Reshaping Load-Dependent Mesh Excitation Waveforms of Spur Gears—An Analytical Framework on Tip Relief Modeling and Design

Tip relief is a critical design feature of modern spur gears, aimed at improving dynamic performance through a typical design strategy involving peak-to-peak minimization of mesh excitations. However, due to the hyperstatic nature of simultaneous tooth engagements, the applied torque not only affects mesh deformation amplitudes as normally considered but also alters mesh excitation waveforms, leaving great challenges for the typical design to meet various operating conditions. This paper develops an analytical framework to reshape mesh excitation waveforms, aimed at flexibly reducing vibration intensities across different operating loads and speeds. The load-dependency of excitation harmonics with tip relief is efficiently characterized by an improved analytical mesh excitation model. A tip relief design method is proposed, which automatically recombines harmonic contents of mesh excitations to adapt target operating speeds. Comparisons with finite element models and experiments confirmed the accuracies of quasi-static and dynamic analyses. Parametric studies and application examples further demonstrate the acceptable feasibility and effectiveness of the present method.