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RESONANCE

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1. Definition and Principle

Resonance is a physical phenomenon by which two mechanical oscillators of frequencies close together, when subjected to weak coupling, tend to synchronize their oscillations in phase opposition. Applied to horology, this principle allows two balance-springs placed within the same Movement to mutually influence one another so as to stabilize their oscillations. The Resonance watch is classified among precision complications. It seeks to improve rate accuracy not by eliminating disturbances, but by neutralizing them through dynamic compensation between the two Regulating organs. This approach is fundamentally different from that of the Tourbillon, which compensates for the effects of gravity through rotation, or of the remontoire d’égalité, which isolates the Regulating organ from irregularities of the Barrel.

2. The origin: Huygens’ observation

The phenomenon of resonance between oscillators was first described by the Dutch physicist Christiaan Huygens in 1665. Observing two pendulums attached to the same beam, he noticed that after a certain amount of Time, their oscillations spontaneously synchronized. He noted that this synchronization was established in phase opposition: the two masses oscillated in opposite directions to one another. Huygens attributed this phenomenon to the transmission of tiny impulses through the shared beam. Resonance, in his view, resulted from a slow and continuous exchange of energy between the two oscillators. This explanation was later confirmed by mechanical analysis. In watchmaking, the same principle applies when two balance-hairsprings are mounted in a Movement whose mechanical support they share.

3. The synchronization mechanism

The synchronization in phase opposition between two coupled oscillators is explained by the energy exchange that occurs between them. When two Balances oscillate in the same direction, their effects on the common frame add up. When they oscillate in opposite directions, these effects cancel out. The state of phase opposition is therefore the only stable state of the system: it is the one that minimizes the energy transmitted to the support. Any external disturbance affecting the frame is then felt simultaneously by both Balances, but in opposite directions. The resulting deviations compensate each other, rather than accumulating. It is this property that gives the resonance watch better resistance to shocks and mechanical disturbances than a single Balance would provide. The stability of the overall Frequency is thus greater than that of each oscillator taken separately.

4. Conditions necessary for resonance

For resonance to be established, two conditions must be met simultaneously. First, the two Balance-springs must present extremely close, ideally identical, natural frequencies. Too large a frequency gap prevents synchronization. In practice, the two regulating organs must be regulated to within a few fractions of a second per day of each other before resonance intervenes to correct the rest. Second, the coupling between the two oscillators must be weak. Too strong a coupling would make the two balances mechanically bound together and deprive them of their oscillatory independence. Too weak a coupling would not transmit the impulses necessary for synchronization. Finding this optimal coupling is one of the central challenges in designing a resonance watch.

5. The coupling between oscillators

In a resonance watch, the coupling between the two balances can be established through several channels. The first coupling mode is mechanical transmission through the common frame: the Main plateand the bridges constitute the propagation path for impulses from one oscillator to the other. This is the most difficult coupling mode to master, as it depends on the rigidity and geometry of the entire Movement. The second mode consists of connecting the two oscillators via a dedicated component, such as a coupling spring. This extremely fine spring transmits impulses with a calculated intensity. It offers a defined and reproducible coupling, independent of the frame. A third approach is air coupling, theoretically possible but difficult to exploit within the dimensions of a watch Movement. In practice, modern designs use a calibrated coupling spring to ensure the robustness and reproducibility of the Resonance.

6. Chronometric Advantages

Resonance gives the watch several concrete chronometric advantages. The first is increased resistance to mechanical shocks. In phase opposition, the effects of an external impulse on the two Balances compensate each other, without accumulating any lasting rate error. The second advantage is Frequency stability. Two oscillators coupled in Resonance exhibit a more stable common Frequency than that of each oscillator alone. Internal fluctuations in one tend to be dampened by the other. The third advantage is the mutual and continuous correction of the two Regulating organs. If one drifts slightly, the Resonance exerts a restoring force on it toward the common Frequency. These advantages are particularly noticeable under conditions of active use, where the watch is subjected to shocks and frequent position changes. Resonance therefore improves accuracy under real wearing conditions, which clearly distinguishes it from other precision Complications.

7. Historical achievements

The first attempts to apply Resonance to portable horology date back to the end of the 18th century. The French Horologist (watchmaker) Antide Janvier made watches with a double Balance taking advantage of the phenomenon of Resonance. Ferdinand Berthoud, another great French Horologist (watchmaker) of the same period, also took an interest in this principle as part of his work on high-precision marine chronometers. However, these achievements remained confidential and without direct descendants. The difficulty of regulating two Regulating organs with sufficiently close Frequency, using 18th-century machining techniques, constituted a major obstacle. It was necessary to wait for the progress of modern Micromechanics for horological Resonance to become a truly mastered and reproducible Complication.

8. Contemporary achievements and design difficulties

The contemporary revival of horological Resonance dates back to the end of the 20th century. It was made possible by advances in manufacturing techniques, particularly the ability to produce two hairsprings nearly identical and to regulate them with sub-second precision per day. The main design difficulty lies in obtaining two balance-springs with sufficiently close frequencies. A discrepancy of more than two to three seconds per day between the two organs is generally prohibitive for establishing stable resonance. The design of the coupling constitutes the second major challenge. A coupling spring that is too rigid turns the two balances into a single oscillator and cancels out the resonance effect. Too flexible, and it fails to transmit the necessary impulses. The geometry of the Movement must also be studied so that the two balances share rigorously symmetrical mechanical conditions. Assembling and regulating a Resonance watch require rare expertise and considerable working time, which explains the extreme rarity of this Complication.