# Low-cost vibration analysis using PC audio and DIY motion sensors

#### Article By : Stephen Woodward This design idea explores the potential of personal computer audio codecs, software oscilloscopes, and spreadsheet math for acquisition of signals produced by simple and cheap DIY motion transducers, to implement high-performance vibration analysis without the high cost.

Vibration analysis is a powerful and non-invasive way to measure, understand, and quantify the internal dynamics of mechanical systems, but the cost of the necessary instrumentation is sometimes a deterrent to personal use.  This design idea explores the potential of personal computer audio codecs, software oscilloscopes, and spreadsheet math for acquisition of signals produced by simple and cheap do-it-yourself (DIY) motion transducers, to implement high-performance vibration analysis without the high cost.

Inexpensive moving magnet velocity transducers

Commercial motion transducers employ a variety of physical effects (piezoelectric, etc.) to sense motion, but one variety that’s easy to make yourself comprises a small hobby-grade rod magnet moving inside a home-wound coil. The output voltage, generated by lines of magnetic force traversing the coil, is proportional to the magnet’s velocity relative to the coil (Figure 1).  It can also be numerically converted to a measure of acceleration (by differentiation) and of displacement (by integration). Figure 1 In a moving magnet velocity transducer, the output voltage, generated by lines of magnetic force traversing the coil, is proportional to the magnet’s velocity relative to the coil.

A simple way to make these transducers consists of a plastic sewing-machine bobbin wound with a couple thousand turns of 40AWG “solderable” insulation (i.e., you don’t need to strip it before soldering—a good chore to avoid when dealing with practically invisible wire!) magnet wire, glued to a wooden dowel drilled to house the magnet and a suitable spring (Figure 2 and Figure 3). Figure 2 DIY moving magnet velocity transducer design. Figure 3 A DIY moving magnet velocity transducer.

Calibration of the transducer to compensate for uncertainties in magnet strength, number of turns on the coil, etc., is easily accomplished using gravity. For the transducer shown, the spring is removed and the assembly held vertical with the coil on the bottom. Then the magnet is placed into the bore and released so that it falls freely. The peak-to-peak voltage (Vpp ) so generated  is recorded as the magnet transits the coil.

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Acceleration of a freely falling object is ~9.8m/s2.  Consequently, free fall through a height of X meters results in a velocity of Vm/s = (19.6X)1/2m/s.  Given X as the distance fallen by the magnet (about 0.2m for the transducer shown), then Vpp = 2K(19.6X)1/2m/s, yielding K=Vpp/2/(19.6X)1/2m/s where K is the transducer velocity calibration constant relating velocity Vm/s to output voltage V: Vm/s = V/K.

Acquisition of the velocity-proportional signal

16- and 24-bit audio I/O hardware typically found in personal computers (so called “sound cards”) combined with oscilloscope-simulating software provides low (or even zero) cost signal acquisition capability that’s almost ideal for vibration analysis. Scaling, triggering and timebase options, frequency analysis, and data file storage are all included.  But one legacy of this input hardware that sometimes poses a significant limitation for vibration analysis, is the bottom end of a frequency response that was, after all, specifically optimized for audible sound acquisition and reproduction.  This limitation can be partially overcome with a little added input external circuitry, as suggested in a recent Design Idea (see “Input buffer and attenuator for sound card oscilloscopes extends low-end frequency response“) and illustrated in Figure 4. Figure 4 Sound card front-end circuit.

Alternatively, post-acquisition numerical software correction can be applied with similar effect.  Empirical adjustment of T is likely to be required to optimize compensation.

Let :    ai: (i = 1 to n) Array of raw AC-coupled input data
t = Time between input samples (typically 1 / 44kHz = 22.73us for digital audio)
T = RC timeconstant of soundcard audio input, typically ~1.5ms to 25ms
di: (i = 1 to n) = Array of corrected output data.
Then:   di = ai + SUM(a1:ai) (e(t / T) – 1)

Data analysis

Simple spreadsheet math can convert the digitized (and optionally low-frequency-corrected) transducer signals into fundamental physics of mechanical motion:

Integration (displacement in meters):  y(i = 1 to n) = SUM(d1:di)t/K
Linear (velocity in m/s): vi (i = 1 to n) = di/K
Differentiation (acceleration in m/s2): g(i = 3 to n – 2) = (di-2 – 8di-1 + 8di+1 – di+2)/(12tK)

Example applications Figure 5 Acceleration of 22 joule muzzle energy spring-piston airgun during firing cycle X axis = seconds, Y = Gs. Figure 6 Dual-channel (stereo) codec acquisition of Y-Z axes target airgun muzzle vibration instant of projectile exit indicated. Figure 7 The author’s set-up for sensing the pump bearing vibration on a (very old) Maytag dishwasher. Figure 8 Analysis of Maytag dishwasher pump bearing vibration.

In closing, credit and gratitude are due to Mr. Jim Tyler for his innovative and creative design, implementation, and application of moving magnet transducers (or as Jim christened them “velocimeters”) to the measurement and refinement of the interior ballistics of precision target airguns. Thanks, Jim! 