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Magnetic gear and magnetic-geared machine (MGM) are the potential solutions in electric vehicles (EVs) powertrains for inherent high efficiency and mechanical simplification. However, the torque density issue of the MGM greatly limits its industrial application. To enhance the torque performance of the MGM, a torque-enhanced magnetic-geared machine with dual-series-winding and its design approach are proposed. The key merits of the proposed design are to achieve a high space utilization with a dual-winding design, with no additional control topologies and power converters required. The auxiliary winding is supplemented and integrated with modulation rings. The relative position of the stator and armature winding are designed and rotated compared to the modulation rings with auxiliary winding, to ensure the auxiliary winding shares the excitation with the armature winding. Accordingly, simplifying the external control topologies. With the proposed design, the torque of the MGM can be significantly enhanced with a single three-phase driving. Theoretical analysis, parameters optimization and electromagnetic verification are given, demonstrating that the proposed machine can achieve an efficiency of 93.2%, generate a torque of 107.2 N·m, and reach a torque density of 10.81 N·m/kg.