Spatial mapping tooth profile design and transmission characteristics analysis of harmonic drive based on scaling factor

IF 2.1 3区工程技术 Q3 MECHANICS Meccanica Pub Date : 2025-02-15 DOI:10.1007/s11012-024-01933-9

Ke Xiao, Feifei Yuan, Jianlin Wang, Linjun Li, Yanfeng Han, Cheng Wang, Xiujie Chen

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Abstract

This study proposes a method for the design of spatial mapping profile for harmonic drives based on scaling factors, and provides an in-depth analysis of their transmission characteristics. Firstly, the tooth profile mapping equations for harmonic drive are established by using the rack approximation method and the fundamental theorem of meshing. Then, scaling factors are introduced, and planar profiles of harmonic drives with varying scaling factors are derived through the application of conjugate theory. This study investigates the effect of scaling factors on the conjugate interval. Especially, loss areas for the quadratic conjugation and two-point conjugation are analyzed. The loss areas for the quadratic conjugation and two-point conjugation increase as the scaling factor increases. According to the nonlinear deformation of the FS teeth in the axial direction, a spatial mapping profile of the harmonic drive is developed, and a finite element method is employed to analyze the Von-Mises stress and contact stress of the HD. A reasonable scaling factor is beneficial to increase the meshing interval and improve the stress distribution of the assembly stress, tooth root bending stress, and tooth surface contact stress of the harmonic drive.

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基于比例因子的谐波传动空间映射齿廓设计及传动特性分析

本文提出了一种基于比例因子的谐波传动空间映射剖面设计方法，并对其传动特性进行了深入分析。首先，利用齿条逼近法和啮合基本定理，建立了谐波传动齿廓映射方程；然后，引入比例因子，应用共轭理论推导出不同比例因子下谐波传动的平面轮廓；研究了标度因子对共轭区间的影响。重点分析了二次共轭和两点共轭的损失面积。二次共轭和两点共轭的损失面积随着比例因子的增大而增大。根据轮齿在轴向上的非线性变形，建立了谐波传动的空间映射轮廓，并采用有限元方法对轮齿的Von-Mises应力和接触应力进行了分析。合理的比例系数有利于增大谐波传动的啮合间隔，改善谐波传动的装配应力、齿根弯曲应力和齿面接触应力的应力分布。

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来源期刊

Meccanica 物理-力学

CiteScore

4.70

自引率

3.70%

发文量

151

审稿时长

7 months

期刊介绍： Meccanica focuses on the methodological framework shared by mechanical scientists when addressing theoretical or applied problems. Original papers address various aspects of mechanical and mathematical modeling, of solution, as well as of analysis of system behavior. The journal explores fundamental and applications issues in established areas of mechanics research as well as in emerging fields; contemporary research on general mechanics, solid and structural mechanics, fluid mechanics, and mechanics of machines; interdisciplinary fields between mechanics and other mathematical and engineering sciences; interaction of mechanics with dynamical systems, advanced materials, control and computation; electromechanics; biomechanics. Articles include full length papers; topical overviews; brief notes; discussions and comments on published papers; book reviews; and an international calendar of conferences. Meccanica, the official journal of the Italian Association of Theoretical and Applied Mechanics, was established in 1966.