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 ) × 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 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)×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
