0.625 whenever the overlap ratio exceeds 1 and grows only when the overlap becomes small. The size factor is material-dependent, YX = 1.03 − 0.006 mmn for hardened and nodular steels, 1.05 − 0.01 mmn for quenched, nitrided and cast steels and 1.075 − 0.015 mmn for grey cast iron, and is thus close to unity for the modules used in aerospace gearing.
AGMA 2003. The geometric factor YJ carries the tooth form factor, the load-sharing ratio, the inertia term, the ratio of the tangential radius at the load point to the pitch radius and the ratio of the transverse to the outer module, all evaluated on the outer section. Because it depends on the effective rather than the total face width, YJ decreases as the face is widened without an increase in contact length, which is the mechanism behind one of the counter-intuitive trends discussed below. The longitudinal curvature factor Yβ is numerically the same quantity as in ISO, and the size factor is 0.5 for outer modules up to 1.6 mm and a linear function of the outer module above it, increasing with module — the opposite of the HB behaviour.
Material, surface-condition and life factors
Only ISO carries a material factor, the relative notch sensitivity YδrelT, defined as the ratio of the sensitivity of the actual gear to that of the reference test gear and computed from the depth of the plastically deformed surface layer ρ′ and qs:
$$Y_{\delta relT}=\frac{1+0.2\,\rho'(1+2q_s)}{1+1.2\,\rho’}$$
Only ISO also carries a root surface condition factor YRrelT, which acts on the allowable stress and depends on the material and on the root roughness RZ (Table 5).
| Material | RZ ≤ 1 μm | 1 μm < RZ ≤ 40 μm |
|---|---|---|
| Hardened steel | 1.120 | 1.674 − 0.529 (RZ + 1)1/10 |
| Non-hardened steel | 1.070 | 5.306 − 4.203 (RZ + 1)1/100 |
| Grey cast iron, nitrided steel | 1.025 | 4.299 − 3.259 (RZ + 1)1/200 |
On the service side, HB uses only a temperature factor, equal to 1 below a blank temperature of 121 °C and to 394/(273 + θM) above it, where θM is the peak blank temperature in degrees Celsius. AGMA uses the reciprocal of that quantity, Kθ, in the denominator of the allowable stress, so the two agree in effect. AGMA’s life factor is a three-branch power law in the equivalent number of cycles NL: 2.75 below 103 cycles, 6.1514 NL−0.1192 between 103 and 3 × 106, and 1.683 NL−0.0323 above that. ISO instead reads YNT from material-specific test curves, which is the more complete treatment, and HB has no separate life factor at all — its fatigue limit must already include the life requirement.
A worked comparison
The combined effect of these differences is best seen on a single pair. Table 6 lists the geometry, material and duty of the reference case: a 27/37-tooth pair of 7.96 mm outer module, 35° mean spiral angle, 20° normal pressure angle and 62 mm face width, running at 8500 r/min with a nominal 5 kW input, 109 cycles, 650 MPa bending fatigue limit, equal hardness on both members, simply supported mountings, an oil temperature of 120 °C and a root roughness RZ of 20 μm.
| Parameter | Value |
|---|---|
| Pinion / wheel tooth number z1 / z2 | 27 / 37 |
| Outer transverse module mt | 7.96 mm |
| Mean spiral angle βm | 35° |
| Normal pressure angle αn | 20° |
| Face width b | 62 mm |
| Design speed n | 8500 r/min |
| Duty and environment | 5 kW input; NL = 109; equal hardness; both gears simply supported; oil at 120 °C; flank roughness 4.8 μm; root roughness 20 μm; σFlim = 650 MPa |
The factors actually evaluated for this pair, and the resulting stresses, are given in Table 7. Where a factor is absent from a standard, the cell is left empty rather than set to unity, because the effect it represents is carried elsewhere in the calculation.
