Induction machines
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| synchronous speed | synchronous speed |
| slip | sai số trượt |
The chase that never finishes
- Three coils, three currents 120° apart: the field rotates at synchronous speed $n_{s} = 120f/p$ and the rotor chases it. Slip $s = (n_{s} - n)/n_{s}$ is the gear ratio of the machine.
- The rotor sees frequency $sf$; the rotor branch appears as $R_{2}'/s$, which splits into copper loss $R_{2}'$ plus the shaft term $R_{2}'(1-s)/s$.
{exercise:uni-ee0931-slip}
The field rotates, the rotor chases
Move the slip and watch the stator field, the rotor and their relative speed; read the rotor frequency off the gap between them.
A 4-pole 50 Hz induction motor runs at 1440 rpm. The slip and rotor frequency are —
Độ khó 1/5 · 100 xu + phần thưởng nhỏ khi hoàn thành lần đầu tiên hôm nay
ns = 120·50/4 = 1500 rpm, s = 60/1500 = 0.04 and the rotor bars see s·f = 2 Hz.
The whole torque chain
- With $V_{th} = 231$ V, $R_{th} = 0.5$, $X_{th} + X_{2}' = 2.4\ \Omega$, $R_{2}' = 0.4\ \Omega$: at $s = 0.04$, $T = 87.8$ N·m, air-gap power 13.8 kW, rotor copper 552 W, shaft 13.2 kW — one chain, three balances.
Breakdown: $s_{max} = 0.163$ at 172 N·m — twice the running point. Locked rotor: 62 N·m; double the rotor resistance and starting torque climbs to 109 N·m. Same peak, different address.
{exercise:uni-ee0932-chain}
The worked machine at s = 0.04 delivers 87.8 N·m. The rotor copper loss is about —
Độ khó 1/5 · 100 xu + phần thưởng nhỏ khi hoàn thành lần đầu tiên hôm nay
P_ag = T·ωs = 13.8 kW; copper takes exactly the slip fraction: 0.04 × 13.8 kW = 552 W.
Where the power goes
- Slip divides the air-gap power: copper gets $s P_{ag}$, the shaft gets $(1-s) P_{ag}$. At 4% slip, 96% of the crossing power reaches the shaft — why these machines run best near synchronism.
{exercise:uni-ee0933-power}
Doubling the rotor resistance of that machine changes —
Độ khó 1/5 · 100 xu + phần thưởng nhỏ khi hoàn thành lần đầu tiên hôm nay
Rotor resistance moves the curve peak toward s = 1 (start), leaving the peak value unchanged; the same running slip now dissipates twice the copper.