Elasto-dynamic Modeling and Modal Analysis of Spider Reducer with Small Tooth Number Difference

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Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (12) : 169-175.

ZHANG Jun，GUO Fan，XIE Sheng-long

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Abstract

In order to solve the problems of teeth breakage and premature fatigue of planetary bearings in spider reducers, this paper proposes a methodology of dynamic modeling for spider reducers with which its dynamic characteristics can be analyzed. With the substructure synthesis technique, a lumped parameter elasto-dynamic model of the spider reducer is established. The transmission system is divided into four subsystems as the input shaft subsystem, the output shaft subsystem, the spider shaft subsystem and translational spider gear subsystem. The differential motion equations of four subsystems are derived by using the Newtonian method. The compatibility conditions of the reducer are derived after considering deflections of bearings, gear pairs, index and eccentric errors of eccentric sleeves. By combining the compatibility conditions with subsystem motion equations, the governing motion equations of the reducer are formulated. With the eigenvalue decomposition, the modal properties of the transmission are analyzed and the lower orders of natural frequencies and corresponding vibration modes are classified. The results show that the lower orders of natural frequencies are far above the rated input rotation frequency of the reducer, thus is not possible to cause structural resonances. Meanwhile, the corresponding vibration modes demonstrate a complicated compound vibration modes of four subsystems. To verify the correctness of theoretical analysis, an impact modal test is carried out to. The comparison of lower orders of natural frequencies reveals a good match between theoretical and experimental results. From this point of view, it can be concluded that the proposed elastodynamic model possesses satisfactory accuracy, hence can be used to predict the steady-state dynamic responses of the system. The present research provides a solid fundament for further dynamic design and structural optimization of the spider reducer.

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Small tooth number difference / Spider reducer / Elasto-dynamics / Deformation compatibility condition / Modal analysis

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ZHANG Jun，GUO Fan，XIE Sheng-long. Elasto-dynamic Modeling and Modal Analysis of Spider Reducer with Small Tooth Number Difference[J]. Journal of Vibration and Shock, 2015, 34(12): 169-175

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