Vibration and Sound Measurements Lab Report

Lab 5: Vibration and

Sound Measurements

Joseph R. Felice

Pennsylvania State University

4/25/2014

Table of Contents

Abstract ........................................................................................................................... i

Introduction ................................................................................................................... 1

Results and Discussion ................................................................................................ 2

Station A: Effect of Amplitude Excitation ...................................................................... 2

Station B: Microphone vs. Accelerometer .................................................................... 6

Station E: Effect of Frequency Excitation ..................................................................... 8

Frequency: 7 Hertz ................................................................................................... 8

Frequency: 30 Hertz ............................................................................................... 10

Frequency: 80 Hertz ............................................................................................... 12

Station E: Effect of Frequency Excitation Discussion ............................................. 14

Frequency: 7 Hertz..................................................................................................... 14

Frequency: 30 Hertz................................................................................................... 14

Frequency: 80 Hertz................................................................................................... 15

Conclusion: Comparative Analysis ........................................................................... 16

References ................................................................................................................... 18

Sample Calculations Appendix .................................................................................. 19

i

Abstract

The purpose of this laboratory experiment was to gain insight into the application

of vibration and sound measurements in regard to basic mechanical systems.

Specifically, instruments such as vibrators and electromagnetic shakers will be used to

observe the effects of amplitude and frequency in relation to vibration and sound

measurements. Three different lab stations labeled A, B and E each housed a different

type of sensor. Station A was equipped with a piezo-electric based vibrator that had

two PCB accelerometers mounted to its surface in a symmetrical fashion. Channel 1 is

equipped with a PCB 393A03 accelerometer and channel 2 is equipped with a PCB

302A accelerometer [1]. The purpose of this configuration was to test the effect of

amplitude excitation on frequency measurements. First screenshots of the voltage

output signal over time were acquired through Tek OpenChoice Desktop software.

Then screenshots of the Fast Fourier Transform (FFT) of the voltage output were

captured for both channels at low and high amplitude excitation. The FFT command on

the TDS 2002 DSO brings the voltage output signal into the frequency domain, thus

demonstrating what voltages are present at each frequency [2]. Station B housed both

a microphone, which is a variable capacitive sensor, and accelerometer. The purpose

of this setup was to measure the voltage output signal and FFT of the accelerometer

and microphone signals. Screenshots of voltage output and the respective FFT of each

channel were also acquired for this station. Station E contained a piezo-electric based

electromagnetic shaker. This shaker was tested at three different frequency levels- 7

Hz, 30 Hz and 80 Hz. At each frequency the voltage was recorded using LabVIEW

SignalExpress tool [1]. Approximately 1,000 data points were collected over a period of

one second. This data was transferred to an Excel spreadsheet where plots of voltage

(Volt) versus time (seconds) were generated. Four of these plots were made at each

frequency for a function generator signal (Channel 1), a small accelerometer (Channel

2), an optical proximity sensor (Channel 3) and a large accelerometer (Channel 4).

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Introduction

Vibration and sound measurements are key components to understanding the

operational aspects of many mechanical systems. Equipment such as vibrators and

shakers are instruments ordinarily used when analyzing the effects of amplitude and

frequency excitation, respectively. Common to both of these instruments is the piezo-

electric transducer.

A piezo-electric transducer consists of a crystal sandwiched between two plates.

When a force is applied to the plates the crystal is deformed. A potential difference is

generated as a consequence of the crystal deformation. This potential difference is

proportional to the applied force on the plates. Hence, the effect of this process is

known as the piezo-electric effect [3].

Piezo-electric transducers are contained within pressure transducers. This

allows them to be used for dynamic measurements. They are also extremely beneficial

in situations where high frequency measurements are necessary for proper data

acquisition [3].

Another type of sensor used in vibration and sound measurements is the variable

capacitive sensor. This sensor generates an analog output voltage signal as a

consequence of a change in the capacitance value. The change in capacitance can be

caused by factors such as temperature variation or humidity. Subsequently, the change

in capacitance due to the influence of these or other physical parameters is converted

into the previously mentioned analog output voltage signal [3].

Image 1: Below is an image of

the piezo-electric transducer [3].

Image 2: To the right is an

image of the variable capacitive

sensor [3].

2 | P a g e

Results/Discussion

Station A: Effect of Amplitude Excitation

Figure 1: Shown above is an image of voltage output for low amplitude excitation of

the vibrator.

Figure 2: Featured here is the voltage output for high amplitude excitation of the

vibrator.

