Issue 10: Operating Deflection Shapes (ODS) by Example
We measure the ODS of our rotating demo machine. It is made of a rectangular aluminum base plate onto which a motor and a rotating shaft are mounted (see picture). The goal is to measure the ODS of the foundation of the machine (the base plate) by measuring vibrations encountered during operation.
The first basic requirement for ODS animation is a geometry of the system under test. For the sake of simplicity, we only analyze the base plate of the demo machine. Eight measurement points on the base plate are defined and a basic geometry created in m+p Analyzer "Geometry Editor" (requires license AN-ODS/AN-eODS):
The partial sensor equipment method is used, with four accelerometers to measure the eight points on the base plate. We need three runs for all points: The reference sensor stays at position 1 the entire time. Three "roving" sensors measure positions 2, 3 and 4 in the first run, then 5, 6, 7 in the second run and finally only one sensor is required to get the measurement of the 8th position.
We first configure the sensors with their respective sensitivity and in our case we activate IEPE supply. Setting the first sensor to "excitation" (while all others are "response") will mark it as the reference sensor for phase referencing. We choose a sample rate of 2,048 Hz and a maximum frequency of 800 Hz in the spectra is sufficient. On the configuration save page we choose "ODS-FRF", which will give us phase referenced spectra. Note: These are "pseudo"-spectra. Because we use amplitude averaging, the actual spectrum doesn’t have useful phase information anymore. Behind the scenes, auto- and crosscorrelation functions are used to generate the "ODS-FRF" with meaningful amplitudes and referenced phases.
When we first started this experiment, we wanted to let the machine run at a fixed RPM and measure the vibrations on the base plate. We expected the motor to introduce enough "random" vibration to excite the bending modes. After setting up the machine, configuring m+p Analyzer and starting the first measurement we saw the following spectra:
This was not what we expected to see! Clearly there are many spikes in the spectrum, which don't seem to be structural vibrations. Closer inspection shows that all of these spikes are at integer multiples of 100 Hz (50 Hz being the power line frequency in Germany). It turns out that every time the motor is under load - meaning, it has to speed up the shaft, those spikes are present . So, we had to change plans: We sped up the shaft and turned off the motor to measure a run-down of the machine. The results look more promising:
While this is still not the most perfect spectrum, it will do for our purpose. This goes to show that even a simple demo machine may have its own quirks. Figuring out the best way to get data is part of the process and often solved with trial and error. There are two regions of interest in this spectrum. In the lower frequency range (~ 0 - 100 Hz), we see high vibrations due to the shaft rotation (~ 0 - 6000 RPM). The area is quite wide because we measured a run-down. Thus, all the different RPMs during operation are now found (smeared) in the spectrum. The second region from ~150 - 500 Hz is where we'll find the structural vibrations of the base plate.
With the measurements acquired by the previously described procedure, we can now start extracting the ODS using the m+p Analyzer "Operating Deflection Shape" wizard. The ODS wizard is a straight forward tool for ODS extraction. In three panes (left to right) we can see all valid measurements, a chart to select the frequency to which the ODS is extracted and the final ODS. Note: The ODS animation window also contains the frequency and an estimated damping ratio using half-power method.
As a final step, we can save the extracted ODS into the workspace. As an example, we extracted the deflection shapes for the first and second bending mode of the base plate at 153 Hz and 485 Hz:
Operating deflection shapes are a great tool to analyze the dynamic properties of a structure under operating conditions. They can help engineers to find and solve structural and acoustic problems. The procedure relies on the structures (machines) "self-generated" vibrations, thus the results are only valid for the given operating condition and only structural properties excited under the given condition are found. A different working condition (e.g. rotating speed) may result in different structural responses. A more general approach to analyze structural properties is modal analysis, which will be a topic in one of our next m+p Analyzer Basics issues.