Stress Calculation and Fatigue Life Evaluation on Cup-Type Flexspline under Bending and Torsion in Harmonic Drive

彎扭作用下諧波減速器杯型柔輪應力分析與壽命評價

蔡力鋼(Ligang Cai) ； 胡秋實(Qiushi Hu) ； 劉誌峰(Zhifeng Liu) ； 楊聰彬(Congbin Yang) ； 張濤(Tao Zhang)

《中國機械工程學刊》 40卷5期 (2019/10) Pp. 471-480

摘要

This paper describes a composite method of calculating multi-tooth root stress and evaluating fatigue life of flexspline (FS) in harmonic drive (HD). In order to accurately describe the stress state of the flexible gear root, a mathematical method combined with simulation method is applied. FS is divided into two parts, the cup part and the teeth part, according to the type of stress. On the cup part, the stress is caused by the support of the wave generator (WG). The bending stress is analyzed using differential equations and appropriately set boundary conditions. The theoretical analysis of meshing teeth in a harmonic drive is brought into the finite element model of FS that is deformed by the outer contour of the wave generator. The simulation is conducted under the action of torque and the meshing generated stress is obtained. Finally, the stress spectrum of the tooth root is acquired according to the flexural and torsion stress, while the maximum radial, the circumferential and shear stress are obtained. After applying the fourth strength theory to calculate the Von-Mises stress, the safety factors of several materials are compared according to the S-N curve and fatigue limit formula.

關鍵字

Harmonic drive ； Flexspline ； Multi-tooth meshing ； Fatigue life evaluation

並列摘要

本文旨在研究杯型柔輪多齒嚙合的復合應力計算和壽命評價方法。為了準確描述柔輪齒根的應力狀態，將數學方法和仿真方法相結合，根據應力的類型，將柔輪分為兩部分：杯體部分和齒輪部分。對於杯體部分，利用微分方程和邊界條件計算彎曲應力。對於齒輪部分，建立齒部模型，在扭轉作用下進行了仿真分析，得到齒輪嚙合應力。最終根據彎曲和扭轉應力，復合得到徑向應力、周向應力和剪切應力的應力譜。在應用第四強度理論計算馮．米塞斯應力後，根據應力－壽命曲線和疲勞極限公式，進行了不同材料疲勞壽命安全系數的對比分析。