Dynamic Analysis of Hula Hoop Motion and Optimized Energy Harvest Circuit

The nonlinear dynamics of hula hoop motion is deciphered in this study by nonlinear dynamic modeling techniques to find solution and stability analysis. This is different from the previous study [1], where a homotopy method is employed. The analysis results are capable of transforming linear reciprocating motion into rotational motion. The dynamic governing equations of the system are first successfully derived by force balance. The non-linear dynamic analysis is next applied to derive approximate, asymptotic solutions. Stabilities associated with all solution are determined by subsequent analysis on the derived asymptotic solutions. In addition, the transformer could be integrated with coils, magnets, and electric circuits to form a portable energy scavenging device. A novel front-end circuit is proposed in this work for harvesting human’s energy. The situation of human’s walking and running is simulated by a shaker. And the ac-like energy is processed by the novel energy harvesting circuit, transformed as a DC voltage suitable for devices successfully. The efficiency of the entire circuit is proven up to 60%, and is an input-powered circuit with no standby power. A complete experimental system is also designed and successfully confirm the existence of the stable nonlinear solutions found by analytical and numerical analysis.

Dynamics of Assembled Structures: Taking Into Account the Surface Defects in Interfaces

In structural dynamics, the prediction of damping remains the biggest challenge. This paper deals with the energy losses caused by micro-slip in a nominally planar interface of a structure. This paper proposes an analytical and experimental study of flexural vibrations of a clamped-clamped beam with innovative position of the interfaces. The objective of this test bench is to characterize the global rheology of the interface. The proposed model aims to characterize this rheology based on local settings of the interface. First, the test bench is described and the choice of the position of the interface is justified. The experimental bench and the dynamic behavior of this structure are presented. We propose to illustrate the mechanism of energy losses by micro-slip by making a comparison between the behavior of a “monolithic” beam and a sectioned beam. Secondly, a modeling of the interface taking into account the surface defect is presented. The energy dissipated by friction in the interface is calculated during a loading cycle. This leads to a computation of the dissipated energy and thus to a nonlinear loss factor. Finally, we confront the loss factor calculated analytically and the measured one.

Torsional Vibration Detection Using High Sampling Rate and High Resolution Keyphasor Information

Torsional vibration excitation in rotating machinery can cause system reliability issues or even catastrophic failures. Torsional vibration detection and monitoring becomes an important step in rotating machinery condition monitoring, especially for those machines driven by a variable frequency drive (VFD), a pulse width modulation motor (PWM), or a synchronous motor (SM), etc. Traditionally, the torsional vibration is detected by a phase demodulation process applied to the signals generated by tooth wheels or optical encoders. This demodulation based method has a few unfavorable issues: the installation of the tooth wheels needs to interrupt the machinery normal operation; the installation of the optical barcode is relatively easier, however, it suffers from short term survivability in harsh industrial environments. The geometric irregularities in the tooth wheel and the end discontinuity in the optical encoder will sometimes introduce overwhelming contaminations from shaft order response and its harmonics. In addition, the Hilbert Transform based phase demodulation technique has inevitable errors caused by the edge effect in FFT and IFFT analyses. Fortunately, in many industrial rotating machinery applications, the torsional vibration resonant frequency is usually low and the Keyphasor® and/or encoder for speed monitoring is readily available. Thus, it is feasible to use existing hardware for torsional vibration detection. In this paper, we present a signal processing approach which used the Keyphasor/encoder data digitized by a high sampling rate and high digitization resolution analog-to-digital (A/D) convertor to evaluate the torsional vibration directly. A wavelet decomposition (WD) based method was used to separate the torsional vibration from the shaft speed, so that the time history of the torsional vibrations can be extracted without significant distortions. The developed approach was then validated through a synchronous motor fan drive and an industrial power generation system. Detailed results are presented and discussed in this paper.

Vibration of Bending-Torsion Coupled Resonance in a Rotor

In certain rotor systems, bending-torsion coupled resonance occurs when the rotational speed Ω (= 2π Ωrps) is equal to the sum/difference of the bending natural frequency ωb (= 2π fb) and torsional natural frequency ωθ(= 2πfθ). This coupling effect is due to an unbalance in the rotor. In order to clarify this phenomenon, an equation was derived for the motion of the bending-torsion coupled 2 DOF system, and this coupled resonance was verified by numerical simulations. In stability analyses of an undamped model, unstable rotational speed ranges were found to exist at about Ωrps = fb + fθ. The conditions for stability were also derived from an analysis of a damped model. In rotational simulations, bending-torsion coupled resonance vibration was found to occur at Ωrps = fb − fθ and fb + fθ. In addition, confirmation of this resonance phenomenon was shown by an experiment. When the rotor was excited in the horizontal direction at bending natural frequency, large torsional vibration appeared. On the other hand, when the rotor was excited by torsion at torsional natural frequency, large bending vibration appeared. Therefore, bending-torsion coupled resonance was confirmed.

