Dual Purpose Tunable Vibration Isolator Energy Harvester: Design, Fabrication, Modeling and Characterization

This dissertation is focused on design, fabrication, characterization, and modeling of a unique dual purpose vibration isolation energy harvesting system. The purpose of the system is to, simultaneously, attenuate unwanted vibrations and scavenge kinetic energy available in these vibrations. This study includes theoretical modeling and experimental work to fully characterize and understand the dynamic behavior of the fabricated dual purpose system. In the theoretical study, both numerical (Runge-Kutta) and analytical (Harmonic Balance Method, HBM) methods are used to obtain the dynamic behavior of the system. The system features a combination of mechanical and electromagnetic components to facilitate its dual functionality. The system consists of a magnetic spring, mechanical flat spring, and dampers. The combination of negative stiffness of the magnetic spring with positive stiffness of the mechanical spring results in lowering the cut off frequency of the system. Lowering the cut off frequency improves the device’s ability to operate in a wider range of frequencies. Results from dynamic measurements and model simulation confirm the ability of the device to function in both vibration isolation and energy harvesting modes simultaneously. The dual-purpose device is able to attenuate vibrations higher than 12.5 [Hz]. The device also produces 26.8 [mW] output power at 1g [m/s2] and 9.75 [Hz]. Performance metrics of the device including displacement transmissibility and energy conversion efficiency are formulated. Results show that for low acceleration levels, lower damping values are desirable and yield higher energy conversion efficiencies and improved vibration isolation. At higher acceleration, there is a trade-off where lower damping values worsen vibration isolation but yield higher conversion efficiencies

Design of Bio-Inspired Multifrequency Acoustic Sensors and Metamaterial Energy Harvesting Smart Structures

