# Homework Help: The torque curve of a indcution motor (laboration task)

1. Nov 28, 2012

### beyondlight

1. The problem statement, all variables and given/known data

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 isnt 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.

$$I_{S400V} (n) = I_{S130V} (n) * ...$$
$$T_{400V} (n) = T_{130V} (n) * ...$$

2. Relevant equations

$$T=\frac{P_δ}{ω_s}$$

3. The attempt at a solution

$$I_{s130} = \frac{P_s}{\sqrt{3}Ucos(\phi) }$$

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

$$I_{s400}=I_{s130}*\frac{1}{3}$$

And for T:

$$T_{s130}=\frac{P_δ}{ω_s}$$

Since $$P_δ$$depends on the voltage as does $$P_s (P_δ=P_s -P_{CuR})$$

then $$T_{s400} = T_{s130}* \frac{1}{3}$$

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)