On the dynamics of a nonlinear energy harvester with multiple resonant zones

The dynamics of a nonlinear vibration energy harvester for rotating systems is investigated analytically through harmonic balance, as well as by numerical analysis. The electromagnetic harvester is attached to a spinning shaft at constant speed. Magnetic levitation is used as the system nonlinear restoring force for broadening the resonant range of the oscillator. The system is modelled as a Duffing oscillator with linear frequency variation under static, as well as harmonic excitation. Behaviour charts and backbone curves are extracted for the fundamental harmonic response and validated against frequency response curves for selected cases, using direct numerical integration. It is found that variation in stiffness, together with asymmetric forcing, gives rise to a novel structure of multiple resonant zones, incorporating mono-stable and bi-stable dynamics. Contrary to previously considered bi-stable energy harvesters, cross-well oscillations are realized through a transition from single-well potential energy to double-well with forward frequency sweep. Furthermore, in-well_oscillations present a hardening behaviour, unlike the well-known softening in-well response of bi-stable Duffing oscillators. The analysis shows that the proposed system has multiple resonant responses to a frequency sweep, influenced by consecutive interacting backbone curves similar to a multi-modal system. This combined effect of the transition to bi-stable dynamics and the hardening in-well oscillations induces resonant response of the harvester over multiple distinct frequency ranges. Thus, the system exhibits a broadened frequency response, enhancing its energy harvesting potential

A time-frequency analysis approach for condition monitoring of a wind turbine gearbox under varying load conditions

This paper deals with the condition monitoring of wind turbine gearboxes under varying operating conditions. Generally, gearbox systems include nonlinearities so a simplified nonlinear gear model is developed, on which the time–frequency analysis method proposed is first applied for the easiest understanding of the challenges faced. The effect of varying loads is examined in the simulations and later on in real wind turbine gearbox experimental data. The Empirical Mode Decomposition (EMD) method is used to decompose the vibration signals into meaningful signal components associated with specific frequency bands of the signal. The mode mixing problem of the EMD is examined in the simulation part and the results in that part of the paper suggest that further research might be of interest in condition monitoring terms. For the amplitude–frequency demodulation of the signal components produced, the Hilbert Transform (HT) is used as a standard method. In addition, the Teager–Kaiser energy operator (TKEO), combined with an energy separation algorithm, is a recent alternative method, the performance of which is tested in the paper too. The results show that the TKEO approach is a promising alternative to the HT, since it can improve the estimation of the instantaneous spectral characteristics of the vibration data under certain conditions

A hypoid gear pair tribo-dynamic model taking into account the rheological behaviour of fully formulated gear lubricants

A fully coupled tribo-dynamic model, capable of predicting the inefficiency and dynamic response of automotive differential hypoid gear pairs, is presented in this study. A gear dynamics solver is coupled with an analytical friction solver, which calculates the viscous shear, as well as the boundary conjunctional friction force. The time varying geometry and contact characteristics of the hypoid gear pair are taken into account by using realistic data available in the literature. The rheological models employed cover a range of two different behaviors: Newtonian and non-Newtonian Eyring (shear thinning). The Chittenden-Dowson equation is used to calculate the central film thickness of the elasto-hydrodynamic teeth conjunctions. The boundary friction force is calculated using the Greenwood & Tripp model. Finally, the actual surface topography of a run-in hypoid gear is obtained using a stylus profilometer. The results indicate an overestimation of the viscous friction by the Newtonian model, as opposed with the non-Newtonian model, mainly due to shear thinning effects. Comparative studies are performed for different operating conditions, namely near or away from resonance, as well as for conditions corresponding to a non-linear sub-harmonic resonance. The frictional damping effect on the dynamic transmission error, which is an indication of the NVH response of the gear pair, is also examin

Comparison between transfer path analysis methods on an electric vehicle

A comparison between transfer path analysis and operational path analysis methods using an electric vehicle is presented in this study. Structure-borne noise paths to the cabin from different engine and suspension points have been considered. To realise these methods, two types of test have been performed; operational tests on a rolling road and hammer tests in static conditions. The main aim of this work is assessing the critical paths which are transmitting the structure-borne vibrations from the electric vehicle's vibration sources to the driver's ear. This assessment includes the analysis of the noise contribution of each path depending on the frequency and vehicle speed range and moreover, the assessment of the path noise impact for harmonic orders which arise due to the physical components of the electric vehicle. Furthermore, the applicability of these methods to electric vehicles is assessed as these techniques have been extensively used for vehicles powered with internal combustion engines