Due to the limited availability and high depletion rates of nonrenewable sources of energy as well as environmental concerns, the scientific community has started to explore many alternative clean sources of energies. It is identified that civil, mechanical and Aerospace structures are always subjected to acoustic noises and vibration which could potentially be used as renewable source of energy. Roads and Industrial noise barriers are used inside industrial facilities alongside the walls, around construction pillars, nearby machinery and other equipment to separate quite work zones, protect walls, deliver extra safety and precautions while diminish sound and vibrational pressure. We hypothesized if these noise barriers/structures could serve dual purposes, while harvest energies from the filtered noises and vibrations, significant energies could be renewed. Such renewable energies could be then used for different purposes, like charging cell phones, wearable devices, powering small electronics and remote sensors etc. Additionally, due to gravity, it is natural that our heavy mechanical equipment runs, operates, walks on the ground which are covered by cosmetic materials. Such materials encounter continuously changing pressure on the surface which is otherwise waisted if not harvested. Keeping these applications in mind for walls/ barriers/ tiles, oin this dissertation, utilizing one unique physics, two different type of renewable energy harvesting technologies are proposed. While proposing the application of harvesting and noise filtering, similar physics/mechanics prevalent in cochlea of human inner ear, further motivated this dissertation to device bio-inspired acoustic bandpass sensor. The harvesting and sensing devices that are conceptualized, analytically modeled, numerically simulated via COMSOL Multiphysics software, optimized, fabricated and tested to present the proof of concept are presented below. All models are numerically 1) A novel three-dimensional piezoelectric energy harvester based on a metamaterial structure is proposed, which is capable of scavenging energy at very low frequencies (\u3c~1kHz) from multi-axial ambient vibrations. The proposed structure and its unit cell exploit the negative mass at local resonance frequencies and entraps the vibration energy as dynamic strain. The captured kinetic energy is then transformed to electric potential using three Lead Zirconate Titanate wafers, optimally embedded in the cell\u27s soft constituent. 2) In the second design, a multi-frequency vibration-based energy harvester unit cell which is inspired from the design of human inner-ear, i.e. a snail-shaped model to enhance differential shear deformation of a membrane is proposed. Next an array of the proposed cell in the form of metamaterial bricks in a wall or a metamaterial tiles on the ground (Meta-tile) are modeled and fabricated to experimentally validated the concept. A spiral snail shaped PVDF membrane is embedded inside a Polydimethylsiloxane (PDMS) matrix that entraps the kinetic energy of the vibration within its structure. Numerical and experimental studies show that the unit cell and the Meta-tiles can harvest electrical power of up to ~1.8 mW and 11 mW against a 10KΩ resistive load, respectively. 3) Concurrent to the development of electronic processing of frequencies, mechanical sensors capable of selecting, processing, filtering specific single or a distinct band of frequencies are contributing an essential role in many sciences, technologies and industrial applications. After developing the energy harvester devices, the next objective of this PhD dissertation is to present a scalable numerical model along with a fabricated proof of concept of a bio-inspired acoustic bandpass sensor with a user-defined range of frequencies. In the proposed sensor, the geometric structure of a human’s basilar membrane is adopted as the main model to capture the sonic waves with a target frequency ranges. Human’s basilar membrane in the inner ear could be investigated in two ways, a) plate type and b) beam type. Both models are numerically and experimentally validated. In the first step, a predictive mathematical model of the proposed bandpass sensor is developed based on a plate type model. Next, the dynamic behavior of beam-type basilar membrane with 100 Zinc-Oxide electrodes is modeled and numerically verified. A sensor array is fabricated with using photolithography techniques with Polyvinylidene Difluoride (PVDF) piezoelectric material as a proof-of-concept. The fabricated plate-type sensor is experimentally tested, and its effective performance is validated in the frequency range of ~3 kHz-8 kHz. Similarly, in beam model the longest electrode is near the Apex region (8 mm x 300 μm x 20 μm thick) and the shortest electrode is near the Base side of the sensor with (3 mm x 300 μm x 110 μm thick) are proposed. Eventually, the effective performances of the proposed acoustic sensors are verified using COMSOL Multiphysics Software and the functionality of the proposed sensor appeared in the frequency range of ~ 0.5 kHz near Apex and to ~ 20 kHz near base side. To run all the required experiments on the fabricated energy harvesters and acoustic sensors in this dissertation, a novel three-dimensional exciter is developed as a miscellaneous work. A high percentage of failures in sensors and devices employed in harsh industrial environments and airborne electronics is due to mechanical vibrations and shocks. Therefore, it is important to test the equipment reliability and ensure its survival in long missions in the presence of physical fluctuations. Traditional vibration testbeds employ unidirectional acoustic or mechanical excitations. However, in reality, equipment may encounter uncoupled (unidirectional) and/or coupled (multidirectional) loading conditions during operation. Hence, to systematically characterize and fully understand the proposed energy harvesters’ and acoustic sensors’ behaviors, a testbed capable of simulating a wide variety of vibration conditions is required which is designed, and fabricated. The developed testbed is an acousto electrodynamic three-dimensional (3-D) vibration exciter (AEVE 3-D), which simulates coupled and decoupled (with unpowered arms) 3-D acoustic and/or 3-D mechanical vibration environments. AEVE 3-D consists of three electromagnetic shakers (for mechanical excitation) and three loudspeakers (for acoustic excitation) as well as a main control unit that accurately calculates and sets the actuators\u27 input signals in order to generate optimal coupled and decoupled vibrations at desired frequencies. In this paper, the system\u27s architecture, its mechanical structure, and electrical components are described. In addition, to verify AEVE 3-D\u27s performance, various experiments are carried out using a 3-D piezoelectric energy harvester and a custom-made piezoelectric beam

Modelling of the circular edge-clamped interface of a hydraulic pressure energy harvester to determine power, efficiency and bandwidth

There is an increasing desire to monitor and control hydraulic systems in an autonomous and battery-free manner. One solution to this challenge is to harvest hydraulic pressure ripples and noise by exploiting the piezoelectric effect. This paper develops a new generalized model of a hydraulic piezoelectric harvester based on a circular edge-clamped flat plate interface with a central piezoelectric stack. Such a model allows the relationships between harvesting performance and structure to be assessed in detail. It is demonstrated that the force-deflection relationship of a circular edge-clamped plate with a central lumped mass follows a cubic hardening Duffing equation. A single degree of freedom (SDOF) lumped-parameter model of the system is established where the nonlinear frequency response resulting from hardening nonlinearities are explored. The input mechanical energy and the output electrical energy both exhibit a quadratic nonlinear relationship with vibration amplitude. The maximum output occurs at the jump-down frequency and the overall energy conversion efficiency of the system is determined. The optimum resistance load for maximum output energy and energy efficiency are obtained as non-dimensional excitation frequency. Experimental validation is performed and good agreement is observed between model results and experimental measurements. The developed model provides important insights into the optimization of power output and response of future hydraulic energy harvesting devices.</p

