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# Automatic Vibration Mode Analysis with ESPI

## Determination of amplitude and phase

 Different measurement positions for automatic calculation of amplitude and phase of vibration
A vibrating object is illuminated with the laser light at two different positions, e.g. at 0° and at 180° of the vibration excitation. The ESPI image will show the deformation amplitude between these two exposure times.  Since, in the general case the phase between the excitation and the object vibration is not known, one cannot be sure to be seeing the maximum amplitude with this double exposure technique. Therefore, in case of sinusoidal excitation, a minimum of 2 different time settings are required to determine the absolute amplitude and phase at each point of the image. For practical reasons, typically more images at different time settings are taken in order to eliminate measuring errors.

## Reference point used

The complete set-up for automatic mode analysis is shown beneath. The object is excited by a shaker.  The vibration signal and the output of a force sensor is recorded with a signal analyzer.
A point-measuring sensor (accelerometer or laser vibrometer) is used to provide the time signal of the vibration of the object at one point in the measuring field. ESPI techniques typically show relative deformations. Therefore, this point is used as reference point for the ESPI measurement. Complimentary it determines the absolute amplitude level of the precise ESPI measurement of relative displacement.

 Principle setup for automatic vibration modal analysis

## Change of amplitude distribution at different phase positions     Real and imaginary part of the amplitude, obtained by multiple measurement at constant frequency with different phase positions Amplitude and phase calculation

In the automatic inspection mode, the system records a minimum 3, but typically 6 to 8 images, at different phases between the recording times and the excitation signal, but at the same frequency. Each image gives an amplitude distribution where the different colours represent different amplitude levels.

When the phase between excitation and recording is shifted, the amplitude is reduced to zero and eventually changes sign.  These images are used to calculate the imaginary and real amplitude of each pixel in the image. While theoretically, only two images are required to calculate real and imaginary amplitude of a sinusoidal function, multiple images are recommended to avoid noise, especially close to the nodal lines, which have small amplitudes. At the same time, the amplitude and phase can be calculated from the real and imaginary part of the vibration for every pixel in the image.
 Calculated absolute amplitude and phase at a certain frequency

## Automatic frequency sweep

This procedure is automatically repeated at different frequencies around each resonant mode.  The amplitude and phase of the force signal and of the reference point are recorded.  If required, the software also can automatically adjust the force to constant level for each frequency step.  With this new frequency, the automatic amplitude and phase measurement is repeated.  The result is a set of images with amplitude and phase distributions at the different measured frequencies.

 Change of absolute amplitude distribution at different frequency positions Change of phase distribution at different frequency positions

In order to minimize the amount of data, typically a frequency range around a resonance is automatically analyzed in 10 to 20 frequency steps.  The software allows the definition of several frequency blocks with different frequency steps and different force levels, which will automatically be analyzed.

## Data export Definition of data exportation and analysis points

The system’s format for the output of data to vibration analysis software packages is the Universal File Format (UFF).  In the ESPI measuring area, a set of measuring nodes can be defined.  At these nodes, the measuring data are automatically exported into a UFF file and can be read by the modal analysis software.  The right side picture shows a measuring field on a plate.  The blue rectangle shows the complete measuring field, the blue crosses indicate the data nodes for export.  The number of nodes and their positions are variable.  Also, the reference point and the point of excitation by the shaker are indicated.

## Summary

Automatic modal analysis with ESPI techniques shows the advantage of non-contact and fast generation of vibration information over the complete measuring area.  The full-field simultaneous measuring technique allows for the analysis of complex vibration modes at the same speed as simple modes. In addition, non-steady events can be investigated.

Details concerning a measurement example in the pdf-file.