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MAPLESOFT
Maple is used by Ulysse Nardin to lengthen the running time of new watches Claude Bourgeois, an engineering consultant and former Centre Suisse d'Electronique et de Microtechnique (CSEM) researcher, used Maple to model and optimize barrel springs made of
Ulysse Nardin, a Swiss watch manufacturer, is a pioneer in the innovative use of new technologies and
materials in wristwatches. This company introduced the first silicon-diamond composite barrel spring in a
wristwatch and continues to produce sophisticated new watches based on cutting-edge designs. Maple, the symbolic and mathematical calculation software from Maplesoft, is a key tool in the research process at Ulysse Nardin.
The architecture of mechanical pocket watches and wristwatches has long been based on the same principle. A leaf spring, which is the barrel spring or main spring, is wound inside a barrel drum. The external part of the spring presses against the inside wall of the drum and is fastened rigidly or linked by an elastic part. The inner end of the spring is fastened to a barrel arbor. By keeping the drum fixed and rotating the barrel arbor, it is easy to understand that the spring is wound around the arbor and potential energy can be accumulated in the system. The covered drum inside, known as the barrel, is the main force that drives the watch.
Because the dimensions of the spring and the drum are limited by the small volume available in watches, the mechanical energy stored in the barrel is also limited. The power reserve of the watch, that is, the running time of the watch »at rest» without user interaction, depends on this stored energy. In most cases, the power reserve of a watch is about 48 hours.
If the density of energy storage (the stored energy to volume ratio) can be maximized, the power reserve of the watch is also increased. This is why Ulysse Nardin initiated the development of a barrel spring made of composite materials giving an elastic limit and impact resistance far superior to the best steels known.
The springs have a silicon core produced on monocrystalline silicon wafers. The surface of this silicon core is then coated with a layer of polycrystalline diamond. Compared with steel, silicon and diamond exhibit less fatigue. Moreover, a main spring created using this technique can be expected to have much greater stiffness, stored energy capacity, and resilience. For given dimensions, it is now thought possible to double the power reserve. This may be beneficial for small watches, especially ladies’ watches, in which the volume available for the barrel is limited.
Another advantage is obtained by using silicon deep etching technology, a photolithographic process which makes it possible to produce complex geometries. Research is under way at Ulysse Nardin to produce a barrel spring with a variable turn width that transmits constant torque. If the torque transmitted to the gear train is constant, the amplitude of the balance oscillation will also be constant. This eliminates the anisochronism related to balance amplitudes, which enables the running precision of the watch to be optimized. The watch designs require the production of several springs that are more than half a metre long on a silicon wafer that is limited to a diameter of 6 inches (15.4 cm). This limits the dimensions of the free spring (preform), which means that a preform that is compatible with the tiling of the springs on the wafer must be selected, while imposing a varying thickness along the spring to obtain constant torque. To meet this challenge, Ulysse Nardin called upon Claude Bourgeois, who developed a modelling and optimization tool based on Maple.
First applications of silicon in watchmaking
Silicon is a very hard material that does not wear easily. It has a low friction coefficient and low density, and higher precision can be achieved in the production of complex parts by silicon machining techniques than with steel. The first applications of silicon were fixed or moving non-deforming parts, such as bearings, escapement parts, pinions, and escape wheels.
The elasticity of silicon was then also put to use, at the heart of the watch, in the spiral spring associated with the balance. To compensate for the high intrinsic thermoelastic drift of silicon, which is incompatible with accurate timekeeping, Claude Bourgeois and a team at the CSEM recommended thermal oxidation of the surface to compensate for the drift. Today, Ulysse Nardin, in partnership with Sigatec, is using this technology to produce its own thermally compensated silicon spiral springs. Sigtec, a company based in Sion, Switzerland, provides the capability to manufacture silicon parts on an industrial scale.
