Traceable Vibration Measurement

DESCRIPTION

The need for accurate measurement of vibration in a wide variety of industrial applications has brought to general attention the necessity of measurement of vibration amplitude in internationally accepted standard procedure and instrumentation. Interferometry is directly connected with the definition of meter and, consequently, is a method able to assure the traceability of displacement (or vibration) measurement [1]. Consequently, the wavelength (or in the case of interferometry, subdivisions of the wavelength) of the laser is the intrinsic measuring unit. Depending on the frequency range, a few methods for measuring the vibrations are available, such as the Fringe Counting Method (FCM), the Minimum Point Method (MPM) and the Sine-Approximation Method (SAM). As stated in the ISO/DIS-5347-1 paper [2], these methods cover the whole frequency range from 1 Hz to 10 kHz. The FCM method can be reliably applied in the range 1-800 Hz, while the MPM is used for measurements in the range 800 Hz-10 KHz and SAM in the range 1 Hz-10 kHz.

MEASURING SYSTEM

The measuring system is a Michelson interferometer with collimated beam, as shown in Fig. 1. A stabilized He-Ne laser @ 632.8 nm is used as light source, S, and the laser beam is expanded and collimated using a beam expander, E (composed of a lens system and a pinhole), and a short focal length lens, L. A beam splitter cube, BS, is used to split the incident collimated laser beam and send it towards the two mirrors of the interferometer. The reference mirror, Mref, is attached to a steering mirror mount for an easier adjustment of the position of the reference beam, while the measuring mirror, Mmeas, is placed on a shaker that will make it vibrate in a controlled way. Namely, the shaker will cause the mirror to vibrate longitudinally back and forth in a sinusoidal manner. An oscilloscope is connected to the output of the photo detector, D, in order to visualize and record the signal. All these components of the measuring system are placed on a vibration isolated optical table. The driving signal for the shaker is controlled by computer software.

In the present interferometer, the displacement of Mmeas corresponding to the distance between two adjacent fringes of the same kind (e. g. intensity minima or maxima) is given by l = λ/2. Thus, the number of fringes of the same kind (integer value) moving in front of the photodetector during one vibration cycle is given by

At higher frequencies, when the value of N is small, the measurement errors become significant. In order to reduce this error we apply the procedure described in [4]. According to it, the corrected value of the displacement amplitude is given by
where V(trs) and V(tre) are photodetector output signals at the start and the end stationary points of the vibration cycle. Vps and Vpe are the peak values preceding the start and end stationary points.

RESULTS

Table 1 Values of V(trs), V(tre), Vps and Vpe and N for each frequency of vibration determined from the experimental curves of fig. 4. The values for the corrected displacements calculated using Eq. (3) are also shown.

CONCLUSIONS

A traceable vibration amplitude measurement was demonstrated for calibration of vibrations purpose. A FCM technique to compute the displacements was used. It is important to note that the "saddle-like" stationary points have slightly different shapes for each vibration frequency due to experimental imperfections or background vibration noise. This fact does not affect our measurements at this level of precision, though. With our experiment, the amplitudes of vibration of the measuring mirror, were of the order of microns, and were measured with a resolution of λ/2. Further work includes an improved quadrature interferometer able of λ/8 or even λ/16 resolution in measurement of displacement.