Testing Your Motor for Torque-Speed Performance To determine optimal power of your dc motor, you must determine the torque-speed (T-) curve, because the motor power is the product of torque and rotational speed, as shown in Equation 1, where P=power (W), T=torque (N-m),  is rotation speed (radians/s). P=T*

(1)

You are trying to optimize power (find the maximum power), which means finding the maximum product of torque and rotational speed. Thus, knowing how torque varies as a function of rotational speed is necessary. A plot, such as Figure 1, is critical to this analysis.

Torque (T)

Peak torque

Free (max) rotational speed

Rotational Speed (w) Figure 1. Torque vs. Rotational Speed Sample Graph There are many ways to determine this relationship. The most rigorous is to actually have the motor lift various weights, determine the moment arm (and thus torque), while measuring the rotational speed for each load. This is complex and hard to do with a small motor. Instead, we will assume the shape of the curve is nearly linear. If that is so, then two points on the graph will fix the line. We will find two points: the free rotational speed (maximum speed) and a heavily loaded (almost maximum torque) conditions. To perform the testing, you will need the following equipment (as shown in Figure 2) (a) Direct current (dc) power supply (b) Voltmeter (to measure dc voltage) (c) Ammeter ( to measure dc current) (d) Tachometer (for rotational speed) – shown in Figure 3. (e) Your motor Note that to read voltage, the voltmeter must be in parallel with the motor (from the power supply) and the ammeter must be in series. If you are having trouble getting readings, you probably do not have the ammeter in series (if you have it in parallel, it bypasses the motor circuit because it has a lower resistance to electron flow.)

voltmeter

Ammeter dc power supply

dc motor

Figure 2. Testing Apparatus The tachometer (Figure 3) is needed to measure the rotational speed. It is both a phototachometer (it emits light and then counts the reflections from the rotating object) and a contact tachometer. You will be using it as a phototachometer. The button to emit the light is on the upper right hand portion of the unit, as shown in Figure 4. You will measure voltage, current, and rotational speed. You will be able to determine the torque from these data using Equation 1, 2, 3 and 4. Remember, Equation 1 relates Power and Torque. Therefore, Equation 1 can be rewritten as Equation 2 T = P/



 Power can be found as the product of voltage and current (since it is direct current)

P=V*I

(3)

where V is voltage (in volts) and I is current (in amps). Therefore, T is found in Equation 4 T = V * I /



Experimental Procedure Step 1. Measure free rotational speed with no load on the motor. Apply as close to 5.0 volts of direct current to the motor with nothing to obstruct the motor shaft (rotating freely). Measure the associated current (in amps). The rotational speed must be measured using the phototachometer. Therefore, you will need to have a small reflective spot on the shaft. The problem is that the

metal shaft is reflective, so you need something to darken it (maybe a Sharpie) and a white line along the shaft (maybe Whiteout). You need contrast!

Figure 3. Phototachometer (front view)

Figure 4. Phototach (side view)

To get a good reading, hold the light button for at least ten seconds. Then let go and press the “Memory” button to check the reading. It should be more than 4000 rpms. To convert the rpms to radians per second, use Equation 5 

 (rad/s) =

2 *  * rpms 60

(5)

Step 2 – Measure with load. Using a rag or gloves, load the motor by pinching the shaft. DO NOT USE YOUR BARE FINGERS. Again, raise the voltage to as near 5.0 volts as possible, then pinch the shaft. Measure voltage, current and rpms and repeat the calculations for Step 1. The tough part is not covering up the reflective part of the shaft with whatever you are using to pinch (or restrict) the shaft! Figures 5 and 6 show the setups for voltage and current readings in close up view.

Figure 5. Current measurement (ammeter) and leads (close up view)

Figure 6. Voltage measurement (voltmeter) setup in close up view