6.5 Steps of experimental procedure
1. Fix the two discs at particular span lengths over the shaft as shown in Fig. 6.7 and place the accelerometers over the discs (can also be kept at bearing locations, however, with that the phase of two discs cannot be analyzed as for the present case).
2. Connect the other end of the accelerometers to any two channels of a Data Acquisition System.
3. Connect the acquisition system to a computer with data processing software (Ex. PULSE software, LabVIEW, etc.).
4. To vibrate the system close to mode I, give an impact the shaft around the mid-span of the shaft so that the two discs vibrate in in-phase as shown in Fig. 6.8.
5. Record the data from the data processing software to observe the vibrational responses of the system and it may contain second natural frequency along with the predominant first natural frequency of vibration (in fact it may contain several other frequencies such as base vibrations, noise etc.).
6. To vibrate the system close to mode II, impact the shaft at two points of the shaft in opposite direction so that the two discs vibrate in out of phase (i.e., near each discs, however, in opposite directions) (Fig. 6.9).
7. Follow step 5 to observe the vibration responses of the system with predominant the second natural frequency of vibration.
Fig. 6.7: Position of two discs on the beam
Fig. 6.8: Giving impact to get mode I vibrations
Fig. 6.9: Giving impact to get mode II vibrations
Precautions:
1. Check whether the discs are fixed tightly to the shaft or not and supports are properly tightened on the base plates.
2. Contact type sensors (e.g., accelerometers) should be firmly attached to discs and for non-contact sensors (e.g., laser vibrometer) the surface should be polished or light reflecting tape to be used to get strong signals.
3. Check for any loose sensors or data-acquisition wirings since it may give no or incorrect signal.
4. The impact to the shaft should be very light and in the acceptable range of the sensors and acquisition system. Otherwise the system gets overloaded and results in erroneous signals.
1. Though the system is given an impact to get vibrated in one of its modes, in practice, the system gets vibrated under both of its natural frequencies. Hence, filtering is required to get the response of the system under a particular frequency to observe the mode shape and its phase difference.
2. Practically, it is very difficult to get a pure mode of vibration (i.e., vibrations with a single frequency) under free vibration. Hence, filtering is used to get response corresponding to a single natural frequency.
6.6 Signal processing
Sometimes the signal obtained can be a mix of multiple frequencies. This unwanted signal comes inadvertently such as from noise, the line frequency, etc. To remove these unwanted signals and to get only the relevant signal, filtering is done. There are different types of filters used for this process. Some of them are Low pass filters, High pass filters, Band pass filters, Band stop filters. Refer to section 6.2 to know how these filters work.
From the FFT plot of the experiment, it is observed that the system has two natural frequencies, approximately at 20Hz and 57Hz. From this, we can say that the system vibrates in mode I at 20Hz and in mode II at 57Hz. Hence, we need to pass the signal with frequencies around 20Hz to get the corresponding mode I response signal. Similarly, 57Hz signal should be passed from the filter and the remaining signals must be attenuated.
In this experiment, a Band pass filter is used, which passes the signals with the frequencies falling inside the band mentioned. To get signal corresponding to mode I, the band is chosen such that the lower cut off frequency is 19Hz and the higher cut off frequency is 21Hz. Similarly, for mode II, the band is from 56Hz to 58Hz.
6.7 Working with the LabVIEW
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To start virtual experiment, first click on the RUN button at the top of the page (see Fig. 6.10).
Fig. 6.10: Starting a virtual experiment
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To stop any experiment (even at the middle of the experiment), press the STOP button at the top of the page (see Fig. 6.11).
Fig. 6.11: To stop the virtual experiment
The manipulations one can perform in a graph are: saving the graph, changing the color/thickness of the curves, zooming a particular portion of the graph, using cursors to locate the position of the peaks, etc.
1. To save a graph, right click on the graph area and select Export Simplified Image . Here choose Save to get the file option and select the path where you want to save the graph (Fig. 6.12).
