5.2.3. Slip

Relationship between slip and rotor speed

Rotor speed n lags behind the synchronous speed n_D 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 n_s in asynchronous machines.

slip speed

n_s = n_rel = n_D - 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:

sn_D = n_D - n

n = n_D - sn_D

n = n_D (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 U_2.0

U_2.0 = C₁ · F · n_D

f_2.0 = p · n_D = f₁

The values of the voltage U induced in the rotor and its frequency f₂ depend on the relative speed n_s 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 n_s

U₂ = C₁ · F · n_s

t₂ = p · n_s

If one establishes the quotient U₂/U_2.0 - resp. f₂/f₁, one derives

and thus

U₂ = s U_2.0

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.