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This paper focuses on the electromagnetic vibration and its reduction in PM brush dc motors. First, the air gap flux density distribution and the radial force density distribution are derived in detail, and compared with the results of the finite element method. Next, two types of vibration sources, called pulsating force and bending moment, are analyzed. Then, two passive improvement methods, called varied PM pole width in axial direction and copper ring, are proposed to reduce the magnetic forces and their vibration, and their principles of the vibration reduction are described in detail. For further explanation, a rotor-skewed motor is used for comparison, and the radial force on the motor is discussed and the influence of four different thicknesses of copper ring on the motor vibration is analyzed. Finally, three 2p/24s sample motors are manufactured and the experimental vibration results confirm the analysis and the proposed improvement technique. [ABSTRACT FROM AUTHOR]