Model and Validation of Static and Dynamic Behavior of Passive Diamagnetic Levitation for Energy Harvesting

This dissertation reports the investigation conducted on the static and dynamic behavior of the passive diamagnetic levitation systems. Attachment of a device to a substrate hinders the optimum performance ability of vibrating devices by altering the dynamic behavior of the moving part whilst introducing higher overall stiffness. The significance of this effect is prominent especially in vibration based energy harvesters as higher stiffness elevates the resonance frequency of the system, making it difficult to tune into ambient low frequencies. Other advantages of the proposed method are given by the removal of mechanical bending elements, which are often the source of energy dissipation through thermo-elastic damping and affects device reliability and durability. In this research, diamagnetically levitated resonators that can be utilized in energy harvesting were proposed and investigated as a possible solution to overcome these problems. Permanent magnets in an opposite neighboring poles (ONP) configuration were used to provide the magnetic field required for levitation. Pyrolytic graphite (PG), which is the known highest diamagnetic material, serves as the levitating proof mass. Experimental results show that the static levitation height has a linear dependence on the thickness and a nonlinear dependence on the area of the levitating proof mass that can be approximated to a third order polynomial equation. Also, the study proved that a thinner proof mass provides a higher air gap while length of the proof mass beyond a certain value (l \u3e10 mm for the experimental system considered in this dissertation) has no significant effect on increasing the air gap. It was also observed that levitation can slightly increase by attaching magnets to a sheet of steel (ferromagnetic material). To the best of my knowledge, this dissertation is the first to address the parameterized studies in the dynamics of diamagnetic levitated objects by permanent magnets. Measurements performed on a diamagnetic levitating prototype system show that the resonance frequencies are lowered by approximately 3- 4 orders of magnitude in levitated systems compared to the attached systems demonstrating the feasibility of using levitating techniques for micro to meso scale energy harvester applications. Also, there is a significant dissimilarity observed in this study compared to the mechanically attached systems: The resonance frequency has a dependence on magnetic field strength, and is shifting towards lower values when increasing the strength of the magnetic field. This indicates that the virtual spring of a levitated proof mass is not a constant and therefore, the resonance frequency of the diamagnetic levitated systems is able to be fine-tuned by varying the magnetic field. Finite Element Method (FEM) models were developed using COMSOL software that can simulate 3D magnetic flux formation of an array of permanent magnets and the diamagnetic levitation. The appropriate magnetic force equation from the two force equations that exist in the literature was established for the static levitation with the help of experimental and simulation results. Moreover, these models are able to provide the magnetic force exerted on diamagnetic objects at different heights, stable levitation height and position and also an indication of the maximum stably levitated size of the diamagnetic material. Future endeavor of this study is to realize the diamagnetic levitation in energy harvesters. The results obtained from this research will not be limited to harvester applications but will also be beneficial to other diamagnetic levitation related systems, as these parameters are fundamental and necessary for the foundation of the research in the field of interest