## Monday, July 10, 2017

### Diagnosing Watches With Electronics

I've been fascinated by mechanical watches since I was a kid. Little machines on the wrist, marking out the passage of time with an unexpected level of accuracy, at least if the watch is in good shape.

To measure accuracy and diagnose issues, watchmakers use a watch timer which listens for and measures intervals between ticks. However, the tools are rather expensive for hobbyists, such as yours truly.

Fortunately, free or low-cost options like Watch-o-Scope ease the burden, but require a sensor and preamplifier. Here's my take on this fun little preamp project.

## Preamplifier

Watch-o-Scope provides a schematic of a circuit that amplifies frequencies within a set band to filter out noise.

The circuit is made of three inverting operational amplifiers in series with active filtering. Here's how that works. A basic version of an inverting op amp circuit looks like this:

 Source: Wikipedia (Jul 6, 2017)
The gain is given by:

To implement an active low pass filter with gain, we place a capacitor in parallel with Rf. For AC signals, the gain of the circuit depends on feedback impedance, Zf, which is the sum of resistance and reactance:

Where:

and, yeah, the j is an imaginary number.

You can see that as frequency increases, Zf decreases. In turn, gain decreases with increasing frequency, thus, we have a low pass filter.

Adding a capacitor in series with Rin creates a high pass filter for the input to the op amp, where impedance, Zin, decreases with increasing frequency:

So that gain increases with increasing frequency; a high pass filter.

You can compute the cutoff frequency of each filter as:

Put it all together and we have a high-gain, band pass amplifier.

You may wonder: what frequencies do we use? To find out, I recorded the unfiltered sound of one of my 100-year-old Elgin size 6 pocket watch movements using the piezo sensor amplified by my eeZeeAmp board set to a gain of about 200:

The signal is just a mess, as you can see. My ears can barely pick out the ticking from the noise. But it is there, and you can see the ticks when you zoom in on the waveform. Using Audacity's filtering capabilities, I eventually eliminated most of the noise:

Most of the important sounds appeared to fall in the range of about 2000-5000 Hz. I had to widen the band, however, for some of my wristwatches.

## Diagnosis

So what can we learn from a watch timer? This trace of my 1957 Bulova 23 Jewel, shows the watch is relatively accurate, relatively clean and with a low beat error.

Perfect accuracy means a daily rate of 0 seconds per day of gain/loss and would show as a series of dots (ticks) perfectly overlaying the horizontal line in the middle. For an old watch, 8 seconds per day is arguably tolerable.

An amplitude of 224° rotation of the balance (270° is ideal), combined with a fairly straight, fairly noiseless trace, suggests a clean and well-lubricated watch. And the beat error, the difference in the amount of time the balance spends rotating in each direction, is minimal.

By taking a longer-term trace, we can discern periodic fluctuations point to flaws in the rotating gears of the watch, called the wheel train. The same Bulova 23 over a 3 hour period is enlightening.

The trace above shows fluctuations in amplitude and rate occurring about five times an hour. Until I learn more about the movement I won't know the cause. Meanwhile the blue shading I added highlights an hourly variation that may point to issues with the center (hour) wheel. The slight overall downward trend in amplitude may be due to the main spring unwinding.

And with that, I now have a suitable circuit for diagnosing my various mechanical watches.

References