How is an
Acceleration Value from an Acceleration Sensor Converted to Velocity
and Displacement?

**Acceleration**, **velocity**, and ** displacement** are parameters indicating the status of vibrating
objects. As is widely known, these parameters are mutually related
in differential and integral term. Acceleration sensors are commonly
used for the measurement of vibration. Therefore, the FFT analyzer
is equipped with integration functions for the conversion of
acceleration values measured to velocity and displacement.
Furthermore, when **calibrating EU (What is EC calibration?)** with acceleration values in m/s2 units, velocity units are
automatically read directly in m/s, and displacement units are
automatically read directly in m. The differential and integral
functions of the FFT analyzer support both differentiation and
integration on the frequency and time axes.

For power spectrums subject to narrow band
analysis, since power at each frequency can be seen as being
equivalent to the square of the amplitude of the sine wave, ** frequency-axis differentiation and integration** in the FFT is
implemented by multiplication and division of angular frequency
ω(i.e. 2π f, f: frequency). In the integration example, the power
spectrum value is found by dividing by ω^{2} with the single
integral, and by ω^{4} with the double integral (equivalent
to ω and ω^{2} respectively for the linear spectrum).
Differentiation and integration of the frequency is commonly used if
only the amplitude value on the frequency axis is required.

**Time axis differentiation and integration** involves numerical pre-processing of the direct time waveform,
followed by an FFT to obtain the power spectrum. By using the time
axis integral, the velocity and displacement time waveforms can be
found from the acceleration waveform, thus permitting reading of
instantaneous amplitude of shock amplitude waveforms.

The point you should notice is about time axis integration. Since integration (with the double integral in particular) requires a large numerical dynamic range, even integration of a time waveform with a wide frequency band results is implemented, the waveform with only the low frequency band results, and the waveform for the high frequency band cannot be observed in practice. As a practical method, a high-pass filter (analog or digital) is used to limit to the targeted frequency band when implementing the time-integration of a time waveform.

Revised:2009/11/16

- Copyright © ONO SOKKI CO.,LTD All Rights Reserved.

Copyright © ONO SOKKI CO.,LTD All Rights Reserved. |
Terms of use | Privacy policy