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Magnetic gears offer significant advantages such as low noise and vibration level, lower maintenance and higher reliability compared to mechanical gears and are suitable for many applications in the industry. The coaxial magnetic gear has been extensively discussed in the literature, since it achieves higher torque densities amongst other magnetic gear configurations. The magnetic field is generated by permanent magnets mounted on the two rotors and a modulator between them. The modulator consists of ferromagnetic segments that are typically encased in a resin in order to increase its stiffness without compromising the generated magnetic field. However, due to the development of radial forces, oscillations of the ferromagnetic segments occur, which lead to torque ripples that affect the operation of the coaxial magnetic gear drive in applications where accuracy is required. This work introduces a computationally lightweight analytical 2D model in order to determine the applied radial force on the ferromagnetic segments at each angle of rotation of the two rotors and henceforth calculate the displacement of these segments using FEA. In this way it is possible to assess the variation of the torque (ripple) versus the angle of rotation of the input or output shaft. A parametric investigation examining the influence of the ferromagnetic segment thickness on the resulting torque ripple of a specific drive was carried out illustrating the benefits of the analytical models developed herein.

Although steel involute gears are the standard solution for gear transmissions, they tend to suffer from poor pitting resistance. Pitting typically occurs when the gear tooth flanks have high equivalent curvature at the contact point and/or when the equivalent curvature is not constant across the contact path leading to high contact pressures and the development of surface fatigue. In this paper a new optimization method is presented to produce spur gear tooth flanks with improved pitting performance compared to involute ones. The tooth flanks are represented as B-spline curves, the control points of which are the variables for the optimization problem. The constraints were designed to ensure that all the examined profiles satisfy the law of gearing and do not contain any cusps or C1 discontinuities. Deterministic and stochastic algorithms were implemented and both closed and open path of contact gear sets were examined to determine the optimum tooth profile. The optimization results show that the maximum equivalent curvature of the optimum profiles is reduced by 83% compared to the corresponding standard profiles, while the deviation from the mean value is reduced by 98%. Both the standard and the optimized gears where examined comparatively also through finite element analysis. For the case selected the maximum contact pressure developed on the optimized gear set was 77% of the respective maximum contact pressure on the standard gear set whereas the corresponding deviation from the mean value was 5%. At the same time, the bending stresses developed in the optimized gear are slightly lower than those in the standard one.

A novel numerical second order transient thermal model for beta-type Stirling engines (TTMS) was developed taking into account the transient heat transfer between the engine cylinder walls and pistons and the working gas in the expansion and compression space in order to determine the total power output and thermal efficiency with higher accuracy. The time-dependent energy equilibriums were formulated by including the transient thermal response of the cylinder walls and pistons until steady state operation was achieved. In addition, the transient response of the heat exchangers (cooler, regenerator and heater) was developed in order to determine more accurately the enthalpy of the working gas that enters or exits each compartment of the engine. The solution of the governing differential equations at each time step can be achieved with the implementation of a conventional fixed point algorithm. Various loss mechanisms were incorporated in order to increase the accuracy of the developed model. The TTMS was applied to the GPU-3 Stirling engine and the thermal response of the engine was calculated. The steady state results were compared to both experimental results and other numerical second order models in the literature which showed that TTMS can predict the thermal efficiency and the power output of the engine with an improved accuracy of as high as 65% and 62% respectively compared to the more advanced second order models published in the literature. The information of the transient response of the engine will be valuable for automotive and other energy applications in the industry.