How to choose the angular step (airgap space discretization) for vibroacoustic simulation?

MANATEE software automatically checks the quality of the discretization input by the user during the simulation. In case of low discretization quality, some warnings are given in MANATEE console.

The number of angular steps is given along 360° of the electrical machine airgap and is defined in the simulation script by

Input.Simu.Na_tot= 8*1000;

MANATEE automatically identifies applicable time and space symmetries when Input.Simu.is_symmetry= 1. If a symmetry of order 8 is identified in space domain, it is the advised to use a multiple of 8 for Na_tot.

The number of angular steps must be chosen to catch the highest electromagnetic force / vibration wavenumber of interest. According to Shannon theorem if the maximum wavenumber to be studied is Input.Simu.Nmax_fft_orders_circ=21 the sampling frequency must be at least 2Nmax_fft_orders_circ (42 in this case). This criterion is not enough because the angular discretization is also used for the calculation of airgap fields, and low force wavenumber harmonics might be created by high wavenumber flux density harmonics due to the quadratic nature of Maxwell stress: the airgap discretization must therefore be set to capture very accurately the airgap flux waveform, as it is the case when calculating electromagnetic torque ripple. In particular to capture slotting harmonics a high number of points must be taken in front of slot opening.

The maximum wavenumber of interest depends on the machine topology and on the application - for instance, large electrical machines used in hydroelectric generators have large yoke diameter to width ratio and large pole numbers, therefore main electromagnetically-excited noise and vibration may involve wavenumbers up to 30 ; on the contrary, vibration of small electric motors with low pole number may only involve wavenumbers up to 4.

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