Development Of A Vibration Based Electromagnetic Energy Harvester (EEH) Using Graphene Silver Conductive Direct-Write Process For Automotive Thermal-Sensor

Vibration Energy Harvesting is the concept of converting the kinetic energy inherent in vibrations to electricity. Vibration comes from many sources either natural vibration or forced vibration and vibration also can cause severe issue that may produce noise,impede stability and generate crack in structure.However,it can be beneficial in energy harvester as one of the power source which can be harvest and turn into electricity. With the development of low power energy harvester in recent years have given many opportunities to these sensors to functioning autonomously and wireless, especially in automotive.Furthermore, microelectromechanical systems (MEMS) concept has been on focus lately and become most important aspect in energy harvesting in micro-size device because the advantages of low-volume,low-weight and integration capability with other MEMS components.A double electromagnetic energy harvester (EEH) with three layer of conductive ink as coil was developed.The coil was made from graphene and silver conductive ink as a replacement of initial copper coil winding which limited for its bulky size and heavy weight.This research had study the conductivity of the conductive ink and development of the EEH’s device and system.EEH device also focused on its layers of the conductive ink coil and output power.The coil was printed on TPU or PET substrate due to their flexibility.Test was done on the conductive ink to find the most conductive material for the coil,which 40% loading composition of graphene and 80% laoding composition of silver gave most lower resistivity which resistivity,R is inversely proportional with current,I.Furthermore,damping test was done to measure damping coefficient of both conductive ink which graphene conductive ink’s damping coefficient is 0.01585 and for silver conductive ink is 0.00654.This damping coefficient will be used to obtain the output power of the EEH.Lastly,vibration experiment was done and from the experiment,EEH produce more power with more layers was printed but the power output was decreased with the increasing of the frequency

Design and Modelling of a Novel Hybrid Vibration Converter based on Electromagnetic and Magnetoelectric Principles