Fig. 6.12: To save a plot
2. To change the appearance of the graph, click on the plot symbol on the top of the graph (Fig. 6.13).
Fig. 6.13: To change the appearance of a plot
3. To zoom the graph click on the magnifying lens symbol at the top of the graph (Fig. 6.14) and select any option to zoom a particular potion of the plot.
Fig. 6.14 To zoom a plot for close observation
4. To know the X and Y axes values of a particular point on the graph use CURSORS.
a. Right click on the graph and from the visible items select cursor legend (see Fig. 6.15).
b. To add a cursor, right click on the cursor legend and select create cursor as shown in Fig. 6.16.
c. Now a cursor will be created with the marker at the origin (see Fig. 6.17).
d. Now drag the cursor to the point where you want to measure the X and Y axes (see Fig. 6.18).The cursor legend shows the x and y co-ordinates of the point.
e. If you want to use multiple cursors follow the steps from b to d (see Fig. 6.19).
Fig. 6.15: Adding cursor legend
Fig. 6.16: Creating a cursor
Fig. 6.17: View of a cursor
Fig. 6.18: Measuring the coordinates using cursor
Fig. 6.19: Using multiple cursors
6.8 Steps in virtual experiment
The virtual experiment procedure is divided into different sections, those needs to be followed one by one to complete the experiment.
Step 1: Press the RUN button at the top to start an experiment. This will take you to the Home page of the experiment (Fig. 6. 20). Press NEXT BUTTON at the end of every page to proceed further in the experiment.
Step 2: Press NEXT BUTTON to proceed. This takes you to the Introduction page (Fig. 6.21), which gives you a brief description about the mode shapes of a system and their significance. This explains about the two mode shapes, the present system has i.e., mode I and mode II.
Step 3 Next comes is the Input page (Fig. 6.22), where you can choose inputs to perform the experiment. Inputs include the type of impact to be given to the system and the type of transducer to collect the data. Once the inputs are finalized by clicking the enter button they can’t be modified for the rest of the experimentation. You need to restart the virtual experiment in such a case to make changes of your choice.
Step 4 : Theoretically calculated natural frequencies are shown in Fig. 6.23.
Step 5 : Next page shows the FFT plot of vibration responses (Fig. 6.24) corresponding to the inputs chosen by the user, from which the frequency of vibration of the system can be obtained. Spend some time in finding answers for the questions put forth for you. Observe that, the system vibrates under a combination of multiple frequencies, though you impacted the system close to the single mode. This is the practical limitation that we can’t escape. However, the predominant peaks can be observed corresponding to the mode at which the system is excited. The theoretically derived natural frequencies are compared with the experimental natural frequencies.
Step 6 : Next page displays the vibrational responses from the two discs (Fig. 6.25). Since the vibration is not because of a single frequency, we need to filter out the unwanted signal from the response signal to get the signal corresponding to the required frequency. Hence, a band-pass filter is used to filter the signal. For example, if the system is impacted in mode I, the second natural frequency signal will be attenuated using the band-pass filter with central frequency corresponding to the mode I (Fig. 6.26).
Step 7: The close view of filtered responses from the two discs will be displayed (Fig. 6.27). Try to find out the phase difference between the masses. In mode I since the masses vibrate in in-phase, the phase difference will be close to zero degrees (since the damping is relatively low for the present system). In mode II, the masses vibrate in out-of-phase, the phase difference will be around 180 degrees.
Step 8: A comparison will be done between the values calculated theoretically and experimentally as shown in Fig. 6.28.
Step 9: A small questionnaire will be put forth for the user (Fig. 6.29) and the feedback on the virtual experiment will be taken from the user (Fig. 6.30).
Fig. 6.20: Home page of the virtual experiment
Fig. 6.21: Basic definitions
Fig. 6.22: User input page
Fig. 6.23: Theoretical natural frequencies of the system
Fig. 6.24: Finding natural frequencies using its FFT plot
Fig. 6.25: Responses from discs
Fig. 6.26: Filtered signals
Fig. 6.27: Close view of filtered signals to find phase difference
Fig. 6.28: Comparison of theoretical and experimental results
Fig. 6.29: Questionnaire
Fig. 6.30: Feedback page