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

189 11

single cycle resolution. This methodology was demonstrated via three tests at various stress levels corresponding to high cycle fatigue behavior. The following conclusions and observations can be made from this study: • A gear single tooth bending fatigue test setup can be used to optically record root crack propagation. • Digital images can be processed to yield tooth contours, which can successfully be compared to gear tooth CMM measurements to scale image field of view. • Digital images can be automatically processed through computerized algorithms to measure cycle-to-cycle maximum crack lengths for large cycle counts. • The minimum crack length able to be measured was around 1.5mm long. • Remaining life after first detection of a crack was between 1500-2000 cycles for the three example measurements. 6. Discussion and Future Work As with all measurements, there are sources of error inherent to the limitations of hardware, data processing approximations,assumptions, and environmentalfactors. As this is a newly proposed measurement methodology,a discussion on sources and approximate magnitude of errors is warranted. The main sources of error in this measurement can be attributed to the following in what the authors believe is the approximate order of most error to least error.

1. Crack Path Approximation Error 2. Contrast Error 3. Digital Image Resolution Error 4. Field of View (FOV) Calibration Error

5. Synchronization Error 6. Lens Aberration Error A description of each of these errors can be summarized as follows:

1. Crack Path Approximation Error – The true fracture surface is curved and as such, length should be measured by fitting a spline to the fracture path to determine true length. In the case of gear tooth bending fatigue the fracture path consists of approximately a single radius of curvature and as such errors from approximating the fracture path do not significantly change qualitative insights gained from this study. However, in terms of absolute error this approximation most likely contributes the most. 2. Contrast Error – Contrast directly effects the ability of the image processing algorithm to correctly detect the location of the crack tip. Sufficient contrast generated through lighting and illumination of the gear end face surface is needed. This error also includes false detection of crack location caused by defects and irregularities on the surface. Polishing the imaged surface to an isotropic or more homogenous topography is recommended. Additional manipulation of lighting and background treatments are recommended. 3. Digital Image Resolution Error – Measurement resolution and therefore maximal achievable accuracy is function of the number of sensors in a CCD or CMOS chip and directly tied to equipment cost. Because this is a direct image correlation technique the size of a pixel is equal to the theoretical minimal achievable displacement resolution. In this study a 20.9-megapixel CMOS sensor was used. 4. FOV Calibration Error – A difference between the true length of the surface in the image and the actual length estimated through the transformation constant will cause error in the measurement. The current method is quite sophisticated utilizing state of the art CMM with sub-micron level accuracy to compare to the digital image defined tooth size.