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 example, the calculation of the equivalent circuit is given in the text output, and can be accessed in Output.Electrical structure.

One can see that the saturation is moderate, with a saturation coefficient K0=1 and an airgap flux close to 2.7 V/Hz. The magnetizing inductance and saturation coefficients as a function of airgap flux can be plot with plot_Lm :

Magnetizing inductance (plot_Lm)

The curve is not completely smooth due to numerical calculations: the saturation model is an iterative model that depends on the parametrized slot geometry and the B(H) curve.

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 radial flux density

Only the radial flux component is calculated in this basic permeance / mmf model, but the tangential component of the airgap flux can be calculated using subdomain model or finite element models available in MANATEE. One can identify besides the fundamental the two stator slotting and winding harmonics at Zs-p=36-3=33 and Zs+p=36+3=38. The rotor slotting harmonics at Zr+p=31 and Zr-p=25 are smaller due to their smaller opening width.

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

Airgap maxwell stress

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 a large radial force harmonic (in red) occurs close to the second circumferential mode of the stator stack (red cross x).

plot_Fr_fft2_stem :

Airgap radial pressure FFT2

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.
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 -8 and -2.

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; in our case it has been automatically removed from the frequency limits because it has no major acoustic role and it would make the graph less readable in linear scale.

To add this main force line from the graph limits one can specify Input.Plot.is_remove2f=0

is_remove2f=0

Similarly, the static force is not displayed. One can display it using Input.Plot.is_remove0f=0

is_remove0f=0

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 680 and 560 Hz) can be visualized using plot_Fteeth_machine(680);plot_Fteeth_machine(560)

Magnetic forces per tooth

One can see that the forces are mainly radial.

Now that the magnetic forces have been analysed one can plot the vibration and noise spectra. The vibration velocity spectrum is given by plot_Vr_fft

Radial velocity spectrum

One can notice that the highest vibration occurs at same frequency of the wavenumber 2 force wave. To further confirm that, one can plot the spectrum with the contribution of each structural mode to the vibration level with 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)

Radial acceleration spectrum

or with the modal contribution (plot_Ar_modal_cont)

Modal contribution to radial acceleration level

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 :

The vibration spectrum with modal contribution shows that at 680 Hz the dominating wave has a wavenumber 2. This can be easily visualized in MANATEE typing plot_ODS(680)

operational deflection shape

The number of points for the deflection can be changed with Input.Simu.Nacc_xy=16

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 A-weighted SWL

This sound power level spectrum (SWL) shows that the acoustic power is clearly radiated by the ovalization mode due to the slotting force of wavenumber 2.
One must distinguish the SWL, which is intrinsic to the acoustic noise source, and the sound pressure level (SPL) which is the sound perceived at a given distance from the machine. The SPL can be plotted using plot_ASPL_fft

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

All the previous graphs are done at the fixed speed specified by Input.Simu.N0, but a sonogram (acoustic noise and vibration at variable speed) has been calculated by extrapolating magnetic loads at variable speed with Input.Simu.type_varspeed = 1