3 | P a g e

Figure 3: Displayed above is the Fast Fourier Transform (FFT) of channel 1 on the

DSO set at a frequency of 50 Hz with the vibrator set at low amplitude. FFT shows the

frequency domain. This demonstrates what voltages are present at each frequency.

Figure 4: Shown here is the FFT of channel 2 on the DSO set at a frequency of 50 Hz

with the vibrator set at low amplitude.

4 | P a g e

Figure 5: Shown above if the FFT of channel 1 with the vibrator set at high amplitude.

Figure 6: Featured here is the FFT of channel 2 with the vibrator set at high amplitude.

5 | P a g e

In Figure 1, both channels one (yellow waveform) and two (blue waveform) are

shown for the vibrator set at low amplitude setting. It is clear that the waveforms for

both these channels are not perfectly smooth. Thus, the corresponding FFT frequency

domain images for channels 1 and 2 shown in Figures 3 and 4, respectively,

demonstrate what an expected behavior pattern for the voltage output is over time as

seen in Figure 1. Several spikes are seen in both FFT images indicating that there are

several minor varying signals contained within the waveforms for each channel, thus

showing that there are several varying voltages occurring at different frequencies.

Channel 2 does seem to have more signal variations present than Channel 1.

In Figure 2, channels 1 and 2 demonstrate the voltage output over time of the

vibrator set at high amplitude. Similar to the case with the vibrator set at low amplitude

these waveforms are not perfectly smooth, indicating the likelihood of varying signals

contained within each waveform. This observation is confirmed by the corresponding

FFT images shown in Figures 5 and 6 where several spikes are easily noted in both

images proving there are several frequencies occurring as voltage varies.

On the vibrator there are two PCB accelerometers mounted in a symmetric

fashion. Channel 1 (yellow waveform) displays the voltage output over time for the PCB

393A03 accelerometer. The sensitivity for this accelerometer is 1,000 mV/g

accompanied by a frequency range of 0.5-2,000 Hz and amplitude range of +/- 5,000 g

pk [4]. Channel 2 is equipped with a PCB 302A accelerometer. The sensitivity for this

accelerometer is 10 mV/g accompanied by a frequency range of 0.7-10,000 Hz and

amplitude range of +/- 500 g pk [1]. When comparing the output signals for channels 1

and 2 both appear very similar in shape.

However, a noteworthy difference is evident in that channel 2 seems to have

more signal variation than channel 1 for both low and high amplitude settings of the

vibrator. This is confirmed by each respective FFT that was recorded for the voltage

output signals of both channels at both amplitude settings as aforementioned. Perhaps

the reason why channel 1 has less signal variations detected in the FFT of the voltage

output could be related to the frequency ranges for each accelerometer. The PCB 302A

(channel 2) has a much larger frequency range of 0.7-10,000 Hz whereas the PCB

393A03 (channel) 1 has a smaller frequency range of 0.5-2,000 Hz. Therefore, channel

2 detects the presence of more signal variations in the FFT of voltage output.

6 | P a g e

Station B: Microphone vs. Accelerometer

Figure 7: Shown here is the voltage output of the microphone vs. accelerometer sound

vibration sensor set at a frequency of 80 Hz.

Figure 8: Above is the FFT for channel 1 showing the microphone vs. accelerometer

setup with the DSO set at a frequency of 50 Hz. The generator remained set at 80 Hz.

7 | P a g e

Figure 9: Here is the FFT for channel 2 showing the microphone vs. accelerometer

configuration with the DSO set at a frequency of 50 Hz. The generator remained set at

80 Hz.

Station B consisted of a microphone vs. accelerometer setup. This was the only

variable capacitive sensor in this experiment. The microphone, of course, being the

part containing the capacitor element. The frequencies observed in Figures 8 and 9 are

expected Fast Fourier Transform (FFT) signals for the voltage output over time seen in

Figure 7. In Figure 7, both channels 1 (yellow sine wave) and 2 (blue sine wave) each

have sinusoidal waveforms for their respective voltage outputs with the generator set at

80 Hz. Therefore, in Figures 8 and 9 only one spike should be observed in each,

corresponding to the expectation that with a consistent sinusoidal change of voltage

over time there is only one frequency.

However, aside from one pronounced spike in each Figures 8 and 9 there are

several other smaller spikes which repeatedly occur following the large initial spike.

