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TECHNICAL PAPERS

Kinematic Analysis of the Ball Screw Mechanism Considering Variable Contact Angles and Elastic Deformations

[+] Author and Article Information
Chin Chung Wei, Jen Fin Lin

Department of Mechanical Engineering, National Cheng Kung University, Tainan, 70101, Taiwan, Republic of China

J. Mech. Des 125(4), 717-733 (Jan 22, 2004) (17 pages) doi:10.1115/1.1623761 History: Received October 01, 2001; Revised April 01, 2003; Online January 22, 2004
Copyright © 2003 by ASME
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References

Figures

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A ball screw and nut mechanism
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The position of ball center in Cartesian coordinates and Frenet coordinates
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Instantaneous position of ball mass element dm
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(a) Ball-nut contact, (b) ball-screw contact
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Sliding velocities and slip angles formed at the ball-screw and ball-nut contacts
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(a) Position of ball center and raceway groove curvature centers with and without applied load (b) the detailed graph to describe the θ angle shown in Fig. 6(a)
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(a) Force balance created at the contact point of the nut, (b) force and moment balances created at a ball
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Flow chart of the numerical analysis in the present model
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Contact angles formed at the ball/screw and ball/nut contact areas
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Elastic deformations formed at the ball/screw and ball/nut contact areas
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Ball’s spinning and revolving angular velocities varying with the screw rotational speed
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The slider-roll ratios evaluated at the (a) ball-screw (b) ball-nut contact area
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Friction coefficients created on the nut and the screw surfaces at various screw rotational speeds
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(a) Normal loads created at the contact areas of the nut and the screw (b) friction forces created at the contact areas of the nut and the screw
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The drag forces and the centrifugal forces created at a ball under various operating conditions
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Variations of the gyroscopic angle β with the screw rotational speed
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The mechanical efficiencies of a ball-screw system evaluated by the present model and the model of Lin et al.
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Contact angles formed at the nut and the screw varying with the helix angle
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Mechanical efficiency of a ball screw system varying with the helix angle of the screw surface
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Friction coefficients created at the ball-screw and the ball-nut contact areas varying with the slide-roll ratio

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