Two-Dimensional Field Analysis on Electromagnetic Vibration-and-Noise Sources in Permanent-Magnet Direct Current Commutator Motors

This paper concerns the modeling of electromagnetic vibration-and-noise sources in permanent-magnet direct current (PMDC) commutator motors. The electromagnetic sources are considered as an electromagnetic field distributed in the air-gap region of a PMDC motor. The latter is then formulated by the two-dimensional field theory in polar coordinates with the consideration of slotting effects and the armature reaction field. Consequently, based on the derived radial electromagnetic field, the radial and tangential magnetic forces acting on the inner surface of the permanent magnets can be expressed as Fourier functions in forms of space and frequency harmonics. The results obtained from the present models agree well with those from the finite-element models. In addition, the measured cogging torque is compared to those calculated by the analytical and finite-element models to validate the formulated electromagnetic field and magnetic forces. Furthermore, experimental investigations are carried out on the electromagnetic vibration-and-noise behavior of a commonly used PMDC commutator motor (such as that in heating, ventilating, and air conditioning (HVAC) systems). By measuring the natural frequencies and the associated mode shapes of the stator, the relationships between the magnetic forces and the measured vibration-and-noise responses are discussed in the frequency domain.