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Commutating Brushless DC Motors<br />

Clamping zener diodes are used to protect<br />

the power MOSFETS from over-voltage<br />

transients produced when the inductive<br />

winding are switched OFF.<br />

Brushless Servo Systems<br />

The brushless DC motor, when properly<br />

commutated, will exhibit the same performance<br />

characteristics as a brushcommutated<br />

DC motor, and for servo analysis the<br />

brushless motor can be represented by the<br />

same motor parameters. It can be modeled<br />

by the equivalent circuit of Figure 16.This<br />

model can be used to develop the electrical<br />

and speed-torque characteristics equations<br />

for brushless DC motors.<br />

The electrical equation is:<br />

VT = IR + Ldl/dt + KB() (1)<br />

W<strong>here</strong><br />

(800) 777-3393<br />

VT = the terminal voltage across the active<br />

commutated phase<br />

I = the sum of the phase currents into<br />

the motor<br />

R = the equivalent input resistance of the<br />

active commutated phase<br />

L = the equivalent input inductance of<br />

the active commutate phase<br />

KB = the back EMF constant of the active<br />

= the angular velocity of the rotor<br />

If the electrical time constant of the brushless<br />

DC motor is substantially less than the<br />

period of commutation, the steady state<br />

equation describing the voltage across the<br />

motor is:<br />

V T = IR+K B (2)<br />

Pancake Resolvers >> Brush Type Motors >><br />

NL<br />

( No Load<br />

speed)<br />

Brushless DC Motors<br />

The torque developed by the brushless DC<br />

motor is proportional to the input current.<br />

T = I K T<br />

V1 V2 Torque<br />

T<br />

Stall<br />

W<strong>here</strong> K T = the torque sensitivity<br />

(oz-in/amp)<br />

If we solve for I and substitute into<br />

Equation (2) we obtain:<br />

V T = T/K TR + K B() (3)<br />

The first term represents the voltage<br />

required to produce the desired torque, and<br />

the second term represents the voltage<br />

required to overcome the back EMF of the<br />

winding at the desired speed. If we solve (3)<br />

for rotor speed, we obtain:<br />

= V T/K B - TR/K BK T<br />

www.axsys.com<br />

><br />

Speed<br />

V T<br />

Figure-17 Speed torque characteristic curves.<br />

(4)<br />

which is the speed-torque equation for a<br />

permanent magnet DC motor.<br />

A family of speed-torque curves represented<br />

by Equation (4) is shown in Figure 17.<br />

The no-load speed can be obtained by substituting<br />

T=0 into (4).<br />

V N

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