Voltage Signals From Dynamic Systems

Spring 2006

OBJECTIVES

1. Increase knowledge of oscilloscope use in measuring voltage signals.

2. Use data acquisition software to obtain and analyze a voltage signal with a personal computer.

3. Examine the errors associated with an analog‑to‑digital conversion.

4. Develop criteria for selecting the sampling frequency and record length required to reconstruct a voltage signal in the time domain.

BACKGROUND

The dynamic behavior of mechanical systems is of paramount importance in many engineering applications. Experimental testing is often used to gain a better understanding of dynamic behavior of a particular mechanical device. The experimental results are used to predict failure mode and to provide data that will result in future improvements. Some examples where experimental testing has had benefits, (1) the reduction in the time required for a computer hard disk head to reach and maintain a desired position, (2) the reduction in the noise generated by a jet engine intake, and (3) the non destructive testing of an airplane wing.

The first step in the experimental dynamic analysis of a mechanical system to is to instrument the mechanical system with the appropriate transducers. The system can then be operated in the usual mode or it may be necessary to excite it by external forcing (e.g., strike the device being tested with an impulse hammer). The voltage signals from the transducers must then be processed and analyzed. The signals may be amplified, filtered to reduce the noise and interference content, and then observed in both the time and frequency domain. The goal of this and the next lab is to become familiar with the tools that the mechanical engineer uses to analyze voltage signals from dynamic systems.

PREPARATORY EXERCISES

1. A data acquisition board has an input voltage range of 0 to 5 V. The board has 8-bit resolution. What is the voltage resolution corresponding to the least significant bit?

2. Find the mean, peak to peak, and RMS values of the following signals. If the value doesn’t exist, say so and why.

a. E = 3.6 V

b. E = ‑5 + 2 sin(8pt) V

c. A square wave with 1.6 V amplitude, 10 Hz frequency, and zero D.C. offset.

Note that the definition of an RMS (root-mean-squared) value for a signal, if the voltage v(t) is the time varying part of the signal, we have

3. Consider a sine wave with 1 V amplitude and 5 Hz frequency.

a. What is the lowest A/D converter sampling frequency will allow you to discern the proper frequency content?

b. What frequency will the signal appear to have if you sample at f_s= 10 Hz (). Use Figure 7.3 of your text to help answer this.

EQUIPMENT

1. Oscilloscope.

2. Function Generator.

3. PICaxe08M microprocessor data acquisition system

Figure 1. Experimental setup.

LABORATORY INSTRUCTIONS

1. Create the following signal using a function generator and an oscilloscope.
E = 2.5 + 1.0 sin(2πt) (volts)

What are the DC, AC-amplitude, and frequency values for this signal?

2. Connect the function generator to the data acquisition system and to the oscilloscope. View the digitally sampled signal by importing the captured data into Excel and plotting it. Reduce the signal amplitude to the point that discretization error becomes apparent on the graph. Move the data to Excel and print out the signal trace for your lab notebook. Is the resolution of the data acquisition system or of the graphics monitor the key factor responsible for the apparent discretization error on the screen?

3. Take at least 1000 samples at the maximum sampling frequency and determine what the average sampling rate is.

4. Next, take 100 samples with t_s = Dt ≈ 0.025 sec (sampling frequency, f_s ≈ 40 Hz). Adjust the frequency of the function generator to each of the values given in

5. Table 1. For each frequency, record and compare information about the time domain and frequency domain plots.

Table 1. Test plan.

6. Repeat step 3 for sampling frequencies at half and one-fourth of this rate. Comment on how well the plots represent the actual input signal.

7. Use the oscilloscope to measure the DC offset, minimum, maximum, and RMS voltages. Also measure the frequency and period of the signal. Record all measurements and oscilloscope settings. Also include a sketch or printout of the signal.

8. Use the function generator to create a triangle wave with 2 volt amplitude, 2 Hz frequency, and 1 volt D.C. offset. Repeat steps 3-5 for the triangle wave.

DISCUSSION QUESTIONS

1. How can you assure that the accuracy of measurements from an oscilloscope is always maximized? Does this involve the gain selection or where zero is positioned?

2. Comment on what the time domain and the frequency domain plots look like. Does the plot represent the signal accurately? Compare your Excel plots with the information that you obtain from the oscilloscope.

3. How can you assure that the accuracy of measurements using an A/D converter is always maximized? Again, does this involve the use of a pre-amp and its gain selection, or where zero is positioned, or even the number of bits of A/D resolution?

Laboratory Grading Form

Specific Item	Possible	Ntbk
Table of Contents	2
Experiment Titled	3
Preparatory Exercises	20
Objectives	5
Date, Time, Place, Ambient Conditions	5
Apparatus/Equipment Sketches. Make the sketch such that you could set up this experiment from you notebook.	10
Equipment Description. Write a sentence for each piece of equipment – to describe what it was used for.	5
Lab Procedure that you did. Record the steps that you made, data that you took, and any comments that would help you conduct this type of work in the future.	20
Calculations	5
Discussion of Results	10
Discussion Questions	10
Organization and Readability	5
Total