Contact Kinematics in the Roller Screw Mechanism

[+] Author and Article Information
Steven A. Velinsky

e-mail: savelinsky@ucdavis.edu
Department of Mechanical and Aerospace Engineering,
University of California,
Davis, One Shields Avenue,
Davis, CA 95616

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 17, 2012; final manuscript received February 25, 2013; published online April 23, 2013. Assoc. Editor: Kwun-Lon Ting.

J. Mech. Des 135(5), 051003 (Apr 23, 2013) (10 pages) Paper No: MD-12-1119; doi: 10.1115/1.4023964 History: Received February 17, 2012; Revised February 25, 2013

This paper investigates the nature of the contact between the load transferring surfaces in the roller screw mechanism, i.e., between the screw and roller threads and between the nut and roller threads. The analysis is applied to both planetary roller screws and recirculating roller screws. Prior work has neglected to take a fundamental approach toward understanding the kinematics of the contact between these components and, as a consequence, detailed analyses of aspects such as contact mechanics, friction, lubrication, and wear are not correctly carried out. Accordingly, in this paper, the principle of conjugate surfaces is used to establish contact at the screw/roller and nut/roller interfaces. The in-plane angles to the contact points are derived and it is shown that for the screw/roller interface, the contact point cannot lie on the bodies' line of centers, as has been the assumption in previous papers. Then, based on the curved profile of the roller thread, the radii of contact on the roller, screw, and nut bodies are also derived. Knowledge of the contact point locations is necessary in order to understand the interaction forces between the key components of the roller screw mechanism. The principal radii of curvature at the contact points and the angle between the principal axes are also derived. Lastly, a brief example is developed showing how the developed theory may be used to design a roller screw for improved stiffness and decreased contact stresses.

