Optimal synchronizability of bearings

TL;DR

This paper demonstrates that the synchronizability of mechanical bearings can be optimized by tuning the mass-radius relation of rotor disks, leading to improved energy distribution and system stability.

Contribution

It introduces a novel analogy between bearings and complex oscillator networks, identifying an optimal mass-radius exponent for maximum synchronizability.

Findings

Optimal exponent for mass-radius relation is approximately 1.

Synchronizability is maximized when contact number and inertia are balanced.

Energy dissipation is evenly distributed among rotors at optimal conditions.

Abstract

Bearings are mechanical dissipative systems that, when perturbed, relax toward a synchronized (bearing) state. Here we find that bearings can be perceived as physical realizations of complex networks of oscillators with asymmetrically weighted couplings. Accordingly, these networks can exhibit optimal synchronization properties through fine tuning of the local interaction strength as a function of node degree [Motter, Zhou, and Kurths, Phys. Rev. E 71, 016116 (2005)]. We show that, in analogy, the synchronizability of bearings can be maximized by counterbalancing the number of contacts and the inertia of their constituting rotor disks through the mass-radius relation, $m\sim r^{\alpha}$, with an optimal exponent $\alpha=\alpha_{\times}$ which converges to unity for a large number of rotors. Under this condition, and regardless of the presence of a long-tailed distribution of disk radii composing the mechanical system, the average participation per disk is maximized and the energy dissipation rate is homogeneously distributed among elementary rotors.