M E - 495 Mechanical and Thermal Systems Lab #8 Laser Vibrometry Lab

pdf

School

San Diego State University *

*We aren’t endorsed by this school

Course

495

Subject

Mechanical Engineering

Date

Apr 3, 2024

Type

pdf

Pages

Uploaded by LieutenantOxide4000

M E - 495 Mechanical and Thermal Systems lab Wednesday Section 3 Lab #8 Laser Vibrometry Lab Group D Department of Mechanical Engineering Professor Hamid Nourollahi Preformed on: February 21st, 2024 Submitted on: February 27th, 2024

Table of Contents Table of Contents 1 The Objective of the Experiment 2 Equipment 4 Experimental Procedure 5 Experimental Results 7 Discussion of Results 11 Lab Questions 12 Conclusion 14 References 15 Table of Figures and Tables Figure 1: PDV 100 Portable Digital Vibrometer Sensor 4 Figure 2: speaker cone 4 Figure 3: Channel tab 5 Figure 4: Experiment 1 data 7 Figure 5: Classical Music Data 8 Figure 6: Rock Music Data 8

The Objective of the Experiment The objective of these experiments is to familiarize students with the process of quantitatively characterizing surface vibrations in a mechanical system. To do so, students will learn to use a Polytec PDV 100 Laser Doppler Vibrometer, which is a tool used to measure the displacement, velocity, and acceleration of mechanical vibrations in a speaker cone when harmonically excited at various frequencies. The final goal for the students is to use the data collected along with empirical data to calculate the damping ratio. The data collected is saved in the form of 4 graphs per type of sound displayed: one graph showing velocity vs time, and the three others showing magnitude vs frequency, so another objective of this experiment is to improve students’ graph interpretation. This experiment also prepares students for real-world situations, for example when bridges are built, a big consideration when doing so is the fact that everything traveling on said bridge creates a vibration, and a similar analysis as the one done in this experiment can be used to test the bridge’s safety. For the first experiment, the speaker is expected to be underdamped because it is old and blown out after years of use. For the second experiment, the rock music will be on the lower end of the frequency spectrum because they have a dominance in bass instruments. These instruments have deep tones that have low frequencies. We expect classical music to have a wider range of frequencies as they have a diverse range of instruments that produce frequencies across the frequency spectrum.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Equations: (Equation 1) ? ? 2 ? ?? 2 + ? ?? ?? + ?? = 𝐹 ? ( ) (Equation 2) ξ = ? ? ??𝑖? (Equation 3) ? ??𝑖? = 2 ?? (Equation 4) β = ?𝑎? −1 [ ξ 1−ξ 2 ] (Equation 5) 𝑃 𝑃 ? = −ξ− ξ 2 −1 2 ξ 2 −1 ? (−ξ+ ξ 2 −1) ω ? ? + −ξ− ξ 2 −1 2 ξ 2 −1 ? (−ξ+ ξ 2 −1) ω ? ? + 1 (Equation 6) 𝐹 ? ( ) = 𝐹 0 ?𝑖?(ω?) (Equation 7) ? ? ( ) = ? ? sin ?𝑖? ω? − ϕ ( ) (Equation 8) ? ? ? ? = 1 1− ω ω ? ( ) 2 ⎡ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎦ 2 + 2ξω ω ? ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ 2 (Equation 9) ? ? = 𝐹 0 ? (Equation 10) ϕ = 2ζω ω ? 1− ω ω ? ( ) 2 ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ Nomenclature: m = mass (kg) c = damping coefficient k = spring constant F(t) = input force = natural frequency (s -1 ) ω ?? = damping ratio ξ s d = amplitude of the periodic steady-state displacement s s = displacement of the spring ϕ = phase angle

Equipment ● PDV 100 Portable Digital Vibrometer Sensor: It is a device used to measure vibrations. It is equipped with sensors that can detect vibrations and provide data. A laser emerges from its lens and focuses on the area in which vibration analysis is desired. Figure 1: PDV 100 Portable Digital Vibrometer Sensor [1] ● The speaker cone is a part of a speaker that outputs sounds from the computer. Its job is to convert electrical signals into mechanical vibrations, producing sound waves that we can hear. Figure 2: speaker cone [1] ● VibrSoft Software: A data analysis software to analyze vibrations and output the data as graphs. ● Audacity Software: A digital audio editor and recording application.

