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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Nomenclature image horizontal field of view image vertical field of view crack length in pixels ℎ camera sensor height camera sensor width M lens magnification ratio γ

image field of view scaling factor

1. Introduction The gear single tooth bending fatigue (STBF) test has been the most common way of directly evaluatingthe tooth bending fatigue performance of a gear [1]. In the STBF test the gear is held statically and a load is cyclically applied to a tooth as opposed to performing the fatigue evaluation on rotating gears [2,3]. As such, STBF is more economical and can utilize conventional servo-hydraulic and electrodynamic shakers rather than relying on specialized gear testers. Spur gears are used such that the gear tooth transverse and normal planes are aligned and parallel to the direction of loading. Planar (2D) approximations of the tooth profile are usually used to describe the state of stress and for the purposes of crack propagation modeling. Placing strain gages in the tooth root has been the traditional way of measuring bending strain for validation of stress prediction models. Very few studies have attempted any level of digital image correlation (DIC) on gear tooth specimens. Raghuwanshiand Parey [4] used DIC to measure gear tooth stiffness in a static but meshed system. Gear teeth shapes were cut from a blank with Wire EDM and root cracks were simulated through Wire EDM as well. As such the gear specimens used do not necessary represent how gears are made for contemporary power transmission drive units. In addition, as the focus of the study was to extract mesh stiffness, crack length was not measured using DIC. Blais and Toubal [5] used a high-speed camera and a commercial DIC software (StrainMaster, LaVision Inc.) to access crack progression in high-density polyethylene (HDPE) gears in a STBF test. Crack length was reported normalized to the maximum crack length for four tests against logarithmically scaled loading cycles. Exact details on how cycle-to-cycle crack length was measured using the StrainMaster software were not reported. 2D strain and stress fields were not shown. Studies by Savaria et al. [6], Masuyama et al. [7], and Pullin et al. [8] all used various commercialDIC software’s to measure 2D strain fields in statically loaded gear tests. Direct measurement of cracks was not performed. This leaves a void of experimental data exploring the utility and limits of DIC to measure cycle to cycle crack propagation measurements in gear teeth. Within the greater body of literature there are several studies utilizing DIC to measure crack lengths and propagation rates in coupon specimens with and without pre-machined cracks. Gehri et al. [9] grouped these techniques into direct and indirect image-based techniques with direct techniques consisting of greyscale thresholding and morphological operations to detect and measure the crack. Indirect techniques relied on spatial shifts allowing subpixel resolutions of displacements in the image. Indirect techniques are typically what is refereed to when referencing DIC and what is typically found in commercial software packages. In this research a direct image-based technique is developed to measure cycle to cycle crack growth rates in a gear tooth bending fatigue experiment. The motivation behind is work is to explore the feasibility and limitations of these methods as applied to tooth root crack behaviour in high-quality automotive-grade case-carburized alloy steel gear teeth. Successful development of these techniques should allow for validation of existing fracture mechanics models used for prediction of gear tooth bending fatigue life, mesh stiffness fluctuations and health monitoring systems.