ASE 369 K Measurements and Instrumentation LAB #9: Impulse-Force Hammer; Vibration of Beams Equipment: Dell Optiplex computer with National Instruments PCI-MIO-16E-4 data-acquisition board and the Virtual Bench Dynamic Signal Analyzer Impulse-Force Hammer (PCB 086C03) Piezoelectric Accelerometer (PCB 302A) Four-channel Amplifier/Signal Conditioner Unit (PCB 482A16 or PCB 482A22) Aluminum beam Objectives: To introduce you to the use of the impulse-force hammer to produce impact forces. To introduce you to the use of frequency response functions for determining the natural frequencies and mode shapes of a vibrating structure. 1 Dynamic Signal Analyzer (DSA) You used the DSA in the digital signal processing lab. You will use the DSA to conduct a spectral analysis of the acquired signals. Start out by loading the default.dsa file from the Edit load settings menu item. 2 Impulse-Force Hammer; Spectrum of an Impulse Impulse-force hammers are widely used in vibration testing to produce short-duration (i.e. impulse) forces and to measure the force produced. The experiments in this section: (1) illustrate the use of a hammer with attached force cell to produce an impulse force, and (2) illustrate the spectrum of the transient force produced by the hammer. The force cell is the piezoelectric type that is calibrated so that force can be obtained from the output voltage. The hammer has the following specifications: Frequency response range: 0 8 khz Max force: 500 lb Sensitivity: 10 mv/lb The hammer can be fitted with different hardness tips to enable the user to vary the duration of the impulsive loads. Note that only one side of the hammer has the piezoelectric cell, the other is for storing a different tip.
2.1 Assess the effect of hammer tip on the spectrum of an impulse force. 2.1.1 Install the soft red vinyl tip fitting on the force-cell end of the impulse-force hammer head. Only screw the tip in so that it is "finger- tight," that is, DO NOT use a wrench or pliers to tighten the tip; but, on the other hand, be sure that it is not loose. 2.1.2 The setup is shown in Fig. 1. Attach a BNC-to-BNC cable from the hammer handle to one of the four input channels of the PCB 4-channel Power Supply, which is to be shared between two lab stations. Attach a BNC-to-BNC cable from the output of the power-supply channel that you are using to ACH 0 of the BNC 2120. Set the gain of that power-supply channel to 10. Inputs (left column) outputs (right column) Dell Optiplex computer w/ Data-acquisition board and DSA software Figure 1. Experiment setup for impulse-force hammer measurements. 2.1.3 Set up the DSA by making the following selections: From the Edit menu: Input Settings: Input: Device = PCI-MIO-16E-4, Coupling = DC, Voltage Range = -10 to 10 V (for both channels); Windowing: Window A=none, Window B=none; Triggering: Type=Analog, Trigger channel=a, level=0.05 V. Frequency Settings: Baseband span = 2000 Hz, # of lines=400. Set up the display to show the time-waveform on Display 1 and the amplitude spectrum on Display 2. Have Display 1 show the real part and Display 2 the linear magnitude. 2.1.4 Holding the hammer still, but poised an inch or so above the desktop of the lab bench, press the SINGLE button on the DSA. At the top of the display you should see trigger wait,
which means it is waiting for the voltage to go above 0.05V before it triggers. Now, tap (NOT hit) the red tip of the hammer on the wood desktop. An impulse-like time history should appear in Display 1. If that does not happen, press RUN rather than single and try again (the problem with RUN is that you can lose your displayed data if you inadvertently cause a trigger, such as by putting the hammer down). If that still doesn t work ask your Lab Instructor for assistance. Once you have the time history and the spectrum of the signal produced by the red hammer tip, save Displays 1 and 2 to files. 2.1.5 Change the baseband span to 4 khz by clicking on the label at the lower right of display 2. Remove the red vinyl tip to expose the white nylon tip and repeat Section 2.1.4. Try to tap the desk with about the same force level that you used in Sect. 2.1.4. 3 Natural Frequencies and Mode Shapes of a Cantilever Beam References: (1) Craig, R. R., Structural Dynamics An Introduction to Computer Methods, Sects. 9.2 and 10.2, John Wiley & Sons, New York, 1981. (2) Vibration of Beams Frequency Response, ASE 369K Class Notes, ASE-EM Department, The University of Texas at Austin, Spring 1997. In this laboratory exercise you will obtain three frequency response functions (FRFs), which constitute part of the data that would be taken in a modal test. These frequency response functions can be used to determine approximate values of the lowest two natural frequencies of the cantilever beam with tip mass (the accelerometer). The accelerometer will be mounted near the tip of the beam on the underside of the beam. The impulse hammer will be used to tap the beam at three locations -- location A, 2 in. from the tip of the beam, will emphasize mode 1; a hit at location B, 5 in. from the tip of the beam, will excite both mode 1 and mode 2, and a hit at location C, 8 in. from the tip of the beam, will also excite both mode 1 and mode 2. Clamp Beam Accelerometer
8 Clamp 5 2 C B A 3.1 Spectrum Analyzer Set-Up 3.1.1 Keep the same trigger settings. Open the Edit menu and under frequency settings select baseband span= 2000 and # of lines = 400. 3.2 Beam, Accelerometer, and Impulse Hammer Set-Up 3.2.1 Make sure that the aluminum beam is securely clamped in the bracket that is bolted to the steel loading frame. Measure the cross-sectional dimensions of the beam: w= in. and t in., and measure the length of the beam from the edge of the clamping bracket to the tip of the beam, L in. Assume that the modulus of elasticity for the aluminum beam is E=10 10 6 psi and that the weight density is 0.10 lb/in 3. 3.2.2 Attach the PCB accelerometer to the bottom side of the beam by tightly threading the short 10-32 stud-bolt in the base of the accelerometer into the tapped hole near the end of the beam. Carefully attach a microdot-to-bnc cable from the accelerometer to the Channel 2 (or 4) INPUT of the PCB amplifier/signal conditioner. Set the amplifier gain of this accelerometer channel to k a = 10. Connect the amplifier OUTPUT of this channel to ACH1 of your BNC connector box. 3.2.3 Install a white-nylon/blue-vinyl tip on the impulse hammer force cell, and attach a BNC-to-BNC cable from the hammer to the Channel 1 (or 3) INPUT of the PCB amplifier/signal conditioner. Set the amplifier gain of this force channel to k f = 10. Connect the amplifier OUTPUT of this channel to ACH0 of your BNC connector box. Have the TA check your set-up of the beam, accelerometer, and hammer. 3.3 Time Histories of Impulse Force and Acceleration Acquire the time history of the impulse force and the time history of the acceleration of the tip of the beam as you strike (tap) the cantilever beam at three different locations.