Supplying wireless sensors from ambient energy is nowadays highly demanded for a higher flexibility of use and low system maintenance costs. Vibration sources are thereby especially attractive due to their availability and the relatively high energy density they can provide. The aim of this work is to realize a hybrid energy converter for vibration sources having low amplitude and low frequency. The idea is to combine two diverse harvesters to realize a higher energy density and at the same time to improve the converter reliability. We focus on the design, modeling, and test of the hybrid vibration converter. For an appropriate converter design, the vibration profiles of several ambient vibration sources are characterized. The results show that the typical frequency and acceleration ranges are between 5 Hz to 60 Hz and 0.1 g to 1.5 g respectively. The proposed converter is based on the magnetoelectric (ME) and electromagnetic (EM) principles. These two principles can be easily combined within almost the same volume, because they generate energy form the same varying magnetic field coupled to the mechanical vibration of the source. Thereby, the energy density is improved as the ME converter is incorporated within the relatively large coil housing of the electromagnetic converter. The proposed converter is based on the use of a magnetic spring instead of the typically used mechanical springs, which applies the repulsive force to the seismic mass of the converter. The applied vibration is transmitted to the converter based on the magnetic spring principle instead of the conventional mechanical springs. Due to the nonlinearity of the magnetic spring, the converter is able to operate for a frequency bandwidth instead of resonant frequency which is the case while using a mechanical spring. Hence, this leads to realize a high converter efficiency even under random vibrations characterized by frequency bandwidth. As well, using magnetic spring principle enables to adjust the resonant frequency of the converter relative to the applied vibration source easily by just adjusting the moving magnet size. For the converter design, a parametric study is conducted using finite element analysis. Two main criteria are thereby taken into account, which are the compactness and the efficiency of the converter. Parameters affecting these two criteria are classified in mechanical, electromagnetic and magnetoelectric parameters. Results show that the combination of the EM and ME principles leads to an improvement of the energy output compared to a single EM or ME converter. The novel hybrid converter is realized and tested under harmonic and real vibration profiles. It comprises two main parts: A fixed part, where the coils and the ME transducer are fixed in order to ensure a good reliability of the converter by avoiding wire movements. A moving part, where the moving magnet of the magnetic spring and the magnetic circuit are placed. The presented converter is reliable and compact, which is able to harvest energy with a maximum output power density of 0.11 mW/cm³ within a frequency bandwidth of 12 Hz for a resonance frequency of 24 Hz under an applied harmonic vibration with an amplitude of 1 mm.Die Versorgung von drahtlosen Sensoren aus der Umgebungsenergie ermöglicht heutzutage eine hohe Einsatzflexibilität und die Senkung des Systemwartungsaufwands. Schwingungsquellen sind aufgrund ihrer Verfügbarkeit und der damit erreichbaren Energiedichte besonders attraktiv. Ziel dieser Arbeit ist es, einen hybriden Energiewandler für Vibrationsquellen mit geringer Amplitude und niedriger Frequenz zu realisieren. Der Ansatz dabei ist, zwei verschiedene Wandler zu kombinieren, um eine höhere Energiedichte zu erreichen und die Zuverlässigkeit zu verbessern. Der Entwurf konzentriert sich auf die Modellierung und den Test des hybriden Vibrationswandlers. Für einen geeigneten Wandlerentwurf werden die Schwingungsprofileigenschaften mehrerer Umgebungsschwingungsquellen untersucht. Die Ergebnisse zeigen, dass die typische Frequenz zwischen 5 Hz und 60 Hz und der Beschleunigungsbereich zwischen 0,1 g und 1,5 g liegen. Der vorgeschlagene Wandler kombiniert das magnetoelektrischen (ME) Prinzip mit dem elektromagnetischen (EM) Prinzip. Diese beiden Prinzipien können innerhalb des fast gleichen Volumens leicht integriert werden, da sie Energie aus der Variation des gleichen Magnetfeldes, das mit der mechanischen Schwingung gekoppelt ist, erzeugen können. Dadurch wird die Energiedichte verbessert, da der ME-Wandler in das relativ große Spulengehäuse des elektromagnetischen Wandlers eingesetzt werden kann. Darüber hinaus basiert der vorgeschlagene Wandler auf der Verwendung von Magnetfedern, um die Repulsivkraft auf die seismische Masse zu realisieren. Aufgrund der Nichtlinearität der Magnetfeder, kann der Wandler in einem breiteren Frequenzbereich betrieben werden, anstatt nur bei der Resonanzfrequenz, wie es bei der Verwendung einer mechanischen Feder der Fall ist. Dies führt dazu, dass der Wandler auch bei zufälligen breitbandigen Schwingungsquellen effizient betrieben werden kann. Darüber hinaus ermöglicht die Verwendung des Magnetfederprinzips eine einfache Einstellung der Resonanzfrequenz des Wandlers in Bezug auf die Schwingungsquelle, durch Einstellen der Größe des beweglichen Magneten. Für den Wandlerentwurf wird eine Parameterstudie mit Hilfe der Finite-Elemente-Analyse durchgeführt. Zwei Hauptkriterien werden dabei berücksichtigt: Die Kompaktheit und die Energieeffizienz des Wandlers. Parameter die diese beiden Kriterien beeinflussen, können in mechanische, elektromagnetische und magnetoelektrische unterteilt werden. Die Ergebnisse haben gezeigt, dass die Kombination der EM- und ME-Prinzipien zu einer Verbesserung der Energieausbeute im Vergleich zu einem einzelnen EM- oder ME-Wandler geführt hat. Der neuartige Hybrid-Wandler wurde realisiert und unter harmonischen und realen Schwingungsprofilen getestet. Der Wandler besteht aus zwei Hauptteilen: Ein festes Teil, an dem die Spulen und der ME-Wandler befestigt sind, um eine hohe Zuverlässigkeit zu gewährleisten indem auf einen beweglichen Draht verzichtet wird, und ein bewegliches Teil, das sich aus einem beweglichen Magneten zusammensetzt. Der vorgestellte Wandler ist zuverlässig, kompakt und in der Lage, Energie mit einer maximalen Ausgangsleistungsdichte von 0,11 mW/cm 3 und einer Bandbreite von 12 Hz bei einer Resonanzfrequenz von 24 Hz unter einer angelegten harmonischen Schwingung mit einer Amplitude von 1 mm zu gewinnen