These new applications required new modeling tools, which were still not widespread in traditional
watchmaking, to model, analyze, and optimize these new types of active structures. Maple was used to model and optimize the oxidized silicon sprung balance resonator. The developed model combined the thermal drift up to third order and the anisotropy of silicon. differential equations that characterized the springs at large displacements were integrated, while taking into account the deviation from the isochronism of the resonator at different balance amplitudes. The shape of the terminal curve of the spiral spring, which enabled the isochronism deviations to be controlled, was then optimized by a convergent iterative calculation, varying the appropriate geometrical parameters.
Maple makes it easy to identify the critical parameters related to the required function and the figures of merit of the system. It also helps to establish analytical macromodels, which are useful elements for analysis and for developing new concepts.
Ulysse Nardin Freak Caliber
The first watch to use the new barrel springs with silicon cores is the Ulysse Nardin Freak Caliber. It has a great advantage: its barrel is placed below the rest of the movement. This means that it occupies a large volume since almost the entire diameter of the watch can be allocated to it. As a result, the power reserve of this watch is more than seven days. Only one manual winding a week is necessary, by means of a grooved bezel under the watch. Another feature of this model is that the hour hand is fixed directly on the barrel drum, which is designed to rotate once every twelve hours. Also, this watch has a karrusel tourbillon, making it very precise.
The Manufacturing of silicon and diamond parts
Through its determination to innovate, the Ulysse Nardin factory today has highly sophisticated production
facilities that benefit from its technological advances. Sigatec was formed as a joint venture between Ulysse Nardin and another Sion-based company called Mimotec SA, a manufacturer of nickel micro-parts. Diamaze Microtechnology SA, based in Chaux-de-Fonds, Switzerland, produces thin or thick coats of polycrystalline diamond. This is the company that coats the silicon core with diamond to produce the diamond barrel springs. A hard spring with a soft heart is possible as a result.
Other Maple applications
While employed at the CSEM, Claude Bourgeois developed many other simulation applications with Maple. These applications involved anisotropic elasticity, piezoelectricity and electromagnetism, as well as gaseous and liquid microfluidics, in particular, during the development of high-performance resonators made of quartz, then of silicon activated by AlN, and many types of MEMS sensors and actuators.
materials in wristwatches. This company introduced the first silicon-diamond composite barrel spring in a
wristwatch and continues to produce sophisticated new watches based on cutting-edge designs. Maple, the symbolic and mathematical calculation software from Maplesoft, is a key tool in the research process at Ulysse Nardin.
The architecture of mechanical pocket watches and wristwatches has long been based on the same principle. A leaf spring, which is the barrel spring or main spring, is wound inside a barrel drum. The external part of the spring presses against the inside wall of the drum and is fastened rigidly or linked by an elastic part. The inner end of the spring is fastened to a barrel arbor. By keeping the drum fixed and rotating the barrel arbor, it is easy to understand that the spring is wound around the arbor and potential energy can be accumulated in the system. The covered drum inside, known as the barrel, is the main force that drives the watch.
Because the dimensions of the spring and the drum are limited by the small volume available in watches, the mechanical energy stored in the barrel is also limited. The power reserve of the watch, that is, the running time of the watch »at rest» without user interaction, depends on this stored energy. In most cases, the power reserve of a watch is about 48 hours.
If the density of energy storage (the stored energy to volume ratio) can be maximized, the power reserve of the watch is also increased. This is why Ulysse Nardin initiated the development of a barrel spring made of composite materials giving an elastic limit and impact resistance far superior to the best steels known.
The springs have a silicon core produced on monocrystalline silicon wafers. The surface of this silicon core is then coated with a layer of polycrystalline diamond. Compared with steel, silicon and diamond exhibit less fatigue. Moreover, a main spring created using this technique can be expected to have much greater stiffness, stored energy capacity, and resilience. For given dimensions, it is now thought possible to double the power reserve. This may be beneficial for small watches, especially ladies’ watches, in which the volume available for the barrel is limited.
