How do you calculate the torque for an electric motor with an air gap?

Calculating the torque of a motor with an air gap involves multiple parameters and steps. The air gap is the space between the stator and the rotor, and it significantly affects the motor's performance. Below are the detailed steps and formulas for calculating the torque of a motor with an air gap.

1. Basic Concepts

Torque (T):

Torque is the rotational force generated by the motor's rotor, typically measured in Newton-meters (N·m).

Air Gap (g):

The air gap is the distance between the stator and the rotor, influencing the distribution of the magnetic field and the motor's performance.

2. Calculation Formulas

2.1 Air Gap Magnetic Flux Density

First, calculate the magnetic flux density (Bg) in the air gap:

where:

Φ is the total magnetic flux (Weber, Wb)

Ag is the area of the air gap (square meters, m²)

2.2 Relationship Between Air Gap Magnetic Flux Density and Current

The air gap magnetic flux density can be related to the stator current (Is) and the air gap length (g) using the following formula:

where:

μ0 is the permeability of free space (4π×10 −7 H/m)

Ns is the number of turns in the stator winding

Is is the stator current (Amperes, A)

g is the air gap length (meters, m)

2.3 Torque Calculation

The torque can be calculated using the following formula:

where:

T is the torque (Newton-meters, N·m)

Bg is the air gap magnetic flux density (Tesla, T)

r is the radius of the rotor (meters, m)

Ap is the surface area of the rotor (square meters, m²)

μ0 is the permeability of free space (4π×10 −7 H/m)

3. Simplified Formula for Practical Applications

In practical applications, a simplified formula is often used to calculate the torque of a motor. A commonly used simplified formula is:

where:

T is the torque (Newton-meters, N·m)

k is a motor constant, dependent on the motor design and geometric parameters

Is is the stator current (Amperes, A)

Φ is the total magnetic flux (Weber, Wb)

4. Example Calculation

Assume a motor with the following parameters:

Stator current 

Is=10 A

Air gap length 

g=0.5 mm = 0.0005 m

Number of turns in the stator winding 

Ns=100

Radius of the rotor 

r=0.1 m

Surface area of the rotor 

Ap=0.01 m²

First, calculate the air gap magnetic flux density Bg:

Summary

Calculating the torque of a motor with an air gap involves multiple parameters, including the air gap magnetic flux density, stator current, air gap length, rotor radius, and rotor surface area. By following the above formulas and steps, the torque of the motor can be accurately calculated.