What this means is that there are other varying signals in the sine waves shown in

Figure 7 that are so small visually the eye cannot detect them, yet they become

noticeable with FFT. Thus, the primary purpose of the FFT command on the DSO 2002

is to bring these minor unnoticeable variations in waveforms to the visual forefront.

8 | P a g e

Station E: Effect of Frequency Excitation

Frequency: 7 Hertz

Graph 1: Above is a graph of voltage (V) versus time (seconds) for the function

generator with the shaker set at 7 Hz (Channel 1).

Graph 2: Shown here is a graph of voltage (V) versus time (seconds) for the small

accelerometer with the shaker set at 7 Hz (Channel 2).

-1

0

1

2

3

4

5

0 0.05 0.1 0.15 0.2 0.25 0.3

Voltage (Volt)

Time (seconds)

Voltage vs. Time -Function Generator Signal

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Voltage (Volt)

Time (seconds)

Voltage vs. Time-Small Accelerometer

9 | P a g e

Graph 3: Featured here is the excitation frequency (Hz) versus Voltage (V) plot for the

first accelerometer with the shaker set at 7 Hz (Channel 3).

Graph 4: Demonstrated above is the voltage (Volt) versus time (seconds) plot for the

large accelerometer with the shaker set at 7 Hz (Channel 4).

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Voltage (Volt)

Time (seconds)

Voltage vs. Time -Optical Proximity Sensor

4.982

4.984

4.986

4.988

4.99

4.992

4.994

4.996

4.998

5

0 0.002 0.004 0.006 0.008 0.01 0.012

Voltage (Volt)

Time (seconds)

Voltage vs. Time -Large Accelerometer

10 | P a g e

Frequency: 30 Hertz

Graph 5: Above is the voltage (Volt) versus time (seconds) for the function generator

with the shaker set at 30 Hz (Channel 1).

Graph 6: Shown here is the voltage (Volt) versus time (seconds) for the displacement

sensor with the shaker set at 30 Hz (Channel 2).

-1

0

1

2

3

4

5

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Voltage (Volt)

Time (seconds)


-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Voltage (Volt)

Time (seconds)

Voltage vs. Time -Small Accelerometer

11 | P a g e

Graph 7: Above is the voltage (Volt) versus time (seconds) plot for the first


Graph 8: Featured above is the plot of voltage (Volt) versus time (seconds) for the

second accelerometer with the shaker set at 30 Hz (Channel 4).

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Voltage (Volt)

Time (seconds)


4.982

4.984

4.986

4.988

4.99

4.992

4.994

4.996

4.998

5

5.002

0 0.002 0.004 0.006 0.008 0.01 0.012

Voltage (Volt)

Time (seconds)


12 | P a g e

Frequency: 80 Hertz

Graph 9: Above is the plot of voltage (Volt) versus time (seconds) for the function

generator with the shaker set at 80 Hz (Channel 1).

Graph 10: Shown here is the graph of voltage (Volt) versus time (seconds) for the

small accelerometer with the shaker set at 80 Hz (Channel 2).

-1

0

1

2

3

4

5

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Voltage (Volt)

Time (seconds)


-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 0.005 0.01 0.015 0.02 0.025

Votlage (Volt)

Time (seconds)


13 | P a g e

Graph 11: Above is the voltage (Volt) versus time (seconds) plot for the first


Graph 12: Featured here is the voltage (Volt) versus time (seconds) plot for the second


-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Voltage (Volt)

Time (seconds)


4.98

4.982

4.984

4.986

4.988

4.99

4.992

4.994

4.996

4.998

5

0 0.002 0.004 0.006 0.008 0.01 0.012

Voltage (Volt)

Time (seconds)


14 | P a g e

Station E: Effect of Frequency Excitation Discussion

Frequency: 7 Hertz

Graph 1 is the plot for voltage (Volt) versus time (seconds) of Channel 1 for the

function generator signal with the shaker set at 7 Hz. The smooth sinusoidal shaped

plot has peak-to-peak amplitude of 4.63 Volts. If interpreted as a sine wave function an

apparent horizontal phase shift of positive 90 degrees is evident shifting the plot to the

left creating, thus generating a cosine plot.

Graph 2 is the plot of voltage (Volt) versus time (seconds) of Channel 2 for the

small accelerometer signal with the shaker set at 7 Hz. The shape of the plot is jagged

and very inconsistent in its pattern. No phase shift is evident. The amplitude of the

initial sine wave form at the start of the plot appears to be 0.023 Volts.

