<p>Rotor asymmetric offset which constitutes an inherent flaw in permanent magnet synchronous motors (PMSMs) manufacturing and assembly adversely affects both the output performance and operational stability of PMSMs. Existing studies mostly focus on the qualitative analysis of single-type rotor asymmetry, lacking systematic quantitative comparison of the effects of static and dynamic asymmetric offsets on motor electromagnetic performance, as well as targeted optimization schemes for performance degradation. To address this gap, this paper first establishes mathematical models of static and dynamic rotor asymmetric offsets, and analytically derives their influence mechanism on air-gap flux density distribution, electromagnetic torque and power quality. Then, the no-load and on-load characteristics of the motor with healthy rotor, statically and dynamically asymmetric rotors are systematically compared via finite element analysis (FEA), quantifying the performance degradation caused by different offset conditions. Finally, to suppress the excessive torque ripple induced by dynamic asymmetric offset, a torque ripple suppression method based on auxiliary notches on stator teeth is proposed, and a multi-objective particle swarm optimization (MOPSO) algorithm is employed to optimize the notch parameters with the objectives of maximizing average torque and minimizing torque ripple. The simulation results show that the optimal parameter combination (notch width of 1.071 electrical degrees, notch depth of 4.446&#xa0;mm) reduces the cogging torque by 11.04% and the torque ripple by 1.38% with a sacrifice (3.07% decrease) in average torque, verifying the effectiveness of the proposed method. This research can provide theoretical reference and engineering guidance for performance optimization of PMSMs with rotor asymmetric defects.</p>