### Objectives

This article shows how to use MANATEE software to mitigate acoustic noise and vibrations due to electromagnetic forces using **notching**.

### Principle

Notching (also sometimes called auxiliary slots, grooves, or dummy slots) consists in removing some magnetic materials on rotor or stator bore lamination in order to generate airgap permeance wave fluctuations that compensate a particular magnetic force wave, resulting in lower NVH level.

The type of force wave and the magnitude of the force wave that is generated using notching depend on the number of notches, notch position (e.g. along d-axis or q-axis for IPMSM rotor notching) and notch shape (e.g. polar, rectangular, semi circular).

The notching effect can be introduced in several MANATEE electromagnetic models:

- permeance / magnetomotive force (PMMF) model, using analytic permeance or numerically calculated permeance (coupling with FEMM)
- subdomain model, using polar notches only
- finite element model, using coupling of MANATEE with FEMM

Generally notch design must be optimized at a given load point, as **it depends on the saturation level in magnetic materials, and for IPMSM on magnet temperature**. This means that for variable speed operation, notching effect must be checked at all points of torque/speed place and different temperatures, it **may also lead to higher noise at some other operating points**. Besides, **one must take care that notching does not increase the torque ripple level**.

MANATEE contains several permeance slot shapes. **It is possible to apply notches on all teeth or to apply notching only on specific teeth or poles**.

### Design methodology

The following steps are recommended to optimally design notching:

- use of an appropriate electromagnetic model (FEMM recommended in most cases)
- make a vibroacoustic analysis of the machine without notches to identify the resonance speed, the force wavenumber and frequency to be damped, as well as its physical origin (see the article on How to find the root cause of noise and vibrations?).
- find the theoretical number of notches to damp the force wave based on analytic equations (see our e-NVH technical training)
- run a parameter sweep on notch shape and notch dimensions at the resonance speed where noise must be damped
- run a multiobjective optimization on the chosen notch shape at variable speed to be sure that the final notch design do not increase torque ripple or noise at other speeds

### GUI implementation

TBC

### Scripting implementation

##### Notch shape parameters

All notch shape parameters are defined inside the machine script, as part of lamination object. The number of stator notch per tooth is defined by

`Input.Geometry.Nnotches`

A polar stator notch shape is defined by

`Input.Geometry.type_shape_notches=0`

while a rectangular stator notch shape is defined by

`Input.Geometry.type_shape_notches=1`

For rectangular stator notch the width is given by

`Input.Geometry.Wnotches`

and the height is given by

`Input.Geometry.Hnotches`

and the notch radius is given by

` Input.Geometry.Rnotches`

Stator notch spacing in radian is defined by

`Input.Geometry.Spnotches`

The existence of stator notches can be activated at some specific tooth numbers using a boolean vector

`Input.Geometry.is_notches`

The number of rotor notch per tooth (or per pole depending on topology) is defined by

`Input.Geometry.Nnotcher`

A polar rotor notch shape is defined by

`Input.Geometry.type_shape_notcher=0`

while a rectangular rotor notch shape is defined by

`Input.Geometry.type_shape_notcher=1`

For rectangular rotor notch the width is given by

`Input.Geometry.Wnotcher`

and the height is given by

`Input.Geometry.Hnotcher`

and the notch radius is given by

` Input.Geometry.Rnotcher`

Rotor notch spacing in radian is defined by

`Input.Geometry.Spnotches`

When 0 the notch are equally distributed over the tooth or pole width.
**To place Npp notches per rotor pole along D-axis one should put Nnotcher=Npp+1 with Spnotcher=pi/p/Npp and for Npp notches per rotor pole along Q-axis one should put Nnotcher=Npp with Spnotcher=pi/p/Npp.**

The existence of rotor notches can be activated at some specific tooth or pole numbers using a boolean vector

`Input.Geometry.is_notcher`

##### PMMF case

For PMMF model it is recommended to activate the computation of the permeance function per slot with FEMM. An elementary slot model is then created to characterize separately the airgap permeance, so the computation time is still very fast.

The stator permeance computation with FEMM is activated with

`Input.Simu.type_perm_modelS = 1;`

The rotor permeance computation with FEMM is activated with

`Input.Simu.type_perm_modelR = 1;`

##### SDM case

SubDomain Model automatically includes equally spaced polar notches on stator tooth tips when Nnotches>0.

##### FEMM case

FEMM model automatically includes the notches when specified in the machine geometry.

### Plot commands

In all cases the permeance per slot or pole can be visualized using plot_Per_slot command.