Graphing Induction motor characteristics

[coltfourfive]

Homework Statement

5HP, 60 hz, 440Vac, 3 phase induction motor.

Graph:
3 Phase Torque vs RPM
Current vs RPM
Mechanical Power (HP) vs RPM
Efficiency vs RPM
Power Factor vs RPM

Homework Equations

I'm having trouble finding equations online relating relating these values. Can anyone give me a pointer in the right direction as to what equations I need to start with?

The Attempt at a Solution

The first part of the problem asked me to create an excel spreadsheet calculating R1 X R2 Xm and Rm for the equivalent circuit for slip values between 0 and 1, given No Load and Locked Rotor Test results for and induction motor and I have that working well, just where to begin with the graphs is confusing me.


Thanks

 

[KataKoniK]

for your question! It looks like you are working on a project related to induction motors and are trying to create graphs for torque, current, mechanical power, efficiency and power factor. To start, you will need to have equations for each of these values. Here are some equations that may be helpful for you:

1. Torque (T) = (3 * P * R2 * V^2)/(ω * s * R1 * Rm)
Where P is the number of poles, R1 and R2 are stator and rotor resistances, V is the supply voltage, ω is the angular velocity and s is the slip.

2. Current (I) = (S * V)/(√(3 * R1^2 + (Xm + Xr)^2))
Where S is the rated power, V is the supply voltage, R1 is the stator resistance and Xm and Xr are the magnetizing and rotor reactances.

3. Mechanical Power (Pm) = (2 * π * N * T)/60
Where N is the speed in RPM and T is the torque.

4. Efficiency (η) = (Pm/Pin) * 100%
Where Pm is the mechanical power and Pin is the input power.

5. Power Factor (PF) = cos(θ)
Where θ is the phase angle between voltage and current.

Using these equations, you can calculate the values for each parameter at different RPM values and plot them on a graph. I would suggest starting with a range of 0-100% for slip and using the corresponding RPM values for each slip value. This will give you a good range of data points to plot on your graphs.

I hope this helps and good luck with your project!