Optimal Tuning of Centrifugal Pendulum Vibration Absorbers

This note provides an analytical proof of the optimal tuning of centrifugal pendulum vibration absorbers (CPVAs) to reduce in-plane translational and rotational vibration for a rotor with N cyclically symmetric substructures attached to it. The reaction forces that the substructures (helicopter or wind turbine blades, for example) exert on the rotor are first analyzed. The linearized equations of motion for the vibration are then solved by a gyroscopic system modal analysis procedure. The solutions show that the rotor translational vibration at order j is reduced when one group of CPVAs is tuned to order jN − 1 and the other is tuned to order jN + 1. Derivation of this result is not available in the literature. The current derivation also yields the better known result that tuning CPVAs to order jN reduces rotational rotor vibration at order j.

Load Optimization of a Nonlinear Mono-Stable Duffing-Type Harvester Operating in a White Noise Environment

This paper investigates electric load optimization of nonlinear mono-stable Duffing energy harvesters subjected to white Gaussian excitations. Both symmetric and asymmetric nonlinear restoring forces are considered. Statistical linearization is utilized to obtain an approximate analytical expression for the optimal load as function of the other systems parameters. It is shown that the optimal load is dependent on the nonlinearity unless the ratio between the harvesting circuit time constant and the period of the mechanical oscillator is very large. Under optimal loading conditions, a harvester with a symmetric nonlinear restoring force can never produce more power than an equivalent linear harvester regardless of the magnitude or nature of the nonlinearity. On the other hand, asymmetries in the restoring force are shown to provide performance enhancement over an equivalent linear harvester.

An Experimental Investigation Into the Performance of a T-Shaped Piezoelectric Flow Energy Harvester

The harvesting of flow energy by exploiting aeroelastic and hydroelastic vibrations has received growing attention over the last few years. The goal in this research field is to generate low-power electricity from flow-induced vibrations of scalable structures involving a proper transduction mechanism for wireless applications ranging from manned/unmanned aerial vehicles to civil infrastructure systems located in high wind areas. The fundamental challenge is to enable geometrically small flow energy harvesters while keeping the cut-in speed (lowest flow speed that induces persistent oscillations) low. An effective design with reduced cut-in speed is known to be the T-shaped cantilever arrangement that consists of a horizontal piezoelectric cantilever with a perpendicular vertical beam attachment at the tip. The direction of incoming flow is parallel to the horizontal cantilever and perpendicular to the vertical and symmetric tip attachment. Vortex-induced vibration resulting from flow past the tip attachment is the source of the aeroelastic response. For a given width of the T-shaped harvester with fixed thickness parameters, an important geometric parameter is the length ratio of the tip attachment to the cantilever. In this paper we investigate the effect of this geometric parameter on the piezoaeroelastic response of a T-shaped flow energy harvester. A controlled desktop wind tunnel system is used to characterize the electrical and mechanical response characteristics for broad ranges of flow speed and electrical load resistance using different vertical tip attachment lengths for the same horizontal piezoelectric cantilever. The variations of the electrical power output and cut-in speed with changing head length are reported along with an investigation into the electroaeroelastic frequency response spectra.

Global “Eclipse” Bifurcation in a Twinkling Oscillator

This work regards the use of cubic springs with intervals of negative stiffness, in other words “snap-through” elements, in order to convert low-frequency ambient vibrations into high-frequency oscillations, referred to as “twinkling”. The focus of this paper is on a global bifurcation of a two-mass chain which, in the symmetric system, involves infinitely many equilibria at the bifurcation point. The structure of this “eclipse” bifurcation is uncovered, and perturbations of the bifurcation are studied. The energies associated with the equilibria are examined.

Application of Cyclostationary Indicators for the Diagnostics of Distributed Faults in Ball Bearings

This paper deals with the detection of distributed faults in ball bearings. In literature most of the authors focus their attention on the detection of incipient localized defects. In that case classical techniques (i.e. statistical parameters, envelope analysis) are robust in recognizing the presence of the fault and its characteristic frequency. In this paper the authors focalize their attention on bearings affected by distributed faults, due to the progressive growing of surface wear or to low-quality manufacturing process. These faults can not be detected by classical techniques; in fact, in this case the signal does not contain impulses at the fault characteristic frequency, but more complex components with strong non-stationary contents. Distributed faults are here detected by means of advanced tools directly derived from the theory of cyclostationarity. In particular three metrics — namely Integrated Cyclic Coherence (ICC), Integrated Cyclic Modulation Coherence (ICMC) and Indicator of Second-Order Cyclostationarity (ICS2x) — have been calculated in order to condense the information given by the cyclostationary analysis and to help the analyst in detecting the fault in a fast fault diagnosis procedure. These indicators are applied on actual signals captured on a test rig where a degreased bearing running under radial load developed accelerated wear. The results indicated that all the three cyclostationary indicators are able to detect both the appearance of a localized fault and its development in a distributed fault, whilst the usual approach fails as the fault grows.