J.B.Francis College of Engineering Mechanical Engineering Department 22-403 Laboratory Experiment #2 Frequency Response Measurements Introduction It is known from dynamic systems that a structure temporarily excited by an external force will vibrate at a frequency defined as the natural frequency. The natural frequency is characteristic of the entire structure and its boundary conditions. An external excitation applied to the structure at the same frequency as the structure's natural frequency will result in resonance. At resonance, the structure will vibrate at higher than normal amplitude levels. Depending upon the overall system design, the amplitude of vibration at resonance can cause unwanted operating conditions as well as a catastrophic failure. This type of system failure can be avoided by determining the structure's natural frequency and maintaining the overall system at an operating condition which will not induce resonance. The natural frequencies of a structure can be determined by measuring frequency response. One means of measuring the frequency response is to impact test the structure. Impact testing is a measurement of the ratio of the structure's transient response to the excitation impulse versus frequency. Technical Objective Using a Dactron Photon II USB acquisition board, impact hammer and an accelerometer, measure the frequency response of a beam with free-free boundary conditions. Compare the first two natural frequencies of the beam to those obtained analytically. Measure the frequency response of a rotor balancing kit and recommend a rotational speed that should be used to balance the rotor. Pre-Lab Assignment 1. Calculate the first two natural frequencies of a beam with free-free boundary conditions given the following parameters and cross section shown in Figure 1: Figure 1: Beam Cross-Section Frequency Response Measurements 1 Mechanical Engineering Department
length - 60" material - Aluminum Equation of Vibration for a Free-Free Beam: 2. List the types of windows that are used when impact testing a structure. Explain the purpose of each window. 3. The ME Lab II course website has a FLASH tutorial overview on the use of the Dactron FFT analyzer - review this file as part of the prelab assignment Background Frequency response measurements are a type of modal testing which can be used to determine the resonant frequencies of a structure. Frequency response testing is accomplished by exciting a system with a known input and simultaneously measuring the corresponding output response. Figure 2 is a block diagram which represents a system with one input (single-point excitation) and the output response. Figure 2: System block diagram X(ω) is the excitation supplied to the structure, Y(ω) is the system's response, and H(ω) is the physical system being analyzed. The ratio of response to excitation versus frequency is defined as the frequency response. The measurement of a system's frequency response can be accomplished in a variety of different ways. The excitation supplied to the structure is commonly generated with an impact hammer or a shaker and a variable voltage source to drive the shaker. The response can be measured using an accelerometer, or a non-contact transducer such as a laser based measurement system. Also, a dynamic signal analyzer or digital acquisition system is required to perform data acquisition and signal processing. Although the selection criteria for choosing a measurement system and the limitations of each will not be covered here, it should be understood that the type of measurement system chosen will have a dramatic effect on the frequency response results obtained. Frequency Response Measurements 2 Mechanical Engineering Department
One common frequency response measurement method utilizes an impact hammer to excite the structure and an accelerometer to measure the response. This type of measurement system requires few hardware components and provides a relatively short measurement time. However, it is important to understand the acquisition techniques depending on the hardware used. Figure 3 shows the instruments that can be used to conduct frequency response measurements by impact testing a structure and utilizing digital data acquisition. Figure 3: Impact testing equipment An impact test generates an impulse excitation, which will result in a transient response. The frequency content of the energy applied to a structure is a function of the stiffness and masses of the contact surfaces. This in turn controls the shape of the force input and the frequency content of the measurement. Because it is not feasible to alter the structure's surface or mass, impact hammers are available with a variety of interchangeable contact surfaces and masses. Altering either the tip or the mass of the impact hammer will result in a change in the frequency content of the measurement. If a hard tip is used, the structure is impacted a shorter duration of time, resulting in an excitation of a higher frequency content. Generally, a tip should be chosen so that the amplitude of the force spectrum is no more than 10 to 20 db down at the maximum frequency of interest. Both noise and leakage are problems which may arise when an impact test is conducted. Noise can be reduced by using a Force Window, which literally forces the sample window to zero after a defined amount of time. Leakage can be found in a system's response if the acquisition software performs a Fourier Transformation on a non-periodic sample window. This error can be reduced by either applying an exponential window to the response signal or adjusting the sample window so that the system decays to a constant displacement of zero. However, if an exponential window is used, the system being analyzed may seem to have a higher damping ratio. Digital data acquisition errors such as clipping and quantization can be reduced by using a technique called half-ranging. Half-ranging can be accomplished by setting the amplitude of the analyzer to approximately two times the maximum signal level being measured. Frequency Response Measurements 3 Mechanical Engineering Department
