Multifractal properties of ball milling dynamics

Controlling Nonlinear Dynamics of Milling Bodies in Mechanochemical Devices Driven by Pendular Forcing

Understanding the dynamics of milling bodies is key to optimize the mixing and the transfer of mechanical energy in mechanochemical processing. In this work, we present a comparative study of mechanochemical reactors driven by harmonic pendular forcing and characterized by different geometries of the lateral borders. We show that the shape of the reactor bases, either flat or curved, along with the size of the milling body and the elasticity of the collisions, represents relevant parameters that govern the dynamical regimes within the system and can control the transition from periodic to chaotic behaviors. We single out possible criteria to preserve target dynamical scenarios when the size of the milling body is changed, by adapting the relative extent of the spatial domain. This allows us to modulate the average energy of the collisions while maintaining the same dynamics and paves the way for a unifying framework to control the dynamical response in different experimental conditions. We finally explore the dynamical and energetic impact of an increasingly asymmetric mechanical force.

Roughness Scaling Extraction Accelerated by Dichotomy-Binary Strategy and Its Application to Milling Vibration Signal

Fractal algorithms for signal analysis are developed from geometric fractals and can be used to describe various complex signals in nature. A roughness scaling extraction algorithm with first-order flattening (RSE-f1) was shown in our previous studies to have a high accuracy, strong noise resistance, and a unique capacity to recognize the complexity of non-fractals that are common in signals. In this study, its disadvantage of a long calculation duration was addressed by using a dichotomy-binary strategy. The accelerated RSE-f1 algorithm (A-RSE-f1) retains the three above-mentioned advantages of the original algorithm according to theoretical analysis and artificial signal testing, while its calculation speed is significantly accelerated by 13 fold, which also makes it faster than the typical Higuchi algorithm. Afterwards, the vibration signals of the milling process are analyzed using the A-RSE-f1 algorithm, demonstrating the ability to distinguish different machining statuses (idle, stable, and chatter) effectively. The results of this study demonstrate that the RSE algorithm has been improved to meet the requirements of practical engineering with both a fast speed and a high performance.

Scale-free networks emerging from multifractal time series

Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterization of empirical data. Here we investigate the effects of the (multi)fractal properties of a signal, common in time series arising from chaotic dynamics or strange attractors, on the topology of a suitably projected network. Relying on the box-counting formalism, we map boxes into the nodes of a network and establish analytic expressions connecting the natural measure of a box with its degree in the graph representation. We single out the conditions yielding to the emergence of a scale-free topology and validate our findings with extensive numerical simulations. We finally present a numerical analysis on the properties of weighted and directed network projections.