Symmetry

The eccentric permanent-magnet (PM) pole technique is widely recognized as an effective technique for reducing cogging torque in surface-mounted PM motors (SMPMMs). This paper proposes a novel analytical approach based on bilinear mapping to determine the optimal PM reduction parameters. In this method, the outer surface of the PM and the stator inner bore are modeled as eccentric circles. Bilinear mapping is then used to transform a slotted stator bore into an equivalent slotless configuration with small slot-openings, allowing the optimal PM reduction to be identified. The key electromagnetic performance characteristics of SMPMMs—including torque, efficiency, mean air-gap flux density, and related parameters—are formulated as explicit mathematical functions of the PM reduction factor. The influence of the optimal PM reduction on both static and dynamic rotor eccentricity is also investigated. The results reveal that the bilinear mapping equations yield two distinct roots for the optimal PM reduction. Once the optimal values are known for a reference motor, those of other motors with different dimensions can be readily derived by scaling according to the ratio of the outer PM radii, without repeating the full calculation process. The proposed method is applicable to various SMPMM geometries, including radial, parallel, and bread-loaf configurations.

This study addresses the common challenges of complex soil behavior and the difficulties in achieving precise control during the construction of large open caissons. A centrifugal model test was conducted to investigate open caisson–fine sandy soil interaction, and the findings were further verified through field testing. Results indicated that during the sinking process, the open caisson–soil interface exhibited slip failure characteristics, while the soil at the cutting edge of the open caisson showed a tendency for inward shear slippage. The horizontal earth pressure along the open caisson sidewall was found to correspond to static earth pressure in the upper section and gradually approached active earth pressure in the lower section. The maximum earth pressure occurred at approximately three-quarters of the embedded depth of the open caisson wall. Furthermore, the friction angle at the soil-open caisson interface was approximately 0.63 times that of the soil friction angle. Based on the observed distribution patterns of earth pressure and skin friction, theoretical calculation formulas were developed. Their accuracy was confirmed through field tests, providing valuable references for the design and construction of large open caisson projects.

We considerthe single-machine group scheduling problem with controllable processing times (i.e., resource allocation) under a common due-window ( ) assignment. The objective is to minimize a total cost composed of earliness, tardiness, due-window-related penalties, and resource consumption. Motivated by realistic production settings such as aerospace component machining and electronics batch assembly, the study addresses the joint optimization of group sequence, job sequence, due-window placement, and resource allocation. For linear and convex resource models, we propose a branch-and-bound ($\widehat{BaB}$) algorithm and efficient heuristics. Numerical experiments show that the $\widehat{BaB}$ algorithm can solve instances with up to 250 jobs and 16 groups. The heuristics ($\widehat{UB}$), including a simulated annealing ($\widehat{SA}$) algorithm, obtain near-optimal solutions with an average error below 0.05% much faster, demonstrating their practical usefulness for real-time scheduling.