Kloß equation

Course of the torque according to the Kloss formula

The Kloss equation or Kloss formula is an approximation for the calculation of asynchronous machines , in which a reduced equivalent circuit is assumed. It is named after the researcher Max Kloss .

Kloss formula:

${\displaystyle {\frac {M}{M_{\mathrm {K} }}}={\frac {2}{\displaystyle {\frac {s}{s_{\mathrm {K} }}}+{\frac {s_{\mathrm {K} }}{s}}}}}$

with the parameters:

• ${\displaystyle {M}}$ =  Torque ,
• ${\displaystyle {M_{\mathrm {K} }}}$ =  Tilting moment ,
• ${\displaystyle {s}}$ =  Slip ,
• ${\displaystyle {s_{\mathrm {K} }}}$ =  Overturning slip

Is assumed a reduced ESB (equivalent circuit diagram) in which the reactance ( ) to be infinite and the copper resistance of the stator winding ( ) of 0 is assumed. The equation represents a general torque relationship that is valid for all asynchronous machines. If the data of the tipping point of a machine are known, it can be used to determine the torque for any slip . ${\displaystyle {X_{\mathrm {h} }}}$ ${\displaystyle {R_{\mathrm {1} }}}$

Application example

The overturning moment of a machine is 500 Nm, the overturning slip is 0.236. How big is the starting torque of the machine when the slip is s  = 1?

${\displaystyle {M_{\mathrm {A} }}={M_{\mathrm {K} }}\cdot {\frac {2}{s_{\mathrm {K} }+1/s_{\mathrm {K} }}}=500\,\mathrm {Nm} \cdot {\frac {2}{0{,}236+1/0{,}236}}=223{,}5\,\mathrm {Nm} }$

literature

• Rolf Fischer: Electrical machines . 14th edition. Hanser, 2009, ISBN 978-3-446-41754-0 .