How to set the harmonic number in the different subdomains ?

In the subdomain method, the harmonic number in the different subdomains determines the size of the matrix system to solve and consequently the accuracy of the solution as well as the processing time.

Default settings

To let MANATEE calculate the optimal number of harmonics in the subdomain model, the values in the default_proj.m are :

Input.Simu.Nhag = 0;                % number airgap space harmonics in subdomain models and surface permanent magnets
Input.Simu.Nhss = 0;                % number stator slot harmonics in subdomain models  
Input.Simu.Nhrs = 0;                % number rotor slot harmonics in subdomain models  
Input.Simu.Nhso = 0;                % number stator slot opening harmonics in subdomain models  
Input.Simu.Nhro = 0;                % number rotor slot opening harmonics in subdomain models  

The computed values are given in the Output as :

Output.Magnetics.sdm.Nhag ;
Output.Magnetics.sdm.Nhss ;
Output.Magnetics.sdm.Nhrs ;
Output.Magnetics.sdm.Nhso ;
Output.Magnetics.sdm.Nhro ;

Manual settings

However, one can manually reduce the harmonics numbers to increase the speed or increase the harmonics numbers to reduce the error (reduce the oscillations in the air gap flux density). For example, here is a sensitivity study of the accuracy and the computation time on the air gap harmonics number :

Illustration of air gap harmonics number versus accuracy, computation time and memory used for subdomain model
Illustration of air gap harmonics number versus accuracy, computation time and memory used for subdomain model

The figure above shows that the error (the blue curve) has already converged for 150 harmonic ranks while the computation time (the orange curve) has slightly increased in comparison with 50 harmonics.

In general, the air gap and surface magnets harmonic number should be at least 5-10 times the number of slots (depending on the air gap length and the slot width and depth) to get at least 5-10 harmonic ranks of permeance and mmf. The harmonic numbers in the slot and slot opening can be chosen between 1 and 5-10 times twice the slot width to slot pitch ratio. The higher is the number of slots and the lower can be the slot and slot opening harmonic numbers.

To manually set the harmonic numbers, replace "0" by the chosen values in the corresponding Input.Simu variables. The user-defined values must be an integer.

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