Blog: Vibrations

Date: 17 December 2015

Copyright © David Boettcher 2005 - 2023 all rights reserved.

I make additions and corrections to this web site frequently, but because they are buried somewhere on one of the pages the changes are not very noticeable, so I decided to create this blog section to highlight new material. Here below you will find part of one of the pages that I have either changed or added to significantly.

The section below is from my second page about technical aspects of watch movements.

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Vibrations

Each swing of the balance from the centre to the point where it reverses and then returns to the centre is called a vibration or beat.

At the start of each vibration, as the balance swings through the centre line, a line joining its axis of rotation to that of the escape wheel, the impulse pin moves the lever and a tooth of the escape wheel is unlocked by a pallet and ‘escapes’. The shape of the pallet face and escape wheel tooth are designed so that, after unlocking, a push called an ‘impulse’, is given to the balance, replacing energy lost by friction. After the escape wheel has turned slightly, the other pallet catches a tooth of the escape wheel and the lever hits the banking pin, locking the escape wheel. The process of unlocking and locking generates an audible tick.

Vph	14,400	16,200	18,000	21,600	28,800	36,000
Ticks/second	4	4.5	5	6	8	10
Ticks/minute	240	270	300	360	480	600
Frequency (Hz)	2	2.25	2.5	3	4	5
Period T (seconds)	0.5	0.44	0.4	0.33	0.25	0.2

Escapements are often characterised by their “vibrations per hour” (vph), sometimes shortened to simply vibrations, or beats per hour (bph). Very old pocket watches run at 14,400, 15,400 or 16,200 vibrations per hour. The 18,000 vph escapement eventually superseded these in the nineteenth century.

For many decades 18,000 vph remained the standard, giving 5 vibrations or ticks per second, since with 3,600 seconds in an hour, 5 ticks per second = 3,600 x 5 = 18,000 vph. The relationship between vibrations and ticks per second is:

\[ vph = 3,600 \times \text{ticks per second} \]

Each tick or vibration represents a swing of the balance from one extreme of its excursion to the other. In physics terms, a cycle is a complete swing of the balance one way and then the other way, returning to where it started, so an 18,000 vph, 5 vibrations per second, balance has a frequency of 2.5 cycles per second, called 2½ Hertz (Hz), and a period of 0.4 seconds.

An 18,000 vph escapement makes one vibration and gives one tick every 0.2 seconds, which is a half period or semiperiod. The relationship between vibrations and semiperiods is:

\[ vph = \frac{3,600}{semiperiod} \]

Higher frequency escapements were used to give watches, especially chronographs or stop watches, greater resolution, which was useful for timing events accurately. Some of these ran at very high frequencies; hundreds of vibrations per second.

The only place where higher frequencies were never used was in marine chronometers, which kept the 14,400 vph rate. With a lever escapement this would give four ticks of the seconds hand per second, but marine chronometers usually have detent escapements which only unlock, and therefore move the seconds hand, on every other vibration. This means that the seconds hand of a marine chronometer moves every half second, which makes it easy to note down time readings to a half second. An 18,000 vph rate would move the seconds hand every 0.4 seconds, which would look odd since over a two second period the hand would move to 0.4, 0.8, 1.2, 1.6 and 2.0 seconds, and higher frequencies would be even more difficult to read precisely.

In the 1950s, higher frequency escapements were introduced to give watches better timekeeping stability. A higher frequency balance stores more energy and is therefore less easily disturbed. These operated at 21,600 vph then 28,800 vph, giving 6 or 8 ticks per second. When electric watches came along higher frequencies were introduced for mechanical watches such as the Girard Perregaux 36,000 vph movement of 1966 and the Zenith El Primero 36,000 vph movement of 1969. The high frequencies introduced problems of retaining lubrication on the pallet jewels, leading to the introduction of the thixotropic 9415 escapement grease.