Another advantage is obtained by using silicon deep etching technology, a photolithographic process which makes it possible to produce complex geometries. Research is under way at Ulysse Nardin to produce a barrel spring with a variable turn width that transmits constant torque. If the torque transmitted to the gear train is constant, the amplitude of the balance oscillation will also be constant. This eliminates the anisochronism related to balance amplitudes, which enables the running precision of the watch to be optimized. The watch designs require the production of several springs that are more than half a metre long on a silicon wafer that is limited to a diameter of 6 inches (15.4 cm). This limits the dimensions of the free spring (preform), which means that a preform that is compatible with the tiling of the springs on the wafer must be selected, while imposing a varying thickness along the spring to obtain constant torque. To meet this challenge, Ulysse Nardin called upon Claude Bourgeois, who developed a modelling and optimization tool based on Maple.
First applications of silicon in watchmaking
Silicon is a very hard material that does not wear easily. It has a low friction coefficient and low density, and higher precision can be achieved in the production of complex parts by silicon machining techniques than with steel. The first applications of silicon were fixed or moving non-deforming parts, such as bearings, escapement parts, pinions, and escape wheels.
The elasticity of silicon was then also put to use, at the heart of the watch, in the spiral spring associated with the balance. To compensate for the high intrinsic thermoelastic drift of silicon, which is incompatible with accurate timekeeping, Claude Bourgeois and a team at the CSEM recommended thermal oxidation of the surface to compensate for the drift. Today, Ulysse Nardin, in partnership with Sigatec, is using this technology to produce its own thermally compensated silicon spiral springs. Sigtec, a company based in Sion, Switzerland, provides the capability to manufacture silicon parts on an industrial scale.
These new applications required new modeling tools, which were still not widespread in traditional
watchmaking, to model, analyze, and optimize these new types of active structures. Maple was used to model and optimize the oxidized silicon sprung balance resonator. The developed model combined the thermal drift up to third order and the anisotropy of silicon. differential equations that characterized the springs at large displacements were integrated, while taking into account the deviation from the isochronism of the resonator at different balance amplitudes. The shape of the terminal curve of the spiral spring, which enabled the isochronism deviations to be controlled, was then optimized by a convergent iterative calculation, varying the appropriate geometrical parameters.
Maple makes it easy to identify the critical parameters related to the required function and the figures of merit of the system. It also helps to establish analytical macromodels, which are useful elements for analysis and for developing new concepts.
Ulysse Nardin Freak Caliber
The first watch to use the new barrel springs with silicon cores is the Ulysse Nardin Freak Caliber. It has a great advantage: its barrel is placed below the rest of the movement. This means that it occupies a large volume since almost the entire diameter of the watch can be allocated to it. As a result, the power reserve of this watch is more than seven days. Only one manual winding a week is necessary, by means of a grooved bezel under the watch. Another feature of this model is that the hour hand is fixed directly on the barrel drum, which is designed to rotate once every twelve hours. Also, this watch has a karrusel tourbillon, making it very precise.
The Manufacturing of silicon and diamond parts
Through its determination to innovate, the Ulysse Nardin factory today has highly sophisticated production
facilities that benefit from its technological advances. Sigatec was formed as a joint venture between Ulysse Nardin and another Sion-based company called Mimotec SA, a manufacturer of nickel micro-parts. Diamaze Microtechnology SA, based in Chaux-de-Fonds, Switzerland, produces thin or thick coats of polycrystalline diamond. This is the company that coats the silicon core with diamond to produce the diamond barrel springs. A hard spring with a soft heart is possible as a result.
Other Maple applications
While employed at the CSEM, Claude Bourgeois developed many other simulation applications with Maple. These applications involved anisotropic elasticity, piezoelectricity and electromagnetism, as well as gaseous and liquid microfluidics, in particular, during the development of high-performance resonators made of quartz, then of silicon activated by AlN, and many types of MEMS sensors and actuators.
