NORTHERN ILLINOIS UNIVERSITY Department of Mechanical Engineering
MEE 390 EXPERIMENTAL METHODS IN MECHANICAL ENGINEERING
©1990-2001 M. Kostic

Objectives: To calibrate a motor-generator type tachometer with a stroboscope; measure a motor-flywheel load torque vs. rpm characteristic; and to measure the motor-flywheel dynamic-startup characteristic and the flywheel mass-moment of inertia.

Go to: Current Setup Photo, or to enlarge the scope and scope screen captured (with triggering) during the motor startup.

This laboratory exercise consists of three parts, which may be treated separately for easier understanding, but all are needed to accomplish the lab objectives. The apparatus, see Figure, consists of a flywheel mounted in the chuck of a variable-speed drill, which electric motor's characteristics are to be investigated later. The motor-flywheel system's rotational speed may be varied by changing the power control-knob setting from position 1 to 7 maximum. Different torque load may be applied on the motor by friction of winded rope around the flywheel on which a hanger with the standard weights is attached at one side, while the other side is held with negligible force. A very small toy-type DC motor is attached to the far end of the flywheel. It is driven by the motor-flywheel and functions as a generator, and will be calibrated and used as a tachometer sensor (speedometer). The sensor's output is wired to an oscilloscope and/or a multimeter, directly and/or through a single-stage R/C low-pass filter (see the Figure). The recommended values are C=1 microfarad for capacitor and R=10 kiloohm for resistor, but could be changed if needed. First, the tachometer will be calibrated, then torque load vs. rpm characteristic will be investigated, and finally, motor-flywheel start-up dynamic characteristic will be measured with an oscilloscope. Lastly, the mass-moment of inertia of the flywheel will be determined.

PART ONE: Calibration of the tachometer. The objective here is to calibrate a small motor-generator in order to be used as a speedometer sensor. It will be referred further on as "tachometer." Since the tachometer shaft is driven by the drill-motor, its generated output voltage will be proportional to the shaft speed.

The calibration is performed by setting the drill-motor power at different level (from minimum to maximum), and measuring the corresponding rotational speed by a stroboscope versus generated tachometer voltage, measured by a multimeter, see the Figure. A white line along a radius of the flywheel is marked to facilitate the use of the stroboscope, see below. The obtained RPM (n) versus voltage (V) data should be correlated with a suitable function {n=n(V), linear or higher order polynomial if necessary}. The calibration function, n=n(V), is characteristic of the tachometer only, not the drill-motor. Therefore, loading of the drill-motor is irrelevant for the tachometer calibration.

After calibration, the tachometer will be used for RPM (or 'n') measurements of drill-motor during the steady state, torque load vs. RPM investigation (PART TWO), and for transient, dynamic investigation of the drill-motor startup (PART THREE).

1. Connect the drill-motor and the stroboscope to power supply. The motor is run without load, i.e. the motor drives only the flywheel and the tachometer. The drill-motor may be set to any of the seven power levels with the power control knob.
2. Connect the multimeter to the "filtered" output of the tachometer (ground-G and filtered-F terminals, see the Figure).
3. Turn ON the drill-motor and the stroboscope. The stroboscope should be set at the highest frequency and switched to RPM (cycles per minute) setting. All frequencies in this lab will be expressed in cycles per minute to match the RPM.
4. The stroboscope light is to be directed towards the flywheel's marked white line and its frequency knob should be slowly rotated from the highest towards lower frequencies until it is synchronized with the flywheel RPM so that the marked white line appears to be stationary. The marked white line will appear stationary (synchronized) if the stroboscope frequency is equal to flywheel RPM (real frequency) divided with any integer, thus making the reading false (still these false aliasing frequencies may be used to determine the real RPM, see below). To make sure that measurement is not affected by aliasing, we have to find the highest possible strobe synchronization frequency. In that case doubling the strobe frequency will make that the single marked white line will appear as two stationary lines, 180 degrees apart. If a stroboscope range is below the measured RPM value, we still could use such a stroboscope by measuring any two successive, synchronized aliasing (false) strobe frequencies, n₁ and n₂. The real frequency (n) is than calculated by: n=n₁n₂/(n₁-n₂). It is left (as a challenge) for you to derive this formula and more general one in our Text, p.495.
5. At least five readings (V and n), as explained above, are to be taken over the full RPM range of the drill-motor.
6. Curve fit the measured data with a suitable function, n=n(V), linear or higher order polynomial if necessary.

PART TWO: Torque (load) versus RPM investigation. The drill-motor torque vs. RPM characteristic at maximum power setting will be investigated. A rope (or string) is winded two times around the flywheel circumference of radius R, see the Figure. A hanger with standard weights (total weight W) is attached on one end of the rope, while the other rope end, tied to a wood piece, is held (anchored) in a groove. WARNING: The flywheel rotational direction MUST BE to pull the hanger with standard weights upward.

In that case, the holding force, F, on the other (anchored) rope end, is much smaller than the W and may be neglected (remember the sliding friction force around a wheel from Dynamics). Then, the torque load on the drill-motor is simply, T=WR. Note that changing the flywheel rotation direction will make force F many times larger than W, that may endanger the experimenter if the rope (string) breaks, or stalling the motor (please, see the above WARNING). By increasing the total weight W (i.e. torque T=WR) at the same (maximum) power setting, the motor RPM will decrease, thus producing the torque vs. RPM motor characteristic data, T=T(n), a very important motor characteristic.

