or the first time, watchmaking has reaped the benefits of an unintuitive, scientific, theoretical, multidisciplinary approach, calling upon mathematics, physics, materials science and the most advanced theoretical mechanics. The spectacular result means that we have now entered a new post-Huygens era. It’s a revolution.

When, on 25 February 1675 in Paris, Christiaan Huygens presented his revolutionary regulator, based on the principle of a balance spring connected to a balance wheel, he had no idea that his invention would dominate watchmaking for the next three centuries. As a scientist, he was uniquely qualified to establish the theoretical foundations for his regulator, which was more precise than any previous systems, but it was not until he teamed up with the royal clockmaker that he was able to put the theory into practice.

The 17th century was in many respects an abominable time to live, punctuated as it was by wars, famines and epidemics, but it was, paradoxically, a scientific golden age. Many technical and theoretical advances were made, including the “calculating clock”, the first embryonic computer, which was invented and designed in 1623 by the German pastor and academic Wilhelm Schickard. It was also in the 17th century that the foundations of modern mathematics were laid.

Nevertheless, back in 1675, while Huygens was able to observe the isochronism of his balance spring, he was unable to provide a theoretical explanation. That would not be possible until differential equations were developed, in the following century.

A largely intuitive development

The paradox of precision watchmaking, which arose out of Huygens’ observations, is that it developed in a largely intuitive manner. Over the ensuing centuries, Huygens’ principle was gradually improved upon and optimised, thanks mainly to advances in metallurgy.

The watchmaking community, tucked away in their mountain retreats, with their eyes turned either up to the stars or down to their minuscule cogs and pinions, rarely encountered any mechanical theorists, who in any case were busy at the time with the extraordinary machines that would power the industrial revolution.

However, its theoretical foundations were never really challenged. And that could be because... there were no theoretical foundations. For generations, watchmaking has remained at a remove from scientific and mathematical theory. Any calculations that watchmakers undertook would generally be focused on the movements of the cosmos, which are essential for telling the time – not on mechanics. Mechanics is an integral part of mathematics and theoretical physics, but it was not until the end of the 19th century that mechanical theories began to be developed. The watchmaking community, tucked away in their mountain retreats, with their eyes turned either up to the stars or down to their minuscule cogs and pinions, rarely encountered any mechanical theorists, who in any case were busy at the time with the extraordinary machines that would power the industrial revolution.

Huygens’ principle was constantly improved upon and gradually perfected by successive generations of watchmakers, and it continued to work flawlessly. There was no reason to give it a second thought. What is more, the trade secrets of watchmaking continued to be passed down from master to disciple, in the privacy of their workshops. And this meant that finishing and decoration came to be the “public face” of the watchmaker’s art.

It was not until the 1970s and ’80s that engineers were first admitted through the manufactory doors. Even then, they were only there to design and install increasingly sophisticated production lines, to adjust the CNC machines and to operate the CAD tools that began to appear in the technical offices. No engineer ever set foot in the workshops where the Huygensian complications were discreetly assembled. That is why, even today, the theoretical underpinnings of mechanical watchmaking have never been fully explored.

Eleven types of mechanical connection

Mechanism design theory, a branch of physics, has identified eleven types of connections that, in combination, can accomplish everything. In order to reach this conclusion, theoreticians had to understand and tame the complex interactions between tightness, weight, dimensions and materials.

When he first made landfall in the watch industry at TAG Heuer, Guy Sémon, a former aerospace consultant and lecturer in theoretical physics (see sidebar), began by looking at the watch from a purely mathematical point of view. First, he tried to take the Huygens regulator to its ultimate expression. In 2011 he unveiled the Heuer Carrera Mikrograph, capable of displaying time in 100ths of a second thanks to two separate escapements, vibrating at 28,800 vph (for the hour, minute and seconds display) and 360,000 vph (50 Hz) for the chronograph hundredths.

Later that same year he took the dual chain concept even further, and introduced the Mikrotimer Flying 1000, vibrating at 500 Hz, which represented the stratospheric frequency of 3.6 million vph. At this level, the watch was able to calculate and display time to one-thousandth of a second! But at this new frequency of 500 Hz, which requires the seconds hand to perform 10 complete rotations each second, Huygensian watchmaking starts to reach its limits. The escapement no longer needs a balance wheel because, at these high speeds, the spring would need to be so stiff (requiring only four coils – that’s ten times stiffer than a normal spring) that the balance is no longer needed for the return.

