Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T02:51:09.116Z Has data issue: false hasContentIssue false

Stiffness Analysis of Linear Guideways Without Preload

Published online by Cambridge University Press:  20 December 2012

D. Shaw
Affiliation:
Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan 30013, R.O.C.
W. L. Su*
Affiliation:
Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan 30013, R.O.C.
*
*Corresponding author (, [email protected])
Get access

Abstract

Theoretical and experimental investigations of the stiffness of non-clearance linear guideways without preload were conducted. A theoretical approach that applied Hertz's contact theory to steel balls to derive the contact angle equation was proposed. The theoretical analysis showed that the stiffness of the linear guideway under variable vertical loads changes nonlinearly with the external load. Therefore, an experimental setup was proposed in which the stiffness curves of three blocks, differing in geometrical shape and assembled with steel balls, were measured under increased vertical load until the guideway began to plastically deform. The results showed that variation in both the width and the thickness of the block does not significantly affect stiffness. A comparison of the theoretical and experimental results revealed a relative error of 4.5%, indicating the correctness of the theoretical model. Based on theoretical equations, the main parameters that affect stiffness are conformity fm, coefficient of contact deformation cδ, reference diameter of the ball Dw, number of load-carrying rows i, number of load-carrying balls in one row Z, and initial contact angle α0. The results are useful for determining the static/dynamic behavior and rigidity of linear guideways in the design stage.

Type
Articles
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Hertz, H., “Über Die Berührung Fester Elastischer Körper,” Journal Für Die Reine Und Angewandte Mathematik, 92, pp. 156171 (1881).Google Scholar
2.Johnson, K. L., Contact Mechanics, Cambridge University Press (1985).CrossRefGoogle Scholar
3.Harris, T. A. and Kotzalas, M. N., Rolling Bearing Analysis, 5th Edition, Taylor & Francis (2006).CrossRefGoogle Scholar
4.Brändlein, J., Ball and Roller Bearings: Theory, Design, and Application, John Wiley (1999).Google Scholar
5.Shimizu, S., “Stiffness Analysis of Linear Motion Guide System,” International Journal of the Japan Society for Precision Engineering, 33, pp. 163167 (1999).Google Scholar
6.Ninomiya, M. and Kato, S., “Analysis of Linear Guide and Ball Screw Stiffness,” International Journal of the Japan Society for Precision Engineering, 33, pp. 173177 (1999).Google Scholar
7.Hsu, K. H., “The Linear Guideway Measurement System Design and Linear Guideway Testing,” M.S. Thesis, Department of Power Mechanical Engineering, National Tsing Hua Univeristy, Taiwan, R.O.C. (2006).Google Scholar
8.Ohta, H. and Tanaka, K., “Vertical Stiffnesses of Preloaded Linear Guideway Type Ball Bearings Incorporating the Flexibility of the Carriage and Rail,” Journal of Tribology, 132, pp. 11021109 (2010).Google Scholar
9.Junzo, O., Ball Bearing Design Calculation Introduction, Nikkan Kogyo Shimbun (2011).Google Scholar
10.Lundberg, G. and Palmgren, A., Dynamic Capacity of Rolling Bearings, Acta Polytechnica Mechanical Engineering Series, 1 (1947).Google Scholar