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<p>Machine tool drives require highly specialized reducers with a&#xa0;significant stiffness especially in the case of the positioning of axis. Several types of stiffness have been highlighted in order to define reducer performance, including torsional stiffness which represents the stiffness of the reducer when a&#xa0;torque is applied to the output and the input is fixed. Measuring and predicting the torsional stiffness are complex tasks.</p><p>The aim of this work is to develop a&#xa0;method that computes the torsional stiffness of a&#xa0;planetary gear train reducer using a&#xa0;numerical and semi analytical approach. All the components that main have a&#xa0;contribution to the torsional stiffness have been identified. For each of them, a&#xa0;special method has been set up to compute its contribution according to its shape and solicitations. The contributions of each part is represented by a&#xa0;lumped parameter stiffness. The global reducer stiffness is computed by adding all the individual stiffnesses in series or in parallel, depending on their position in the reducer.</p><p>Long parts such as shafts are modelled using beam theory. For all gear meshes (sun/planets and planets/ring), the gear meshing stiffness is computed using a&#xa0;thin-slices approach. The bearing are modelled using a&#xa0;combination of the Harris and the Johnson models. The planets are studied using an approach based on continuum model. The model focuses on capturing the most flexible parts of the system. Additionally, the influence of the ratio and the optimisation of components like bearings are also investigated.</p>

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Modelling and computation of the torsional stiffness of a planetary gear train

  • 期刊论文

  • 发表日期：

    2025年8月28日

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  • C. Chevrel-Fraux,
  • P. Casanova,
  • M. Royet

摘要

Machine tool drives require highly specialized reducers with a significant stiffness especially in the case of the positioning of axis. Several types of stiffness have been highlighted in order to define reducer performance, including torsional stiffness which represents the stiffness of the reducer when a torque is applied to the output and the input is fixed. Measuring and predicting the torsional stiffness are complex tasks.

The aim of this work is to develop a method that computes the torsional stiffness of a planetary gear train reducer using a numerical and semi analytical approach. All the components that main have a contribution to the torsional stiffness have been identified. For each of them, a special method has been set up to compute its contribution according to its shape and solicitations. The contributions of each part is represented by a lumped parameter stiffness. The global reducer stiffness is computed by adding all the individual stiffnesses in series or in parallel, depending on their position in the reducer.

Long parts such as shafts are modelled using beam theory. For all gear meshes (sun/planets and planets/ring), the gear meshing stiffness is computed using a thin-slices approach. The bearing are modelled using a combination of the Harris and the Johnson models. The planets are studied using an approach based on continuum model. The model focuses on capturing the most flexible parts of the system. Additionally, the influence of the ratio and the optimisation of components like bearings are also investigated.