But with this balance-less movement, we reach physical limits: the lever starts to have trouble keeping up, the regulating organ suffocates, the transmission between barrel and escape wheel gets out of sync, and there is no longer sufficient energy to power each impulse. The result is an imbalance in dynamics and energy. For Guy Sémon, this impasse was the starting point for his explion of new mechanical regulation technologies.

A detour into magnetism and the “vibrating beam”

On the strength of his mastery of arcane scientific theory, he began exploring new, unorthodox (for watchmaking) connections between energy and how it is regulated. His first venture outside the Huygens galaxy was the Concept Watch Pendulum. The escape wheel and lever are still there, but the heart of the system, the sprung balance, is replaced by a magnetic stator and rotor. The device consists of four magnets. Two of these magnets (one positive and one negative – magnetised in only one direction) are arranged face-to-face around the circumference and held in place by a fixed soft-iron support that forms a kind of Faraday cage.

The escapement no longer needs a balance wheel because, at these high speeds, the spring would need to be so stiff (requiring only four coils – that’s ten times stiffer than a normal spring) that the balance is no longer needed for the return.

At the centre, on the same axis as the balance wheel and held in place by a traditional bridge, two magnets are arranged on a rotating mobile and thus alternate their positive and negative poles, which creates a magnetic field alternately on either side of the device. This system achieves levels of performance comparable with those of a balance spring, yet it falls short of COSC temperature sensitivity requirements. It was an interesting experiment, but difficult to implement on an industrial scale.

Concept Watch Pendulum

Guy Sémon and the multidisciplinary scientific teams with which he surrounded himself therefore turned their attention to a different mechanical avenue, one that had not yet been explored in watchmaking.

The principle from which they drew their inspiration, the theory of “vibrating strings” or beams, was discovered by French mathematician d’Alembert a few years before Huygens. Essentially, in place of the oscillation of a traditional concentric balance spring, this principle involves inducing vibration in a thin blade at very high frequency. In theory, the “perfect vibrating string” posited by d’Alembert, with infinite flexibility, constant tension, perfect elasticity and insensitivity to gravity, transmits a wave uniformly along its entire length. The wave therefore has an isochronous oscillation.

It’s an impressive exercise, but given that this “beam” can only oscillate at very high frequencies, its industrial and commercial applications are limited.

The challenge was to find the closest practical approximation to this theoretical perfect wave. The principle settled upon by Guy Sémon and his team was conceptually simple, combining three “vibrating beams”. An exciter beam attached to the lever and an oscillator consisting of a thin “beam” are united by a “coupler” that is itself also a “beam”. By exciting the oscillator so that it gets as close as possible to the “perfect wave” of the theory, it begins to vibrate at perfectly defined frequencies. It can be adjusted using an eccentric that lengthens or shortens the vibrating beam, a little like tuning a guitar. This new type of “non-Huygensian” oscillator is therefore linear – like a string.

There is very little inertia and practically no amplitude (it vibrates very quickly, but the oscillations are very low), which means that the system consumes less energy than a sprung balance – another benefit of high frequencies, since the power reserve can be a lot higher. Regulated in this way, the TAG Heuer Mikrogirder concept watch “vibrates” at the mind-boggling frequency of 7,200,000 vph, or 1,000Hz, which gives it the ability to measure 1/2000th of a second (TAG Heuer prefers to talk of 5/10,000ths). Thanks to the dual escapement system, the “normal” Huygensian chain for the time indications and the “vibratory” chain for the chronograph at 1/2000th do not affect each other at all.

It’s an impressive exercise, but given that this “beam” can only oscillate at very high frequencies, its industrial and commercial applications are limited. (To find out more, read our article from 2013, “TAG Heuer: Waves and magnetism in the service of regulation”, available on europastar.com)

TAG Heuer Mikrogirder

In search of a new “universal” regulator

Guy Sémon was appointed CEO of TAG Heuer at the end of 2014. He decided to renew his quest for a new type of “universal” regulator, like Huygens’ principle but far more precise. He had been thinking about it for some time, but in order to succeed, he had to bring several different universes together: the field of compliant mechanisms, which had emerged in the 1990s, along with theoretical physics and materials science.

This new type of oscillator requires a material that is insensitive to both magnetism and temperature, while at the same time being highly flexible.