1. Set the apparatus as depicted in the Figure above. The rope should be winded two times around the flywheel circumference. Attach the hanger at one rope end and anchor the other end with a wooden block (piece). Connect the multimeter to the filtered tachometer output terminals. Set the drill motor power to maximum setting.
2. WARNING-Keep your hands and eyes away from moving elements! Verify that motor-flywheel rotation is in the direction to pull the hanger with the weights upward, see the above. Note that opposite direction may endanger the experimenter if the rope (string) breaks. Make sure the rope winds are spiral (orderly, not crossing over) to provide "smooth" flywheel sliding. Otherwise, the flywheel may be winding the rope with the weights upward until they hit the base board with a possibility of injuring people standing nearby.
3. Measure and record the flywheel diameter (verify if it is D=2*R=2*6.3 cm). Measure and record the hanger weight (W_H) and put 2 N (Newton) standard weight (W_S) on the hanger. The total weight will be W=W_H+W_S.
4. Turn the drill-motor ON, measure and record the tachometer output voltage V, and turn the drill-motor OFF.
5. Repeat the above measurements for several (five or more) diferent standard weiths up to 12 N or so.
6. Calculate torque T=WR and RPM (n) using the calibration correlation n=n(V) from PART ONE experiment results.
7. Plot the torque (T) on vertical axis vs. RPM (n) data on horizontal axis. Curve fit the data with a suitable function, T=T(n), linear or higher order polynomial if necessary.

PART THREE: Dynamic Start-up Characteristic. The motor-flywheel start-up RPM vs. time characteristic at maximum power setting and without load will be measured using an oscilloscope. During the start-up, from the moment when the drill-motor is turned ON, it will accelerate from zero speed to its steady equilibrium speed for a set power and load.

An exponential-like curve, approaching the equilibrium speed N, should be obtained. Using the results from PART ONE, n=n(V), and PART TWO, T=T(n(V)), and curve fitting the measured data with an exponential function, n(t)=N(1-e^-Ct), for example (C to be determined), the RPM (n) vs. time (t), and the torque (T) vs. time (t), the motor-flywheel start-up characteristics may be obtained. Furthermore, the slope of n=n(t) is angular acceleration, a=a(t)=dn/dt, for a given time (t). Using the formula from Dynamics, we may calculate the mass-moment of inertia of the shaft-flywheel system, I=T(t)/a(t). The latter, being the mass-geometric property, should not be dependent of time, and may be calculated using the well known formula from Statics, I=integral(r²dm), or I=mR²/2=(p /2)r bR⁴ for a disk or cylinder of radius R, thickness or length b, and density r . The mass-moment of inertia I=T(t)/a(t) should be calculated for several values of t and agreement between themselves and the value calculated from the mass-geometric properties of the flywheel system. Any discrepancy should be discussed and justified.

1. Set the apparatus as depicted in the Figure above, but without the weight load. Set the drill motor power to maximum setting, since we are going to use the T(n(V)) correlation from PART TWO above. Connect the filtered tachometer output terminals (F & G) to the multimeter and channel one of the oscilloscope. Connect the unfiltered tachometer output terminals (S & G) to channel two of the oscilloscope in order to compare it with the channel one reading.
2. Set the oscilloscope trigger to capture the tachometer signal during the start-up. You will have to set up trigger in SINGLE SWEEP mode, rising slope and appropriate level, and use pre-triggering if needed (probably not). Please review the Oscilloscope lab (and its Handout) as demonstrated to you earlier. You will probably have to "play" with different settings (voltage scale in DC mode, time scale, and trigger settings) until you are satisfied with the captured start-up tachometer signal on the scope screen. The scope STORE button has to be depressed to store the trace of the beam on the screen. Do not forget to press RESET button (to "rearm" the scope) for the next trigger sweep. The SAVE button may be used (in AUTO trigger mode) to save the zero reference sweep.
3. Read and record the voltage (V) for at least eight time (t) values across the start-up range from the scope screen using the scope time (S_t) and voltage (S_V) division scales.
4. Calculate the rotational speed using the tachometer calibration result, n(t)=n(V(t)), from the PART ONE. Calculate the corresponding torques using the torque vs. RPM result, T(t)=T(n[V(t)]), from the PART TWO.
5. Using the Least Square Method, curve fit the n-t data { n(t)=N(1-e^-Ct), see the above} and calculate the corresponding angular acceleration a(t)=(p/30)dn/dt. Then, calculate the mass-moment of inertia of the flywheel system, I,  for several values of time, during the start-up.
6. Calculate the mass-moment of inertia of the flywheel system using its mass-geometric properties, for example, by approximating its shape as one or more disks or cylinders.
7. Compare the values and discus the results.

NOTE 1: You need to work with and report all units and make any conversion if necessary.

NOTE 2: Your previous Lab assignment and Lab report are due before the demonstration of the next Lab. It is the best for you if you do your lab experiments right after the demonstration while TA is still in the Lab. Also, you have to perform the uncertainty analysis for every experimental lab and include it in your lab report.

Go to TOP

Professor M. Kostic's Web Site: www.kostic.niu.edu *Usage Policy & © Copyright by M. Kostic