The Study of Stress Intensity Factor for Cracked Gear Tooth by Using Weight Function Method

以權函數法對含裂紋齒輪應力強度因子之研究

施延欣(Yan-Shin Shih) ； 葉忠泓(Ghung-Hong Yeh)

《中原學報》 27卷3期 (1999/09) Pp. 69-75

https://doi.org/10.6358/JCYU.199909.0069

摘要

對於齒輪含齒根裂紋的齒之應力強度因子，利用適當的應力場以及權函數的積分計算，可求得較為正確之結果。在本文中，裂齒所受之負載可分解為一在x方向的點力，一在y方向之點力，以及一彎曲力矩作用。在Flasker的假設當中，由y方向點力所造成的應力場被視為常數；在本文中，對於此彎矩所造成之應力場可以三種方式來探討。在第三種方式中，是以一端固定之平板來模擬裂齒之狀態，並以彈性力學的理論來求解裂齒所受到之應力場；因此可得到較為合理之裂齒所受應力場以及裂紋尖端之應力強度因子。此外，Flasker 在求取權函數時所用的方程式，皆須經過多次反覆的微分與積分計算，過程太過於繁雜，因此，本文所提出的多項式可更容易且簡便的用以計算權函數。

關鍵字

權函數法 ； 應力強度因子 ； 齒輪

並列摘要

For a cracked gear tooth, the stress intensity factor is integrated by weight function method. The accuracy of result depends on the selection of the stress field and weight functions. In this study the loading is resolved to a point force in x direction, a point force in y direction and a bending moment shown in Figure2. The bending stress due to the point force in y direction is considered as the constant through the cross section by Flasker. In this work, the bending stress due to the point force in y direction is determined by three approaches. For third approach, the gear tooth is simulated as one end fixed, and the stress is determined by the theory of elasticity. The stress field of third approach is more reasonable and leads to a reasonable stress intensity factor. Additionally, the weight functions used by Flasker are the complicated formulas of integration. These weight functions are simplified to the polynomial equations and the stress intensity factor becomes easy and convenient to determine.

並列關鍵字

gear tooth ； stress intensity factor ； weight function method