The new theory of compliant mechanisms is based on new premises, and creates new connections based not on the interaction between separate components, but on the deformation of their materials. This concept of compliance is particularly relevant to robotics, where it is used to perform tasks that require subtle applications of strength, acting on “stiffness” and transforming into “flexibility”. This includes, for example, tasks such as grasping fragile or highly deformable objects, assembling tightly fitting components, or deburring. In the case of watches, this new theory provides a means of replacing an element made up of several fixed or mobile parts – an oscillator, for example – with a one-piece “compliant” structure.

Theoretical physics comes to the rescue with the theoretical underpinnings of this new kind of oscillator, called a “parametric oscillator”, which is used in physical optics, and for resonators in laser instruments. As Guy Sémon readily admits, this theoretical field is “extremely modern and very complex.” The third field of exploration is materials science.

This new type of oscillator requires a material that is insensitive to both magnetism and temperature, while at the same time being highly flexible. These requirements rule out all known metals. After drawing a blank at Delft University in the Netherlands, which is in the vanguard of this new mechanical theory, Guy Sémon expanded his search to the University of Arizona at Albuquerque. No luck. He then went to the University of Utah, which takes a keen interest in nanotechnology. There, Guy Sémon says he “lucked out”, and found a nano-structured material that was highly flexible. This material would enable him to create balance springs out of carbon nanotubes, which would be used in the El Primero 21 unveiled by Zenith in Basel this year (see Europa Star Chapter 3/17), but would not make it to the Defy Lab.

This experience with carbon nanotubes indirectly contributed to Guy Sémon’s development of the new oscillator. By combining the first two ingredients – theoretical physics and its “parametric” oscillators, with mechanical compliance theory – to optimise the shape of the oscillator, and by using silicon, which can be chemically etched (as we have seen with microprocessors for years), Guy Sémon and his team could move on to defining and making their oscillator.

In physics, an oscillator is a flexible beam with a given stiffness. In order to produce an oscillation, a mass is introduced. In order to achieve linear oscillation, the various parameters have to be filtered. The final product is a single monocrystalline silicon component measuring 0.5 mm thick (compared with around 5 mm for a standard regulator), in place of the 31 or so parts of a Huygens regulator, as shown in the diagram below.

The energy supply for this oscillator is a fairly classic barrel and gear train. But, once the escape wheel has supplied energy to the oscillator, we leave the traditional watchmaking chain behind. The escape wheel comes into contact with two small teeth (see diagram) which set the monobloc oscillator and its components in motion.

The oscillator starts to beat – or breathe – with a very small amplitude of +/- 6° (compared with around 300°) at an extraordinary frequency of 15 Hz, three times greater than that of the El Primero. But even with this high frequency, the power reserve is around 60 hours, 10% more than the El Primero. (Guy Sémon has no intention of leaving matters there, and is targeting power reserves of 100 hours, even as much as 150 hours.)

Le mouvement de la Defy Lab

Multiple benefits

The advantages of this revolutionary oscillator are manifold. There is no need for assembly or adjustment. No more contact and friction means no need for lubrication. Not only is energy consumption reduced, the device is largely impervious to incidental energy variations and changes of position. Not only is it extraordinarily precise, varying by around 0.3 seconds per day (the COSC standard is -4 to +6 seconds per day, or a total maximum of 10 seconds per day), but it also maintains the same degree of precision for 95% of its power reserve.

Insensitive to gravity, magnetism and temperature (thanks to a layer of silicon oxide), this double-patented oscillator is also triple-certified: for chronometry by the Besançon Observatory; for thermal resistance by ISO-3159, which it comfortably exceeds; and for magnetism by ISO-764, which it exceeds by 18 times, given that it can withstand 1,100 Gauss.

Zenith was chosen for the public debut of the “Sémon oscillator” in a watch named the Zenith Defy Lab – “Defy” was the name of a case from the 1960s, which has been completely revamped for the occasion. Beyond its debut appearance, the oscillator is destined to equip the majority of watches produced by LVMH or, as a minimum, the more “horological” brands in the group – Hublot, TAG Heuer and Zenith. The operation resembles Omega’s approach to the co-axial escapement developed by George Daniels. But, strategically, this operation is even more important for LVMH, because it will help the group to attain even greater autonomy. Combined with its self-sufficiency in balance spring development thanks to carbon nanotubes (see sidebar), it will ensure the group is insulated from any strategic dependency. Guy Sémon and his scientific teams have now been promoted to head up a major research centre. But that’s a different story (one that you will be able to read very soon.)

Photograph: Fabien Scotti | Arcade Europa Star