## Tuesday, February 23, 2021

Constitution and operating principle of an asynchronous motor

An asynchronous motor has two parts:

The stator consists of three coils supplied by a balanced three-phase network; line voltage U, and line current, I. It creates a magnetic field rotating at the frequency of rotation: ns = f / p (p is the number of pairs of poles)

The rotor rotates at a frequency of rotation n slightly lower than ns.
A relation links these two parts: the slip g = (ns-n) / ns --- n = ns. (1 - g)
we denote by W the speed of rotation of the rotor, it is expressed in rad / s.

We have W = 2.π.n (if n is in rev / s) and W = 2.π.n / 60 (if n is in rev / min)

The coupling

The smallest voltage listed on the motor nameplate should be across a winding. Depending on the three-phase network used, the coupling will be star or delta.

Examples:

.

stator power

Absorbed power :

Pa = U.I. √3.cos j (electrical power in W)

I: Line current in (A)

cos j: motor power factor

Losses by Joule effect:

If R is the resistance measured between two phase terminals: Pjs = 3 / 2.R.I² (electrical power in W)
If R is the resistance of a winding: in this case the stator coupling must be taken into account
star coupling: pjs = 3.R.I² (electrical power in W)

triangle coupling: pjs = 3.R.J² (electrical power in W)

Magnetic losses: pfs = Constant

Power transmitted to the rotor: Ptr = Pa - pjs - pfs

rotor power

Losses by Joule effect: pjr = g.Ptr (electrical power in W)

Electromagnetic power: Pem = Ptr - pjr and Pem = Tem.W (mechanical power in W)

Mechanical losses: pméc = Constant

Useful power: Pu = Tu .W and also by Pu = Ptr - pjr - pméc

Yield:

Motor efficiency: h = Pu / Pa

No-load test (Tu = 0 N.m and n = ns): we then have pméc + pfs = Pa0 - pjs0

Load test: Tu = Pu / W = Tr in steady state

Constitution and operating principle of an asynchronous motor

An asynchronous motor has two parts:

The stator consists of three coils supplied by a balanced three-phase network; line voltage U, and line current, I. It creates a magnetic field rotating at the frequency of rotation: ns = f / p (p is the number of pairs of poles)

The rotor rotates at a frequency of rotation n slightly lower than ns.
A relation links these two parts: the slip g = (ns-n) / ns --- n = ns. (1 - g)
we denote by W the speed of rotation of the rotor, it is expressed in rad / s.

We have W = 2.π.n (if n is in rev / s) and W = 2.π.n / 60 (if n is in rev / min)

The coupling

The smallest voltage listed on the motor nameplate should be across a winding. Depending on the three-phase network used, the coupling will be star or delta.

Examples:

.

stator power

Absorbed power :

Pa = U.I. √3.cos j (electrical power in W)

I: Line current in (A)

cos j: motor power factor

Losses by Joule effect:

If R is the resistance measured between two phase terminals: Pjs = 3 / 2.R.I² (electrical power in W)
If R is the resistance of a winding: in this case the stator coupling must be taken into account
star coupling: pjs = 3.R.I² (electrical power in W)

triangle coupling: pjs = 3.R.J² (electrical power in W)

Magnetic losses: pfs = Constant

Power transmitted to the rotor: Ptr = Pa - pjs - pfs

rotor power

Losses by Joule effect: pjr = g.Ptr (electrical power in W)

Electromagnetic power: Pem = Ptr - pjr and Pem = Tem.W (mechanical power in W)

Mechanical losses: pméc = Constant

Useful power: Pu = Tu .W and also by Pu = Ptr - pjr - pméc

Yield:

Motor efficiency: h = Pu / Pa

No-load test (Tu = 0 N.m and n = ns): we then have pméc + pfs = Pa0 - pjs0

Load test: Tu = Pu / W = Tr in steady state