Isochronism
As isochronism (from the Greek .: isochronous equal length constant) the property of a mechanical vibration system for vibration is called regardless of the vibration height (amplitude) is always the same time requiring. The term (other terms: isochrony, tautochrony) is of central importance for the technology of mechanical clocks. If a constant oscillation range of the oscillation system cannot be guaranteed for watches, deviations from isochronism lead to rate errors.
The term is often used ambiguously. In contrast to the above definition, an oscillation system is called isochronous if it has a constant oscillation period with a constant oscillation amplitude. The oscillation itself is isochronous (i.e. of the same length) under this condition. The system, however, is usually not an isochronous one, because a different amplitude may result in a different period of oscillation. You can call this conditional or limited isochronism.
It should also be mentioned that the statement ascribed to Galileo, that a gravity pendulum oscillation system is an isochronous one, only applies to small deflections (see pendulum ; see below).
A mechanical oscillating system consists of a body (mass), which a restoring force (reversing force, counter-torque) tries to return to this central position when it is deflected from a central position (zero position). In mechanical watch technology only bodies are used that can be deflected around an axis of rotation. These are the gravity pendulum ( Galilei ), the balance wheel ( Huygens ) and (of minor importance) the torsion pendulum. Back-driving forces are the gravitation of the gravity pendulum and spring forces (spiral spring in the balance wheel, torsion spring in the case of the torsion pendulum).
Theoretically, an oscillating system oscillates isochronously if the restoring force increases linearly (proportionally) with the deflection angle. This is neither the case with the gravity pendulum nor with the balance wheel, whereas the torsion pendulum has this property. In practice, however, it has been shown that the torsion pendulum is inferior to the gravity pendulum and the balance-wheel-spiral oscillation system for reasons not to be discussed here and is not suitable for precision watches.
The isochronism error of the gravitational pendulum is due to the fact that the restoring force is mathematically determined by the sine of the deflection angle (i.e. it is not linear). The balance-spring oscillation system could in principle behave isochronously if the balance spring provided an exactly linear restoring force. However, this can only be achieved for small amplitude ranges, so that this system cannot be called isochronous.
In mechanical clocks, therefore, non- isochronous oscillation systems are used (apart from the torsion pendulum and the pendulum with a small oscillation range described below).
The endeavors of watchmakers were and are therefore directed on the one hand to make the oscillation system oscillate with constant amplitude and on the other hand to keep the size of the restoring force (of the balance spring or torsion spring) stable depending on the deflection ( conditional isochronism ). A multitude of influences oppose this (influence of the escapement on the oscillation system, temperature fluctuations, friction problems, shocks caused by movement of the watch, fluctuating drive torque, material fatigue in springs, etc.). The construction of precise mechanical clocks requires that all these influences are minimized by suitable measures ( free escapement , compensation pendulum or balance , jewel bearings, optimized materials, constant drive torque, etc.).
The gravity pendulum has a special feature in that, in the range of very small amplitudes, the oscillation is to be regarded as isochronous, because then mathematically the sine of the deflection angle can be replaced by the deflection angle and the restoring force thus has a linear dependence on the deflection angle with great accuracy. For example, the period of oscillation of a pendulum with an average amplitude of 2 ° does not change noticeably with amplitude fluctuations of ± 1 °. Precise pendulum clocks are therefore operated with small deflection angles, although the aim is of course to have an amplitude that is as constant as possible. Only with the invention of the Graham escapement could pendulum clocks with small pendulum swings be built.
Huygens discovered that a gravity pendulum theoretically behaves isochronously when it swings on a cycloid path instead of a circular path. In order to achieve this, he invented the tautochronous pendulum suspension ( cycloid pendulum ). The pendulum is suspended from a thin thread or a thin leaf spring, which is placed against cycloid-shaped jaws during the oscillation. This forces the pendulum onto a cycloidal path. This way of making the period of oscillation of the gravity pendulum independent of the deflection has not proven itself, in particular because of the associated friction problems.
In watch literature, the imprecise terms "isochronism of the spiral", "isochronous spiral" or the like are used. to find. However, a hairspring cannot be used as a speed regulator without a balance and can therefore not be called isochronous (or an isochronism can be assigned to the hairspring). Mostly, spirals are meant which, through a special shape (end curves / Breguet , Phillips , Gerstenberger), provide an approximately linear restoring force (constant directional moment) for the oscillating system in the working area. But spirals, whose design (arrangement of the attachment points) enables mutual compensation of opposing interfering influences (Caspari, Grossmann ), are given this attribute. The causes of the disturbance can come from the hairspring itself as well as from other components of the watch.
Individual evidence
- ^ Rudi Koch: BI-Lexicon Clocks and Time Measurement, VEB Bibliographisches Institut Leipzig
- ↑ Fritz von Osterhausen: Callweys lexicon. Callwey, Munich 1999, ISBN 978-3766713537 .
- ↑ Martinek Rehor: Mechanical watches. VEB Verlag Technik Berlin
- ^ Meschede: Gerthsen Physik. Jumper
- ↑ Recknagel: Physics Mechanics. VEB Verlag Technik Berlin
- ^ Edouard Phillips: Mémoire sur le spiral réglant des chronomètres et des montres. 1860, accessed April 1, 2017 (French).