Graph 3 plots the voltage (Volt) versus time (seconds) of Channel 3 for the

optical proximity sensor with the shaker set at 7 Hz. The shape of the plot is mostly

smooth and yields amplitude of 0.22 Volts for the sinusoidal segments. No phase shift

is apparent.

Graph 4 demonstrates the plot of voltage (Volt) versus time (seconds) of Channel

4 for the large accelerometer signal with the shaker set at 7 Hz. The plot is smooth in

shape and generates maximum amplitude of 0.014 Volts. No phase shit is evident.

Frequency: 30 Hertz

Graph 5 is the plot for voltage (Volt) versus time (seconds) of Channel 1 for the

function generator signal with the shaker set at 30 Hz. The shape of the curse is a

smooth sinusoidal plot. It has amplitude of 4.68 Volts. If this plot is viewed as a sine

wave function there is an apparent horizontal phase shift of positive 45 degrees. This

causes the plot to shift slightly leftward, however, not to the degree it did in Graph 1

where the cosine plot was yielded as a result of that plot’s 90 degree horizontal phase

shift.

Graph 6 is a plot of the voltage (Volt) versus time (seconds) of Channel 2 for the

small accelerometer with the shaker set at 30 Hz. The shape of the plot is very rigid

and yields amplitude of 0.135 Volts. There is no apparent phase shift.


optical proximity sensor with the shaker set at 30 Hz. The plot is a smooth sinusoidal

curve and in fact is very characteristic of a sine wave function. In this case, it is

apparent that there is a phase shift of negative 90 degrees, shifting the plot to the right.

15 | P a g e


large accelerometer signal with the shaker set at 30 Hz. Amplitude of 0.0105 Volts is

evident. No phase shift is apparent in this plot.

Frequency: 80 Hertz

Graph 9 demonstrates the plot of voltage (Volt) versus time (seconds) of Channel

1 for the function generator signal with the shaker set at 80 Hz. The shape of the

function is smooth and appears to be very similar to the behavior of a cosine wave

function. This plot generates amplitude of 4.65 volts. If interpreted as a sine function it

is evident that there is a phase shift of positive 90 degrees causing the plot to move

leftward horizontally into its current cosine position.


small accelerometer with the shaker set at 80 Hz. The shape of the curve is smooth

and maintains the characteristics of a sine wave function. This plot yields amplitude of

0.248 Volts. There is a phase shift of negative 45 degrees evident causing a horizontal

rightward shift.


optical proximity sensor signal with the shaker set at 80 Hz. The shape of the plot is

smooth and has the characteristics of a typical cosine wave function. This plot yields

amplitude of 0.75 Volts. If viewed as a sine wave function a horizontal phase shift of

positive 90 degrees is apparent shifting the plot leftward into its current cosine plot

position.

Graph 12 is the plot of the voltage (Volt) versus time (seconds) of Channel 4 for

the large accelerometer signal with the shaker set to 80 Hz. The shape of the plot is

smooth and generates maximum amplitude of 0.12 Volts. No phase shift is apparent.

16 | P a g e

Conclusion: Comparative Analysis

Station A: Effect of Amplitude Excitation was a piezo-electric sensor based

vibrator setup. Station B: Microphone vs. Accelerometer was the only laboratory setup

with a capacitive based sensor. When the voltage outputs over time of Station A are

compared with the output of Station B both similarities and differences become evident.

For instance, both channels 1 and 2 for the voltage outputs in Stations A and B

are smooth waveform patterns. Despite this similarity there is still a very noticeable

different between these signals. In Station A, the signals for channels 1 and 2 for the

low amplitude setting of the vibrator have a much smaller period than the signals for

these respective channels have for the voltage output in Station B. The period for the

low amplitude excitation setting of the vibrator at Station A for channel 1 was 5

milliseconds and for channel 2 was 4.375 milliseconds. At Station B, the period for

channel 1 was 11.875 milliseconds and for channel 2 was 12.5 milliseconds.

Longer periods for the capacitive based sensor in comparison to the shorter

periods for the piezo-electric based vibrator set at low amplitude of excitation seem to

indicate a time difference in how each sensor responds to its assigned stimuli.

Evidently, charging the capacitor of the microphone at Station B to acquire a voltage

output response takes longer than it does for low amplitude of excitation to deform the

crystal in the piezo-electric transducer to acquire a voltage output signal at Station A.

This changes when the setting of the vibrator at Station A is adjusted to high amplitude

of excitation.

