= Gear pitting area fraction
{title2=$\phi=A_{\rm pit}/A_{\rm inspected}$}
The \b[gear pitting area fraction] measures how much of a stated tooth-flank inspection region is classified as affected by <gear surface pitting>:
$$
\phi=\frac{A_{\rm pit}}{A_{\rm inspected}},\qquad 0\le\phi\le1.
$$
Both areas must use the same geometric convention. A projected photograph, an unwrapped flank map and an actual curved surface need not assign the same areas. The <gear pitting inspection mask> specifies which part of the flank is included, so that an apparent change of damage is not merely a change of inspected region.
For an original image-counting example, let the inspected region contain $N$ equal-area pixels and let $n$ be classified as pitted. If their common scale is $s$ length units per pixel,
$$
\phi=\frac{ns^2}{Ns^2}=\frac nN.
$$
Thus $n=2400$ out of $N=120000$ gives $\phi=0.02$, or $2\%$. The common scale cancels from the ratio; uncertainty in the classification boundary, perspective distortion or the inspection mask does not. <Image segmentation> should therefore be checked against the actual surface, with consistent illumination and a recorded threshold or classification rule.
Combining regions requires area weighting. Suppose one region has $0.6\,\mathrm{mm^2}$ of pits within $30\,\mathrm{mm^2}$ and another has $1.2\,\mathrm{mm^2}$ within $120\,\mathrm{mm^2}$. Their fractions are $2\%$ and $1\%$, but the combined fraction is $1.8/150=1.2\%$, rather than the unweighted average $1.5\%$.
The ratio measures extent under its chosen convention, not pit depth, lost volume or a universal remaining life. A 2009 NASA endurance study paired repeated gear inspection with vibration and oil-debris monitoring. Its test rig used accelerometers, shaft timing signals and an inductive debris sensor, giving observations of different aspects of the evolving damage.<Gear Fault Detection Effectiveness as Applied to Tooth Surface Pitting Fatigue Damage by David G. Lewicki and others>[Printed pp. 1–5, apparatus, instrumentation, test procedure and inspection comparisons]{ref} A surface fraction can complement these measurements, but it does not make their signals interchangeable.
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