Assignment #1 Frequency Response Measurements of a Beam with Free Ends In this assignment, a beam with free-free boundary conditions will be analyzed to determine the first two natural frequencies. Analytical calculations of the beam's first two natural frequencies will be used as a comparison of the results obtained through impact testing. Although this assignment is not intended to cover every facet of impact testing, it should show that impact testing can be used to obtain the natural frequency of a structure. Procedure 1. Turn on the computer at the lab workstation. 2. Using the microdot-bnc cables provided, connect the impact hammer and accelerometer to channels #1 and #2 respectively of the Dactron Photon II USB DAC Board. 3. Examine the Aluminum beam provided. Record all information required to calculate the first two natural frequencies of the beam with free end conditions. 4. Attach the accelerometer to one end of the beam using a small amount of wax and attempt to avoid any possible node points. 5. Open the RT Pro Photon 6.06 software from the programs menu or from the desktop icon. In the new project window select: Modal Data Acquisition 6. In the upper right hand side of the screen select signals. Check all available boxes for channels one and two. Click OK Frequency Response Measurements 4 Mechanical Engineering Department
7. Now select the channel icon to set acquisition parameters for each channel. Set the parameters in accordance with the figure below. Click OK *Note if channel 1 overloads with this setting change MaxVolts to 1.0 Frequency Response Measurements 5 Mechanical Engineering Department
8. Click the trigger icon and fill in the settings as seen in the figure below. Click OK 9. In the frequency range dropdown menu select 1000Hz and select 1024 points. Change the window setting to none. View the figure below for verification of correct acquisition settings. Frequency Response Measurements 6 Mechanical Engineering Department
10. Click the Average button and fill in as seen in the figure below. 11. From the menu bar select window>2d display>two-pane horizontal. In the upper window right click and select contents From the input candidates list select input1(t) for the impact time trace. Right click on the bottom pane and select contents. Choose the input2(t) for the response time trace. Select ok. The existing plots are for coherence (top) and FRF (bottom). To ensure accuracy in testing observe the coherence after each test. Note that a value closer to one (1) for the coherence trace means an accurate FRF at that frequency. 12. Click the start button and impact the beam at the same location for five averages. Notice the time trace for the response and click on the FRF for this test. Select cursor>add normal cursor from the menu bar. Click and drag the cursor near the first peak in the FRF. Select Cursor>find nearest peak from the menu bar. Compare this value to the calculated value for the first natural frequency of the beam. Do the same for the second peak in the FRF Be sure to take screen shots for the post lab analysis (Shift+Print Screen and paste into Paint). Frequency Response Measurements 7 Mechanical Engineering Department
13. Click End Test. From the window drop down menu select force/exponential. Click the window icon and fill in the fields as seen in the figure below. 14. Start a new measurement and impact for another five averages. Be sure to impact the same location for each of the five frames. Observe the FRF and the response time trace. Take screenshots. Notice the difference in the response with the window applied. 15. Change the points value to 4096 and select none from the window dropdown menu. Take five averages and screenshots. Locate the peaks in the FRF and notice the value for the amplitude of each peak compared to the amplitude in the windowed test. Assignment #2 Rotor Balance Kit Frequency Response Measurements The purpose of this assignment is to conduct an impact test on a rotor balancing kit. After inspecting the rotor kit, it should be evident that an analytical calculation of the system's natural frequency can not be easily obtained. However, by impact testing the structure, the system's natural frequencies can be determined. With the natural frequency of the system known, rotational speed balancing recommendations can be made. Frequency Response Measurements 8 Mechanical Engineering Department
Procedure 1. Examine the rotor kit supplied. The configuration of the rotor, motor, bearing supports, shaft, and probe mounts should be identical to figure #4. Figure #4 Rotor balancing kit 2. Set the points to 512, lines to 200, frequency to 500HZ in RT Pro Photon and select none from the window dropdown menu. 3. The probe mount located next to the rotor is used to measure vibration levels during balancing exercises. Attach the accelerometer to the rotor kit at an appropriate location where the frequency response can be measured. 4. Lifting the rotor kit base, place the assembly on the air bubble material provided. 5. Conduct an impact test on the rotor kit, noting the resultant trace on the computer screen. 6. After the five averages ensure that the coherence is good. Take screen shots of the FRF and Coherence plots with cursors showing the values of each of the peaks. 7. If desired, move the accelerometer to a new location and continue impact testing the structure. Take screenshots of the frequency response and coherence traces. 8. When finished testing close RT Pro Photon without saving the project. Frequency Response Measurements 9 Mechanical Engineering Department
Appendix A: Post-Lab Analysis 1. Calculate the first two natural frequencies of the beam with free-free end conditions. 2. Compare the analytical solutions to the measured natural frequencies. Explain why these values may have differed. 3. Explain why the beam was suspended from the ceiling in the manner that it was. Can the bungee-cord supports be used to measure the frequency response of a beam with free-free boundary conditions? 4. Is the location of the accelerometer of importance when measuring the natural frequency of the beam? 5. Explain the purpose/effects of using a force window on the impulse signal. 6. List two ways of reducing leakage present in the response signal. 7. Explain the significance of measuring coherence. 8. What is the first natural frequency of the rotor balancing structure? 9. Pictorially show the location where the response of the structure was measured during impact testing. Is there any significance to the location(s)? 10. Explain why the rotor kit was placed on the foam during the impact test. 11. Recommend a rotational speed(s) that should be used to balance the rotor. Explain why this rotational speed(s) should be used. Frequency Response Measurements 10 Mechanical Engineering Department