  Electrical Machines - Basic vocational knowledge (Institut für Berufliche Entwicklung, 144 p.)  5. Asynchronous motors  5.2. Operating principles  5.2.1. Torque generation 5.2.2. Asynchronous principle 5.2.3. Slip

### 5.2.3. Slip

Relationship between slip and rotor speed

Rotor speed n lags behind the synchronous speed nD and one refers to rotor “slippage”. The relative difference n between both speeds, which expresses the relative movement between the stator rotating field and the rotor, is characterised as slip speed ns in asynchronous machines.

slip speed

ns = nrel = nD - n

The quotient resulting from the slip speed and the rotating field speed has been defined as the slip s

slip Example:

An asynchronous motor has been connected to a mains voltage of f1 = 50 Hz frequency. How great is the slip s given a rated speed n = 960 rpm?

Solution:

The rotor rated speed of n = 960 rpm at f1 = 50 Hz should be aligned to the next synchronous speed n = 1000 rpm.

Thus, the slip can be calculated The slip accepts at rated load of motors values ranging between one and eight per cent. Greater slip values usually arise in less powerful motors. If we incorporate the speed limit values of the asynchronous machine in motor operation into the equation, we derive the following values for the slip s:  A solution according to the rotor speed yields the following:

snD = nD - n

n = nD - snD

n = nD (l - s)

Rotor voltage and rotor frequency

Value and frequency of rotor voltage in idling rotors.

The voltage generated by idling rotors is characterized as rotor idling voltage U2.0

U2.0 = C1 · F · nD

f2.0 = p · nD = f1

The values of the voltage U induced in the rotor and its frequency f2 depend on the relative speed ns between the stator rotating field and the rotor, that is to say, the slip. These values are there called slip voltage resp. slip frequency.

Value and frequency of the rotor voltage given any slip speed ns

U2 = C1 · F · ns

t2 = p · ns

If one establishes the quotient U2/U2.0 - resp. f2/f1, one derives and thus

U2 = s U2.0 resp. with

w = 2 · p · f

w2 = s · w1

The voltage (U2) induced in the rotor and its frequency f2 are proportional to the slip.