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23 — Calculators

Synchronous speed, slip and torque

The nameplate says 1455 revolutions; the head says 1500. The difference is the slip, and it is not an inaccuracy but the precondition for the motor producing any torque at all.

Input

Readable from the rated speed: around 2900 rpm means one pole pair, around 1450 rpm two.

The speed under load. It is always below the synchronous speed.

Result

Synchronous speed
—1/min
SlipHigh slip means soft behaviour under load and higher rotor losses.
—%
Rated torque at the shaft
—Nm
Torque referred to synchronous speedThe difference from the previous figure is exactly the slip.
—Nm
Rotor lossesThey arise inevitably from the slip and heat the rotor.
—kW

A guide, not a design to standard. We give no warranty for the correctness of the results, the applicable standards and case-by-case verification govern.

Worked example

The default case the calculator starts with, worked through once. Change the values above and it recalculates immediately.

Inputs

Supply frequency
50 Hz
Number of pole pairs
2 (4-pole)
Rated speed from the nameplate
1,455 1/min
Rated power
30 kW

Result

Synchronous speed
1,500 1/min
Slip
3 %
Rated torque at the shaft
197 Nm
Torque referred to synchronous speed
191 Nm
Rotor losses
0.928 kW

Formula

  • n_synchronous = 60 · f / p
  • s = (n_synchronous − n) / n_synchronous
  • M = P · 60 / (2π · n)
  • P_rotor = P · s / (1 − s)

Assumptions and standards

  • The synchronous speed depends only on frequency and pole pairs, not on the motor itself.
  • Torque is calculated from the shaft power delivered and the actual speed.
  • The rotor losses are the share of the air-gap power that remains as heat in the rotor. They are a lower bound — friction and the fan add to them.

Frequently asked

Why does an induction motor never run synchronously?

Because it produces torque from the relative motion between the rotating field and the rotor. Without slip no voltage would be induced in the rotor, no current would flow and no torque would arise. Slip is therefore not a weakness but the operating principle.

What does high slip indicate?

That the motor gives way more in speed under load — soft behaviour, which can be desirable with shock loads. The price is higher rotor losses, since those go directly with the slip.

Does slip change on a variable frequency drive?

The synchronous speed follows the frequency; at the same load torque the slip stays roughly the same in absolute revolutions, not in percent. At low frequency the percentage slip therefore grows.

Calculating is the easy part.

A formula gives you a number. Designing a plant also demands installation method, grouping, discrimination, the standards in force and a look at the installed base. That is what we take on.

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