PSI - Issue 57

Haelie Egbert et al. / Procedia Structural Integrity 57 (2024) 179–190 Haelie Egbert et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Figure 7(b) by Point B. The length of the crack was approximated by the linear distance between the end points of the crack. In pixels, this was represented by the distance formula:

) 2

) ( 2

(

i cr

, x A x B (2) In Eq. (2), is the length of the crack at loading cycle , , and , are the horizontalcoordinates in pixels of Point A and B in the crack, and , and , are the vertical coordinates in pixels. Figure 7 shows the cropped image of the digitized crack and the corresponding length measurement. Until this point, the images and measurement methodology has been presented in units of pixels, but the tooth area covered by any given pixel has been undefined. To properly define this in physical units, the digitally decomposed binary image is compared to a measurement of the gear tooth in order to determine the proper scaling factor. The test gear was first measured using a gear coordinate measurement machine (CMM). It allowed for the measurement of the entire outside contour of the gear. To extract the tooth surface contour from the digitally decomposed TIFF images, morphological image processing techniques were employed. These techniques changed the pixel in question based upon its neighboring pixels’ values. For example, the operation “remove” sets the pixel value being analyzed to 0 if the pixel above, below, and on either side of it is a 1, creating a boundary of white pixels outlining the gear shape. This command , , y A y B , L P P = − P P + −

Figure 7. Cropped binary representation of the imaged gear tooth crack (a) without measurement and (b) showing the simplified length calculation