This paper develops the dynamic equations of motion for the planetary roller screw mechanism (PRSM) accounting for the screw, rollers, and nut bodies. First, the linear and angular velocities and accelerations of the components are derived. Then, their angular momentums are presented. Next, the slip velocities at the contacts are derived in order to determine the direction of the forces of friction. The equations of motion are derived through the use of Lagrange's Method with viscous friction. The steady-state angular velocities and screw/roller slip velocities are also derived. An example demonstrates the magnitude of the slip velocity of the PRSM as a function of both the screw lead and the screw and nut contact angles. By allowing full dynamic simulation, the developed analysis can be used for much improved PRSM system design.
Dynamics of the Planetary Roller Screw Mechanism
Manuscript received November 3, 2014; final manuscript received March 2, 2015; published online August 18, 2015. Assoc. Editor: James Schmiedeler.
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Jones, M. H., Velinsky, S. A., and Lasky, T. A. (August 18, 2015). "Dynamics of the Planetary Roller Screw Mechanism." ASME. J. Mechanisms Robotics. February 2016; 8(1): 014503. https://doi.org/10.1115/1.4030082
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