Multi-simulation: rotor stepped skew effect in open-circuit, variable-speed

Tutorial summary
Project name tuto_BPMSM_05
Machine name machine_BPMSM_A
Source project tuto_BPMSM_02
Description Sensitivity study on rotor skew

In this example the open-circuit project tuto_BPMSM_02_test is copied pasted in a new project named tuto_BPMSM_05_test to find the optimal magnet skew angle with respect to acoustic noise at variable speed. The sensivity analysis is activated by using

Input.Simu.type_sensitivity = 1;

The single input variable to be varied is the rotor skew angle rate, expressed in stator slot pitch, given by

Input.Simu.names_var={'skew_rater'};

The skew rate is evenly varied from 0 to 1.2 stator slot pitch with 27 different values using

Input.Simu.types_var=[0]; %continuous variable
Input.Simu.types_val=[0]; % Value defined by interval
Input.Simu.type_sampling=[0]; % linspace sampling
Input.Simu.bds_contvar={[0 1.2]}; %Values between 0 and 1.2
Input.Simu.Nval_contvar=[27]; % 20 values

The output variable that is tracked during the sensitivity analysis is the maximum sound power level calculated from N0_min to N0_max rpm:

Input.Simu.names_resp={'LwrA_max'};

In the GUI all these parameters are gathered in the Workflow group / Sensitivity tab. You have to click "Add Input" to set the variation of skew_rater:

Setup of the input
Setup of the input

Then you have to click on "Add Output" to add Lwra_max:

Workflow group (Sensitivity tab)
Workflow group (Sensitivity tab)

The default skew shape is linear, it is defined by the machine parameter Input.Geometry.type_skew_geoR. Finally the electromagnetic skewed model based on 5 magnet segments is activated using

Numerical group (Magnetics tab)
Numerical group (Magnetics tab)
Input.Simu.type_skew = 2;          
Input.Simu.Nskew_slices = 5;  

The maximum noise and cogging torque levels as a function of the skew rate can be plot using plot_MS_all_resp_var

150. Effect of the rotor skew rate on the maximum sound power level radiated by a variable-speed PMSM (MANATEE software output)
Effect of the rotor skew rate on the maximum sound power level radiated by a variable-speed PMSM (MANATEE software output)
Evolution of cogging torque as a function of stepped-skew angle
Evolution of cogging torque as a function of stepped-skew angle

One can see that the maximum noise in open-circuit variable speed condition, which is dominated by a zero-th wavenumber, is minimized close to (4/5)=0.8 stator slot pitch together with cogging torque.

The optimal skew angle depends on the type of the force wave responsible for noise and depends on the load condition, so the optimal skew rate is not always (N-1)/N stator slot pitch for N magnet segments.

This simulation only takes a few sconds so MANATEE software allows to quickly optimize the skew geometry in terms of torque ripple, acoustic noise & vibrations and electromagnetic performances.

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