1. The torque-speed characteristics of a DC motor have been...

1. The torque-speed characteristics of a DC motor have been determined, as shown in Figure 1 below. Note that u is the voltage applied to the motor armature, ?m and ?m are, respectively, the output torque and angular velocity of the motor shaft. From this plot, • Obtain the motor constant, torque constant, and armature resistance of the motor. • When the motor is rotating at 100 radians per second, what is the back emf voltage induced at the armature? • When the motor is producing 2x10^-3 Nm of torque, how much power is dissipated as heat at the motor windings? Figure 1: Torque-speed characteristics of a DC motor

Transcript

00:01 In this question, we are given speed characteristics of a dc motor.

00:09 So now let us draw the speed characteristics of the dc motor.

00:15 Here it is x -axis and on x -axis, sorry, y -axis, y -axis removes torque and on x -axis, we have our frequency or we can say speed, omega m in radian per second and here is our graph.

00:34 So these are our two lines here.

00:38 So this line indicates the omega as omega is 160 radian per second and for this line, omega is 200 radian per second.

00:50 For this line, the value of torque is given as 4 into 10 to power minus 3 of newton meter.

00:59 So we have to find the motor constant, the torque constant and torque constant and the amateur resistance.

01:20 Now let us first find the motor constant.

01:24 As we know, the value of k2 motor constant will be, one data is given also here as here.

01:34 For this voltage is given here as u equals to 20 volts and for the upper graph, voltage is given here as u equals to 24 volts.

01:47 Now we know k2 is equal to v2 upon omega 2 as the motor constant is equal to voltage upon frequency.

01:57 So the motor constant will be, for second graph will be 24 upon here, it is 24 and for it is 200.

02:06 So 24 by 2v.

02:07 So the value of k2 will be 0 .12.

02:12 Now similarly, finding k1.

02:15 So k1 will be v1 upon omega 1.

02:19 So here v1 is 20 and for omega 1 is 160.

02:24 So k1 will be equal to 0 .125.

02:29 Now for torque constant, for torque constant, for torque constant, we have torque at 200 radian per second as 4 into 10 to power minus 3.

02:50 In this figure, yeah, for 200 radian per second, we have torque as 410 to power minus 3.

02:57 So now finding the torque for 160.

03:00 So here we can write, let x be the torque for 160.

03:09 So dividing both equations will be get 4 upon 10 to power minus 3 upon x into 200 by 160...

Question

Please give Ace some feedback