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1. Study on Dynamic Behaviors of Hypoid Gears Under Variable Tidal Current Energy Harvesting Conditions

   https://doi.org/10.3390/machines13030178  

   Huang, Dequan; Li, Yan; Zheng, Xingyuan; Li, Gang (March 2025, Machines)

   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. 

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2. System Tautochronic Path for Pendulum Vibration Absorber Based on Simple Harmonic Oscillator Transformation

   https://doi.org/10.1115/1.4067078  

   Valadbeigi, Nima; Monroe, Ryan; Geist, Bruce (December 2024, Journal of Vibration and Acoustics)

   Centrifugal pendulum vibration absorbers (CPVAs) are essentially collections of pendulums attached to a rotor or rotating component or components within a mechanical system for the purpose of mitigating the typical torsional surging that is inherent to internal combustion engines and electric motors. The dynamic stability and performance of CPVAs are highly dependent on the motion path defined for their pendulous masses. Assemblies of absorbers are tuned by adjusting these paths such that the pendulums respond to problematic orders (multiples of average rotation speed) in a way that smooths the rotational accelerations arising from combustion or other nonuniform rotational acceleration events. For most motion paths, pendulum tuning indeed shifts as a function of the pendulum response amplitude. For a given motion path, the tuning shift that occurs as pendulum amplitude varies produces potentially undesirable dynamic instabilities. Large amplitude pendulum motion that mitigates a high percentage of torsional oscillation while avoiding instabilities brought on by tuning shift introduces complexity and hazards into CPVA design processes. Therefore, identifying pendulum paths whose tuning order does not shift as the pendulum amplitude varies, so-called tautochronic paths, may greatly simplify engineering design processes for generating high-performing CPVAs. To illustrate this new approach and results, a tautochronic cut-out shape producing constant period system motion is obtained for a simplified problem involving a mass sliding in the cut-out of a larger mass that is free to translate horizontally without friction in a constant gravitational field, where the translating base mass replaces the rotating rotor in the centrifugal field. 

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3. The Effects of Gravity on the Response of Centrifugal Pendulum Vibration Absorbers1

   https://doi.org/10.1115/1.4051030  

   Tchokogoué, Darryl; Mu, Ming; Feeny, Brian F.; Geist, Bruce K.; Shaw, Steven W. (December 2021, Journal of Vibration and Acoustics)

   null (Ed.)

   Abstract This article describes the effects of gravity on the response of systems of identical, cyclically arranged, centrifugal pendulum vibration absorbers (CPVAs) fitted to a rotor spinning about a vertical axis. CPVAs are passive devices composed of movable masses suspended on a rotor, suspended such that they reduce torsional vibrations at a given engine order. Gravitational effects acting on the absorbers can be important for systems spinning at relatively low rotation speeds, for example, during engine idle conditions. The main goal of this study is to predict the response of a CPVA/rotor system in the presence of gravity. A linearized model that includes the effects of gravity and an order n torque acting on the rotor is analyzed by exploiting the cyclic symmetry of the system. The results show that a system of N absorbers responds in one or more groups, where the absorbers in each group have identical waveforms but shifted phases. The nature of the waveforms can have a limiting effect on the absorber operating envelope. The number of groups is shown to depend on the engine order n and the ratio N/n. It is also shown that there are special resonant effects if the engine order is n = 1 or n = 2, the latter of which is particularly important in applications. In these cases, the response of the absorbers has a complicated dependence on the relative levels of the applied torque and gravity. In addition, it is shown that for N > 1, the rotor response is not affected by gravity, at least to leading order, due to the cyclic symmetry of the gravity effects. The linear model and the attendant analytical predictions are verified by numerical simulations of the full nonlinear equations of motion. 

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4. System Tautochronic Path for Pendulum Vibration Absorber Based on Simple Harmonic Oscillator Transformation

   https://doi.org/10.1115/DETC2024-143621  

   Valadbeigi, Nima; Monroe, Ryan; Geist, Bruce (August 2024, American Society of Mechanical Engineers)

   Centrifugal pendulum vibration absorbers (CPVAs) are essentially collections of pendulums attached to a rotor or rotating component or components within a mechanical system for the purpose of mitigating the typical torsional surging that is inherent to internal combustion engines and electric motors. The dynamic stability and performance of CPVAs are highly dependent on the motion path defined for their pendulous masses. Assemblies of absorbers are tuned by adjusting these paths such that the pendulums respond to problematic orders (multiples of average rotation speed) in a way that smooths the rotational accelerations arising from combustion or other non-uniform rotational acceleration events. For most motion paths, pendulum tuning indeed shifts as a function of the pendulum response amplitude. For a given motion path, the tuning shift that occurs as pendulum amplitude varies produces potentially undesirable dynamic instabilities. Large amplitude pendulum motion that mitigates a high percentage of torsional oscillation while avoiding instabilities brought on by tuning shift introduces complexity and hazards into CPVA design processes. Therefore, identifying pendulum paths whose tuning order does not shift as the pendulum amplitude varies, so-called tautochronic paths, may greatly simplify engineering design processes for generating high-performing CPVAs. This paper expands on the work of Sabatini, in which a mathematical condition for tautochronicity is identified for a class of differential equations that includes those that arise in the modeling of the motion of a pendulum in a centrifugal field. The approach is based on a transformation from the physical coordinate to a standard Hamiltonian system. We show that transforming a nonlinear oscillator made tautochronic through path modification actually transforms the nonlinear oscillator into a simple harmonic oscillator. To illustrate the new approach and results, the technique is applied to the simplified problem of determining the cut-out shape that produces tautochronic motion for a mass sliding in the cut-out of a larger mass that is free to translate horizontally without friction. In the simplified problem, centrifugal acceleration is replaced by constant gravitational acceleration and rotation of the rotor inertia is replaced by the translation of the large base mass. 

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5. Bluff Body, Piezoelastic Oscillator: Reduced-Order Model, Vortex-Induced Vibrations, and Energy Harvesting

   https://doi.org/10.1115/DETC2024-143647  

   Bellei, Andrés; Balachandran, Balakumar (August 2024, American Society of Mechanical Engineers)

   Energy harvesting from flow-induced vibrations has gained substantial attention in the last two decades due to the rising demand for renewable and sustainable energy sources, as well as the widely availability of these sources, offering a viable alternative in areas where other ambient energy sources may not be readily accessible. Flow-induced vibrations of bluff bodies are characterized by complex nonlinear dynamics, for which accurate models are currently lacking. In this work, a circular cylinder attached to the free end of a piezoelastic cantilever is considered for energy harvesting. When placed in a flow, this system undergoes vortex-induced vibrations. A reduced-order model is developed to understand fluid-structure interactions of this system. A wake oscillator has been used to describe vortex-induced vibrations and a finite-element model has been used to model the piezoelastic cantilever. The developed model is used to explore the interplay amongst the fluid, structure, and piezoelectric element. The results obtained are compared to experimental data from literature, in terms of the vibration amplitude, vibration frequency, and power obtained. Modifications to the wake oscillator model are examined to better reflect the fluid-structure interactions. It is found that there is a trade-off between accurately predicting the vibration amplitude and accurately predicting the vibration frequency. 

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