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电机功率P、转矩T、转速N之间的关系
公式导出由功率的定义式导出转矩与转速上式表达式可以表示为
公式导出
由功率的定义式导出转矩与转速
P
(
w
)
=
W
(
j
)
t
(
s
)
=
F
(
N
)
×
x
(
m
)
t
(
s
)
=
F
(
N
)
×
x
(
m
)
t
(
s
)
=
F
(
N
)
×
V
(
m
/
s
)
=
T
(
N
⋅
m
)
R
(
m
)
×
2
π
R
(
m
)
N
(
r
a
d
/
s
)
=
2
π
T
(
N
⋅
m
)
N
(
r
a
d
/
s
)
\begin{align} P(w)&=\frac{W(j)}{t(s)}\\ &= \frac{F(N)\times x(m)}{t(s)}\\ &=F(N)\times \frac{x(m)}{t(s)} \\ &=F(N)\times V(m/s)\\ &=\frac{T(N \cdot m )}{R(m)}\times 2\pi R(m) N(rad/s)\\ &=2\pi T(N \cdot m)N(rad/s)\\ \end{align}
P(w)=t(s)W(j)=t(s)F(N)×x(m)=F(N)×t(s)x(m)=F(N)×V(m/s)=R(m)T(N⋅m)×2πR(m)N(rad/s)=2πT(N⋅m)N(rad/s)
由于平时转速的单位是
r
a
d
/
m
i
n
rad/min
rad/min功率的单位是
k
w
kw
kw
上式表达式可以表示为
P
(
w
)
=
2
π
T
(
N
⋅
m
)
N
(
r
a
d
/
s
)
1000
×
60
=
3.14
×
2
T
N
1000
×
60
=
T
×
N
9549.2965
≈
T
×
N
9550
\begin{align} P(w)&=\frac{2\pi T(N \cdot m)N(rad/s)}{1000\times 60}\\ &=\frac{3.14\times2TN}{1000\times 60}\\ &=\frac{T\times N}{9549.2965}\\ &\approx \frac{T \times N}{9550} \end{align}
P(w)=1000×602πT(N⋅m)N(rad/s)=1000×603.14×2TN=9549.2965T×N≈9550T×N
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