Tipping point (asynchronous machine)

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Points K1 and K2 mark the breakdown moments of an asynchronous motor

The tipping point is the point on the torque-speed characteristic of an asynchronous machine (ASM) at which it develops its maximum torque, the breakdown torque . It is also the highest point on the torque / speed characteristic. If the asynchronous machine is subjected to a greater motor or generator load than the breakdown torque during operation, it stops or spins: it "tips over". The tipping point is in the machine's overload range and should therefore only be reached for a short time. In the overload range, the machine heats up excessively.

It will be in 50 Hz operation , which means that the following formulas can be assumed for the data of the breakdown point : The breakdown torque depends on the square of the ratio of stator voltage to stator voltage frequency. A higher stator current flows into the ASM when there is a high voltage and a low frequency. The level of the stator current determines the level of the rotor current. The torque is proportional to the product of the two. ${\displaystyle R_{1}\ll X_{1}}$

Overturning moment

The breakdown torque is the maximum torque available for a short time .

${\displaystyle {M_{K}}={\frac {m\cdot U_{1}^{2}}{4\pi \cdot n_{1}}}\cdot {\frac {1-\sigma }{R_{1}(1-\sigma )+{\sqrt {R_{1}^{2}+X_{\sigma }^{2}}}}}\approx {\frac {m\cdot U_{1}^{2}}{4\pi \cdot n_{1}\cdot X_{\sigma }}}}$

Overturning slip

The perpendicular from the tipping point to the speed axis marks the tipping slip .

${\displaystyle {s_{K}}={\frac {R'_{2}}{\sqrt {R_{1}^{2}+X_{\sigma }^{2}}}}\approx {\frac {R'_{2}}{X_{\sigma }}}}$

Kloß formula

The Kloß formula is an approximation equation for asynchronous machines to determine the torque as a function of the speed or the slip.

${\displaystyle {\frac {M}{M_{K}}}={\frac {2}{\left({\frac {s_{K}}{s}}+{\frac {s}{s_{K}}}\right)}}}$

Explanation of the individual symbols

Equivalent circuit diagram of an asynchronous machine

variable	meaning
${\displaystyle s}$	Asynchronous machine slip
${\displaystyle s_{K}}$	Tilting slip of the asynchronous machine
${\displaystyle M}$	Moment of the asynchronous machine
${\displaystyle M_{K}}$	Breakdown moment of the asynchronous machine
${\displaystyle R_{1}}$	Stator resistance of the asynchronous machine
${\displaystyle X_{1}}$	Stator reactance of the asynchronous machine
${\displaystyle R'_{2}}$	related rotor resistance of the asynchronous machine
${\displaystyle X'_{2}}$	related rotor impedance of the asynchronous machine
${\displaystyle X_{h}}$	Main reactance of the asynchronous machine
${\displaystyle \sigma }$	Scatter factor of the asynchronous machine: ${\displaystyle {\sigma }=1-{\frac {X_{h}^{2}}{(X_{1}+X_{h})(X'_{2}+X_{h})}}}$
${\displaystyle X_{\sigma }}$	${\displaystyle {X_{\sigma }}={\sigma \cdot (X_{1}+X_{h})}}$
${\displaystyle m}$	Number of strands, for the asynchronous machine 3
${\displaystyle U_{1}}$	Phase voltage of the asynchronous machine
${\displaystyle n_{1}}$	Speed ​​of the asynchronous machine with vanishing moment of resistance in ${\displaystyle s^{-1}}$