Models of transverse vibration of gear based on mindlin’s theory

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Journal of Vibration and Shock ›› 2011, Vol. 30 ›› Issue (12) : 230-234.

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Models of transverse vibration of gear based on mindlin’s theory

LI Xiang-peng; ZHANG Chun-hui; WANG Shi-ying

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Abstract

Gear was simplified to three medium thick annular plates with the outer diameters of reference circle, addendum circle and dedendum circle respectively，according to the structural characteristics of a cylindrical gear with a hole in the center and its ratio of the thickness to radius beyond the scope of the classical thin plate theory. The frequency equations for transverse vibration of the medium thick annular plate were derived with the free boundary conditions based on Mindlin’s theory and solved computationally with the help of MATLAB. The solutions are in best agreement with those from the finite element method and also with the experimental results only when the diameter of gear equals to one of its reference circle. The conclusion has certain theoretical significance to guide to design the vibration system of ultrasonic gear honing.

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mindlin’s theory / gear / medium thick annular plate / transverse vibration

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LI Xiang-peng;ZHANG Chun-hui;WANG Shi-ying. Models of transverse vibration of gear based on mindlin’s theory[J]. Journal of Vibration and Shock, 2011, 30(12): 230-234