For high amplitude of excitation on the vibrator the periods were 15 milliseconds

and 17.5 milliseconds for channels 1 and 2, respectively. Now, when compared to the

microphone vs. accelerometer setup the period for the voltage output waves are less

than the periods observed for the vibrator. Thus, at high amplitude of excitation it takes

longer for the piezo-electric crystal in the vibrator to deform and yield a voltage output

than it does to charge the plates in the capacitor of the microphone to generate a

voltage output.

The FFT of the voltage output for Station B was less active than the FFT of the

vibrator for low and high amplitude excitation settings. Apparently, when charging the

capacitor plates of the microphone there was less signal variation in the output voltage

than there was for the crystal deformation of the piezo-electric element at Station A.

Station E: Effect of Frequency Excitation was also a piezo-electric based

vibration sensor. All of the graphs for the function generator with the frequencies set at

7, 30 and 80 Hz yielded smooth curves similar in behavior to cosine waveforms. At 7

Hz and 80 Hz if viewed as sine waves a horizontal phase shift of positive 90 degrees is

observed meaning a shift to the left describes their current cosine positions. For the

17 | P a g e

setting of 30 Hz, if this plot were viewed as a sine function a horizontal phase shift of

positive 45 degrees is evident.

All of the plots for the small accelerometer at 7, 30 and 80 Hz observe a gradual

but still noteworthy increase in the amplitude. At 7 Hz the amplitude was 0.023 Volts.

When the setting was adjusted to 30 Hz the amplitude plotted was 0.135 Volts. When

increased to the final observed setting of 80 Hz the amplitude increased to a value of

0.248 Volts. Obviously, higher settings of frequency for the electromagnetic shaker

yield larger values for amplitude.

The voltage (Volt) versus time (seconds) for the optical proximity sensor shows

varied values for the amplitude. At 7 Hz, the amplitude of the plot is 0.22 Volts. When

increased to 30 Hz, the amplitude increases to 1.224 Volts. Then at the final setting of

80 Hz the amplitude declines to 0.75 Volts. In this case, the medium level of frequency

achieved the highest value of amplitude. The medium level at 30 Hz acquiring the

largest value of amplitude at 1.224 Volts perhaps does make sense in that the piezo-

electric based shaker can still operate safely. If the highest frequency at 80 Hz were to

have acquired the largest amplitude, the shaker may have needed to be fanned in order

to cool it down since at large amplitudes and high frequencies overheating can occur

[5].

The plots for the large accelerometer for the shaker settings of 7, 30 and 80 Hz

represent amplitudes of 0.014, 0.0105 and 0.012 Volts, respectively. In this case, the

lowest frequency setting acquired the largest amplitude. As aforementioned this makes

sense given that under these circumstances overheating of the shaker is unlikely to

occur under these circumstances (i.e. low frequency, high amplitude).

18 | P a g e

References

[1] ME 345W Lecture Notes, Spring 2014, “ME 345W Lab # 5 Vibration and Noise Measurements Handout,” Slide 2. Penn State University, Angel Course Webpage. Middletown, PA. [2] Tektronix, 2014, “FFT Tutorial,” from http://www.tek.com/support/faqs/what-fft-fast-fourier-transform-math-function-oscilloscope-useful. [3] ME 345W Lecture Notes, Spring 2014, “Vibrations Measurement,” Slides 1-5. Penn State University, Angel Course Webpage. Middletown, PA. [4] ME 345W Lecture Notes, Spring 2014, “PCB 393A03 H,” Slide 1. Penn State University, Angel Course Webpage. Middletown, PA. [5] Piezo Nano Positioning, 2014, “Electrical Requirements for Piezo Operation,” from http://www.physikinstrumente.com/en/products/prdetail.php?sortnr=400600.75.

19 | P a g e

Sample Calculations Appendix

Figure 2: Featured here is the voltage output for high amplitude excitation of the

vibrator. The white arrow represents one period for the voltage output of channel 2.

Period, T = (3.5 grid divisions)*(5.00 milliseconds) = 17.5 milliseconds

Graph 10: Shown here is the graph of voltage (V) versus time (seconds) for the small

accelerometer with the shaker set at 80 Hz. The black arrow represents the amplitude.

Amplitude = 0.14 Volts + 0.108 Volts = 0.248 Volts

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 0.005 0.01 0.015 0.02 0.025

Votlage (Volt)

Time (seconds)


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Vibration and Sound Measurements Lab Report

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