Targeted Energy Transfer and Modal Energy Redistribution in Automotive Drivetrains

The new generations of compact high output power-to-weight ratio internal combustion engines generate broadband torsional oscillations, transmitted to lightly damped drivetrain systems. A novel approach to mitigate these untoward vibrations can be the use of nonlinear absorbers. These act as Nonlinear Energy Sinks (NESs). The NES is coupled to the primary (drivetrain) structure, inducing passive irreversible targeted energy transfer (TET) from the drivetrain system to the NES. During this process, the vibration energy is directed from the lower-frequency modes of the structure to the higher ones. Thereafter, vibrations can be either dissipated through structural damping or consumed by the NES. This paper uses a lumped parameter model of an automotive driveline to simulate the effect of TET and the assumed modal energy redistribution. Significant redistribution of vibratory energy is observed through TET. Furthermore, the integrated optimization process highlights the most effective configuration and parametric evaluation for use of NES

Isothermal Elastohydrodynamic Lubrication Analysis of Heavily Loaded Hypoid Gear Pairs

A numerical model able to predict the pressure distribution and the film thickness in heavily loaded elliptical EHL contacts is developed and presented in this study. The operating conditions, such as the contact load and the velocities of the mating surfaces, are representative of the corresponding conditions present in automotive differential hypoid gear pair units. The EHL solver presented is able to predict the minimum and central film thickness of the lubricating oil as well as the pressure distribution assuming isothermal and Newtonian conditions. Results are presented for a full quasi-static meshing cycle. A comparison between the numerically calculated values of the central and the minimum film thickness is performed against the corresponding values produced using the Chittenden-Dowson formula. A very good agreement is observed between the values of the central film thickness. However, it is shown that the minimum film thickness values using the Chittenden-Dowson formula can deviate up to 40% compared with the corresponding values which are calculated numerically

Film Thickness Investigation in Heavily Loaded Hypoid Gear Pair Elastohydrodynamic Conjunctions

Introduction: Hypoid gear pairs are some of the most highly loaded components of the differential unit in modern automobiles. Prediction of wear rate and generated friction require determination of lubricant film thickness. However, only very few investigations have addressed the issue of thin elastohydrodynamic films in hypoid gear pairs. The main reason for dearth of analysis in this regard has been the need for accurate determination of transient contact geometry and kinematics of interacting surfaces throughout a typical meshing cycle. Furthermore, combined gear dynamics and lubrication analysis of any pairs of simultaneous meshing teeth pairs is required. Simon [1] was among the first to deal with these issues. He used Tooth Contact Analysis (TCA) in order to calculate the instantaneous contact geometry and load for any teeth pair during their meshing cycle. However, in his study, the load carried by the hypoid pair was quite low, making the application of the results limited and not entirely suitable for real life operating conditions of typical hypoid gear pairs of vehicular differentials, which is of interest in the current paper. Xu and Kahraman [2] performed numerical prediction of power losses and consequently the film thickness for highly loaded hypoid gear pairs. However, in their study only the one-dimensional Reynolds equation was employed. Consequently, the effect of lubricant side leakage in the passage through the contact was ignored. A more recent study by Mohammadpour et al. [3] employed realistic gear geometry data (through the use of TCA) for calculation of film thickness time history through mesh. The two-dimensional Reynolds equation, accounting for the side leakage of the lubricant, was solved numerically. It was shown that the side leakage component of the entraining velocity can significantly influence the film thickness. With regard to hypoid gear dynamics, several studies should be mentioned. Wang and Lim [4] studied the dynamic response of hypoid gear pairs under the influence of time varying meshing stiffness. Yang and Lim [5] created a model able to predict the dynamic response of a hypoid gear pair by taking into account the lateral translations of their shafts due to the compliance of the supporting bearings. Karagiannis et al. [6-7] studied the dynamics of automotive differential hypoid gear pairs by taking into account the velocity dependent resistive torque at the gear caused by aerodynamic drag and tyre-road rolling resistance. The study integrated the gear dynamics with the generated viscous and boundary conjunctional friction

