원형 핀과 구멍의 접촉에서 헤르츠 응력장 가정을 위한 조건
Conditions for Assuming Hertzian Stress for the Contact between a Circular Pin and Hole
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This paper focuses on the conformal contact problem. A typical example of conformal contact is the contact between a pin and hole. In particular, this paper focuses on the condition for assuming a contact stress field to be a Hertzian pressure profile by using well-known classical solutions associated with Hertzian contact. Persson first developed the conformal contact analysis method around half a century ago, but there have been no significant improvements since then. The present research also adopted this method, but developed new solutions from the viewpoint of application to structural design. The analysis began with a comparison between Persson° Øs conformal contact stress and the Hertzian stress fields. The next step was to check the differences in the normalized stress values of both. This study used the tolerance for the difference in the peak stresses of Persson° Øs solution and the Hertz solution to validate the Hertzian assumption. This gave the range for the difference in radii of the pin and hole when the contact force and mechanical properties of the material are specified. The results showed that, at a tolerance of 5%, the Hertzian assumption is valid if half of the contact angle is less than 35°ý. In addition, the Hertzian assumption holds even for a relatively long contact length, in contrast to the general incomplete contact problem. This paper discusses these results along with other aspects of the application to the design.
Abstract
This paper focuses on the conformal contact problem. A typical example of conformal contact is the contact between a pin and hole. In particular, this paper focuses on the condition for assuming a contact stress field to be a Hertzian pressure profile by using well-known classical solutions associated with Hertzian contact. Persson first developed the conformal contact analysis method around half a century ago, but there have been no significant improvements since then. The present research also adopted this method, but developed new solutions from the viewpoint of application to structural design. The analysis began with a comparison between Persson° Øs conformal contact stress and the Hertzian stress fields. The next step was to check the differences in the normalized stress values of both. This study used the tolerance for the difference in the peak stresses of Persson° Øs solution and the Hertz solution to validate the Hertzian assumption. This gave the range for the difference in radii of the pin and hole when the contact force and mechanical properties of the material are specified. The results showed that, at a tolerance of 5%, the Hertzian assumption is valid if half of the contact angle is less than 35°ý. In addition, the Hertzian assumption holds even for a relatively long contact length, in contrast to the general incomplete contact problem. This paper discusses these results along with other aspects of the application to the design.
참고문헌 (6)
- Hertz, H., "Über die Berührung fester elastische Köper", J. Reine und angewandte Mathematik, 92, pp.156~171 (1882)
- Mindlin, R. D., "Compliance of elastic bodies in contact", J. Appl. Mech, 16, pp.259~268 (1949)
- Cattaneo, C., "Sul contatto di due corpi elastici : distribuzione locale degli sforzi", Rendiconti dell’ Academia nazionale dei Lincei, 27(6), pp.342~ (1938)
- Hills, D. A., "Mechanics of Fretting Fatigue, Chap. 3" (1994), Kluwer Academic Publishers
- Johnson, K. L., "Contact Mechanics, Chaps. 4, 7" (1985), Cambridge Univ. Press
- Persson, A., "On the Stress Distribution of Cylindrical Elastic Bodies in Contact", 박사, pp.1964