Experimental Procedure Experiment 1: 1. Open both Vibrsoft and Audacity software 2. On the Vibrsoft applications, locate the top bar menu and select “Acquisitions”. From there click on “Settings” from the drop-down menu. a. A pop-up menu will come up. Click the “Channel” tab and ensure that the settings are the same as the figure below. Figure 3: Channel tab [1] b. Click on the “General” tab and make sure that “peak hold” is selected and set to “3” 3. Make sure that the 'Analyzer 1' window is selected (its top bar should be blue, not gray). 4. Choose Analyzer → Domain → Time to switch the window to the time domain. 5. Repeat steps 4 and select Analyzer±Signal±Velocity 6. Open three windows by selecting Window±New Window 7. Change the domain of these three windows to frequency by selecting Analyzer±Domain±FFT 8. Change one of each window to Displacement, Velocity, and Acceleration 9. Tile the windows either vertically or horizontally. 10. Turn on the cursor by selecting Analyzer±Cursor 11. Change the cursor to 10 seconds on the velocity window and 1kHz on the frequency domain. 12. Open Audacity.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

13. Locate Generate±Tone a. A pop-up menu will come up. On the drop-down menu, locate “waveform” and choose “sine”. b. Frequency/Hz setting: 1000 Hz c. Amplitude: 1 d. Length: 30 e. “Generate Tone” f. Click “Play Button” 14. On the Vibrsoft application click “Acquisition” ± “Continuous” 15. Let the analysis run for 15 seconds and Click “Acquisition” ± “Stop” 16. Stop the music on Audacity 17. On the Vibrsoft application right-click and get the “auto scale” on each screen. 18. Take a screenshot of the results. Experiment 2: 1. Choose a classical music track either from YouTube. Play the selected track for approximately 20 seconds using the same procedure outlined in Experiment 1. 2. Capture a screenshot of the frequency data displayed during playback. 3. Select a bass-rich music track from the rock, electronic, or hip-hop genre, again from YouTube. 4. Play the chosen bass-rich track for around 20 seconds, employing the same method as in step 1. 5. Take a screenshot of the frequency data exhibited during the playback of the bass-rich track.

Experimental Results Experiment 1: Figure 4: Experiment 1 data

Experiment 2: Figure 5: Classical Music Data Figure 6: Rock Music Data

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Data Reduction: When calculating the damping ratio, , it is necessary to take the following ζ determinations into consideration: ? = 63 𝑔 ?? * 9. 81 ? ? 2 = 618 𝑁 ? . ? = 7 ?𝑔 = 297.13 ω ? = ? ? Data gathered in Experiment 1 and equations 1, 2, 3 and 6 from the lab manual were utilized to calculate , the damping ratio ± . ζ ζ = 𝑎???𝑎? ?𝑎??𝑖?𝑔 ??𝑖?𝑖?𝑎? ?𝑎??𝑖?𝑔 ? ? 2 ? ?? 2 + ? ?? ?? + ?? = 𝐹 ? ( ) (0.239 s)) [(7 * 10 −6 ?𝑔)(2000 ?/? 2 )] + ? (?. 31978 ?/?) + [(618 𝑁/?) (5. 089 * 10 −5 ?)] = ?𝑖? (2π (1 ?𝐻𝑧) 𝐶 = 2. 978 𝑁*𝑆 ? = ζ = 𝐶 𝐶(??𝑖?𝑖?𝑎?) 𝐶 2 ?*? = 0.716 ζ = 2.978 2 (618.03 * 7*10 −3

The damping ratio has been determined to be underdamped ( 0.716 < 1), This is to be expected, as the speaker and components utilized in the experiment have been worn and “blown out” from years of repeated experimentation in the lab. There is no real reason to solve for the damping ratio again for experiment 2, as; even though the music is different, it is impossible to calculate the damping coefficient for an unknown forcing function, F(t). As can be seen in the provided graphs, the frequency spectrums between classical and bass music are similar, but distinct from one another. Classical music tends to be more dynamic compared to the somewhat monotonous noise of rock music. Rock music has overall a lower magnitude at similar frequencies to rock music.

