Cross-correlation analysis among tooth profile and helix deviations

• Published in: Forschung im Ingenieurwesen 2023-09, Vol.87 (3), p.1009-1017
• Main Authors: Yamazaki, Daisuke, Iba, Daisuke, Low, Jing Chong, Moriwaki, Ichiro
• Format: Article
• Language: English
• Subjects: Correlation analysis; Correlation coefficients; Cross correlation; Deviation; Engineering; Gear teeth; Mathematical analysis; Mechanical Engineering; Originalarbeiten/Originals; Phase shift
• ISSN: 0015-7899; 1434-0860
• DOI: 10.1007/s10010-023-00696-1

The purpose of this study is to evaluate the overall relationship between tooth profile and tooth helix deviations, which cause noise and vibration during meshing, by representing the information obtained from the tooth surface of gears as networks. In the previous study, the method to visualize the relationship among tooth helix deviations as a network was proposed using the measurement data of gear surfaces. In that study, at first, the correlation coefficients that can express the phase difference between deviations were calculated. Secondly, setting each gear tooth as a node constructed the phase difference network. In the network, the magnitude of the correlation coefficient is the thickness of the edge connecting the nodes. However, the phase difference network could not evaluate the periodicity of the short wavelength components of the tooth surface shape included in the deviation data. Therefore, this study proposes a method to analyze the characteristics between deviations using a cross-correlation function that can detect the periodicity between two profiles. The presented study also investigates a preprocessing method suitable for extracting the periodic shapes left on the tooth surface. As a result of calculating the cross-correlation function between tooth surface deviations and displaying them as contour lines, it was found that the entire information on tooth surface deviations could be easily checked from a bird’s eye view.