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Basic Electric Motor Torque Equation

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Equation:        T = FR


T = Torque, lb-ft
F = Force, lb
R = Radius, or distance which force is applied from pivot location, ft

Torque Developed:

The equation for torque developed in a DC motor can be derived as follows.

The force on one coil of wire F =i l x B Newton

Note that l and B are vector quantities

Since B = φ/A where A is the area of the coil,

Therefore the torque for a multi turn coil with an armature current of Ia:

T = K φ Ia

Where φ is the flux/pole in weber, K is a constant depending on coil geometry, and Ia is the current flowing in the armature winding.

Note: Torque T is a function of force and the distance, equation (2) lumps all the constant parameters (eg. length, area and distance) in constant K.

The mechanical power generated is the product of the machine torque and the mechanical speed of rotation, ωm


Pm = ωm T

= ωm K φa

DC Motors

It is interesting to note that the same DC machine can be used either as a motor or as a generator, by reversing the terminal connections.


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