| Quantity | HB | ISO 10300 | AGMA 2003 |
|---|---|---|---|
| YFa | 2.3285 | 2.3285 | — |
| Ysa | 1.6531 | 1.830 | — |
| Overlap / load application factor | Yε = 0.5694 | Yε = 0.625 | — |
| Load-sharing factor | Yγ = 0.7163 | YLS = 0.7132 | — |
| Helix / longitudinal curvature factor | YLC = 0.9865 | YBS = 1.3327 | Yβ = 1.0448 |
| Root stress distribution / geometric factor | Yb = 1.8041 | — | YJ = 0.245 |
| Inertia factor | Yi = 1.000 | — | — |
| Test-gear stress correction YST | 1.775 | 2.000 | — |
| Size factor YX | 0.6883 | 0.9975 | 0.5536 |
| Relative notch sensitivity YδrelT | — | 1.0081 | — |
| Root surface factor YRrelT | — | 0.9567 | — |
| Life factor YNT | — | 1.000 | 0.9376 |
| Temperature factor | Yθ = 0.906 | — | Kθ = 1.000 |
| Calculated stress σF | 524.7 MPa | 1301.8 MPa | 365.2 MPa |
| Allowable stress σFP | 558.9 MPa | 1250.8 MPa | 487.5 MPa |
The ranking is unambiguous: ISO returns a calculated stress 2.5 times HB’s and 3.6 times AGMA’s, and it is the only one of the three documents for which this pair fails, with σF above σFP. Three mechanisms produce the gap. The dynamic factor differs strongly, because ISO resolves the operating point against the resonance regions and returns 1.887 here against 1.258 for AGMA, while HB’s empirical expression returns 1.00 for this accuracy grade and speed. The face load distribution factor differs for the reason set out above, since ISO’s KFβ of 1.452 multiplies its own contact factor by 1/0.74, whereas HB and AGMA return values close to unity for simply supported gears at full load. And the geometry-side factors differ in a consistent direction: ISO’s stress correction factor is 11 % above HB’s and its test-gear factor 13 % above, while its size factor of 0.9975 sits between HB’s 0.688 and AGMA’s 0.554. The tooth form factor and the load-sharing factor, by contrast, are nearly identical in HB and ISO (2.329 versus 2.329 and 0.716 versus 0.713), which shows that the 30° tangent and the different iteration schemes converge to essentially the same critical section.
How design parameters move the answer
Sweeping one parameter at a time around the reference case exposes disagreements that are more consequential than the absolute offset, because they change the direction of a design decision (Table 8).
| Parameter increased | HB σF | HB σFP | ISO σF | ISO σFP | AGMA σF | AGMA σFP |
|---|---|---|---|---|---|---|
| Face width b | lower | higher | lower | higher | higher | no geometric dependence |
| Mean spiral angle βm | extremum (minimum within 0–40°) | lower | extremum (maximum within 0–40°) | higher | higher | no geometric dependence |
| Normal pressure angle αn | higher | higher | higher | higher | lower | no geometric dependence |
| Pinion tooth number z1 | lower | higher | lower | higher | lower | no geometric dependence |
| Outer transverse module mt | lower | lower | lower | lower | lower | no geometric dependence |
| Design speed n | lower | higher | lower | none | lower | no geometric dependence |
Four of these deserve comment. The face width is the sharpest reversal: in HB and ISO the stress falls as b grows, because the load per unit width falls faster than any geometric factor rises, whereas the AGMA calculation gives a rising stress, since YJ depends on the ratio of the effective contact width to the total width and therefore falls as the face is widened at constant contact length. The spiral angle is the parameter on which the three standards disagree most, because it acts primarily through the overlap ratio: as εvβ crosses 1, the ISO overlap factor locks at 0.625, the HB load application factor switches branch, and the HB load-sharing factor turns on at εvγ = 2, which produces an interior extremum in both standards — a minimum for HB and a maximum for ISO — while AGMA’s stress rises monotonically. The pressure angle reverses sign for AGMA, whose geometric factor improves as the pressure angle increases, against HB and ISO where the total overlap ratio falls and the load application factor with it. And the speed dependence of the ISO dynamic factor is region-based, so a change in tooth number, module or speed can move the operating point into another resonance branch and reverse a trend that the parameter sweep would otherwise show as monotonic.
