Eigenvalue Analysys of Graph Laplacian Representing Helix Deviation Network

EasyChair Preprint no. 13365

Abstract

The purpose of this study is to evaluate the relationship between tooth profile and tooth trace deviation, which has been impossible in conventional gear accuracy evaluation, by expressing gear profile deviation as a network. In addition, the effect of mounting errors in gear manufacturing on the phase difference network has not been studied in detail. In this study, a graph Laplacian was created from the adjacency matrix of the network consisting of tooth trace deviation curves, and eigenvalue analysis was performed to investigate the effect of mounting error on the tooth trace deviation network. By normalizing the graph Laplacian matrix of the tooth profile deviation curve of the gear created by the hobbing simulation and replacing it with a mechanical vibration system consisting of a spring and a mass by performing eigenvalue analysis, the intrinsic characteristics of the tooth profile deviation network of the hobbed gear could be interpreted more easily.

Keyphrases: adjacency matrix, eigenvalue analysis, Graph Laplacian, Helix deviation, Installation error, network theory

@Booklet{EasyChair:13365,
  author = {Yuichiro Seo and Daisuke Iba and Daisuke Yamazaki and Jing Chong Low and Kunitoshi Kawano},
  title = {Eigenvalue Analysys of Graph Laplacian Representing Helix Deviation Network},
  howpublished = {EasyChair Preprint no. 13365},

  year = {EasyChair, 2024}}