= Gear face load factor
{title2=$K_{H\beta}$}
A <gear face load factor> quantifies the effect of nonuniform load across the engaged <gear face width>. For the contact-load convention in <ISO 6336-1:2006>, $K_{H\beta}$ compares maximum line-load intensity with the mean intensity over the stated width:
$$
K_{H\beta}=\frac{w_{\max}}{F_m/b}.
$$
Here $F_m$ is the total load represented by that distribution and $b$ is its evaluation width. A uniform distribution gives1; an edge-concentrated distribution gives a larger value. The numerator and denominator must refer to the same load convention and operating condition.<ISO 6336-1:2006>[§7.4.2, equation(38), printed p.41, maximum versus mean load intensity]{ref}
For an original illustrative distribution over $b=20\,\mathrm{mm}$,
$$
w(z)=50\left[1+0.6\left(\frac{2z}{20\,\mathrm{mm}}-1\right)\right]\,\mathrm{N/mm},
$$
total load is1000N, mean line load is50N/mm and maximum line load is80N/mm. Thus $K_{H\beta}=1.6$. A uniform distribution with the same width and total load gives1. The <gear contact pattern> can cover the whole width in both cases.
\Image[/gear-face-line-load.png]
{title=Equal total gear-face loads with different maximum-to-mean line-load ratios}
For ideal elastic line contact at fixed geometry and material, <Hertzian contact> pressure scales with the square root of line load. The corresponding <gear contact-stress load factor> is therefore $\sqrt{1.6}\approx1.265$ in this simplified comparison. Multiplying the contact pressure itself by1.6 would confuse a load-intensity ratio with a stress ratio. This scaling does not replace a complete gear-rating calculation.
The manufacturer's treatment connects face-load assessment to shaft-support placement, shaft stiffness and loaded contact quality.<Elements of Metric Gear Technology by SDP-SI>[§17.2.12, printed T-164, and Table17-11]{ref} A value inferred from a toy line-load profile is consequently useful for understanding the factor, while a real design must obtain the relevant distribution or factor from a method appropriate to its geometry and load state.
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