The torque curve of a indcution motor (laboration task)

[beyondlight]

Homework Statement

I have to measure the entire torque curve and stator-current of a inductive motor from idle running speed to 0 rpm. This will bee done for 130 V instead of 400 V because the energy loses will be too high if it is done with a stator voltage of 400V. Question: How does the inductive motors stator-current and torque vary with the stator-voltages amplitude? Find the formulas to re-calculate the already measured torque and stator-current so it is valid for the 400V case which isn't measured. It has to be valid for all rotational speeds n rpm. So it will be treated as an unknown constant through the deduction. Because for example the current at 130V and a specific rotational speed will be calculated for 400V at same rotational speed. Explain in words why the stator- current and torque vary like this.

[tex]I_{S400V} (n) = I_{S130V} (n) * ...[/tex]
[tex]T_{400V} (n) = T_{130V} (n) * ...[/tex]

Homework Equations

[tex]T=\frac{P_δ}{ω_s}[/tex]

The Attempt at a Solution

[tex]I_{s130} = \frac{P_s}{\sqrt{3}Ucos(\phi) }[/tex]

Since the ratio of 400/130 is 3 we can express

[tex]I_{s400}=I_{s130}*\frac{1}{3}[/tex]And for T:

[tex]T_{s130}=\frac{P_δ}{ω_s}[/tex]

Since [tex]P_δ [/tex]depends on the voltage as does [tex] P_s (P_δ=P_s -P_{CuR})[/tex]

then [tex]T_{s400} = T_{s130}* \frac{1}{3}[/tex]Now if this is correct (havent taken the resistance losses into account) how do i make it dependent of n? (n is the rotational speed in rpm)

 

[Valkarie]

The reason why the torque and stator-current vary with the stator-voltage amplitude is due to the fact that a higher stator voltage produces more mechanical power in the motor. This increase in power is a result of the increased stator current, which produces a stronger magnetic field that interacts with the rotor magnets. This stronger magnetic field increases the torque produced by the motor, allowing it to rotate faster. Additionally, the increase in stator voltage also increases the stator current, which leads to an increase in the stator resistance losses. This increase in stator resistance losses results in an overall decrease in efficiency of the motor.