考慮愛波斯坦方圈測磁或變壓器，電流乙個週期所做的功為w
ww，即為損耗,
w =∫
t1t2
u(t)
i(t)
dt\displaystyle w= \int _^u(t)i(t)dt
w=∫t1t
2u(
t)i(
t)dt
由於u(t)
=ndϕ
dt=n
adb(
t)dt
=n⋅a
dbdt
\displaystyle u(t)=n \frac = n \frac = n\cdot a \frac
u(t)=n
dtdϕ
=nd
tadb
(t)
=n⋅a
dtdb
，h (t
)=ni
(t)l
\displaystyle h(t)= \frac
h(t)=l
ni(t
)這裡 n代表線圈匝數， a代表鐵心截面積，l
ll 代表磁路平均長度，所以
w =∫
t1t2
u(t)
i(t)
dt=∫
t1t2
n⋅a⋅
i(t)
db=∮
a⋅l0
n⋅i(
t)l0
db=v
∮hdb
\displaystyle w= \int _^u(t)i(t)dt = \int _^ n \cdot a \cdot i(t) db = \oint a\cdot l_0 \frac b = v \oint h b
w=∫t1t
2u(
t)i(
t)dt
=∫t1
t2n
⋅a⋅i
(t)d
b=∮a
⋅l0
l0n
⋅i(t
)db
=v∮h
db即 ∮ hd
b=wv
\displaystyle\oint h b = \frac
∮hdb=v
w為單位體積的材料在乙個週期內消耗的能量。
使用scipy中simps函式進行積分；資料來源： 磁滯迴線原始資料27qh085牌號。
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import cubicspline
from scipy.integrate import simps
# 讀取資料
data = pd.read_excel(
'csdn_1.7t磁滯迴線.xlsx'
)data.describe(
)
磁場強度, a/m 磁極化強度, mt
count 865.000000
865.000000
mean -
0.099143
1.371792
std 21.209575
1334.475407
min-
43.522999
-1705.40002425%
-12.869000
-1525.90002450%
-0.386400
5.58000075%
12.510000
1520.000000
max43.612999
1705.400024
em_e
me,磁路有效體積為v
ev_e
ve，密度為 ρ
\rho
ρ，則50hz下的磁滯損耗為0.277w/kg：
simps(
-y,x)
/1000
*(m_e/rho)
/m_e*
50, simps(
-y,x)
/7650
/1000*50
(0.27743683004581576
,0.2774368300458158
)