= Gear face load distribution
<Gear face load distribution> describes how tooth-contact load is spread across the engaged <gear face width>. Equal total transmitted <force> can produce different local loads when shafts tilt, supports deform or tooth traces are imperfect. A geometrically available <gear effective face width> therefore does not establish uniform loading. The manufacturer's tooth-flank <gear face load factor> accounts for support arrangement and the expected quality of contact under load.<Elements of Metric Gear Technology by SDP-SI>[D815 technical section, §17.2.12, printed T-164 and Table17-11, tooth-flank load distribution factor]{ref}
For a simple axial line-load model, let $w(z)$ have units $\mathrm{N/mm}$ over $0\le z\le b$. Its total normal <force> is
$$
F_n=\int_0^b w(z)\,dz.
$$
Uniform loading gives $w=F_n/b$. An illustrative tilted distribution is
$$
w(z)=\frac{F_n}{b}\left[1+\lambda\left(\frac{2z}{b}-1\right)\right],\qquad 0\le\lambda\le1.
$$
Its integral remains $F_n$, while its largest line load is $(1+\lambda)F_n/b$. With $F_n=1000\,\mathrm N$, $b=20\,\mathrm{mm}$ and $\lambda=0.6$, the two edges carry20 and80N/mm, compared with the50N/mm mean. The peak-to-mean ratio1.6 characterizes this constructed model; it is not a substitute for the manufacturer's standard factor calculation.
The <gear contact pattern> can reveal where mating tooth flanks touch, but an unloaded marking test alone does not measure the operating force density. A loaded comparison must specify applied <torque>, shaft positioning and support deformation. In <helical gears>, changing tooth-contact lines and multiple simultaneous contacts also require a consistent choice of time and projected width. A wider tooth can reduce mean load per width while still suffering a concentrated edge load; width and alignment must be considered together.
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