Complications
andrea~ provides a fascinating, in-depth exploration of F.P. Journe's Resonance watches, approaching the complex horological phenomenon through the lens of control theory. His post, rich with technical diagrams and mathematical equations, offers a unique perspective on how two independent balance wheels can achieve synchronization. This article distills the community's engagement with andrea~'s original post, offering further insights and debates on the mechanics and benefits of resonance.
Have you ever heard of a feedback loop? If you haven't, I can best describe it as a way in which a system can actively detect its output through a sensor and make changes to its variables in order to achieve and maintain a certain desired state automatically.
Control theory is a branch of mathematics mainly used in Electrical, Automation and Robotics engineering, extremely useful for the autonomous operation of devices.
Example: control systems are extremely prevalent in the aerospace field, used to maintain the orientation of satellites, to autopilot planes and missles and to program robots used for space exploration.
But I'm not here to discuss aerospace (unless we're talking Breitling 😉). Here's how control theory can be applied to mechanical watchmaking, in the form of the resonance synchronization found in clocks and watches by Breguet, Janvier and Journe among others.
We can describe the coupling of the two balance wheels of a Resonance through this system of ordinary differential equations (for the sake of simplicity I'll just leave the definition of some of the variables for the answers to any eventual questions, just know that Theta describes the angular position of the balances, omega is the angular velocity of such balances and k signifies the rigidity of the base plate, through which the sound waves propagate in order for the coupling to happen).
As we all know, our beloved mechanical watches don't contain any electronics, so the way in which the oscillators control one another can be described as passive reciprocal control. This makes the system "open", which means that it lacks a feedback loop.
If we assume that the watch is kept wound, the oscillations of the balance wheels can be described through this graph: as you can see, the amplitude is kept constant and the oscillators are in phase opposition, in such a way they are able to compensate one another, thus stabilizing the system. (The simulation was performed using MATLAB and Simulink).
What I love about watchmaking is that it can be appreciated through many lenses, and science is one of them. Hopefully I was clear enough in my explanation. Feel free to ask any questions, I'll try to answer them if I can.
The Chronomètre à Résonance represents F.P. Journe's entry in the Souveraine collection, distinguished by its resonance complication. This reference utilizes the principle of resonance between two independent escapements to enhance chronometric precision.
The 40mm case is crafted in 18k rose gold with a fixed bezel and sapphire crystal. The silver dial houses the manual-winding caliber 1499 movement, offering a 42-hour power reserve. Water resistance is rated to 30 meters, and the watch is completed with a leather strap.
This reference appeals to collectors focused on haute horlogerie complications and independent watchmaking. The resonance mechanism positions this piece as a technical showcase within F.P. Journe's manual-winding offerings. Production began in 2000, establishing this as part of the brand's contemporary catalog for collectors seeking advanced chronometric functions.
inspiring science. Love it, Filip
How do they compensate and stabilize each other? Through vibrations on the mainplate? Or maybe movements in the air?
The mechanical coupling happens through vibrations, and the mainplate is the means to achieve it, since both oscillators are mounted on top of it.
I wonder if they're using any special materials on the mainplate to enhance the coupling... I'd expect something more rigid would be better? No doubt shape would matter as well... I guess I'm wondering how much this effect has been optimized with modern materials and techniques, or if it's currently at the stage of "here's something cool Breguet tried, let's see if it still works decently today"
No new materials are being used, the mainplate is either brass (found in early versions) or rose gold, but the results are good regardless.
Haha, looks like I would have to get a brass resonance to satisfy my optimization tendencies then! That's very bad news for my wallet though, I guess I'll have to stick with admiring my little CS for now...
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