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TAG Heuer is the first to explore new avenues for regulating mechanical watches.
MIKROGIRDER
It’s 1747, ten years before Thomas Mudge adapts the lever escapement to portable watches. Jean le Rond d’Alembert, a famous French mathematician and encyclopaedist, published his theory on “vibrating strings”... What is that exactly? In mathematics, it was the first wave equation. It describes “the variation in time and space of an undulating quantity”, for example a length of string that starts vibrating. Or, to take another – well-known – example, this equation is used to measure the effects of the wave generated by a troop marching in time across a bridge. The bridge starts to vibrate rhythmically, triggered by a wave that can lead to its destruction. But what has this equation got to do with mechanical watchmaking?
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- Guy Semon
Although it found no practical application for a long time, d’Alembert’s equation found an important use in civil engineering. It paved the way for the development of “vibrating string extensometer” gauges, which can measure the deformations in concrete caused by variations in constraint in large buildings, towers, dams and nuclear power stations. It is also used to calculate the movements that could disturb the cables on a suspension bridge, the catenaries of a railway line, or, quite simply, the strings of a guitar. It only started being used in watchmaking in 2012, having been taken up by the rational intuition of Guy Semon, Head of Research and Development at TAG Heuer.
A SHORT STEP BACK
But to get to this stage, we need to take a step back.
It all started in 2003, when TAG Heuer bought the idea of the V4 “concept watch” from Jean-François Ruchonnet. But the development and production of this new type of watch, using transmission belts instead of the traditional gear trains, required know-how and specific technical skills that were beyond those of the world of watchmaking. Having decided to develop and sell this avant-garde product come what may, TAG Heuer called upon consultants from other areas, such as the automobile industry, aeronautics and avant-garde technologies. This was how Guy Semon, physicist, mathematician, engineer, university lecturer and former employee of the French National Defence Department, came into contact with the teams at TAG Heuer. This was in 2004. In 2007, TAG Heuer asked Guy Semon to join the company in order to set up a Research and Development department worthy of the name. Jean-Christophe Babin, at the time CEO of TAG Heuer, was pursuing a very innovative vision of what research and development should be for his brand, which, despite its classical watchmaking, had made a name for itself with technological advances in the field of precision and timekeeping performance.
THE INTRINSIC LIMITS OF THE SPRUNG BALANCE
Guy Semon started work using tools such as theory, maths and physics, that were unusual for traditional watchmakers.
He soon discovered that the traditional pairing of balance and spring, invented in 1675 by Christiaan Huygens and improved by Thomas Mudge a century later, had serious limits when you tried to increase its frequency in order to measure very short time intervals.
At BaselWorld in 2011, TAG Heuer presented its Mikrotimer Flying 1000, vibrating at 500Hz, or the staggering figure of 3.6 million vibrations/hour. At this frequency, the watch could measure and display times down to 1/1000th of a second!
To achieve this spectacular result, TAG Heuer continued its research into the dual chain technology which started the same year with the Heuer Carrera Mikrograph, which could display the 100th of a second thanks to two different regulating organs, oscillating 28,800 vibrations/hour, for the hours, minutes and seconds, and at 360,000 vibrations/hour, or 50Hz, for the chronograph display to 1/100th of a second. But at the frequency of 500Hz that the brand has now achieved, where the seconds hand makes ten full revolutions per second, we start to go beyond the boundaries of Huygensian watchmaking: the escapement no longer needs a balance because at this high speed the spring would have to be so stiff (specifically, only four coils, or 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 the barrel and the escape wheel gets out of sync, the amount of energy required per impulse is no longer sufficient. The result is an imbalance in dynamics and energy. For Guy Semon, this was the starting point for looking into a new technology for regulation.
D’ALEMBERT COMES BACK ON STAGE
In theory, the “perfect vibrating string” posited by d’Alembert, with infinite flexibility, constant tension, perfect elasticity and insensitive to gravity, transmits a wave uniformly along its entire length. The wave therefore has an isochronous oscillation.
In practice, the closest approximation to this theoretical perfect wave had to be found. The principle chosen for this seems simple and combines 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!
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- The MIKROGIRDER 5/10000th microblade regulator
But, as in any classical movement, the mechanical power is transmitted in a non-constant way to the escape wheel pinion. In order to compensate for this non-constant transmission of energy, the angle of escapement must be as low as possible. The escape wheel therefore has double the usual number of teeth, 40 instead of 20. Consequently, the traditional function of “rest” acts to limit the speed and prevent any racing out of control. The geometry of the point of contact between the lever and the escape wheel was also revised in order to maximise this compensation. For the inertia of transmission, a “system of decoupling the link between the escape pinion and escape wheel” was designed in the form a spring that is wound when the transmission is under load and at the moment of the drop restores the energy so that the “acceleration of the escape wheel reaches its maximum, independently of the transmission”. The kinetic energy propagates in the exciter, transforms into potential energy and is transmitted to the “vibrating beam of the coupler”. The latter transmits “exciting energy” that reaches the end of the “oscillating beam”, resulting in displacement according to the vibratory mode, which is that of the desired frequency. There is very little inertia and practically no amplitude (it vibrates very quickly, but the oscillations are very low): the system therefore consumes less energy than a sprung balance. Another benefit, therefore, of high frequencies, since the power reserve can be a lot higher.
A REGULATING ORGAN SPECIALLY ADAPTED FOR VERY SHORT TIME INTERVALS
Regulated in this way, the TAG Heuer Mikrogirder concept watch “vibrates” at the mind-boggling frequency of 7,200,000 vibrations/hour, or 1,000Hz, which is good for measuring 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.
