Asynchronous machine

The asynchronous machine is also a rotating field machine. The stator is identical to the stator of the synchronous machine, whereas the rotor is passive in the most common version of this machine type, the so-called squirrel cage rotor.

1 Structure

2 Cage rotor

• Conductive rods are located in the grooves of the runner plate package.
• The rods are connected to each other at the front by short-circuit rings.
• Together, these components form a cage (similar to a hamster cage).
• The rods are designed at an angle to reduce harmonics in the rotating magnetic field.

3 Start-up of the ASM

• The stator generates a rotating magnetic traveling wave in the stationary part with the angular velocity: \(\omega _\mathrm {s} = \frac {\omega _0}{p}\).
• The stationary rotor experiences a time-varying field with the frequency \(\omega _\mathrm {s}\).
• The rotating magnetic field penetrates the rotor and induces a voltage with the frequency \(\omega _\mathrm {s}\).
• The induced voltage results in a current flow, since the rotor windings are short-circuited.
• The induced rotor current opposes the change of the stator field perceived by it (Lenz’s law).
• The stator field and the rotor current interact via the Lorentz force, leading to the formation of a torque.
• The torque acts in the direction of the stator’s rotating magnetic field.
• The rotor begins to rotate.

4 Operation of the ASM

• As the rotor speed increases, the rotor perceives an increasingly slower change of the stator field: \(\omega _\mathrm {r} = \omega _\mathrm {s} - \omega _\mathrm {mech}\).
• With increasing speed, both the magnitude and the frequency of the induced voltage in the rotor decrease.
• The magnitude of the torque decreases.
• When the rotor and the stator field rotate at the same frequency, synchronous speed is reached.
• The rotor windings no longer experience a change in the magnetic field.
• The induced current and the torque of the machine become zero.
• Due to friction effects, the rotor is slowed down again, leading to the renewed formation of torque.
• In the steady-state condition, a speed slightly below the synchronous speed is established.

5 Speed/torque characteristic curve

The speed/torque characteristic curve of an asynchronous machine is non-linear and can be divided into several sections. The characteristic curve is often plotted as shown in Figure 3 using the slip \(s\). The slip refers to the percentage deviation of the mechanical rotational speed of the rotor \(n_\mathrm {r}\) from the electrical rotational speed \(n_\mathrm {s}\) of the supplying network in the stator. \begin {equation} s = \frac {\omega _\mathrm {s} - \omega _\mathrm {r}}{\omega _\mathrm {s}} \end {equation}

A slip of \(s=1\) (\(100\%\)) therefore corresponds to the machine being at a standstill or a speed of \(n=0\), while a slip of \(s=0\) corresponds to mains-synchronous operation, which can never occur with an asynchronous machine, however, as the torque would be zero in this case. The speed/torque characteristic curve is also known as the Kloss characteristic curve and can be calculated using equation 2: \begin {equation} M = \frac {2\cdot M_\mathrm {K}}{\frac {s_\mathrm {K}}{s} + \frac {s}{s_\mathrm {K}}}\label {GlKloss} \end {equation}

For large machines, the slip corresponds very closely to the percentage losses of the machine: \begin {equation} \eta \approx 1-s \end {equation}

asynchronous machine A three-phase asynchronous motor has the following information on its nameplate:

• Rated power: \(10\,\)kW
• Rated speed: \(1440\,\frac {\mathrm {U}}{\mathrm {min}}\)

• Frequency: \(50\,\)Hz
• Breakdown torque: 25%

Calculate the rated torque, the tipping torque and the starting torque. \begin {align*} P_\mathrm {N} &= M_\mathrm {N}\cdot \omega _\mathrm {N} = M_\mathrm {N}\cdot 2\pi n_\mathrm {N}\\ M_\mathrm {N} &= \frac {P_\mathrm {N}}{2\pi n_\mathrm {N}} = \frac {10\cdot 10^3\,\mathrm {W}}{2\pi \cdot 1440 \frac {1}{60\,\mathrm {s}}} = 66,31\,\mathrm {Nm}\\ s_\mathrm {N} &= \frac {\omega _\mathrm {s} - \omega _\mathrm {r}}{\omega _\mathrm {s}}\\ &=\frac {2\pi \cdot 1500 \,\frac {1}{60\,\mathrm {s}} - 2\pi \cdot 1440\,\frac {1}{60\,\mathrm {s}}}{2\pi \cdot 1500 \,\frac {1}{60\,\mathrm {s}}}\\ & = 0,04 \end {align*}

To calculate the other moments, equation 2 is calculated for the cases of nominal operation and standstill. \begin {align*} M &= \frac {2\cdot M_\mathrm {K}}{\frac {s_\mathrm {K}}{s} + \frac {s}{s_\mathrm {K}}}\\ M_\mathrm {K} &= \frac {M_\mathrm {N}}{2}\cdot \left (\frac {s_\mathrm {K}}{s_\mathrm {N}} + \frac {s_\mathrm {N}}{s_\mathrm {K}}\right )\\ &= \frac {66,31\,\mathrm {Nm}}{2}\cdot \left (\!\frac {0,25}{0,04} + \frac {0,04}{0,25}\!\right ) = 212,54\,\mathrm {Nm}\\ M_\mathrm {A} &= \frac {2\cdot 212,54\,\mathrm {Nm}}{\frac {0,25}{1} + \frac {1}{0,25}} = 100,02\,\mathrm {Nm} \end {align*}