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Complex networks from space-filling bearings.

J J Kranz1,2, N A M Araújo3,4, J S Andrade1,5

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This study explores two-dimensional space-filling bearings, revealing a hierarchical network structure. Analytic results show tunable scale-free properties in these disk packings, impacting their behavior.

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Area of Science:

  • Physics
  • Materials Science
  • Network Science

Background:

  • Two-dimensional space-filling bearings are critical components in mechanical systems, enabling rotation without slip.
  • Understanding the contact network topology is essential for predicting bearing performance and failure modes.

Purpose of the Study:

  • To analyze the contact network structure of the first family of two-dimensional space-filling bearings composed of four-disk loops.
  • To derive analytic expressions for key network properties and investigate their dependence on bearing parameters.

Main Methods:

  • Hierarchical construction of the contact network for four-disk loop bearings.
  • Derivation of analytic expressions for clustering coefficient and degree distribution.
  • Analysis of average shortest path length and percolation properties.

Main Results:

  • The contact network exhibits bipartite scale-free behavior.
  • The degree exponent is tunable and depends on specific bearing parameters.
  • Characterization of network properties like clustering, degree distribution, shortest path, and percolation.

Conclusions:

  • The hierarchical construction provides a framework for understanding complex bearing networks.
  • The identified scale-free properties offer insights into the robustness and behavior of these disk packings.
  • This work contributes to the fundamental understanding of granular materials and mechanical networks.