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- The TAG HEUER MIKROGIRDER
What about reading these times? The fractions of 1/100th, 1/1000th and 1/2000th of a second are read off against a scale around the circumference of the dial and displayed by a central hand that makes 20 revolutions a second. A second scale, at 12 o’clock, is divided into fractions of three seconds, while a third scale, at 3 o’clock, displays the tenths of a second. The system is theoretically suitable for all frequencies, but below 50Hz it has a tendency to block. So this new type of regulating organ, while perfectly adapted for measuring very short times, is less adapted to the simple display of hours, minutes and seconds. It is therefore unlikely to supersede the good-old “Swiss” lever escapement.
PENDULUM
The year before, in 2010, TAG Heuer and Guy Semon’s team presented another entirely different regulating organ that dispensed with the traditional spring in favour of its magnetic equivalent: the Pendulum Concept Watch. Here, the escape wheel and lever are maintained. But it is the heart of the system, the sprung-balance, that is replaced by a magnetic stator and rotor. Even more radical than the “Girder”, this system moves away from traditional watchmaking towards the mysteries of physics, almost verging on quantum physics.
STATOR AND ROTOR TO THE FORE
The device that replaces the spring consists of four magnets. Two of these magnets, one positive and one negative and magnetised in only one direction, are arranged face-to-face on the circumference, held in place by a fixed soft-iron support that forms a kind of Faraday cage. 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. For this to work, the magnets had to have a special shape in order to “linearise” their force (because one of the problems with magnets is that their force decreases rapidly in inverse proportion to the square of the distance separating them) and to arrange them very carefully, so that they can be controlled in three dimensions to ensure that they provide sufficient linear torque to return the alternate oscillations of the balance.
On paper, the advantages of this system jump off the page: the magnetic fields are insensitive to gravity and shocks and thus to the two congenital weaknesses of the traditional balance spring. Add to this a simplicity of assembly that makes the watchmaker’s work a lot easier. But a serious problem remained nevertheless: magnets are very sensitive to temperature. So the problem was how to develop a magnet that was as insensitive as possible to the temperature differences that could affect its precision? In a way, the people at TAG Heuer were confronted with the same problem presented by the balance spring before the invention of Elinvar by Guillaume in the 1920s. But if this major challenge, as well as others regarding the energy density of magnets, their production, their physical dimensions, the linearity of magnetic torque as a function of amplitude, could be overcome, the theoretical Pendulum, with its 6Hz, its 43,200 vibrations/hour, no loss of amplitude and the possible modulation of its frequency without overloading its power supply, could offer genuine advantages for precision and performance.
ON THE FRINGES OF QUANTUM PHYSICS
Three years later, these problems seem to have been solved, using the theory of magnetism, spatial geometry and genetic algorithms...
It is difficult to go into the detail of this high-level research here, because the concepts used are so specialised. Suffice it to say, however, that the magnets used are made of a complex ferromagnetic alloy that comprises cobalt, samarium and gadolinium. The particularity of the latter element, one of the rare earth elements, is that it acts as a “variable for adjusting the magnetic field”. In other words, by correctly dosing the amount of gadolinium, you can compensate for variations in the magnetic field caused by temperature, with the alloy acting like a shield that absorbs heat differences.
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The “linearity of torque as a function of amplitude” is another obstacle overcome. If the magnetic field created by the magnets is and remains constant, the torque generated by the rotor will only depend on the amplitude. But the lines of the magnetic fields created do not remain solely inside the plane of the pendulum, since they reach the surrounding space as well. This “iron loss” acts like a kind of magnetic friction. Using modelling, the “geometry of the static magnets has to be adapted” so that the lines of magnetic force are perfectly aligned and “guided in the plane of the magnets”. Only in this way can a constant mechanical torque be obtained on the axis of the balance for a given amplitude. It was in the research for this geometry that the complex genetic algorithms were employed to obtain the linearity of torque by successive topological optimisations.
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- The TAG HEUER CARRERA MIKROPENDULUMS
- The TAG Heuer Carrera MikroPendulumS, with two magnetic Pendulums replacing the hairsprings, one for telling time and one for timekeeping. Composed of 454 working components, its watch chain turns at 12Hz and its chronograph chain turns at 50Hz (60 minutes power reserve). The chronograph tourbillon, the world’s fastest, controls the 1/100th of a second, beats 360,000 times an hour and rotates 12 times a minute. The case is forged from a fully biocompatible chrome and cobalt alloy, which is harder than the titanium alloy used in aviation and surgery. The case design, with its stopwatch-like placement of the crown at 12 o’clock, is based on the 2012 Aiguille d’Or winner, the TAG Heuer Carrera Mikrogirder, and the Carrera 50 Year Anniversary Jack Heuer edition. The two tourbillon Pendulums and their solid rose gold bridges (18-carat 5N) are visible through the fine-brushed anthracite dial. The hand applied “100” at 12 o’clock is also in solid rose gold. The chronograph minutes counter is at 12 o’clock, chronograph seconds at 3 and the chronograph power reserve at 9. The 1/100th of a second scale appears on the silver flange. The strap is hand-sewn anthracite grey alligator, very high-tech in style and soft to the touch.
The end result is that the Pendulum system achieves levels of performance that are comparable with those of a balance spring, yet which fall short of the COSC requirements, which express sensitivity to temperature as the daily rate variation measured by degree of temperature difference. Specifically, this is 0.6 seconds/day/ºC for the COSC, against 1 second/day/ºC for the Pendulum presented this year at BaselWorld. An excellent mechanical, mathematical and physical performance
Escapements
Girard-Perregaux – Buckling towards constant force
Omega – George Daniels’s legacy
Audemars Piguet – The best of both worlds
Urban Jürgensen – Innovation in the service of tradition
Source: Europa Star August - September 2013 Magazine Issue
