from numpy import linspace, meshgrid, pi, repeat, sum as np_sum, zeros, mean
from ....Functions.Winding.comp_cond_function import comp_cond_function
[docs]def comp_wind_function(self, angle=None, Na=2048, alpha_mmf0=0, per_a=1):
"""Computation of the winding function for the lamination.
By convention a tooth is centered on the X axis
Parameters
----------
self : LamSlotWind
A LamSlotWind object
angle : ndarray
Space discretization to compute the winding functions
Na : int
Number of angular points for the winding function (not used if angle is set)
alpha_mmf0 : float
Angle to shift the winding function (Default value = 0)
per_a : int
Spatial periodicity factor
Returns
-------
wf: ndarray
Winding function Matrix (qs,Na)
"""
# Space discretization
if angle is None:
angle = linspace(0, pi * 2 / per_a, Na, endpoint=False)
else:
Na = angle.size
qs = self.winding.qs # number of phases
# Number of point on rad and tan direction
Nrad, Ntan = self.winding.get_dim_wind()
Zs = self.slot.Zs # Number of slot
Zs0 = int(Zs / per_a)
slot_angle = self.slot.comp_angle_active_eq()
slot_opening = self.slot.comp_angle_opening()
wind_mat = self.winding.get_connection_mat(Zs)
# sum wind_mat along Nlay_rad axis
wind_mat = np_sum(wind_mat, axis=0)
# angle of the center of the slots
# By convention a tooth is centered on the X axis
alpha_slot = linspace(0, 2 * pi / per_a, Zs0, endpoint=False) + pi / Zs
# angle of the lay in a slot (Nlay point, end and begin excluded)
alpha_lay = linspace(-slot_angle / 2, slot_angle / 2, Ntan + 1, endpoint=False)[1:]
if alpha_mmf0 != 0:
angle = (angle - alpha_mmf0) % (2 * pi)
wf = zeros((qs, Na))
for n in range(Ntan):
# [Na, Zs]
Xalpha_slot, Xangle = meshgrid(alpha_slot + alpha_lay[n], angle)
Xwind = zeros((1, Zs0, qs))
Xwind[0, :, :] = wind_mat[n, 0:Zs0, :]
# Extended winding matrix [Na, Zs, qs]
Xwind = repeat(Xwind, Na, axis=0)
# Single winding function in every slot and angle for nth layer [Na, Zs]
Xwf = -0.5 * comp_cond_function(Xalpha_slot, slot_opening, Xangle)
for q in range(qs):
# winding function of qth phase (sum over layers) [qs, Na]
wf[q, :] += np_sum(Xwind[:, :, q] * Xwf, axis=1)
if per_a > 1:
wf = wf - mean(wf, axis=1)[:, None]
return wf
