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$rad/min$
• 功率的单位是$kw$

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​​​