Experts in Vibration – we design your test and measurement solutions ## Issue 9: Operating Deflection Shapes (ODS)

In this edition of our m+p Analyzer Basics series, we explain the basics of Operating Deflection Shapes.

### What are "Operating Deflection Shapes"?

Operating Deflection Shapes (sometimes called "Operational Deflection Shapes" or ODS) provide additional insight into vibration problems by visualizing the vibration pattern of a structure. In contrast to modal analysis, which can give similar insight, operating deflection shapes are extracted from measurement data acquired during real-world operation, hence the name "operating" deflection shapes. Typically, an ODS is presented in the frequency domain, as can be seen in this animation of a car frame at 16.4 Hz:

Show example For a given frequency, the amplitudes and relative phases of all measurement points are extracted and applied to a geometry to visualize the deformation pattern. To clarify the process, let’s have a look at a very basic example. We consider only two points, where the phase of point 2 is referenced to point 1. The two spectra might look like this:

We can find three regions of interest marked by three cursors:

1. At the first cursor, we can see that both points show approximately the same amplitude and their phases are identical as well. The ODS from this configuration would look like this:

Show example Both points move in phase with the same amplitude.

2. At the second cursor, the second point has significantly smaller amplitude than point 1. Also, a phase shift of 90° is observed. The ODS for this configuration looks like this:

Show example The animation shows large movement of point 1 and the very small amplitude of point 2.

3. At the third cursor, both points again show the same amplitude but their phases are shifted by 180°. The ODS looks like this:

Show example The phase shift of 180° means that the two points move in exact anti-phase to each other.

This example shows that an ODS is really just an animation of the amplitude and phase relations of the measured points. One might argue that it is quite easy to draw this information directly from the chart. This may be true for this simple example, but for more complex geometries like the car ODS above with many measurement points, it would be much more difficult.

### Prerequisites for ODS measurements

Geometry: A geometry consisting of the locations of the measurement points on the structure is required. Typically, this means x-, y-, z-coordinates for each measurement point and defined connecting lines between these points. m+p Analyzer offers an easy to use Geometry editor for this task, which is sufficient for simple geometries. In case of more complex geometries the .stl file format (Standard Triangulation/Tesselation Language format) may be used to import geometries from a CAD software.

Phase referenced spectra: Because ODS requires phase information and "normal" spectra generally have random phase, additional treatment for phase referencing is required. Normally, this is done by choosing a reference sensor and referencing the phases of all sensors to it. This implies that the phase of the reference sensor becomes zero for all frequencies, as it is referenced to itself. Note: Data from the reference sensor and all other sensors needs to be acquired simultaneously! In m+p Analyzer, phase referenced spectra are calculated using auto- and crosspower spectra. For a given measurement point:

... the autopower spectrum results in the amplitude spectrum.

... the crosspower spectrum to the reference provides the phase referenced spectrum.

Steady state operation: Depending on how the data is acquired a steady state operation (or a least reproducible state) of the machine may be necessary. Generally, two approaches to data acquisition may be chosen:

1. Full sensor equipment with single measurement: This is a straightforward approach where sensors are applied to all desired locations. In a single run, data from all sensors is acquired simultaneously. The advantage of this approach is that it is quick as only one measurement run is required. However, this may require a large number of sensors and input channels on the front-end.

2. Partial sensor equipment with repeated measurements: With this approach, we can get all measurements done using as few as two sensors. One sensor - the reference sensor - remains at the same location for the entire test. The second sensor - the roving sensor – is successively moved to the remaining measurement locations and at each position a measurement is taken. While this approach requires less hardware, a steady state condition of the machine is required to make the individual measurements "compatible". This is because we "stitch" together measurements from different runs, and we need to make sure that the vibration pattern of the machine is identical for each run. The easiest way to achieve this, is to run the machine at constant RPM.

Are you interested in learning more about ODS measurement? Read the next issue of m+p Analyzer Basics, where we go through an example demonstrating how to measure and extract ODS using m+p Analyzer.

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