Design, Modelling and Fabrication of a Hybrid Energy Harvester

As sources of energy are becoming more scarce and expensive, energy harvesting is receiving more global interest and is currently a growing field. Energy harvesting is the process of converting ambient energy, such as vibration, to electrical energy that can power a multitude of applications. Vibration energy is the by-product of everyday life; it is generated from any perceivable activity. While typically viewed as noise, there is a strong potential for harvesting this energy and deploying it to useful applications. The focus of this thesis will be using vibration as the ambient source of energy. Hybrid energy harvesters employ more than one of the harvesting technologies. In this thesis, two hybrid harvesters that utilize piezoelectric, magnetostrictive, and electromagnetic technologies are designed, modelled, and tested. Both of these harvesters have beams that are spiral in shape. The use of the spiral geometry allows the system to have a lower natural frequency as opposed to the traditional cantilever beam, while still maintaining a high volume of active material. The first harvester that is discussed is the P-MSM harvester. It utilizes piezoelectric and magnetostrictive material. Both materials are configured in a spiral beam geometry and allowed to resonate independently. The resonance frequency of these two materials is designed to create wideband energy harvesting. This allows the harvester to be operating efficiently even if the ambient vibration shifts a small amount. The second harvester that is discussed is the P-MAG harvester. It utilizes piezoelectric and electromagnetic technologies. It also incorporates a spiral geometry for the piezoelectric layers and includes a magnet attached at the centre. The magnet is placed in the centre of the spiral to reduce the natural frequency of the system and to also actively contribute to the harvesting. This harvester has two sources operating at the same resonant frequency, which allows it to have a larger power output than if the sources were separated. Finally, finite element analysis was used to model both harvesters. ANSYS was used for the piezoelectric material and COMSOL was used for the electromagnetic material. The results are compared to the experimental and are in good agreement.4 month

Development of Acoustic Metamaterial Noise Barriers and Simultaneously Harvesting Energy Using Smart Materials

In our surroundings abundant energy, we either feel through component vibration or hear noises from acoustic sources. Harvesting these unused and untapped green energy in the form of ambient vibration, and acoustic sounds is an emerging field of research in recent years. Utilization of the energy within a wide band of the frequency spectrum originated from the vibrational sources alone stands as one of the most promising ways to power small electronic devices, smartphones, local structural health monitoring sensors, home, and workshop appliances. These abundant sources of green energy are available in almost all the engineering industries, workshops, manufacturing facilities, construction zones, and in our daily operations. Particularly aerospace, mechanical, and civil sectors have plenty of such scenarios where the energy used is lost through vibration and acoustic noises. Continuously running machinery in a workshop, ambient vibration in a manufacturing facility, vibrating wings of an aircraft, high dB aircraft noise near airports, noise in metallurgical plants, power plants, vehicle noise near a roadside facility, etc. are few examples of the ambient source of energy that can be harvested which are otherwise wasted. If a suitable mechanism is devised, the vibration and acoustic noise sources can be equipped to trap and reclaim the energy to create local power sources. Researchers proposed many such methods in the past two decades. However, only recently researchers including us proposed that carefully engineered metamaterials can also be used for energy harvesting. Metamaterials are man-made materials that behave uniquely and possess exclusively desired properties that are not found in natural materials. Usually, it is the combination of two or more materials and can be engineered to perform specific tasks that are not possible with traditional materials. These were initially discovered in photonics while working with electromagnetic radiation. An electromagnetic counterpart of wave propagation in mechanics, i.e. phononics with acoustic waves were found to be affected by the metamaterials. These acoustic metamaterials when carefully designed are also capable of affecting the wave propagation characteristics through fluids such as air. Many acoustic metamaterials have gone beyond its definition but still, characterize the waveguiding properties. They are classified under the passive modalities of acoustics to affect the sound and vibration mitigation. Incorporation of smart materials while constructing acoustic metamaterial, can enhance the multifunctionality of these materials in both passive and active ways. A prospective application field for such acoustic metamaterials is energy harvesting from low-frequency vibrations. Conventionally, passive acoustic metamaterials are visualized as noise barrier materials to filter roadside and industrial noises. This application can get extended to the aerospace application where mitigation of engine noise inside the cabin is challenging. Irrespective of their target applications, acoustic metamaterials integrated with smart materials can scavenge the very green energy that they are designed to absorb and mitigate. First, in this research work, a recently proposed method of creating Acoustoelastic Metamaterial (AEMM) is used to investigate further if that can be used to harvest energy from the industrial noise barriers. It is known that noise barriers are designed to minimize noise outside the boundary like the noise barriers seen beside the highways. Construction materials like concrete, steel, vinyl, wood, or earth mounds are used in the industrial sound barriers that can reduce the sound pressure level (dB) on the other side of the barriers. In this work, a novel metamaterial wall (MetaWall) is proposed to redefine the industrial sound isolation wall using the integrated AEMM units. In this part, wave isolation and energy harvesting capabilities of the acoustic metamaterial is fused to propose MetaWall unit bricks, which are made of rubber-metal-concrete composite, as an industrial building material. Secondly, it is proposed that such acousto-elastic metamaterial (AEMM) models can also be used in the aerospace industry to power the online NDE/SHM sensors, e.g. piezoelectric wafer active sensors which are widely used. Hence, further in this part, a rigorous study is made to find the actual power required by the online NDE / SHM sensors such that a similar amount of power can be harvested by the AEMM model and stored in a battery for scheduled scans. The ultimate goal of this second study is to minimize the size of the proposed AEMM model to make it suitable for aerospace applications on-board. With changes in the materials of the cell constituents, it is shown that the power outputs from a similar model can be significantly altered and further optimized. A parametric study is also performed to show the variation of the output power. Finally, based on the learning a plate-type metamaterial is proposed to harvest a required optimum amount of energy from the ambient vibration with dominant frequency as low as 100Hz. In the third section, a spiral-shaped acoustic metamaterial is proposed which has dual functionality of noise filtering and energy harvesting over a wider range of frequencies. A work in progress presented with a proposed timeline to complete the dissertation. This acoustic metamaterial has a comparatively high reflection coefficient closer to the anti-resonance frequencies, resulting in high sound transmission loss. The filtered noise is trapped inside the cell in the form of strain energy. The spiral design is also sensitive to the vibration due to trampoline shaped in highly flexible polymeric piezoelectric material attachments inside the cell. This also makes it capable of harvesting energy using vibration. This is a promising acoustoelastic metamaterial with multifunctionality properties for future applications. Hence, it is claimed that if metamaterials are employed to reduce or suppress the noise and make use of the trapped energy which is any way wasted could be harvested to power the local electronic devices. The new solution could make a transformative impact on the 21st century’s green energy solutions. Calculated placement of smart materials in the cell-matrix can help to extract the strain energy in the form of power. The acoustic metamaterial cell designs presented in this research have the capability of isolating noise and reducing diffraction by trapping sound in a wide range of frequencies and at the same time recover the trapped abundant energy in the form of electrical potential using piezoelectric materials