Tribodynamics of hydraulic actuated clutch system for engine-downsizing in heavy duty off-highway vehicles

Engine downsizing is desired for modern heavy-duty vehicles to enhance fuel economy and reduce emissions. However, the smaller engines usually cannot overcome the parasitic loads during engine start-up. A new clutch system is designed to disconnect the downsized engine from the parasitic losses prior to the idling speed. A multi-scale, multi-physics model is developed to study the clutch system. Multi-body dynamics is used to study the combined translational–rotational motions of the clutch components. A micro-scale contact model is incorporated to represent the frictional characteristics of the sliding surfaces. Although the clutch is designed for dry contact operation, leakage of actuating hydraulic fluid can affect the interfacial frictional characteristics. These are integrated into the multi-body dynamic analysis through tribometric studies of partially wetted surfaces using fresh and shear-degraded lubricants. Multi-scale simulations include sensitivity analysis of key operating parameters, such as contact pressure. This multi-physics approach is not hitherto reported in the literature. The study shows the importance of adhesion in dry clutch engagement, enabling full torque capacity. The same is also noted for any leakage of significantly shear-degraded lubricant into the clutch interfaces. However, the ingression of fresh lubricant into the contact is found to reduce the clutch torque capacity

Comparison between transfer path analysis methods on an electric vehicle

A comparison between transfer path analysis and operational path analysis methods using an electric vehicle is presented in this study. Structure-borne noise paths to the cabin from different engine and suspension points have been considered. To realise these methods, two types of test have been performed; operational tests on a rolling road and hammer tests in static conditions. The main aim of this work is assessing the critical paths which are transmitting the structure-borne vibrations from the electric vehicle?s vibration sources to the driver?s ear. This assessment includes the analysis of the noise contribution of each path depending on the frequency and vehicle speed range and moreover, the assessment of the path noise impact for harmonic orders which arise due to the physical components of the electric vehicle. Furthermore, the applicability of these methods to electric vehicles is assessed as these techniques have been extensively used for vehicles powered with internal combustion engines.The authors would like to acknowledge the COST ACTION TU1105 for supporting this research

Impact of optical coherence tomography on diagnostic decision-making by UK community optometrists: a clinical vignette study.

PURPOSE: In recent years, there has been widespread investment in imaging technologies by community optometrists in the UK, most notably optical coherence tomography (OCT). The aim of the current study was to determine the value of OCT in the diagnosis of posterior segment diseases in a representative sample of community optometrists using a clinical vignette methodology. METHODS: A group of community optometrists (n = 50) initially completed a standardised training package on OCT interpretation followed by a computer-based assessment featuring 52 clinical vignettes, containing images of healthy (n = 8) or glaucomatous (n = 18) discs or healthy (n = 8) or diseased (n = 18) fundi. Each vignette featured either a single fundus/disc photographic image, or a combination of a fundus/disc image with the corresponding OCT scan. An expert panel confirmed that the fundus images presented alone and those in combination with OCT data were of a similar level of difficulty and that the cases were typical of those seen in primary care. For each case, the optometrist selected their diagnosis from a pull-down list and reported their confidence in their decision using a 10-point Likert scale. Pairwise comparisons of the fundus image alone and fundus image/OCT combination were made for both diagnostic performance and confidence. RESULTS: The mean percentage of correct diagnoses using fundus imaging alone was 62% (95% CI 59-64%) and for the combination of fundus image/OCT was 80% (95% CI 77-82%). The mean false negative rate with fundus alone was 27% reducing to 13% with the OCT combination. Median confidence scores for fundus imaging alone was 8.0 (IQR 7.0-8.0) and 8.3 (IQR 8.0-9.0) for the combination. Improvements in performance and confidence were statistically significant (p < 0.001). CONCLUSION: The results from this vignette study suggests that OCT improves optometrists' diagnostic performance compared to fundus observation alone. These initial results suggest that OCT provides valuable additional data that could augment case-finding for glaucoma and retinal disease; however, further research is needed to assess its diagnostic performance in a routine clinical practice setting