Frequency Domain Characteristics in Nonlinear Trimmer Dynamics #SWI2023

Philips Drachten is one of the Philips largest development and production centers in Europe. Here, we work together with more than 2000 people on Personal Health products, such as the newest shavers, Avent Mother & Childcare products, OneBlades, Ladyshaves and beard trimmers.

At Philips we use dynamical models to simulate and analyze the dynamic motion (i.e., vibrations) of the trimmer, in order to optimize performance. A simple but relevant model is one in which a dc-motor is coupled to a mass spring damper system (the cutting element). Individually, each system have linear dynamics. However, the interconnection between them is nonlinear (due to the eccentric motion), which makes the whole system nonlinear.

Mathematical Challenge

The motor current through the electric part consists of a dc-component and a sinusoidal component. Simulations have shown that there is an operating frequency at which the amplitude of the sinusoidal part of the motor current is minimal. The main challenge is to find an approach, based on the equations of motion, to identify such frequency characteristics in the nonlinear dynamics of the trimmer.

Goals

• Based on the equations of motion, identify frequency characteristics in nonlinear dynamics
• Identify and quantify possible implications and/or advantages in terms of power consumption

Possible exploitation

Better understanding of the trimmer dynamics helps Philips develop trimmers with improved performance. Performance is also not only related to shaving/trimming, but also eg. energy consumption.