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Analyzing a Timeless Tradition Found in Ultra-Luxury Watches

Engineers at HEPIA, HES-SO Geneva use the COMSOL Multiphysics^® software to model and simulate the acoustics of a minute repeater, a rare and sophisticated mechanism in watchmaking. With the software, the engineering team use the boundary element method to carry out optimization calculations based on surrogate models.

By Mackenzie McCarty
August 2026

Some luxury watches feature a minute repeater — a complex mechanical function in which tiny hammers strike tiny gongs to produce distinct musical chimes signifying the hours, quarter-hours, and minutes of the day. Activated on demand by a button or lever, minute repeaters were originally designed to tell time in the dark. Today, they are considered pieces of art, worn to represent status, craftsmanship, and a link to the past.

Building these intricate mechanisms requires significant skill and extreme precision to achieve just the right chime tones. Hundreds of small components are involved, highlighting the importance of an optimized design. Engineers at the Institute of Technology (inTECH) at the School of Engineering, Architecture and Landscape (HEPIA) in Geneva, part of the HES-SO University of Applied Sciences and Arts Western Switzerland, used the COMSOL Multiphysics^® software and a simplified 2D model to simulate the acoustic performance of a minute repeater.

We spoke with Roland Rozsnyo, a researcher and lecturer on mathematics at HEPIA, about his use of COMSOL Multiphysics^® in the horology industry and specifically with the minute repeater. He discussed how the software can be used to optimize the hammer's impact location on the watch's gong, or timbre, to enhance both the radiated acoustic intensity and the spectral content of the sound while also addressing the computational efficiency of the simulations performed. The acoustic signature is a key quality attribute of these luxury watches, and optimizing its sound production process is critical for user satisfaction and product differentiation. Numerical modeling was used extensively due to the complexity of acoustic propagation in small mechanical structures and the need for high-fidelity simulations.

What is the minute repeater, and what role does it play in modern watchmaking?

"The minute repeater remains one of the most prestigious and rare features in watchmaking. It is mainly found in high-end and ultra-luxury watches produced in very limited quantities (Figure 1). Although it is no longer a practical necessity in modern life, it retains a very strong symbolic value, representing extreme mechanical mastery and centuries of horological tradition. Customers are still attracted to minute repeaters for their emotional, artistic, and patrimonial value. The sound itself, its musicality, and the unique acoustic signature of each watch make the minute repeater a true object of art rather than a simple timekeeping function.

The minute repeater is programmed to chime the time on command. Watchmakers wish to have a very nice sound, and they wish to understand what the key parameters are to have this nice sound for a given frequency. The principle of a minute repeater watch is that you have a gong, and this gong is struck by a hammer, creating a vibration that propagates to the glass or to a vibrating membrane, and this radiates the sound into the air."

How do you use COMSOL Multiphysics^® to optimize the acoustic performance of the minute repeater?

"Initially, a theoretical comparison between the finite element method (FEM) and the boundary element method (BEM) is conducted in COMSOL Multiphysics^®. FEM requires meshing both the solid and surrounding air volume, resulting in a high computational burden. In comparison, BEM only requires meshing the boundaries, significantly reducing memory and time requirements in acoustics, especially in unbounded domains. The study revealed that BEM provides similar acoustic results to FEM but substantially reduced computation time and resources (Figure 3).

The COMSOL Multiphysics^® simulation used a simplified 2D model of the minute repeater mechanism in order to optimize its acoustic performance (Figure 2). The hammer–gong interaction is modeled with multibody dynamics, simulating contact, spring, and damping effects to generate structural vibrations.

BEM is used to compute the radiated sound field in the frequency domain using the acceleration at the structural boundaries. A surrogate model based on deep neural networks (DNNs) trained on BEM data was used to approximate the acoustic response with reduced computational cost. The efficient global optimization (EGO) algorithm was used to enable fast optimization iterations. The simulations determine which hammer impact positions optimize acoustic intensity and tonal quality while minimizing a defined cost function. This also demonstrates a significant reduction in computation time while providing a framework for advanced horological acoustic design.

To properly capture high audible frequencies in a one-meter air volume around the watch using FEM, extremely fine meshes are required (typically at least five elements per wavelength), which leads to very large models in terms of memory and computation time. With BEM, only the watch geometry is meshed, while the air domain is handled implicitly through the integral formulation. Although the system matrices are dense, they remain much smaller than FEM volumetric matrices. This results in significant memory savings and faster overall computation, especially in 3D and at high frequencies.

The BEM results allow us to analyze acoustic radiation, sound intensity, directivity, and the influence of case geometry with a very good balance between physical accuracy and numerical efficiency."

