Impact of Profile Shifting on Gear Tooth Stresses at Extended Center Distances: A Comparative Study Using Hertz, AGMA, and FEA

This study investigates how increasing the center distance of straight spur gears from 218.75 mm to 220 mm and 222 mm through positive profile shift coefficients affects tooth contact characteristics for machine design. Maximum Hertzian contact stress is evaluated using Hertz theory, AGMA standards, and finite element analysis (FEA) in Ansys Workbench 2022 R1, with FEA results validated against theoretical predictions (deviations < 5%). Comparing an unshifted case (xl =0, x2 =0) with two shifted cases (Shift 1: <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$x$</tex> 1=0.117, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$x$</tex>2=0.394; Shift 2: x1=0.324, x2=1.045), all methods confirm that extending the center distance via positive profile shifting significantly reduces contact stress—by 5.7% (Hertz), 5.5% (AGMA), and 5.3% (FEA) in Shift 2 versus the unshifted case. Von Mises stress also decreases, improving fatigue strength and minimizing deformation risks. These findings underscore the efficacy of profile shifting for optimizing gear reliability at extended center distances, provided coefficients are judiciously chosen.