表面に周期的に分布する半楕円体状の接触圧力による半無限弾性体内部の応力解析 (第2報 接触面の形状寸法と周期の比の影響について-数値解析結果)

URI http://harp.lib.hiroshima-u.ac.jp/it-hiroshima/metadata/7208
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Title
表面に周期的に分布する半楕円体状の接触圧力による半無限弾性体内部の応力解析 (第2報 接触面の形状寸法と周期の比の影響について-数値解析結果)
Title Alternative
The analysis of stress distribution in a semi-infinite elastic body by periodically spaced semi-ellipsoid contact pressures (2nd Report Effect of the ratio of the size of contact area to the spacing of load bearing asperities-Numerical calculations)
Author
氏名 片山 剛之丞
ヨミ カタヤマ ゴウノジョウ
別名 Ktayama Gonojo
氏名 山下 尚義
ヨミ ヤマシタ ナオヨシ
別名 Yamashita Naoyoshi
NDC
423
Abstract

The classical theory of contact between elastic bodies was first published by H. Hertz in 1881. The problem actually solved by Hertz,however,was a very restricted one; it concerned two elastic bodies in static contact under the action of a steady resultant force acting normal to the tangent plane at the point of contact. The surfaces of the two bodies are assumed to be smooth and continuous in the neighbourhood of the region of contact,with radii of curvature which are large compared with the actual dimensions of the contact area. lt is immediately clear that the Hertzian analysis cannot hold for rough surfaces. The designer is frequently confronted with the problem of estimating the appropriate value for the allowable contact pressure in gears,or anti-friction bearings. One of reasons for this difficulty is the lack of the knowledge for the effect of surface roughness on the contact fatigue. In the previous report,we derivated the theoretical equations for the stress field in a semi-infinite elastic body by normally loaded,periodically spaced semi-ellipsoid pressures. lt is intended that this model represent the contact problem of two nominally flat surfaces. One of the surfaces was assumed to be covered with asperities whose tips were represented by the ellipsoid of the same height. The effect of spacing of load-bearing asperities and the form and sizes of contact areas upon the state of stress within the body is studied. It is shown that the maximum octahedral shear stress occurs at the surface as the contact-spot spacing becomes small. Further,as the neighbour asperities approach together,the magnitude of tensile stress at the circumterential point of a circular contact on the surface becomes large. We discuss the variation of two shear stresses near the surface under the rolling motion. It is shown that the amplitude of the shear stress acting on a Z=const.-plane is larger than one of the shear stress acting in a direction inclined at an angle of 45 deg. to the direction of the two principal stress. Thus,it is suggested,from the above numerical calculations,that damage to the surface of curved elastic pairs in contact under cyclic loading starts from the point of very shallow depth below the surface.

Journal Title
広島工業大学研究紀要
Volume
10
Spage
173
Epage
180
Published Date
Jan-76
Publisher
広島工業大学
ISSN
3851672
NCID
AN0021271X
Language
jpn
NIIType
Departmental Bulletin Paper
Text Version
出版社版
Relation URL
Old URI
Set
it-hiroshima