| 摘要: | 本文旨在解決赫氏接觸(Hertzian contact)下之 切線問題,所發展出的分析(analytical)及數值 (numerical)技巧能解出原本只有赫氏正向壓力 (Hertzian pressure)作用之兩接觸體,如果再加上切線力F/sub x/、F/sub y/及力矩M/sub z/作用時,其接 觸區域內的剪應力分布。 根據Cattaneo對靜態接觸(static contact)問題所 求出之結果,接觸區域內之剪應力可分解成兩 個臨界運動(impending motion)狀態的型式。本文中 作者進一步利用平面運動學之瞬時中心 (instantaneous center)觀念,將切線力F/sub x/、F/sub y/ 及力矩 M/sub z/表示成瞬時中心(.zeta.,.eta.)的函 數;在圓形接觸區域的情況下,找出切線力與瞬 時中心位置之間的解析關係式;在橢圓接觸區 域的情況下,利用數值技巧找出切線力與瞬時 中心位置之間的關係式;由這些關係式可解出 切線力(F/sub x/,F/sub y/,M/sub z/)作用時之瞬時中 心(.zeta.,.eta.),並因此獲得接觸區域內任意一點 的剪應力分布。
The purpose of this paper is to develop analytical and numerical techniques for tangential problems of two elastically identical bodies in Hertzian contact. When tangential forces F/sub x/, F/sub y/ and twisting moment M/sub z/ are applied to two bodies already in Hertzian contact, the techniques may be used to find tangential stress distributions in the contact region. According to Cattaneo's results for static contact problems, the resulting component of tangential traction over the entire contact region is composed of two tractions under the condition of impending motion. By making use of the concept of instantaneous center (IC) for the impending motions, we find the relations between (F/sub x/, F/sub y/, M/sub z/) and (.zeta.,.eta.), the coordinates of the IC. For circular contact patches under Hertzian pressure, these relations are given by analytical expressions. For elliptical contact patches under Hertzian pressure, a numerical algorithm has been developed to find the relations between (F/sub x/, F/sub y/, M/sub z/) and(.zeta.,.eta.). These results may be used to find (.zeta.,.eta.) for given values of (F/sub x/, F/sub y/, M/sub z/). Then tangential stresses at any point in contact region may be determined. |