Only the module behaves consistently across all three documents, where an increasing module lowers the calculated stress everywhere, although HB’s extremum shifts with module because the overlap ratio is sensitive to it.
Safety factors across seven gear sets
Because the stresses differ by a factor of three, the computed safety factors must be compared case by case rather than inferred from the stress ranking. Seven geometrically similar pairs, spanning 21 to 39 pinion teeth and 10.0 to 5.513 mm outer module under otherwise identical duty, are collected in Table 9.
| Set | z1 / z2 | mt (mm) | HB | ISO 10300 | AGMA 2003 |
|---|---|---|---|---|---|
| 1 | 39 / 53 | 5.513 | 1.349 | 0.593 | 1.158 |
| 2 | 36 / 49 | 5.972 | 1.350 | 0.642 | 1.201 |
| 3 | 31 / 42 | 6.935 | 1.314 | 0.751 | 1.295 |
| 4 | 27 / 37 | 7.960 | 1.331 | 0.961 | 1.335 |
| 5 | 26 / 35 | 8.270 | 1.300 | 1.104 | 1.343 |
| 6 | 25 / 34 | 8.600 | 1.280 | 1.252 | 1.375 |
| 7 | 21 / 29 | 10.000 | 1.152 | 1.598 | 1.460 |
The three series cross. For fine-pitch, high-tooth-count gears (sets 1–3) ISO is by far the most severe, returning safety factors below unity while HB and AGMA both accept the design with margins above 1.15. For coarse-pitch, low-tooth-count gears (set 7) the order reverses: ISO returns 1.598, AGMA 1.460 and HB only 1.152, so HB becomes the most conservative of the three. Between sets 4 and 6 the three curves intersect and the ordering is ambiguous. ISO’s safety factor also varies far more across the sweep — from 0.59 to 1.60, a factor of 2.7 — than HB’s (1.15 to 1.35) or AGMA’s (1.16 to 1.46), which means ISO is the most sensitive of the three to tooth number and module and HB the least. Any statement of the form “standard X is more conservative than standard Y” therefore holds only inside a band of gear geometry, and the band should be stated explicitly whenever such a comparison is used in a design review.
Practical consequences
Three conclusions follow from the structure of the documents and are independent of the specific numbers above.
The AGMA calculation is the shortest of the three by a wide margin — eight factors instead of thirteen or fourteen — because the geometric factor YJ absorbs tooth form, load sharing, contact-line length and inertia into a single tabulated quantity. That economy is appropriate for general commercial duty, where the accuracy of the input data does not justify a finer decomposition, but it also means that the effect of a design change on the individual mechanisms is invisible in the result. The ISO and HB calculations retain the decomposition, at the cost of a longer procedure, and are the appropriate choice where load-carrying capacity is the design driver.
The two ISO-derived documents are not interchangeable. HB, written in 1985 against an earlier ISO text, lacks the transverse load-sharing factor KFα, the material notch sensitivity YδrelT, the root surface factor YRrelT and a separate life factor, and its reliability table is truncated at two classes. It therefore returns systematically lower stresses and, for fine-pitch gears, more optimistic safety factors. Its range of validity — high tooth counts, small modules, the accuracy grades and mounting arrangements covered by its tables — should be respected, and outside that range the ISO 10300 procedures are the safer choice. ISO, conversely, is the most severe of the three for fine-pitch gearing and the least severe for coarse-pitch, low-tooth-count gearing, and it is the only one of the three whose dynamic factor responds explicitly to resonance, which matters at the pitch-line velocities typical of aero-engine bevel gears.
Finally, the parameter sensitivities in Table 8 should be read before any single-parameter optimisation is attempted. The spiral angle, the pressure angle and the face width each change the sign of their influence between standards, and the sign changes are traceable to identifiable mechanisms — the overlap ratio crossing unity, the effective-to-total width ratio inside YJ, and the resonance branches of the ISO dynamic factor. A design that is improved under one document can be degraded under another for the same nominal change, and only the mechanism-level comparison identifies which of the three is responding to the physics rather than to a tabulation boundary.