def calc_Zc(f, Rd, r, mu_r, rho):
n = np.shape(Rd)[0]
Zc = np.empty((n), np.complex128)
for i in range(n):
m = np.sqrt(2 * np.pi * f * mu_r[i] * 4 * np.pi * 10**-7 / rho[i])
mr = m * r[i]
# print(mr)
A = special.ber(mr) * special.beip(mr) - special.bei(
mr) * special.berp(mr)
B = special.bei(mr) * special.beip(mr) + special.ber(
mr) * special.berp(mr)
C = special.berp(mr)**2 + special.beip(mr)**2
# print('B/C=',B/C,'A/C=',A/C)
# print('A/C=',A/C)
alphaR = (mr / 2) * (A / C)
alphaL = (4 / mr) * (B / C)
# print('alphaL = ',alphaL)
Rc = Rd[i] * alphaR
Xc = np.pi * f * 10**-4 * mu_r[i] * alphaL
Zc[i] = Rc + 1j * Xc
print(Zc[i])
return Zc
def heatrate(lw, dw, i, f):
rw = dw / 2
rate = [0, 0]
Bx = fBcalc.BxSol(i, rc, rw)
#i,a,r in order where i= current, a= radius of coil, r= distance from center
rho_cg = 3.57 * 10**(3)
rho_si = 3.57 * 10**(
-8
) #Reference https://www.engineeringtoolbox.com/resistivity-conductivity-d_418.html
# Calculation for derived variables
rw = rw * 100
ur = 1
u = ur * 4 * math.pi * 10**(-7)
k = math.sqrt((8 * (math.pi**2) * f * ur) / rho_cg)
#print(k*rw)
Q = 2*(special.ber(k*rw)*special.berp(k*rw) + special.bei(k*rw)*special.beip(k*rw))\
/(k*rw)/((special.ber(k*rw))**2 + (special.bei(k*rw))**2)
rw = rw / 100
new_k = math.sqrt(2 * math.pi * u * f / rho_si)
#print(new_k*rw)
aw = math.pi * rw * rw
beta = math.pi * f * aw * Q / (u)
rate[0] = beta * (float(Bx.subs(x, lc / 2)**
2)) / (2695 * math.pi * rw * rw * 952.177)
rate[1] = beta * (
float(Bx.subs(x, (lc - lw) / 2)**2 + Bx.subs(x, (lc + lw) / 2)**2) /
2) / (2700 * math.pi * rw * rw * 929)
return rate
def uniform_loading(r, x, a, rou_p, l):
if x <= r:
kerpa = sp.kerp(a)
berx = sp.ber(x / l)
keipa = sp.keip(a)
beix = sp.beip(x / l)
w = rou_basalt * uniform_h * (a * kerpa * berx - a * keipa * beix +
1) / rou_p
else:
berpa = sp.berp(a)
kerx = sp.ker(x / l)
beipa = sp.beip(a)
keix = sp.kei(x / l)
w = rou_basalt * uniform_h * (a * berpa * kerx -
a * beipa * keix) / rou_p
return w
def power(lw, dw, i, f):
rw = dw / 2
Bx = fBcalc.BxSol(i, rc, rw)
#i,a,r in order where i= current, a= radius of coil, r= distance from center
rho_cg = 3.25 * 10**(3)
rho_si = 3.25 * 10**(
-8
) #Reference https://www.engineeringtoolbox.com/resistivity-conductivity-d_418.html
# Calculation for derived variables
rw = rw * 100
ur = 1
u = ur * 4 * math.pi * 10**(-7)
k = math.sqrt((8 * (math.pi**2) * f * ur) / rho_cg)
#print(k*rw)
Q = 2*(special.ber(k*rw)*special.berp(k*rw) + special.bei(k*rw)*special.beip(k*rw))\
/(k*rw)/((special.ber(k*rw))**2 + (special.bei(k*rw))**2)
rw = rw / 100
print(k)
new_k = math.sqrt(2 * math.pi * u * f / rho_si)
print(new_k)
aw = math.pi * rw * rw
beta = math.pi * f * aw * Q / (u)
#beta is a constant and total power is beta times Bx**2 integrated
#over the length of the workpiece
# Bx involves ellipticl integrals of the first kind and the second kind and
# its analytical integral is not possible using python
# Approach: Evaluate Bx at a set number of points and implement different types of
# numerical integration methods like simpsons, trapezoidal etc.
# Maybe define a good criteria of how many points to take versus the computation power consumed for evaluating the numerical integrals
# Origin redefined to the center of end coil of the solenoid
# Defining linspace in such a way that the distance between two points in the workpiece remains fixed to an order where Bx doesn't change significantly
# i.e. lw/(number of points) = constant -- this is not the best way because derivative of Bx is large near the end of coil and linspace is constant
# distance between each successive x points be 0.0001 m
num_pts = int(lw / 0.0003)
x_arr = linspace((lc - lw) / 2, (lc + lw) / 2, num=num_pts)
Bx_sq_arr = np.empty(num_pts, dtype='float')
for i in range(num_pts):
temp = Bx.subs(x, x_arr[i])
Bx_sq_arr[i] = temp**2
P = beta * trap(Bx_sq_arr, x_arr)
rate = P / (lw * 2700 * math.pi * rw * rw * 910)
return rate
def calc_Zc1(f, Rd, r, mu_r, rho):
n = np.shape(Rd)[0]
Zc = np.empty((n), np.complex128)
for i in range(n):
m = np.sqrt(2 * np.pi * f * mu_r[i] * 4 * np.pi * 10**-7 / rho[i])
mr = m * r[i]
# print(mr)
a = special.ber(mr) + 1j * special.bei(mr)
b = special.berp(mr) + 1j * special.beip(mr)
c = 1j * a / b
# print('a=',a)
# print('b=',b)
# print('c=',c)
alphaR = (mr / 2) * np.real(c)
alphaL = (4 / mr) * np.imag(c)
# print('alphaL = ',alphaL)
Rc = Rd[i] * alphaR
Xc = np.pi * f * 10**-4 * mu_r[i] * alphaL
Zc[i] = Rc + 1j * Xc
print(Zc[i])
return Zc
import numpy as np
from scipy import linalg
from scipy import constants as C
from scipy import special
conductors_equivalent_radius = 0.001 * np.array([
6.18, 4.74, 9.03, 49.65, 49.65, 7.22, 4.055, 6.18, 4.74, 9.03, 49.65,
49.65, 7.22, 4.055
])
conductors_rho = 10**-10 * np.array([
172.41, 0.185, 0.29731, 2.1121, 2.1121, 0.029667, 0.19264, 172.41, 0.185,
0.29731, 2.1121, 2.1121, 0.029667, 0.19264
])
f = 50
mu = 4 * np.pi * 10**-7
r = conductors_equivalent_radius
rho = conductors_rho
m = np.sqrt(2 * np.pi * f * mu / rho)
print(rho)
print(r)
print(m)
A1 = m * r / 2
A2 = 4 / (m * r)
B1 = special.ber(m * r)
B2 = special.bei(m * r)
C1 = special.berp(m * r)
C2 = special.beip(m * r)
aR = A1 * ((B1 * C2 - C1 * B2) / (C1**2 + C2**2))
aL = A2 * ((B2 * C2 - C1 * B1) / (C1**2 + C2**2))
print(aR)
print(aL)