Use SINGLE to arm the trigger each time (if that doesn t work use RUN). 3.3.1 Display the time waveform of CH0 on Display 1. Choose to display the real part. This will display the impulse-force hammer output. 3.3.2 Display the time waveform of CH1 on Display 2.Choose to display the real part. This will display the accelerometer time-history. 3.3.3 Tap the center of the top surface of the beam 8 in. from the tip of the beam (location C). If you don't get a trigger, call on the TA to help you. There should be a single impulse peak (or perhaps double-humped peak) for the force signal, and the time history of the acceleration should appear to be the superposition of a high-frequency sinusoidal signal and a very low-frequency sinusoidal signal. When you think you have acceptable time histories of acceleration and force, show your graphs to the TA before continuing. Save both displays to files. 3.3.4 Tap the center of the top surface of the beam 5 in. from the tip of the beam (location B), using the same good technique you developed in Step 3.3.3. There should be a single impulse peak for the force signal, and the time history of the acceleration should again appear to be the superposition of a highfrequency sinusoidal signal and a low-frequency sinusoidal signal. When you think you have acceptable time histories of acceleration and force, save the displays to files. 3.3.5 Tap the center of the top surface of the beam 2 in. from the tip of the beam (location A). There should be a single impulse peak for the force signal, and the time history of the tip acceleration should appear to be a low-frequency sinusoidal signal. Your force signal should not have several distinct peaks. (As you hit closer to the tip of the beam, it gets harder and harder to hit the beam only once. The beam can bounce back up and hit your hammer tip before your hand can pull the hammer back away from the beam.) When you think you have acceptable time histories of acceleration and force, show your graphs to the TA before continuing. Save both displays to files. 3.4 Impulse-Force Spectrum and Accelerance FRFs Use the thick plate for this section. Display the amplitude spectrum of the impulse-force hammer and also the frequency response function (FRF). The FRF is the ratio of the tipacceleration/impulse-force, or CH1/CH0 and has units of volts/volts. 3.4.1 Setup Display 1 as follows: CH0, amplitude spectrum, linear magnitude. 3.4.2 Setup Display 2 as follows: CH1, frequency response, linear magnitude. Change the baseband span to 400 Hz. This setup will cause Display 2 to display the FRF, i.e. acceleration/input-force.
Homework: 3.4.3 Tap the center of the top surface of the beam 8 in. from the tip of the beam (location C), using the same good technique you used in Sect. 3.3.3. There should be a fairly smooth spectrum for the force signal, and the FRF should have a small peak at about 30 Hz and a larger peak at about 220 Hz. When you think you have an acceptable force spectrum and FRF, show your graphs to the TA before continuing. Save the displays to files. 3.4.4 Tap the center of the top surface of the beam 5 in. from the tip of the beam (location B). There should be a fairly smooth spectrum for the force signal, and the FRF should again have a peak at about 30 Hz and a peak at about 220 Hz. When you think you have an acceptable force spectrum and FRF, save the displays to files. 3.4.5 Tap the center of the top surface of the beam 2 in. from the tip of the beam (location A). There should be a fairly smooth spectrum for the force signal, and the FRF should have a large peak at about 30 Hz, but no peak (or only a very small one) at about 220 Hz. (If your force spectrum is very humpy, you probably allowed the hammer to make multiple hits. As you hit closer to the tip of the beam, it gets harder and harder, in fact, it gets virtually impossible, to hit the beam only once. The beam can bounce back up and hit your hammer tip before your hand can pull the hammer back away from the beam. Keep trying until you get a fairly smooth force spectrum.) Save the displays to files. 1. Using the sensitivity information of the force cell, plot on the same graph the force-time response for the red and white vinyl hammer tip. 2. From the impulse test, plot the amplitude spectrum of red and white vinyl hammer tip. Discuss your plots. 3. Plot both the time history and amplitude spectrum for the beam at the three different locations. Briefly describe your observations. 4. Plot the accelerance FRF s for the three positions on the beam. Briefly describe your plots. 5. Compare the theoretical vibrational modes to the measured vibrational modes (from the FRF). RRC, 11/94, Latest revision: 4/2003, NC Ravi, modified 01/2004