Research Papers

Hybrid Modeling of Ball Screw Drives With Coupled Axial, Torsional, and Lateral Dynamics

[+] Author and Article Information
Chinedum E. Okwudire

Manufacturing Automation Laboratory, University of British Columbia, 6250 Applied Sciences Lane, Vancouver, BC, V6T 1Z4, Canada

Yusuf Altintas

Manufacturing Automation Laboratory, University of British Columbia, 6250 Applied Sciences Lane, Vancouver, BC, V6T 1Z4, Canadaaltintas@mech.ubc.ca

J. Mech. Des 131(7), 071002 (May 27, 2009) (9 pages) doi:10.1115/1.3125887 History: Received October 21, 2008; Revised March 22, 2009; Published May 27, 2009

It has been a common practice to assume that the torsional and axial dynamics are totally decoupled from the lateral dynamics of the screw when modeling ball screw drives. However, experiments show that there is a considerable coupling between them, which could adversely affect the positioning accuracy and fatigue life of the drive. In this paper, the lateral dynamics of the screw is explicitly incorporated into the hybrid finite element model of ball screw drives. The ball screw is modeled by Timoshenko beam elements, and the balls, joints, bearings, and fasteners are modeled as pure springs. Rigid components are modeled as lumped masses. The proposed screw-nut interface model, which includes the effects of lateral vibrations, is shown to predict the coupling between axial, torsional, and lateral dynamics of ball screw drives. The effects of this dynamic coupling on the positioning accuracy of the drive are also presented with experimental proof. The proposed model provides a more realistic platform for a designer to optimize the drive parameters for high speed-high acceleration machine tool applications, where the ball screw vibrations limit the fatigue life of the mechanism, bandwidth of the servo systems, and positioning accuracy of the machine.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Mechanical components of a ball screw feed drive

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Figure 11

Simulated deformed shapes of three modes of the ball screw

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Figure 12

(a) Measured and (b) simulated relative amplitude of the table’s vibration; (c) measured and (d) simulated modal displacement of the table due to a mode of around 228 Hz (predicted around 267 Hz) as the table moves from position to position along ball screw

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Figure 13

Simulated shape of ball screw drive due to the mode around 228 Hz (predicted at around 267 Hz) showing severe bending of the ball screw at the locations X=160 mm and X=300 mm

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Figure 2

Timoshenko beam element

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Figure 3

(a) Bolted joint—example of a semirigid joint interface and (b) simple model of semirigid joints

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Figure 4

(a) Spring model of balls in the screw-nut interface and (b) orientation of contact normal

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Figure 5

Inclined plane representation of ball screw thread

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Figure 6

(a) Relationship between ball coordinates and screw coordinates and (b) lumping to nodes based on the rigid ball screw assumption

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Figure 7

Position vectors for ball-contact points

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Figure 8

(a) Test bed—single-axis ball screw drive and (b) schematic representation of test bed model

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Figure 9

(a) Simulated and (b) measured FRF between torque applied to motor and axial displacement of point 1 (see Fig. 8) on table

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Figure 10

(a) Simulated and (b) measured FRF between torque applied to motor and lateral displacement of point 2 (see Fig. 8) on ball screw




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