Research Papers: Applications

Vertical Stiffnesses of Preloaded Linear Guideway Type Ball Bearings Incorporating the Flexibility of the Carriage and Rail

[+] Author and Article Information
Hiroyuki Ohta

Department of Mechanical Engineering, Nagaoka University of Technology, 1603-1 Kamitomioka, Nagaoka, Niigata, 940-2188 Japanohta@mech.nagaokaut.ac.jp

Keisuke Tanaka

Department of Mechanical Engineering, Nagaoka University of Technology, 1603-1 Kamitomioka, Nagaoka, Niigata, 940-2188 Japan

J. Tribol 132(1), 011102 (Nov 10, 2009) (9 pages) doi:10.1115/1.4000277 History: Received April 06, 2009; Revised September 20, 2009; Published November 10, 2009; Online November 10, 2009

This article deals with the vertical stiffnesses of preloaded linear guideway type ball bearings (linear bearings) incorporating the flexibility of the carriage and rail. First the vertical stiffnesses of light and medium preloaded linear bearings were measured, as well as the outward carriage deformations in the width direction. Compared with the stiffnesses calculated by the conventional rigid model (assuming the carriage and rail are rigid, except for the contact points with the balls), the measured stiffnesses were about 40% less. In preloaded linear bearings under a vertical load, the side faces of the carriage deformed outward. The deformations were minimal at the top, increased toward the bottom, and had a tendency to be greater under either a larger preload or a smaller vertical load. The measured stiffnesses and outward carriage deformations cannot be explained using the conventional rigid model. To overcome these problems with the conventional rigid model, a flexible model (taking into account the flexibility of the carriage and rail) is presented in this article. The flexible model deformations were estimated through finite element (FE) analysis. The Hertzian contacts between the balls and the carriage or rail also were considered. With relative errors of 9–21%, the calculated stiffnesses using the flexible model more closely matched the measured stiffnesses. Also, the calculated outward carriage deformations matched the measured deformations well. Clearly, there is a better match between the calculated results of the flexible model and the measurements than with the conventional rigid model.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Test linear bearing

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Figure 2

Vertical stiffness measuring apparatus

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Figure 3

Vertical displacement measuring points

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Figure 4

Outward carriage deformation measuring method

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Figure 5

Vertical load versus vertical displacement

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Figure 6

Outward carriage deformations

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Figure 7

Ball-raceway contact in rigid model (Fv=0)

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Figure 8

Ball-raceway contact in flexible model (Fv>0)

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Figure 9

Positions of raceway groove curvature centers in flexible model

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Figure 10

Overview of finite element model

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Figure 11

Cross section of finite element model

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Figure 13

Vertical stiffness calculation flow chart

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Figure 14

Calculated deformations of carriages

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Figure 15

Calculated deformations of raceway grooves of the carriage and rail

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Figure 12

Areas under pressures qic and qir



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