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Research Papers

Improved Screw–Nut Interface Model for High-Performance Ball Screw Drives

[+] Author and Article Information
Chinedum E. Okwudire

Department of Mechanical Engineering,  University of Michigan, G.G. Brown Laboratory, 2350 Hayward, Ann Arbor, MI 48109okwudire@umich.edu

J. Mech. Des 133(4), 041009 (May 18, 2011) (10 pages) doi:10.1115/1.4004000 History: Received April 04, 2010; Revised April 04, 2011; Published May 18, 2011; Online May 18, 2011

Emerging applications of ball screw drives such as semiconductor inspection, fiber optic alignment, medical equipment, and miniature robotic actuators typically make use of ball screws that are compact, stiff, and precise. Existing models for the screw–nut interface stiffness of ball screw drives are however unable to accurately describe the dynamics of compact and stiff ball screws because they are derived based on the assumption that the portion of the screw within the nut is rigid. This paper proposes a new screw–nut interface stiffness model, which incorporates the elastic deformation of the screw within the nut using Timoshenko beam shape functions. The new model is shown, via simulation and experiments, to provide more accurate predictions of the natural frequencies of compact and stiff ball screw/nut assemblies compared to the existing models. It is therefore more suitable for use in the design simulation/evaluation of high-performance ball screw drives where compactness and rigidity are required.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Miniature ball screw/nut assemblies (source: Ref. [3])

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Figure 2

Single and double Nut preload of the screw–nut interface (source: Ref. [5])

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Figure 3

(a) Spring model of balls in screw–nut interface; (b) orientation of contact normal

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Figure 4

Inclined plane representation of ball screw thread

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Figure 5

Relationship between ball-centered and screw-centered coordinates

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Figure 6

Pictorial representation of the Shape Function method

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Figure 7

Position vectors for ball contact points

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Figure 8

More details of Shape Function method

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Figure 9

Integration limits for region 1 and region 2

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Figure 10

Simulation setup consisting of ball screw attached to clamped nut

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Figure 11

Three modes studied in simulations (mode shapes and natural frequencies are based on the Rigid Ball Screw model using nominal parameters)

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Figure 12

Comparison of percentage discrepancy (δ) in the natural frequencies of three modes of the simulation set up predicted by the Shape Function and Rigid Ball Screw models as a function of dbs , Lbs , Lnut , and kball

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Figure 13

Comparison of the consistency of the mode shapes (MAC) of three modes of the simulation set up predicted by the Shape Function and Rigid Ball Screw models as a function of dBS , LBS , LNut , and kBall

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Figure 14

Experimental setup—Ball screw/nut assembly in free-free condition. Inset: details of ball screw thread profile showing estimation of β.

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Figure 15

Comparison of measured and simulated FRFs in the axial direction from force applied at one end of ball screw to displacement at the other end of the ball screw

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Figure 16

Comparison of measured and simulated FRFs in the lateral direction from force applied at one end of ball screw to displacement at the other end of the ball screw

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