The generation mechanism of cogging torque was studied, and the twodimensional(2D) model of the permanent magnet couplings(PMC) was established by using finite element electromagnetic simulation software Ansoft Maxwell. The reasons for the increase in output torque and torque fluctuation range of cylindrical permanent magnetic couplings with slotted conductor copper sleeve were analyzed. According to the generation mechanism of the cogging torque, the influence of the relationship between the slot number and the pole number on the cogging torque was further analyzed, and the cogging torque and output torque characteristic curves of PMC under different slot width duty cycle and permanent magnet duty cycle were also obtained by simulation. Then the parameter optimization methods for weakening the cogging torque, increasing the output torque and reducing the torque fluctuation were given. It provides some theoretical reference for the design and application of PMC.