The interaction between the permanent magnets and the armature teeth of the PMSM generates cogging torque. It causes vibration and noise. Therefore, this paper establishes the analytical formula of the cogging torque of the motor with auxiliary slots on the surface of the rotor. It shows that reasonable slots can weaken the cogging torque. But it’s essential to determine whether the air-gap flux density harmonics will increase appreciably by slotting. A V-type IPMSM with 8-pole, 48-slot is modeled to analyze the cogging torque. Two new rotor slot shapes—inwardly biased slots and outwardly biased slots—are proposed and researched to reduce the cogging torque of the V-type IPMSM. And they are compared with the traditional symmetrical auxiliary slots. Research shows that the inwardly biased slots and the symmetric auxiliary slots can obtain a better effect on the cogging torque than the outwardly biased slots. By the symmetrical auxiliary slots, the cogging torque is weakened by 75.88%, but the torque ripple increases from 22.36% to 29.60%. By the inwardly biased slots, the cogging torque is weakened by 75.64%, and the torque ripple drops from 22.36% to 12.95%. The inwardly biased slots could successfully suppress the torque ripple.

Avoiding the ablation on the rail surface and obtaining large enough electromagnetic thrust to push the armature forward to high speed are two core contents of the electromagnetic launch technology. Reducing the ablation on the rail surface as much as possible can effectively extend the service life of the electromagnetic launcher (EML). The greater the electromagnetic thrust, the greater the initial velocity of the armature launched by the EML. The ablation on the rail is closely related to the temperature of the rail surface, and the electromagnetic thrust is proportional to the inductance gradient in the rails. The water flowing through cooling channels in rails can take away most of the heat generated by megaampere current flowing through the rails and armature in a few milliseconds. In this way, serious ablation on the rail can be avoided. Although the cooling channels are very helpful to reduce the ablation on rails, if the location distribution of the cooling channels in rails is not appropriate, the inductance gradient in the rails will be affected. This will affect the electromagnetic thrust in the EML. Therefore, the expressions of the inductance gradient in the rails with or without cooling channels are deduced and verified by the FEA in this article. The influence of the position distribution of the cooling channel on the inductance gradient in rails is analyzed. The results show that, with the increase of frequency, the influence of cooling channels on the inductance gradient in the rails diminishes gradually; if the distance between the cooling channels and the surface of the rails is greater than a certain value, the inductance gradient is no longer influenced by the cooling channels. At last, the relationship among L $^\prime$ , L $_{\mathbf{1}}$ , and L $_{\mathbf{2}}$ are fit in this article. It can be used to find the rail parameters that meet both thermal management and electromagnetic driving force requirements.

The inductance gradient is one of the most critical parameters in the electromagnetic rail launcher (ERL). It determines the electromagnetic force and efficiency in the ERL. In general, the inductance gradient in the rails is treated as a constant. However, the inductance gradient in the rails changes dynamically during the launching process. It is very important for the electromagnetic driving force in the launching process to accurately solve the time-varying inductance gradient. For this reason, a method for establishing the analytical calculation of the time-varying inductance gradient is proposed in this article. The results show that the application conditions of the proposed method are ( $s$ / $w>2$ and $s$ / $h>1$ ), and the shortest side length of the rail must be greater than 20 mm. At last, in order to verify the applicability of this method, the inductance gradients in five different ERLs injected with the pulse current are calculated and the results obtained are compared with the FEA. The research shows that the inductance gradient in the initial stage changes significantly due to the rapidly changing current frequency. After an interval, it tends to be a constant, which is the result of the stabilization of the current. It is consistent with the results reported in the literature. And if the rail dimensions meet the applicable conditions, the maximum error between the method in this article and the FEA is less than 5%.

To address the issue of coil misalignment in magnetically coupled wireless power transfer (WPT) systems, which causes fluctuations in mutual inductance, a reduction in the magnetic coupling coefficient, and a decline in transmission efficiency, this paper proposes a misalignment tolerance WPT system. The system utilizes a novel dual-layer vertical DD (DVDD) coil coupling mechanism, featuring an innovative magnetic core design. A mathematical model of the DVDD mechanism has been developed and analyzed to characterize its output properties. Comparative evaluation of equivalent mutual inductance variation and coupling coefficient retention demonstrates the DVDD's superiority over conventional magnetic coupling mechanisms. The DVDD mechanism achieves a 14.5% improvement in coupling coefficient retention compared to traditional DD magnetic coupling mechanisms. Furthermore, the newly designed magnetic core achieves 26.6% material reduction relative to conventional full-coverage designs while preserving 98% of the magnetic coupling coefficient retention rate in the full-coverage magnetic core. These combined improvements ensure enhanced operational stability in dynamic WPT systems. A WPT system prototype implementing the DVDD magnetic coupling mechanism was developed. Experimental and simulation results demonstrated close agreement, confirming the enhanced misalignment tolerance of the DVDD mechanism and the feasibility of the lighter magnetic core design.

The inductance gradient is a vital parameter in the electromagnetic rail launcher, holding significant sway over the electromagnetic force and operational efficiency. Traditionally, the inductance gradient has been assumed to maintain a constant value for the sake of simplicity. However, in reality, it dynamically transforms throughout the launching process. Thus, achieving a precise conclusion for the time-varying inductance gradient becomes an utmost priority for the electromagnetic driving force during launch. Therefore, this article presents a novel approach utilizing the backpropagation (BP) neural network to address the challenge of accurately determining the time-varying inductance gradient. The testing set exhibits exceptional performance with an R-square (R $^{{2}}$ ) value of 0.99982, indicating a high degree of correlation. The mean absolute error (MAE) is measured at 0.61273, highlighting the accuracy of the neural network in predicting values. Furthermore, the mean bias error (MBE) is found to be $-$ 0.033674, indicating a minimal systematic deviation. These results underscore the suitability of the BP neural network for precise calculations of inductance gradients. The effectiveness of the proposed approach is validated through a rigorous comparative analysis, comparing the obtained results with those reported in diverse scientific literature.