Calculation
M/Mk = 2 / (s/sk + sk/s)
The Kloss equation describes an induction motor's torque-slip curve solely from the ratio of slip to breakdown slip, without equivalent-circuit data.
Busch 2006, Abschnitt 8.4.3.3, Gl. (8.65) Kloßsche Näherungsgleichung
Induction motor torque ratio (Kloss equation)
The Kloss equation describes an induction motor's torque-slip curve solely from the ratio of slip to breakdown slip, without equivalent-circuit data.
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Result
Select a target and calculate.
Understand the inputs
- Torque ratio M/Mk — Ratio of torque at the considered slip to breakdown torque; reaches its maximum of 1 at s=sk.
- Slip s — Motor operating slip at the considered point.
- Breakdown slip sk — Slip at which the motor develops its maximum (breakdown) torque.
Example
s=0.04 and sk=0.2 give M/Mk=2/(0.2+5)=0.385.
Assumptions and limits
Simplified equivalent circuit neglecting stator resistance (valid mainly for larger machines); saturation, current displacement and starting transients are excluded.
Understand Induction motor torque ratio (Kloss equation)
This calculator determines the ratio of torque to breakdown torque of an induction motor at any slip, without requiring equivalent-circuit values.
What does this quantity describe?
The Kloss approximation describes the torque-slip curve solely via the ratio of operating slip s to breakdown slip sk: M/Mk=2/(s/sk+sk/s). At s=sk, the maximum M/Mk=1 is reached.
Formula and variables
M/Mk = 2 / (s/sk + sk/s)
M/Mk = 2/(s/sk + sk/s)
| Symbol / input | Meaning |
|---|---|
| Torque ratio M/Mk | Ratio of torque at the considered slip to breakdown torque; reaches its maximum of 1 at s=sk. |
| Slip s | Motor operating slip at the considered point. |
| Breakdown slip sk | Slip at which the motor develops its maximum (breakdown) torque. |
Choose the inputs correctly
s is the operating slip at the considered point, sk the breakdown slip at which the motor develops its maximum torque.
How to use the calculator
Determine s from speed measurement and synchronous speed ((ns−n)/ns); derive sk from a datasheet or from the ratio of breakdown to rated torque.
Worked example
s=0.04 and sk=0.2 give M/Mk=2/(0.2+5)=0.385.
Understand the result and units
For s≪sk the curve is approximately linear (stable operating region); for s≫sk torque falls again.
s and sk are dimensionless slip values between 0 and 1. M/Mk is dimensionless.
Typical applications
Estimating induction motor torque at any operating point without a full equivalent circuit, and teaching the shape of the torque-slip curve.
Assumptions, limits and common mistakes
Simplified equivalent circuit neglecting stator resistance, valid mainly for larger machines; saturation, rotor current displacement and starting transients are excluded.
Common mistake: Do not confuse sk with rated slip; breakdown slip is well above normal operating slip.
Frequently asked questions
What is “Induction motor torque ratio (Kloss equation)” used for?
Estimating induction motor torque at any operating point without a full equivalent circuit, and teaching the shape of the torque-slip curve.
Where do the input values come from?
s is the operating slip at the considered point, sk the breakdown slip at which the motor develops its maximum torque.
What does the result not cover?
Simplified equivalent circuit neglecting stator resistance, valid mainly for larger machines; saturation, rotor current displacement and starting transients are excluded.