Modelling and simulation of the dynamical response of coaxial magnetic gear transmissions admitting computationally lightweight and robust solutions for torque modelling and power losses

Abstract

Coaxial magnetic gears (CMGs) have been of great interest amongst researchers and the industry since their introduction two decades ago. Magnetic gears possess significant advantages compared to mechanical gears such as higher performance in terms of attained speeds, versatility, vibration attenuation, backdrivability and efficiency. However, some drawbacks limit their wide adoption in the industry. Even with the use of rare-earth permanent magnets and implementing sophisticated designs the torque density of magnetic gears is significantly lower compared to mechanical gears. Increasing the torque density is a major issue in magnetic drivetrains and has been extensively discussed in the literature. However, the calculation of the torque is typically performed through FEA and/or numerical methods, thus increasing the computational cost for optimization processes. Furthermore, slippage that occurs during transient operation of CMG drives is a phenomenon that should be thoroughly investigated since it limits their operation when high acceleration/deceleration is present. The analysis of slippage in the literature has been conducted by mainly implementing FE transient simulations or with other iterative methods, without giving additional insights on the complex dynamical phenomena of CMGs and with high computational cost. Finally, power losses due to eddy current and core losses are a significant drawbacks in CMG drives and should be examined since high values of power losses could lead to excess heat that could increase the temperature of the system leading to degradation of the permanent magnets and the CMG as a whole. The power losses are usually calculated implementing FE transient simulations that require high computational cost and therefore limiting optimization methods aiming towards the reduction of eddy current and core losses. The objective of this thesis is to introduce two analytical 2D models for fast and efficient calculation of the applied torques for every rotation angle, geometry configuration and constitutive parameters of the magnets using the Maxwell Stress Tensor. The first model refers to the standard CMG drive, while the second to the Halbach-array CMG drive, due to its comparative advantages. The results obtained from the models were compared against those obtained from FEA. The calculated torques at the inner and outer rotor were in perfect agreement with FEA, however the analytical models were more than two orders of magnitude faster. In addition, an analytical calculation of the torque ripple in coaxial magnetic gear drives is made possible using the proposed models. An investigation of the influence of the modulator ring on stall torque was performed illustrating that there is an optimum arc length for the ferromagnetic segment to maximize torque density. Furthermore, the dynamical equations of the coaxial magnetic gear drive were formulated and a model was developed to simulate the dynamical response of the system without the requirement of torque calculation at each time step that significantly decreases computational cost. The slippage phenomenon was thoroughly investigated in the present thesis. It was demonstrated that the governing equations of the dynamical response of the coaxial magnetic gear are the same with the dynamical equation of the driven pendulum. A non-dimensional criterion was formulated for the prediction of the dynamical behavior of the CMG drive during transient operation. Finally, it was demonstrated that the dynamical response of the CMG drive could exhibit chaotic behavior under certain conditions. With the developed analysis, besides the significant reduction of the computational cost important insights regarding the complex dynamical phenomena during the operation of CMG drives are obtained. Moreover, a detailed analysis regarding the calculation of power losses during the operation of CMGs has been conducted. Using the analytical calculation of the magnetic induction the eddy current losses in the permanent magnets of the CMG and the core losses on the modulator ring were obtained. An investigation on the effect of the magnet segmentation to the power losses was conducted, illustrating that eddy current losses can be significantly reduced by applying this technique. Finally, a detailed design of a CMG drive is presented showcasing the important designs aspects for manufacturing a robust and efficient CMG drive. A detailed analysis regarding the bearing tolerances and their subsequent effect on the natural frequencies of the CMG drive is conducted illustrating its significance as a design aspect.