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Research Papers: Design of Mechanisms and Robotic Systems

Static Load Distribution and Axial Stiffness in a Planetary Roller Screw Mechanism

[+] Author and Article Information
Folly Abevi

Research and Product Development Engineer,
SKF Transrol,
148 Rue Felix Esclangon,
Chambéry 73000, France
e-mail: folly.abevi@skf.com

Alain Daidie

Institut Clément ADER,
INSA (Institut National des Sciences Appliquées),
Université de Toulouse,
3 Rue Caroline Aigle,
Toulouse 31400, France
e-mail: alain.daidie@insa-toulouse.fr

Michel Chaussumier

Institut Clément ADER,
INSA (Institut National des Sciences Appliquées),
Université de Toulouse,
3 Rue Caroline Aigle,
Toulouse 31400, France
e-mail: michel.chaussumier@insa-toulouse.fr

Marc Sartor

Institut Clément ADER,
INSA (Institut National des Sciences Appliquées),
Université de Toulouse,
3 Rue Caroline Aigle,
Toulouse 31400, France
e-mail: marc.sartor@insa-toulouse.fr

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received May 11, 2015; final manuscript received September 27, 2015; published online November 16, 2015. Assoc. Editor: Ettore Pennestri.

J. Mech. Des 138(1), 012301 (Nov 16, 2015) (11 pages) Paper No: MD-15-1367; doi: 10.1115/1.4031859 History: Received May 11, 2015; Revised September 27, 2015

In this paper, an original approach is proposed to calculate the static load distribution and the axial stiffness of a planetary roller screw (PRS) mechanism. Assuming that the external loading is shared equally over an arbitrary number of rollers, only a sector of the system is represented to save on computing time. The approach consists in using a structure of bars, beams, and nonlinear springs to model the different components of the mechanism and their interactions. This nonlinear model describes the details of the mechanism and captures the shape of the nut as well as the bending deformation of the roller. All materials are assumed to operate in the elastic range. The load distribution and the axial stiffness are determined in three specific configurations of the system for both compressive and tensile loads. Further, the influence of the shape of the nut is studied in the case of the inverted PRS. The results obtained from this approach are also compared to those computed with a three-dimensional finite-element (3D FE) model. Finally, since the calculations appear to be very accurate, a parametric study is conducted to show the impact of the bending of the roller on the load distribution.

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References

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Abevi, F. K. , 2013, “ Development of a Support Tool for the Preliminary Design of a Planetary Roller Screw Under Complex Loadings,” Ph.D. thesis, Institut Clément ADER (ICA) of INSA de Toulouse, France, http://www.theses.fr/2013ISAT0038
Johnson, L. K. , 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.

Figures

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Fig. 1

(a) Inverted PRS and (b) standard PRS [15]

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Fig. 2

Studied inverted PRS with two flanges at its initial position

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Fig. 3

Discrete model of components of the inverted PRS

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Fig. 4

Discrete model of the PRS mechanism

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Fig. 5

BCs on the screw without the representation of the corresponding rigid elements

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Fig. 7

Meshing of the nut in CONFIG 1

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Fig. 8

Meshing of the nut in CONFIG 2

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Fig. 9

Meshing of the nut in CONFIG 3

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Fig. 10

Axial stiffness curves in CONFIGs 1, 2, and 3 with a bending flexible roller

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Fig. 11

Load distribution at the screw–roller side in a CC in CONFIGs 1, 2, and 3

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Fig. 12

Load distribution at the screw–roller side in a TC in CONFIGs 1, 2, and 3

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Fig. 13

Load distribution at the nut–roller side in a CC in CONFIGs 1, 2, and 3

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Fig. 14

Load distribution at the nut–roller side in a TC in CONFIGs 1, 2, and 3 for a bending flexible roller

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Fig. 15

Load distribution against the external load at screw–roller interface in CONFIGs 1, 2, and 3 for a nonflexible roller

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Fig. 16

Load distribution against the external load at screw–roller interface in CONFIGs 1, 2, and 3 for a bending flexible roller

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Fig. 17

Load distribution against the external load at nut–roller interface in CONFIGs 1, 2, and 3 for a nonflexible roller

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Fig. 18

Load distribution against the external load at nut–roller interface in CONFIGs 1, 2, and 3 for a bending flexible roller

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