Asymptotic Fourier decomposition of tooth forces in terms of convolved air gap field harmonics for noise diagnosis of electrical machines

The electromagnetic excited audible noise of electrical machines can be mostly attributed to radial forces on stator tooth‐heads. The methodology proposed in this paper uses numerical field simulation to obtain the magnetic air gap field of electrical machines and an analytical‐based post‐processing approach to reveal the relationship between air gap field harmonics and the resulting force wave.

The simulated air gap field is sampled in space and time and a two‐dimensional Fourier transform is performed. The convolution of the Fourier transformed air gap field by itself represents a multiplication in space time domain. During the convolution process, all relevant combinations of field waves are stored and displayed using space vectors.

The effectiveness of the proposed approach is shown on an example machine. Particular examples of individual force waves demonstrate how the approach can be used for practical application in analysis of noise and vibration problems in electrical machines. The proposed method is compared to the result of a Maxwell stress tensor calculation. It shows that the deviation is small enough to justify the approach for analysis purposes.

The combination of analytically understood force waves and the use of numerical simulation by means of air gap field convolution has not been proposed before.