Discussion of Results Using the spring constant and the mass of the speaker cone which are respectively, it is possible to solve for the natural frequency of the speaker, 618 𝑁/? 𝑎?? 7 ?𝑔 which is 297.13 Hz. These values were then used to determine the damping coefficient with a value of All values needed to solve for the damping ratio are accounted for. The 2. 978 𝑁*𝑆 ? . damping ratio is 0.716. Based on the damping ratio the speaker is underdamped because < 1. ζ This is what was expected from the hypothesis because the speaker is old and blown out from years of use. Sources of error could have occurred from the microphone picking up on noise from the background and other experiments occurring inside of the laboratory. The blown speaker could have also been a source of error. For experiment two, there is no need to solve for the damping ratio again because we are unable to calculate the damping coefficient for an unknown forcing function. The damping coefficient is needed to solve for the damping ratio. As can be seen in Figure 5, classical music has a peak in its magnitude after the 200 Hz mark. In Figure 6, the rock music created a peak under 200 Hz. Classical music has a wide range of frequencies but rock music has a heavy focus on bass instruments which produce low frequencies.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Lab Questions 1. Determine the phase angle for the data from the first experiment. ● The phase angle can be determined utilizing the following equation: = = 1.73° ϕ = ?𝑎? −1 [ 2ξω ω? 1−( ? ω? ) 2 ] ?𝑎? −1 [ 2(0.716)(6.283) 297.13 1−( 6.283 297.13 ) 2 ] 2. Find c when the system is critically damped. ● To find C when the system is critically damped, the following equation may be used: = ζ = 𝐶 𝐶? 𝐶 2 ?? 𝐶 = 2 ζ ?? 𝐶 = 2 (0. 716) 618 * 7 * 10 −3 𝐶 = 2. 97 3. What can you say about the frequency contents of the two music pieces in Experiment 2? ● Classical music exhibits a broader frequency range compared to rock music, and its peaks are more prominent in higher frequencies, particularly those above 200 Hz. On the other hand, rock music, featuring heavy use of bass instruments, has peaks at lower frequencies, typically below 200 Hz. The distinctive frequency characteristics in both genres are shaped by their instrumentation, production techniques, and stylistic preferences.

4. How is 'bass' of music related to frequency? ● "Bass" in music refers to the low-frequency range, typically between 20 Hz and 250 Hz. It represents the lower end of the audible spectrum, with longer sound waves and fewer cycles per second. Bass sounds are characterized by their depth and lower pitch, serving as a foundation in musical compositions, and instruments and equipment designed for handling these frequencies contribute to a balanced audio experience.

Conclusion The goal of this laboratory experiment is for students to get a better understanding of the physical properties of waves as they exit a speaker cone. Students are also introduced to a PDV 100 Portable Digital Vibrometer Sensor and all of its features. The sensor is also able to examine the difference between A over-damped, Under-damped, and critically damped systems. In addition to that students are also able to use the sensor to examine the difference in properties between classical and rock music. In conclusion, it is found for experiment one that our system is underdamped or less than 1. This is seen through the graphs' relationships as well as the calculated data that shows our system to be overdamped. This is because we are using an older “blown out” speaker and we see this system behavior. In the next experiment, it is found that rock music has a lower manitou at similar frequencies compared to classical music. It is also found that Classical music tends to be more dynamic than rock music. This lab served as an excellent introduction to the concept of vibrational analysis and how the damping ratio affects a system. Having an opportunity to use and gather a greater understanding of the PDV 100 Portable Digital Vibrometer Sensor has allowed me to understand the vibrational properties coming from a speaker cone. Team D for M E495 lab section 3 thanks the instructor, Professor Hamid Nourollahi, and Teaching Assistant Rishabh Guwalani for their guidance and support during the completion of the laboratory exercise and creation of this lab report.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version