Vibration analysis is a powerful, 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 for personal use. This design idea explores the potential of personal computer audio codecs, software oscilloscopes, and mathematical spreadsheets for acquiring signals produced by simple and inexpensive do-it-yourself (DIY) motion transducers, in order to implement high-performance vibration analysis without high cost.

**Inexpensive Moving Magnet Speed Transducers**

Commercial motion transducers use a variety of physical effects (piezoelectric, etc.) to detect motion, but an easy-to-make-your-own variety includes a small amateur-grade rod magnet moving inside a household winding reel. The output voltage, generated by the magnetic lines of force passing through the coil, is proportional to the speed of the magnet relative to the coil (**Figure 1**). It can also be digitally converted into a measurement of acceleration (by differentiation) and displacement (by integration).

**Figure 1** In a moving magnet speed transducer, the output voltage, generated by magnetic lines of force passing through the coil, is proportional to the speed of the magnet relative to the coil.

A simple way to make these transducers is from a plastic sewing machine coil wound with a few 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 virtually invisible wire!) magnetic wire, glued to a drilled wooden dowel to house the magnet and a suitable spring (**Figure 2** and **picture 3**).

**Figure 2** DIY moving magnet speed transducer design.

**Figure 3A **DIY moving magnet speed 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 is held vertical with the coil at the bottom. Then the magnet is placed in the bore and released so that it falls freely. The peak-to-peak voltage (**V _{dp }**) thus generated is recorded when the magnet passes through the coil.

The acceleration of an object in free fall is about 9.8 m/s^{2}. Therefore, a free fall from a height of X meters results in a velocity of **Vm/s = (19.6X) ^{1/2}Mrs**. Given X as the distance traveled by the magnet (about 0.2 m for the transducer shown), then

**V**giving

_{dp }= 2K(19.6X)^{1/2}Mrs**K=V**where K is the speed calibration constant of the transducer relating the speed Vm/s to the output voltage V:

_{dp}/2/(19.6X)^{1/2}Mrs**Vm/s = V/K.**

**Acquisition of the signal proportional to the speed**

The 16- and 24-bit audio I/O hardware typically found in personal computers (called “sound cards”) combined with oscilloscope simulation software provides low (even zero) cost which is almost ideal for vibration analysis. Scaling, triggering and timebase options, frequency analysis and data file storage are all included. But a legacy of this input hardware that sometimes poses a significant limitation for vibration analysis, is the lower end of a frequency response that has, after all, been specifically optimized for the acquisition and reproduction of audible sounds. This limitation can be partially overcome with a small additional external input circuit, as suggested in a recent design idea (see “Input buffer and attenuator for sound card oscilloscopes extend low-end frequency response “) and illustrated in **Figure 4**.

**Figure 4 **Sound card front circuit.

Alternatively, post-acquisition digital software correction can be applied with a similar effect. An empirical adjustment of T will probably be necessary to optimize the compensation.

Either: a_{I}: (i = 1 to n) Array of AC coupled raw input data

t = Time between input samples (typically 1/44kHz = 22.73us for digital audio)

T = RC time constant of sound card audio input, typically ~1.5ms to 25ms

D_{I}: (i = 1 to n) = Table of corrected output data.

So 😀_{I} = one_{I} + SUM(a_{1}:a_{I}) (e^{(t / T)} – 1)

**Data analysis**

Simple mathematical calculations can convert the digitized (and possibly low-frequency corrected) transducer signals into the fundamental physics of mechanical motion:

Integration (displacement in meters): y_{I }(i = 1 to n) = SUM(d_{1}😀_{I})t/K

Linear (speed in m/s): v_{I} (i = 1 to n) = d_{I}/K

Differentiation (acceleration in m/s^{2}): g_{I }(i = 3 to n – 2) = (d_{i-2} – 8d_{i-1} + 8d_{th+1} – D_{th+2})/(12tK)

**Application examples**

**Figure 5 **Acceleration of a 22 joule muzzle energy spring air pistol during the firing cycle X axis = seconds, Y = Gs.

** **

**Figure 6 **Dual-channel (stereo) codec acquisition of the YZ axes targets the air gun muzzle vibration instant of the indicated projectile exit.

** **

**Picture 7 **Author’s setup to detect pump vibrations on a (very old) Maytag dishwasher.

**Picture 8 **Maytag dishwasher pump bearing vibration analysis.

In conclusion, credit and gratitude is due to Mr. Jim Tyler for his innovative and creative design, implementation and application of moving magnet transducers (or as Jim called them “velocimeters”) to the measurement and refinement of the interior ballistics of the precision target. compressed air guns. Thanks Jim!

*Stephen Woodward’s relationship with *EDN*The DI column goes back a long way. A total of 64 submissions have been accepted since the publication of his first contribution in 1974.*

**Related content**