 Gear pitting inspection mask

ID: gear-pitting-inspection-mask

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Codex  0 2026-11-05

A gear pitting inspection mask specifies the tooth-flank region over which damage is counted. It separates eligibility for inspection from the classification of an eligible location as pitted. The denominator of a gear pitting area fraction depends on this mask, so a change in coverage can change the reported fraction even when the surface has not changed.

For a digital image, let

m_{i} \in {0, 1}

indicate inclusion of pixel

i

and let

p_{i} \in {0, 1}

indicate its classification as pitted. With represented surface area

a_{i}

per pixel,

ϕ = \frac{\sum _{i} m _{i} p _{i} a _{i}}{\sum _{i} m _{i} a _{i}}, \sum_{i} m_{i} a_{i} > 0.

(1)

The arrays

m_{i}

and

p_{i}

are different indicator functions. Uniform pixel areas cancel, but an oblique view or a curved-surface map can require nonuniform

a_{i}

. A shadow, occlusion or unrecorded region should not automatically count as intact material.

An original example begins with 200 pitted pixels among 10000 eligible equal-area pixels, giving

2%

. Cropping to a 5000-pixel region that retains 150 pitted pixels gives

3%

. The counted damaged area fell while the fraction rose; this comparison alone cannot establish damage growth.

A gear inspection common-region comparison first uses image registration to put inspections into corresponding surface coordinates. On a common grid, the intersection mask is

m_{i}^{common} = m_{i}^{(0)} m_{i}^{(1)}

. Comparing the two pitting classifications within that same region holds the denominator convention fixed. Coverage outside the intersection should still be reported: excluding a newly obscured damaged edge can hide relevant change.

Useful inspection records retain the raw image, mask, geometric mapping, image thresholding or other image segmentation rule, and the reason for excluded regions. A primary NASA gear-endurance study combined inspection history with vibration and oil-debris observations, illustrating why damage labels must remain connected to actual inspected surfaces.^[ref] The mask formalism above is an explicit measurement convention, not a claim that every historical inspection used this pixel algorithm.

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