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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4. Crack Propagation Rates In the early stages of the crack propagation phase, the contrast between the gear face and initial crack is typically too small for the computerized measurement algorithm to detect. Application of the measurement algorithm corresponded to the beginning frame at which the program could distinguish the crack from the gear tooth surface. This generally occurred past the 4,000th out of 6,207 frames of the TIFF file, which resulted in crack length analysis over the last 10% of the tooth life. Crack length measurements, , for three individual tests are shown in Figure 9. These three tests corresponded to maximum tooth root bending stress values of 1,183, 1,238, and 1,348 MPa and fatigue lives of 49,846, 21,096, and 23,092 cycles, respectively. The length in mm is plotted against the ratio C of the current cycle to the total cycles . It is observed that the first detectible crack happens at a cycle ratio of about 0.968 for the 1,183 MPa stress test, 0.932 for the 1,238 MPa stress test and 0.901 for the 1,348 MPa stress test.

Figure 9. Measured gear tooth root crack lengths under 1183 MPa with failure life of 49,846 cycles, 1238 MPa with failure life of 21,096 cycle and 1348 MPa with failure life of 23,092 cycles. The final crack lengths from the digital image measurement were 7.26 mm for the 1,183 MPa stress test, 6.11 mm for the 1,238 MPa stress test and 7.57 mm for the 1,348 MPa stress test. A CMM measurement of the tooth fracture surface on the gear indicates the length being 8.56 mm, which has been plotted for reference as the fracture length. The difference was because the image filtering techniques described removed frames where the tooth was completely separated. As such the last frame considered in the imaging is the loading cycle immediately prior to the cycle in which fracture occurred. 5. Summary and Conclusions A methodology has been proposed for the measurement of cyclic crack growth during the last portion of the crack propagation phase of a gear tooth root fatigue failure. The methodology utilizes the SAE standard gear single tooth bending fatigue test setup and integrates high-speed photography to record several minutes prior to the onset of tooth failure in the single tooth bending test. To achieve this, a triggering system was developed which monitors the real time load applied to the gear tooth and sends a TTL pulse to the camera when a low force condition is met, indicating the exact moment of tooth failure. The high-speed imaging was done utilizing macro lens equipment to achieve high resolution images of the gear tooth root. A frame rate which is an integer multiple of the loading rate and set to 25x higher than the loading rate was used. This ensured sufficient time resolution such that an image was captured at the highest applied load and that moment was consistent from cycle to cycle. Digital images were calibrated to the size of the tooth and used to measure crack length during each cycle, yielding cyclic crack growth rate measurements with