Copyright © 2013 by ASME
Topics: Screws , Rollers , Thread
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Strandgren, C. B., 1954, “Screw-Threaded Mechanism,” U.S. Patent No. 2,683, 379.
Andrade, A., Nicolosi, D., Lucchi, J., Biscegli, J., Arruda, A. C. F., Ohashi, Y., Mueller, J., Tayama, E., Glueck, J., and Nosé, Y., 2001, “Auxiliary Total Artificial Heart: A Compact Electromechanical Artificial Heart Working Simultaneously With the Natural Heart,” Artif.Organs, 23(9), pp. 876–880. [CrossRef]
Rosenburg, G., Pierce, W. S., Snyder, A. J., Weiss, W. J., and Lamson, T., 1991, “The Pennsylvania State University Roller Screw Electric Total Artificial Heart: 205 Days Survival in the Calf,” Proceedings of the 13th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Orlando, FL, IEEE, Piscataway, pp. 2087–2089.
Takatani, S., Takami, Y., Nakazawa, T., Jacobs, G., and Nose, Y., 1995, “Double Chamber Ventricular Assist Device With a Roller Screw Linear Actuator Driven by Left and Right Latissimus Dorsi Muscles,. ASAIO J., 41(3), pp. M475–M480. [CrossRef] [PubMed]
Gromov, V. V., Misckevich, A. V., Yudkin, E. N., Kochan, H., Coste, P., and Re, E., 1997, “The Mobile Penetrometer, a Mole for Sub-Surface Soil Investigation,” Proceedings of the 7th European Space Mechanisms and Tribology Symposium, Noordwijk, The Netherlands, pp. 151–156.
Wander, J., Byrd, V., and Parker, J., 1995, “Initial Disturbance Accommodating Control System Analysis for Prototype Electromechanical Space Shuttle Steering Actuator,” Proceedings of the American Control Conference, Seattle, WA, pp. 3961–3964.
Marks, S., Cortopassi, C., DeVries, J., Hoyer, E., Leinbach, R., Minamihara, Y., Padmore, H., Pipersky, P., Plate, D., Schlueter, R., and Young, A., 1997, “The Advanced Light Source Elliptically Polarizing Undulator,” Proceedings of the Particle Accelerator Conference, Vancouver, B.C., Canada, pp. 3221–3223.
Brandenburg, G., Brückl, S., Dormann, J., Heinzl, J., and Schmidt, C., 2000, “Comparative Investigation of Rotary and Linear Motor Feed Drivesystems for High Precision Machine Tools,” Proceedings of the 6th International Workshop on Advanced Motion Control, Nagoya, Japan, pp. 384–389.
Dupont, P. E., 1990, “Friction Modeling in Dynamic Robot Simulation,” Proceedings of the IEEE International Conference on Robotics and Automation, Cincinnati, OH, pp. 1370–1376.
Kjellqvist, P., Ostlund, S., and Carlsson, F., 1999, “Electromechanical Actuator for Active Suspension of a Rail Vehicle,” Ninth International Conference on Electrical Machines and Drives, Paper No. 468, pp. 263–267.
Kjellqvist, P., 2002, “Experimental Evaluation of an Electromechanical Suspension Actuator for Rail Vehicle Applications,” International Conference on Power Electronics, Machines and Drives, June 4–7, Paper No., 487, pp. 165–170.
Jones, M. H., and Velinsky, S. A., 2012, “Kinematics of Roller Migration in the Planetary Roller Screw Mechanism,” ASME J. Mech. Des.134(6), p. 061006. [CrossRef]
Velinsky, S. A., Lasky, T. A., and Chu, B., 2009, “Kinematics and Efficiency Analysis of the Planetary Roller Screw Mechanism,” ASME J. Mech. Des., 131, p. 011016. [CrossRef]
Sokolov, P. A., Ryakhovsky, O. A., Blinov, D. S., and Laptev, I. A., 2005, “Kinematics of Planetary Roller–Screw Mechanisms,” Vestn. MGTU, Mashinostr., 1, pp. 3–14 (in Russian).
Ryakhovsky, O. A., Blinov, D. S., and Sokolov, P. A., 2002, “Analysis of the Operation of a Planetary Roller–Screw Mechanism,” Vestn. MGTU, Mashinostr., 4, pp. 52–57 (in Russian).
Blinov, D. S., Ryakhovsky, O. A., and Sokolov, P. A., 1996, “Numerical Method of Determining the Point of Initial Thread Contact of Two Screws With Parallel Axes and Different Thread Inclinations,” Vestn. MGTU, Mashinostr., 3, pp. 93–97 (in Russian).
Sokolov, P. A., Sorokin, F. D., Ryakhovsky, O. A., Blinov, D. S., and Laptev, I. A., 2006, “Force Between Working Surfaces of the Thread Turns of a Planetary Roller–Screw Mechanism,” Vestn. MGTU, Mashinostr., 1, pp. 61–72 (in Russian).
Yang, J., Wei, Z., Zhu, J., and Wei, D., 2011, “Calculation of the Load Distribution of a Planetary Roller Screw for Static Rigidity,” J. Huazhong Univ. Sci. Technol., 39(4), pp. 1–4.
Kozyrev, V. V., 1987, “Comparison of the Stiffness of Ball and Roller Transmission of the Screw and Nut Type,” Sov. Eng. Res., 7(5) pp. 34–37.
Otsuka, J., Osawa, T., and Fukada, S., 1989, “A Study on the Planetary Roller Screw. Comparison of Static Stiffness and Vibration Characteristics With Those of the Ball Screw,” Bull. Jpn. Soc. Precis. Eng., 23(3), pp. 217–23.
Tselishchev, A. S., and Zharov., I. S., 2008, “Elastic Elements in Roller-Screw Mechanisms,” Russ. Eng. Res., 28(11), pp. 1040–1043. [CrossRef]
Otsuka, J., Fukada, S., and Osawa, T., 1987, “Fundamental Study of Planetary Screw-Structure and Coefficient of Friction,” Bull. Jpn. Soc. Precis. Eng., 21(1), pp. 43–48.
Jin, Q., Yang, J., and Sun, J., 1998, “Research on the Friction Mechanism of the Planetary Roller Screw,” J. Huazhong Univ. Sci. Technol., 26(6), pp. 82–83.
Sokolov, P. A., Blinov, D. S., Ryakhovskii, O. A., Ochkasov, E. E., and Drobizheva, A. Y., 2008, “Promising Rotation-Translation Converters,” Russ. Eng.Res., 28(10), pp. 949–956. [CrossRef]
Kreyszig, E., 1983, Advanced Engineering Mathematics, Wiley, New York.
Ohwovriole, M. S., and B.Roth, 1983, “A Theory of Parts Mating for Assembly Automation,” 4th Symposium on Theory and Practice of Robots and Manipulators, Zaborow, Poland, Polish Scientific, Warsaw, pp. 1–17.
Beck, J., RidaM., Farouki, T., and Hinds, J. K., “Surface Analysis Methods,” IEEE Comput. Graphics Appl., 6(12), pp. 18–36. [CrossRef]
Lenarčič, J., and Stanišić, M. M., 2010, Advances in Robot Kinematics: Motion in Man and Machine, Springer, Dordrecht, Springer.
Lemor, P. C., 1996, “The Roller Screw, an Efficient and Reliable Mechanical Component of Electro-Mechanical Actuators,” Proceedings of the 31st Intersociety Energy Conversion Engineering Conference (IECEC 96), pp. 215–220.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.


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Fig. 1

Exploded view of relevant roller screw components (www.rollvis.com)

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Fig. 2

Cross-sectional cut of contact between the screw (dark gray) and roller (dark gray)

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Fig. 3

In-plane contact between the screw and roller (exaggerated for clarity)

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Fig. 4

Frenet frame at the screw contact

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Fig. 5

Contact normal for the screw surface

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Fig. 6

In-plane contact between the nut and roller (exaggerated for clarity)

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Fig. 7

Cross section of the roller showing the roller profile

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Fig. 8

Slope of the profile and the contact angle

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Fig. 9

Complete in-plane contact diagram

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Fig. 10

Angle between the axes of the principal radii of curvature at the screw/roller interface

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Fig. 11

Principal radii of curvature versus contact angle

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Fig. 12

Contact pressure and Hertzian deflection versus contact angle

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Fig. 13

Minimum screw contact angle versus roller profile radius




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