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Calculation of time dependent mesh stiffness of helical planetary gear system using analytical approach

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Abstract

Time-dependent mesh stiffness is a most important reason of vibration and dynamic excitation in gear sets. In this research, analytical formulas of the helical gear set and the planetary gear system are combined to calculate the time-dependent mesh stiffness of the helical planetary gear system. For this purpose, at the first step, the analytical equations are derived for the spur gear pair. Then by dividing a helical tooth into the several independent thin spur tooth slices, the helical gear pair mesh stiffness is extracted. Finally, these equations are extended to the helical planetary gear system. The suggested analytical results and those which obtained by the finite element method (FEM) are compared and are in good agreement when the helix angle is less than 15 degrees. Also, the helical planetary gear system mesh stiffness in different cases such as fixed carrier, fixed sun gear and fixed ring gears is calculated. These results show that the value of mesh frequency ratio in each case scales the mesh stiffness shapes in the rotation angle direction. In other words, mesh frequency ratio parameter determines the number of meshing period in each rotation of planets.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, Isfahan, 81744-73441, Iran

    Mohsen Rezaei, Mehrdad Poursina, Shahram Hadian Jazi & Farhad Haji Aboutalebi

Authors
  1. Mohsen Rezaei
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  2. Mehrdad Poursina
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  3. Shahram Hadian Jazi
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  4. Farhad Haji Aboutalebi
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Corresponding author

Correspondence to Mehrdad Poursina.

Additional information

Recommended by Associate Editor Sungsoo Na

Mohsen Rezaei is a Ph.D. student of the Mechanical Engineering under supervision of Prof. M. Poursina since 2014, at the University of Isfahan, Isfahan, Iran. His research interests include the dynamics of gears, beam and plate theory and F.G.M. He received the B.Sc. and M.Sc. degrees in "Agricultural Machinery Engineering" from Shiraz University in 2010 and in "Mechanical Engineering" from Yasouj University in 2014, respectively.

M. Poursina is an Associate Professor of the Mechanical Engineering at the University of Isfahan, Isfahan, Iran. His research interests include the dynamics of gears, metal forming, machine design and optimization. He received the B.Sc., M.Sc. and Ph.D. degrees in mechanical engineering from Isfahan University of Technology, Isfahan, Iran in 1994, 1998 and 2003, respectively. During his Ph.D. he spent a sabbatical period at the Faculty of Engineering, University of Porto, Portugal.

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Rezaei, M., Poursina, M., Jazi, S.H. et al. Calculation of time dependent mesh stiffness of helical planetary gear system using analytical approach. J Mech Sci Technol 32, 3537–3545 (2018). https://doi.org/10.1007/s12206-018-0704-9

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  • DOI: https://doi.org/10.1007/s12206-018-0704-9

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