The secret of the beard trimmer
The challenge
Philips is one of the world’s largest manufacturers of hair machinery, from styling tongs and razors to beard trimmers. Those trimmers display strange behavior: at the right speed, the electric motor suddenly hardly feels the counterforce of the blade that shoots back and forth. Four mathematicians manage to model this behavior in less than a week.
In just a week, a team of four mathematicians achieved the rare feat of delivering an exact solution to a puzzling behaviour found in Philips’ beard trimmers. Their work at the SWI (Study Group Mathematics with Industry) showcased the power of creative mathematics in unravelling complex phenomena.
The mathematics
Led by Danny Dirksz from Philips Personal Health, the team sought to comprehend the unexpected behaviour arising from the interaction between the electric motor and the blade’s spinning motion. Traditional linear techniques failed to provide answers, leading them to tap into the expertise of SWI.
Through non-dimensionalization and asymptotic solutions, the mathematicians deciphered the exact formula for the electric motor’s wobbling behaviour.
Eric Sandin Vidal, a PhD candidate from VU University in Amsterdam, praised the novel techniques employed, which simplified complex calculations and revealed crucial insights into the trimmer’s properties.
The result
The mathematical breakthrough will significantly enhance Philips’ understanding of their devices. With the analysis method applicable to other non-linear systems, this successful collaboration opens doors for solving mathematical challenges that can occur in various products. To me SWI showed the added value of different perspectives and backgrounds. A truly successful week!
“SWI showed that different perspectives and backgrounds have the potential to deliver great results. Truly successful!”
Danny Dirksz – Philips
Additional information
The popular proceedings for this challenge (in Dutch) provide a more detailed explanation. And the scientific proceedings (in English) describe the mathematical details for this and other challenges from SWI 2023.