| 摘要: | 本文以邊界元素法為基礎,使用副區域、二 次元素、四分點元素與奇異曳引力四分點元素 等數值分析技巧,來求得彈性體內部裂紋的應力 強度因子;在分析的過程中,假設彈性體在接觸應 力的作用下,裂紋面可以部分張開部分接觸。 本文以懸臂梁的模式來求得齒輪在傳遞負 荷時,齒面受到接觸應力的作用下,齒輪內部的水 平與垂直裂紋的應力強度因子;並且探討該應力 強度因子與受力點、摩擦係數、裂紋位置、裂 紋長度等因素的關係。 發現齒根全部折斷的發生原因主要是由於 彎曲力矩所引起的拉應力,裂紋起先發生在齒根 附近,最後,裂紋則以張開型模式延伸。而表面碎 裂的發生原因主要是由於表面應力集中所引起 的剪應力,裂紋起先發生在節圓附近,最後,裂紋 則以滑移型模式延伸。在分析時,雖以齒輪為例 ;但本文所採用的方法與技巧,可廣泛的應用在各 種受接觸應力作用的構件上。
In this study, it is shown that the multidomain boundary element technique may be used to obtain stress intensity factors of subsurface cracks under contact stress fields. In particular, we analyze subsurface horizontal and vertical cracks. Crack surfaces may be partially open and partially in contact. To illustrate the usefulness of this technique, a gear tooth with subsurface cracks is analyzed. The gear tooth is simulated by a cantilever beam. Stress intensity factors are found to be dependent upon the following parameters: the location of the applied load、the location of crack and the crack length. We find the breakage at gear root is mainly caused by tensile stresses due to bending. Cracks in the root region propagate with opening mode. Case crushings are caused by shear stresses produced by contact forces. These happen when cracks near the pitch circle propagate with sliding mode. |