Do you combine modeling with experimental testing?

"Yes, modeling is systematically combined with experimental testing. At HEPIA, our applied acoustics group has full instrumentation to characterize watch acoustics, including an anechoic chamber (Figure 4) and dedicated acoustic and vibratory measurement systems. We routinely compare simulation results with experimental measurements. This allows us not only to validate the numerical models but also to improve them by better identifying certain physical parameters that are difficult to estimate purely theoretically. This hybrid approach ensures that our simulations remain reliable and industrially relevant."

Do you think there's room for modeling and simulation to expand and evolve in the watchmaking industry?

"Yes, of course. I would say the watch industry is only at the beginning of using simulation. They've used a lot of mechanical simulations, but now they are using more and more multiphysics simulations. With features like optimization and now surrogate modeling, this is very new. We've shown that the use of surrogate modeling combined with multiphysics simulation led to an optimization process that was approximately seven times faster than a classical approach based solely on direct numerical simulations.

More generally, this result illustrates the substantial computational gains that can be achieved with this methodology. While the exact acceleration factor depends on the problem, model complexity, and parameter space, surrogate-based approaches consistently provide significant reductions in computation time, making large parametric studies and optimization workflows feasible within industrial time constraints while preserving good physical accuracy. We have many parameters to study, and surrogate modeling really has reduced the computational costs in terms of time. We try to find all the possibilities to reduce the time, and COMSOL Multiphysics^® now offers the tools to do that."

What other aspects of COMSOL Multiphysics^® do you use in horology?

"We use computational fluid dynamics to study lubrication and oil propagation, as well as the aerodynamic friction of a balance spring. We also have magnetic simulation to study the parts of the watch that are made of steel and the magnetic perturbation. We also use something called a drop test to test if the watch is waterproof. This test sets a watch into 40°C water under pressure and then removes the watch and puts a small drop of 5°C water on the glass. This causes a thermal shock, which makes steam appear on the glass. If the steam disappears after one minute, it means the watch is waterproof. If not, it's not waterproof. However, in new watches, they use specific coatings, which means thermal conductivity and glass thickness are not always the same, so the standard test no longer gives the right results. They wish to use simulation to understand how to do that, so we modeled it.

It's a multiphysics simulation with three coupled physics: a laminar flow coupled to heat transfer with phase change and moisture transport. This is all at a very small scale too, which adds to the challenges of any experimental testing. There are sensors that are able to check the temperature behavior of the watch while cooling in the air. We check that the simulation is correct and was validated."

How do you use simulation apps in your work?

"We developed simulation apps in projects for companies we collaborate with. The most recent collaboration was with Kugler Bimetal, a metallurgical company that is making bimetallic parts. For this process, we have a part coming from an oven at 1100^°. It should be cooled with pulsed air, and the cooling process should be completely controlled because if the cooling is too fast or too slow, it will not give the good material properties in the final part.

People who are working on that process in the factory are not specialized in simulation. So, as part of a three-year project, we developed an app that is able to calculate the cooling very simply (Figure 5). It is designed for industrial operators. Our idea is to spread simulation to people who are not specialists. The operators can just check the results and check that what is happening is correct and change parameters quickly. It allows them to quickly explore the influence of manufacturing parameters such as geometry, materials, and thermal conditions on the mechanical and thermal behavior of bimetallic parts. They can understand, 'If I set this parameter, it is better.' They can do it directly in the factory. We set the key parameters, such as the oven temperature, which can be modified in the app as an initial condition, and it will give a different cooling. People can change that very easily. It is not possible to have a computer in the factory, so they use tablets or mobile phones.

The results show a significant reduction in physical trials, better understanding of the process, and improved reproducibility of the manufactured parts. The app acts as a true decision-support tool integrated into the production workflow."

Acknowledgements

Roland Rozsnyo would like to gratefully acknowledge the following people for their assistance in the research described in this Q&A, including Romain Boulandet, an associate professor at HEPIA, HES-SO Geneva, specialized in numerical and experimental acoustics; Marc Chambordon, a research assistant at HEPIA, HES-SO Geneva (MSc in microtechnology); Víctor Sánchez Mejía, a research assistant at HEPIA, HES-SO Geneva (MSc in mechanical engineering), and Gaétan Simonnot, a mechanical engineer and research assistant at HEPIA, HES-SO Geneva. In addition, Rozsnyo would also like to acknowledge Alexandre Masserey, a scientific collaborator at HEPIA (PhD in applied mathematics), for developing the simulation app for Kugler Bimetal.