Modeling and solving for transverse vibration of gear with variational thickness
来源期刊：中南大学学报(英文版)2013年第8期
论文作者：QIN Hui-bin(秦慧斌) Lü Ming(吕明) SHE Yin-zhu(佘银柱) WANG Shi-ying(王时英) LI Xiang-peng(李向鹏)
文章页码：2124 - 2133
Key words：gear with variational thickness; Mindlin moderately plate theory; transverse and flexural vibration model; resonant frequencies of vibration
Abstract: A analyzed model of gear with wheel hub, web and rim was derived from the Mindlin moderate plate theory. The gear was divided into three annular segments along the locations of the step variations. Traverse displacement, rotation angle, shear force and flexural moment were equal to ensure the continuity along the interface of the wheel hub, web and rim segments. The governing differential equations for harmonic vibration of annular segments were derived to solve the gear vibration problem. The influence of hole to diameter ratios, segment thickness ratios, segment location ratios, Poisson ratio on the vibration behavior of stepped circular Mindlin disk were calculated, tabletted and plotted. Comparisons were made with the frequencies arising from the presented method, finite elements method, and structure modal experiment. The result correlation among these three ways is very good. The largest error for all frequencies is 5.46%, and less than 5% for most frequencies.
QIN Hui-bin(秦慧斌)1, 2, Lü Ming(吕明)1, SHE Yin-zhu(佘银柱)1, WANG Shi-ying(王时英)1, LI Xiang-peng(李向鹏)1
(1. College of Mechanical Engineering, Taiyuan University of Technology, Taiyuan 030024, China;
2. School of Mechanical Engineering & Automation, North University of China, Taiyuan 030051, China)
Abstract:A analyzed model of gear with wheel hub, web and rim was derived from the Mindlin moderate plate theory. The gear was divided into three annular segments along the locations of the step variations. Traverse displacement, rotation angle, shear force and flexural moment were equal to ensure the continuity along the interface of the wheel hub, web and rim segments. The governing differential equations for harmonic vibration of annular segments were derived to solve the gear vibration problem. The influence of hole to diameter ratios, segment thickness ratios, segment location ratios, Poisson ratio on the vibration behavior of stepped circular Mindlin disk were calculated, tabletted and plotted. Comparisons were made with the frequencies arising from the presented method, finite elements method, and structure modal experiment. The result correlation among these three ways is very good. The largest error for all frequencies is 5.46%, and less than 5% for most frequencies.
Key words:gear with variational thickness; Mindlin moderately plate theory; transverse and flexural vibration model; resonant frequencies of vibration
