# Result interpretation : Graphical Output (Model)

MANATEE is split in four models : Electrical, Electromagnetics, Structural mechanics, and Acoustics. Each of these model use the result of the previous one for its computation and has its own set of plot commands. One can analyse each step of the computation by combining these graphs.

### Electrical Model

Electrical model post processings includes the visualization of saturation effects (inductances, saturation coefficient), voltage and current waveforms and FFTs, skin effect factors, etc.

In this open-circuit example, no electrical post processing is relevant.

### Electromagnetic Model

The electromagnetic model post processings include time, space and FFT representations of torque, back emf, permeance, magnetomotive forces, flux densities and magnetic forces.

In this example, the airgap flux density spatial distribution can be plotted with plot_B_space :

Rotor airgap flux density (radial and tangential)

The graph is only given up to 180° because symmetries are automatically detected and used to reduce computational time when Input.Simu.is_symmetry=1.

The radial component of the airgap Maxwell stress 2D FFT can be plotted with plot_Fr_fft2 :

Stator radial pressure FFT2 and natural frequencies

In this first graph the 2D Fourier transform of the radial magnetic force is displayed in “time frequency” (abscissa in Hz) and “spatial frequency” (ordinates in wavenumbers). Negative spatial wavenumbers corresponds to force waves rotating in opposite direction to positive spatial wavenumbers. In that case one can see that the largest forces occur at r=0, f=0 Hz and r=2p, f=2fs (twice the fundamental electrical frequency) which corresponds to the force wave arising from the square of the fundamental flux density.

Some additional force harmonics of wavenumber 0 occur at multiples of 18fs, which corresponds to the rotation frequency times the least common multiple between slot and pole numbers: LMC(Zs,2p)fR=LCM(36,4)fR=36fR=36fs/p=18fs which is in agreement with the theory. The lowest positive wavenumber is 2p which agrees with the theoretical value of GCD(Zs,2p)=2p at no-load.

This second graph shows a stem plot of radial force harmonics. The force harmonics have been automatically labelled with an estimation of the best analytical formula fitting with numerical results based on a theoretical analysis of main force harmonics.

The static component (f=0 Hz) is automatically removed as it does not contribute to noise & vibrations. The scale limits of the force FFT should be carefully reviewed; the largest force line should be at twice the fundamental frequency, with a 2p spatial wavenumber. This is the “fundamental force harmonic”, it would be present even in an ideal machine with purely sinusoidal flux distribution. Depending on the machine topology and speed range this fundamental force might have an important vibroacoustic role or not (the higher is the wavenumber, the stiffer is the stator yoke). In the present example, its frequency is too low to create a significant resonance. To focus on the other harmonics, one can exclude this fundamental force by setting

`Input.Plot.is_remove2f = 1`

The following new graph is obtained: plot_Fr_fft2_stem :

Airgap radial pressure FFT2 without fundamental force harmonic

One can see that the numerical calculations are in agreement with theoretical analytical calculations given in the text output of MANATEE: the main force lines have a wavenumber 0 and 4.

### Structural Model

For magnetic vibration calculations, MANATEE projects the Maxwell stress tensor on the stator and rotor structures. The magnetic force wave at a given frequency (for instance 2fs=100 Hz and 36fs=1800 Hz) can be visualized using plot_Fteeth_machine(2*Output.Electrical.freq0)

Tangential & radial magnetic forces per tooth at f=100Hz
Tangential & radial magnetic forces per tooth at f=1800Hz

The forces at 2fs have a 2p=4 wavenumber as expected, and are mainly radial. Magnetic forces at 36fs have a 0 wavenumber as expected, and contain both a strong radial and tangential component.

The natural frequencies are displayed in the text output of the command. They can also be plotted using plot_nat_freq

Natural frequencies

The mode 0 which is important is here found to be close to 7500 Hz, while the mode 4 is close to 6000 Hz.

Now that the magnetic forces have been analyzed one can plot the vibration and noise spectra at specified speed 1500 rpm.

The first interesting graph is the radial vibration spectrum with the contribution of each structural mode to the vibration level using plot_Vr_modal_cont

Modal contribution to radial velocity level

Similarly, the radial acceleration spectrum can also be plotted, either without the modal contribution (plot_Ar_fft) or with the modal contribution (plot_Ar_modal_cont).

The operational deflection shape (ODS) analysis consists in visualizing the structural deflections at a given frequency. It can be done within MANATEE environment to compare simulation results and experimental results, usually based on accelerometer measurement along the stator circumference. The ODS also helps validating the nature of a vibration wave (direction of rotation, pulsating or travelling wave). The number of accelerometers is defined in the simulation project file with :

```Input.Simu.Nacc_z=4;                % number of radial accelerometers along the axial direction for the Operational Deflection Shape Input.Simu.Nacc_xy=8;               % number of radial accelerometers along the circumference for the Operational Deflection Shape```

The 2D FFT and theory showed that at 1800 Hz a pulsating force wave was present, this can be checked with plot_ODS(1800)

Operational Deflection Shape

### Acoustic Model

The modal contribution to each spectrum line of the A-weighted acoustic noise power can be visualized with plot_ASWL_modal_cont

Modal contribution to each spectrum line of the A-weighted acoustic noise power

The sound power spectrum is not very rich because the simulation is done in open-circuit. The overall acoustic noise level is very small because no strong resonance occurs at 1500 rpm.

All the previous graphs are done at the fixed speed specified by Input.Simu.N0, but some spectrograms (acoustic noise and vibration at variable speed) have been calculated with Input.Simu.is_spectro_synthesis = 1. Some variable speed post processings are therefore available.