Useful Equations

I have been researching some useful equations that I will use to theoretically model my DC Brushed motors. So far the equations have been pulled together from two separate groups of lecture notes and Electrical Machines, Charles Gross.

The inputs I will be recording into the system will be the current (I) and voltage (V), this will be from a power supply screen. I will use equation 1 to measure my value of k for my motors. I will require a speed sensor of some sort. Finding the change in motor speed over a known voltage change will give a value for k.

My motors are relatively slow and the power (P) is very small therefore I will use a simple DC Motor model as this will give reasonable accuracy, this gives equations 1 and 2.

Equations:

1. kw=V
2. kI=T

The k in both equations is called the motor constant. w is the angular velocity rad/s.

Force (F) generated by the motor is a product of the current, core length (l), number of coils (n) and magnetic flux density (B).

3. F=BIln

From equation 3 the torque can be calculated.

4. T=nIlBd

In equation 4 d denotes the perpendicular distance the force is generated from the axis of rotation.

Combining equations 4 and 2 to find a formula to give the motor constant.

5. kI=nIlBd ==> k=nlBd ==> k=nAB

A is the area of the windings. I will calculate my value of k using equation 5. I will compare this to my recorded value.

The equation for motor efficiency (E) is power input (Pin) divided by power output (Pout).

6. E=Pout/Pin x100

The equations for power are derived from the simple DC motor model.

7. Pout=Tw
8. Pin=VI

Therefore we can re-write the efficiency equation.

9. E=Tw/VI

This will give a theoretical efficiency of the motors. The next steps are finding the equations to model the dynamic inertia effects of the system along with all of the frictional losses.

More on this next post, for now I have more reading to do.