Objectives
This article shows how to use MANATEE software e-NVH simulation software to identify the main Maxwell force harmonics depending on e-machine topology, load state and main parameters.
Principle
Magnetic stress waves can be identified by a wavenumber r and a frequency f noted (f,r). As both radial & tangential stress harmonics are a quadratic function of flux density, these stress waves can also be decomposed as the product of airgap flux density waves. Flux density waves can themselves be decomposed as the product of airgap permeance waves and magnetomotive force waves, using same notation.
Resonances due to electromagnetic forces depend on both their excitation frequencies and their spatial distribution (wavenumber); besides, the stator response is the highest for low wavenumber stress waves. It is therefore important to be able to identify the main wavenumbers and frequencies of magnetic stress waves, as well as their physical origin to take adapted noise mitigation actions.
The wavenumbers and frequencies of stress waves mainy depend on discrete parameters of the e-machine such as stator/rotor slot number, flux barrier number, pole number, phase number.
Scripting implementation
MANATEE offers several command lines to analyze the theoretical content of magnetic stress waves:
- find_harmonic_XXX_fr: identifies the origin of a specific stress wave (f,r)
- find_harmonic_XXX_r: identifies the origin of all stress waves of wavenumber r
- find_harmonic_XXX_f: identifies the origin of all stress waves of frequencies f
As the force characteristics depend on the load state some specific scripts are used in PMSM such as:
- find_harmonic_PMSM_open_circuit_XXX: identifies stress waves related to rotor to rotor flux interactions only (force harmonics due to permanent magnets, includes cogging torque)
- find_harmonic_PMSM_partial_load_XXX: identifies stress waves related to stator to rotor flux interactions only (includes torque ripple)
- find_harmonic_PMSM_full_load_XXX: identifies stress waves related to stator to stator flux interactions only
- find_harmonic_PMSM_XXX: identifies all stress waves related to rotor to rotor, rotor to stator and stator to stator flux interactions
For different electrical machines one can find the corresponding scripts:
- find_harmonic_PMSM_XXX for Permanent Magnet Synchronous Machines (interior or surface magnets)
- find_harmonic_WRSM_XXX for Wound Rotor Synchronous Machines
- find_harmonic_SCIM_XXX for Squirrel Cage Induction Machines
The results of these functions can be sorted by decreasing vibration magnitude (therefore the lowest wavenumbers are favoured) or by favouring their frequency diversity. By default, MANATEE v1.08.02 is favouring the identification of stress waves rather than vibration waves.
Example
To identify the stress waves present in Prius PMSM 48s8p e-motor in open circuit the following command gives:
The input arguments are the following:
- p: number of pole pairs
- Zs: number of stator slots
- Nmax_lines: max number of stress waves to be identified (optional)
- rmax: max wavenumber of stress waves to be identified (optional)
- freq0: electrical frequency (optional)
- fmax: max frequency to be analyzed (optional)
- is_inner_rotor: 1 for inner rotor, 0 for outer rotor stress waves (optional)
- rot_dir: rotation direction of the fundamental (optional)
- is_modulation_effect: 0 to desactivate slot modulation effect (optional)
- Ks_max: max rank of stator permeance waves (optional)
- Hr_max: max rank of rotor mmf waves (optional)
To analyze the stess waves occuring in partial load (armature field effect) in 48s8p IPMSM:
The input arguments are the following:
- p: number of pole pairs
- Zs: number of stator slots
- qs: number of phases
- Nmax_lines: max number of stress waves to be identified (optional)
- rmax: max wavenumber of stress waves to be identified (optional)
- freq0: electrical frequency (optional)
- fmax: max frequency to be analyzed (optional)
- is_inner_rotor: 1 for inner rotor, 0 for outer rotor stress waves (optional)
- rot_dir: rotation direction of the fundamental (optional)
- is_modulation_effect: 0 to desactivate slot modulation effect (optional)
- Ks_max: max rank of stator permeance waves (optional)
- Hr_max: max rank of rotor mmf waves (optional)
- Hs_max: max rank of stator mmf waves (optional)
GUI implementation
TBC
See also
The theoretical content of magnetic forces is used to add informative data to all e-NVH MANATEE post processing such as order tracking analysis.