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 :

Airgap flux density
Airgap flux density

One can see that due to slotting effect, the rotor mmf 11p harmonic as been enhanced as 11p=Zs-p=48-4=44.

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

FFT2 of radial pressure on stator
FFT2 of radial pressure on stator

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 6fs, which corresponds to the rotation frequency times the least common multiple between slot and pole numbers: LMC(Zs,2p)fR=LCM(48,8)fR=48fR=48fs/p=12fs 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.

plot_Fr_fft2_stem :

FFT2 stem plot of radial pressure
FFT2 stem plot of radial pressure

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, indeed 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 Prius example, this wavenumber is too large to create a significant resonance. This force line can be excluded to focus on the other harmonics by setting

Input.Plot.is_remove2f = 1

The following new graph is obtained: plot_Fr_fft2_stem :

FFT2 stem plot of radial pressure (2f removed)
FFT2 stem plot of radial pressure (2f removed)

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 8.

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 667 and 800 Hz) can be visualized using plot_Fteeth_machine(667)

Teeth forces (667 Hz)
Teeth forces (667 Hz)

and plot_Fteeth_machine(800)

Teeth forces (800 Hz)
Teeth forces (800 Hz)

One can see that the forces are mainly radial, and have respectively a wavenumber of 8 and 0.

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

Stator natural frequencies
Stator natural frequencies

One can see that the ovalization mode of the stack is close to 650 Hz as found by FEA in this article. The mode 0 which is important is here found to be close to 4500 Hz, which is also consistent with the article.

Now that the magnetic forces have been analyzed one can plot the vibration and noise spectra at specified speed 1000 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

Radial velocity spectrum
Radial velocity spectrum

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 shows that at 667 Hz, two vibration waves of wavenumber -8 and +8 (opposite rotating directions) exist. This can be checked with plot_ODS(667)

Operational Deflection Shape (ODS) at 667Hz
Operational Deflection Shape (ODS) at 667Hz

The resulting wave is a pulsating wave due to opposite traveling direction.

Acoustic Model

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

Order contribution to A-weighted global noise
Order contribution to A-weighted global noise

The sound power spectrum is not very rich because the simulation is done in open-circuit. One can see that the main acoustic noise contributor at that particular speed is the breathing mode of the stator stack, but he magnetic noise overall all is very small (35 dBA) so it should be covered by mechanical noise. You can obtain the Sound Pressure Level spectrum with plot_SPL_fft:

90. A-weighted sound pressure level spectrum
A-weighted sound pressure level spectrum

A third octave analysis of the SWL can also be displayed with plot_ASWL_13oct

1/3 octave A-weighted acoustic noise spectrum
1/3 octave A-weighted acoustic noise spectrum

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.

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