Calculating DC-motor parameters from a measuring curve

Question

Update: The following question is about an exercise. I don't have more information and I can't do any measuring.

I've got four measuring curves from a DC-motor.

1. input voltage
2. load moment
3. current
4. rational speed

The goal is to calculate the anchor resistance (R), constant of friction (Cr), moment constant (km) and the generator constant (ke).

My approach would be:

The anchor resistance is measured with a blocked motor. Rational speed has to be 0. I would divide U by I at 0.01s $$R_{anchor}=\frac{U}{I} | \omega=0$$

The constant of friction has to be measured with no load. I would us the part between 0.2 and 0.5 seconds.
$$C_r = \frac{K_m \cdot i - M_l}{\omega}$$

The moment constant: $$K_m = \frac{M_m}{i}$$
which is either
$$ K_m = \frac{5\cdot 10^{-3}Nm}{417\cdot 10^{-3}A} = 0.012 \frac{Nm}{A}$$ or $$ K_m = \frac{10 \cdot 10^{-3}Nm}{758\cdot 10^{-3}A} = 0.013 \frac{Nm}{A} $$

1st question: which one would I choose? Can I round it to 0.1 and treat it equally?

The generator constant:
This has to be measured with no load too.
$$ k_e = \frac{U_0 - R\cdot i}{\omega} $$

As you can see, the labeling at w = 0 and at Ml = 0 are missing.

My 2nd and most important question: Is it possible to solve this without knowing the values from 0.1 to 0.5 seconds, thus my approach would be wrong or is there an error in this task?

Answer 1

Edit the question and apply the SI units as well.

1. Regarding your calculated \$k_m[\dfrac{Nm}{A}]\$, it can be prone to error of your instruments. Typically it is linear and begins to drop at higher currents, so you shall evaluate it at nominal current.

2. The \$k_e[\dfrac{V\cdot s}{rad}]\$ shall be measured with a coupled motor that spins your generator, therefore the current is zero. You do measure the angular velocity and generated voltage.

The relationship shall be very close to \$k_e=k_m\$.

EDIT:

The \$k_m[\dfrac{Nm}{A}]\$ has to be measured with locked rotor, too.

EDIT2:

example motor datasheet

Lets choose the most similar motor. If you convert the BEMF constant \$ \dfrac{1.56 V}{1000rpm}\$ to SI units: link and do \$k_m={k_e}\$ you get 0.01489 Nm/A, which is the same as declared - 14.9mNm.

So your motor is unrealistic. It shall have \$k_e\approx 0.012[\dfrac{V\cdot s}{rad}]\$, therefore at 15V it should reach \$1250 s^{-1}\approx 12krpm\$ , clearly a fake example.

At this point it has no sense to further calculate anything. Tell to your prof. that at least they could use a model of a real motor.

EDIT3:

If you look for hint, I do think what they want:

$$U=R_a\cdot I+k_e\cdot \Omega$$ $$15V=R_a\cdot I_1+k_e\cdot \Omega_1$$ $$15V=R_a\cdot I_2+k_e\cdot \Omega_2$$

You have two equations with two variables to solve \$R_a, k_e\$

Then:

$$M = M_l + F\cdot\Omega$$ $$M - M_l - F\cdot\Omega = 0$$ $$k_m\cdot I - M_l - F\cdot\Omega = 0$$

---

$$k_m\cdot I_1 - M_{L_1} - F\cdot\Omega_1 = 0$$ $$k_m\cdot I_2 - M_{L_2} - F\cdot\Omega_2 = 0$$

Again 2 equations, solve \$F, k_m\$

My 2nd and most important question: Is it possible to solve this without knowing the values from 0.1 to 0.5 seconds, thus my approach would be wrong or is there an error in this task?

That won't be the result they want.

Answer 2

Your aproach is right if you can test motor in locked or no load condition. But you have 2 sets of values to calculate required constants, and you don´t need more.

First question: The motor torque is the sum of load torque and friction, friction depends on speed.

Motor current * Km=Load moment+Friction constant * Speed

You have current,Load moment and speed in 2 points, so you can calculate Friction constant, and after moment constant.

Second question:

Uo-R * i=Ke * speed

You have Uo=15 V, 2 values of current and speed. You can calculate R , and after you can get Ke.