Human-powered inertial energy harvesters: the effect of orientation, location and activity on the obtainable electrical power

Human-powered inertial energy harvesting is an emerging technology that can power electronic devices using electrical energy scavenged from human motion. Traditional energy harvesters generate energy only from a single axis, and are referred to one degree-of-freedom (1-DOF) energy harvesters. In this thesis, a two degree-of-freedom (2-DOF) energy harvester consisting of two orthogonal 1-DOF energy harvesters is studied. This research theoretically and experimentally investigates the effect of orientation, location and activity on the obtainable power from 2-DOF human-powered inertial energy harvesters.An on-body measurement study has been conducted to collect acceleration data from five key locations on the body during both walking and running. The collected data have been analyzed to evaluate the harvestable power along different orientations of both 1-DOF and 2-DOF inertial energy harvesters. The results show that the orientation of 1-DOF generators on the body greatly affects the output power. 2-DOF generators can maintain a more constant power output with rotation, thus are more reliable than 1-DOF generators. For 1-DOF generators, and for each location and activity, only 6% of the tested orientations harvest over 90% of the maximum power. For 2-DOF generators, this is increased to 32%, showing a considerable improvement.To validate the analytical results, 1-DOF mechanical- and magnetic-spring electromagnetic generators have been designed and prototyped. A novel design has been proposed to linearise magnetic springs for low frequency use. Experimental validation shows that the design exhibits a linearity of 2% across a ±25 mm displacement range, presenting a significant improvement over the state-of-the-art. A 2-DOF inertial generator that consists of two orthogonal 1-DOF mechanical-spring generators has been tested at three locations around the knee while running. At each location, the 2-DOF generator has been rotated to four different angles. The results show that 2-DOF generators can generate over 81% of the maximum power in all orientations. For 1-DOF generators, it is only 35%