Induction machines

Seven motors in ten

• Around seven of every ten industrial motors are squirrel-cage 鼠笼式 induction machines. They have no brushes and only one moving part.
• The secret is a field that rotates by itself. This lesson follows the rotor as it chases that field.

The rotating field

• Three coils 120° apart, fed with currents 120° apart in time, make a rotating field 旋转磁场 of constant size.
• It turns at the synchronous speed 同步转速 $n_{s} = \dfrac{120f}{p}$ rpm, with $f$ in Hz and $p$ the number of poles.

Slip

• The rotor chases the field but never quite catches it. The shortfall is the slip 转差率 $s = \dfrac{n_{s} - n}{n_{s}}$.
• The rotor bars see the field slide past at frequency $sf$, so every rotor quantity follows from the slip.

Where the power goes

• In the equivalent circuit the rotor appears as $R_{2}'/s = R_{2}' + R_{2}'\dfrac{1-s}{s}$. The first part is rotor copper loss; the second is the shaft.
• So slip divides the air-gap power $P_{ag}$: copper gets $sP_{ag}$ and the shaft gets $(1-s)P_{ag}$.

Worked example: the nameplate

The torque–slip curve

• Torque rises with slip, peaks at the breakdown torque 最大转矩, then falls. The peak sits where $R_{2}'/s$ equals $\sqrt{R_{th}^{2} + (X_{th} + X_{2}')^{2}}$.
• More rotor resistance moves the peak towards starting without changing its height. The wound rotor 绕线转子 sells exactly this.

Worked example: the torque chain

Three common slips

Recap