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

Chin Chung Wei; Jen Fin Lin

doi:10.1115/1.1623761

Journal of Mechanical Design | Volume 125 | Issue 4 | TECHNICAL PAPERS

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TECHNICAL PAPERS

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

Chin Chung Wei, Graduate Student and Jen Fin Lin, Professor

[+] 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

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References

Figures

Sliding velocities and slip angles formed at the ball-screw and ball-nut contacts

View Large | Save Figure | Download Slide (.ppt)

(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)

View Large | Save Figure | Download Slide (.ppt)

(a) Force balance created at the contact point of the nut, (b) force and moment balances created at a ball

View Large | Save Figure | Download Slide (.ppt)

Flow chart of the numerical analysis in the present model

View Large | Save Figure | Download Slide (.ppt)

Contact angles formed at the ball/screw and ball/nut contact areas

View Large | Save Figure | Download Slide (.ppt)

Elastic deformations formed at the ball/screw and ball/nut contact areas

View Large | Save Figure | Download Slide (.ppt)

Ball’s spinning and revolving angular velocities varying with the screw rotational speed

View Large | Save Figure | Download Slide (.ppt)

The slider-roll ratios evaluated at the (a) ball-screw (b) ball-nut contact area

View Large | Save Figure | Download Slide (.ppt)

Friction coefficients created on the nut and the screw surfaces at various screw rotational speeds

View Large | Save Figure | Download Slide (.ppt)

(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

View Large | Save Figure | Download Slide (.ppt)

The drag forces and the centrifugal forces created at a ball under various operating conditions

View Large | Save Figure | Download Slide (.ppt)

Variations of the gyroscopic angle β with the screw rotational speed

View Large | Save Figure | Download Slide (.ppt)

The mechanical efficiencies of a ball-screw system evaluated by the present model and the model of Lin et al.

View Large | Save Figure | Download Slide (.ppt)

Contact angles formed at the nut and the screw varying with the helix angle

View Large | Save Figure | Download Slide (.ppt)

Mechanical efficiency of a ball screw system varying with the helix angle of the screw surface

View Large | Save Figure | Download Slide (.ppt)

Friction coefficients created at the ball-screw and the ball-nut contact areas varying with the slide-roll ratio

View Large | Save Figure | Download Slide (.ppt)

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Wei C, Lin J. Kinematic Analysis of the Ball Screw Mechanism Considering Variable Contact Angles and Elastic Deformations. ASME. J. Mech. Des. 2004;125(4):717-733. doi:10.1115/1.1623761.

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

References

Figures

A ball screw and nut mechanism

The position of ball center in Cartesian coordinates and Frenet coordinates

Instantaneous position of ball mass element dm

(a) Ball-nut contact, (b) ball-screw contact

Sliding velocities and slip angles formed at the ball-screw and ball-nut contacts

(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)

(a) Force balance created at the contact point of the nut, (b) force and moment balances created at a ball

Flow chart of the numerical analysis in the present model

Contact angles formed at the ball/screw and ball/nut contact areas

Elastic deformations formed at the ball/screw and ball/nut contact areas

Ball’s spinning and revolving angular velocities varying with the screw rotational speed

The slider-roll ratios evaluated at the (a) ball-screw (b) ball-nut contact area

Friction coefficients created on the nut and the screw surfaces at various screw rotational speeds

(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

The drag forces and the centrifugal forces created at a ball under various operating conditions

Variations of the gyroscopic angle β with the screw rotational speed

The mechanical efficiencies of a ball-screw system evaluated by the present model and the model of Lin et al.

Contact angles formed at the nut and the screw varying with the helix angle

Mechanical efficiency of a ball screw system varying with the helix angle of the screw surface

Friction coefficients created at the ball-screw and the ball-nut contact areas varying with the slide-roll ratio

Tables

Errata

Discussions

Related Content

Journals

Conference Proceedings

eBooks

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

References

Figures

A ball screw and nut mechanism

The position of ball center in Cartesian coordinates and Frenet coordinates

Instantaneous position of ball mass element dm

(a) Ball-nut contact, (b) ball-screw contact

Sliding velocities and slip angles formed at the ball-screw and ball-nut contacts

(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)

(a) Force balance created at the contact point of the nut, (b) force and moment balances created at a ball

Flow chart of the numerical analysis in the present model

Contact angles formed at the ball/screw and ball/nut contact areas

Elastic deformations formed at the ball/screw and ball/nut contact areas

Ball’s spinning and revolving angular velocities varying with the screw rotational speed

The slider-roll ratios evaluated at the (a) ball-screw (b) ball-nut contact area

Friction coefficients created on the nut and the screw surfaces at various screw rotational speeds

(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

The drag forces and the centrifugal forces created at a ball under various operating conditions

Variations of the gyroscopic angle β with the screw rotational speed

The mechanical efficiencies of a ball-screw system evaluated by the present model and the model of Lin et al.

Contact angles formed at the nut and the screw varying with the helix angle

Mechanical efficiency of a ball screw system varying with the helix angle of the screw surface

Friction coefficients created at the ball-screw and the ball-nut contact areas varying with the slide-roll ratio

Tables

Errata

Discussions

Related Content

Journals

Conference Proceedings

eBooks

(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)