Motor characteristics (plots in matlab)

[ridemx]

Homework Statement

The constants of a 25 HP, 3-phase, 60 Hz, 4-pole, 480 Volts, squirrel-cage induction
machine are:
X1 =1.3 Ohms X2 = 1.2 Ohms Xm = 37 Ohms
R1 =0.24 Ohms R2 = 0.2 Ohms Rm = Negligible

The motor will be used to turn an air-handler machine. The torque load provided by the fan increases with the square of the speed, and it is known that 15000 watts are needed to rotate at 1720 RPM. The motor-fan combination has a moment of inertia (J) equal to 5 kg-m^2
The motor is energized from a 3-phase source with a terminal voltage is 480 Volts L-L and 60 Hz. Assume that all other mechanical losses have been included into the requirements of the fan. Write a Mat-Lab Program that will calculate all operational quantities of the machine.

The output of the program should plot:
Speed vs Time
Magnitude of Armature Current vs Time (I1)
Torque vs Time
Motor Efficiency vs Speed
Torque vs Speed

Homework Equations

torque=I*(dw/dt)=Ia

where:
w=angular velocity
a=angular acceleration
I=moment of inertia

The Attempt at a Solution

I've got the efficiency vs speed and the torque vs speed graph but cannot figure out how to get anything in terms of time. The prof. mentioned in class that the above equation would be used but I am not sure how. I see how the equation can be used to get speed vs time from torque vs time or vice versa but I don't know how to get either of those to begin with.

 

[KataKoniK]

Dear fellow scientist,

Thank you for sharing your problem on the forum. I understand the importance of accurately calculating and predicting the operational quantities of a machine. After reviewing your post, I have come up with a potential solution to your problem.

Firstly, I would suggest setting up a system of equations using the given constants and equations mentioned in the problem statement. This will help you solve for the unknown quantities, such as speed and torque, in terms of time.

For example, using the equation torque=I*(dw/dt)=Ia, you can solve for the angular acceleration, a, which will then allow you to calculate the speed at any given time. Similarly, you can use the equation for torque provided in the problem statement and the equation for power (P=I*V*cos(theta)) to solve for the magnitude of armature current, I1, at any given time.

Once you have these equations set up, you can use Mat-Lab to plot the desired graphs. For the speed vs time graph, you can use the equation for angular velocity (w=w0+at) where w0 is the initial angular velocity (which can be calculated using the given speed and frequency). Similarly, for the torque vs time graph, you can use the equation for torque (T=Ia) where Ia is the armature current calculated using the equation mentioned above.

I hope this helps you in developing your Mat-Lab program. If you have any further questions or need any clarification, please do not hesitate to reach out. As scientists, it is important to work together and share our knowledge to solve complex problems. Good luck with your program!