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This study investigates dynamic behaviors of hypoid gear rotor systems under variable tidal current energy harvesting conditions through numerical simulations and experimental validation. The study examines dynamic responses of a hypoid gear rotor system induced by cyclical tidal current variations, which generate fluctuating loads and bidirectional rotational speeds in tidal energy conversion systems. Two hypoid gear pairs, modified through precise manufacturing parameters, are evaluated to optimize tooth contact patterns for bidirectional tidal loading conditions. A coupled torsional vibration model is developed, incorporating variable transmission error and mesh stiffness. Experimental validation of dynamic performances of hypoid gear pairs was conducted on a bevel gear testing rig, which can measure both torsional and translational vibrations across diverse tidal speed profiles. The experimental results demonstrate that second-order primary resonances exhibit heightened vibration intensity during flow-reversal phases. This phenomenon has significant implications for system power efficiency and acoustic emissions. The findings extend the current understanding of hypoid gear optimization for tidal energy-harvesting applications. 

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. 

Considering the elasticity of gear solid bodies, the load applied to gear teeth will force theoretically separated gear teeth to get into engaging state in advance. This phenomenon is named as the extended tooth contact (ETC). Effects of the ETC directly influence the time-varying mesh stiffness of gear pairs and subsequently alter nonlinear dynamic characteristics of gear transmission systems. Time-vary mesh stiffness, considering effects of the ETC, is thus introduced into the dynamic model of the gear transmission system. Periodic motions of a gear transmission system are discussed in detail in this work. The analytical model of time-varying mesh stiffness with effects of the ETC is proposed, and the effectiveness of the analytical model is demonstrated in comparison with finite element (FE) results. The gear transmission system is simplified as a single degree-of-freedom (DOF) model system by employing the lumped mass method. The correctness of the dynamic model is verified in comparison with experimental results. An incremental harmonic balance (IHB) method is modified to obtain periodic responses of the gear transmission system. The improved Floquet theory is employed to determine the stability and bifurcation of the periodic responses of the gear transmission system. Some interesting phenomena exist in the periodic responses consisting of “softening-spring” behaviors, jump phenomena, primary resonances (PRs), and super-harmonic resonances (SP-HRs), and saddle-node bifurcations are observed. Especially, effects of loads on unstable regions, amplitudes, and positions of bifurcation points of frequency response curves are revealed. Analytical results obtained by the IHB method match very well with those from numerical integration.