Tooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis

Abstract Deformation of the flexspline is the basis of analyzing tooth trajectory and designing tooth profile. Considering the tooth influence on the position of equivalent neutral layer, a piecewise method for calculating the deformation of flexspline assembled with a cam wave generator is presente...

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Autores principales:	Yunpeng Yao, Xiaoxia Chen, Jingzhong Xing, Liteng Shi, Yuqi Wang
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Harmonic drive Deformation calculation Cam wave generator Force analysis Equivalent neutral layer Ocean engineering TC1501-1800 Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/86408e4046ee4b2385d759ac6a387f3e
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spelling	oai:doaj.org-article:86408e4046ee4b2385d759ac6a387f3e2021-11-14T12:05:51ZTooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis10.1186/s10033-021-00621-z1000-93452192-8258https://doaj.org/article/86408e4046ee4b2385d759ac6a387f3e2021-11-01T00:00:00Zhttps://doi.org/10.1186/s10033-021-00621-zhttps://doaj.org/toc/1000-9345https://doaj.org/toc/2192-8258Abstract Deformation of the flexspline is the basis of analyzing tooth trajectory and designing tooth profile. Considering the tooth influence on the position of equivalent neutral layer, a piecewise method for calculating the deformation of flexspline assembled with a cam wave generator is presented in this paper. Firstly, a mechanic model of a ring of uniform thickness in contact with a rigid cam is established. The displacements of the ring inside and outside an unknown wrapping angle are determined by the geometric constraints of the cam profile and the equilibrium relationship, respectively. Meanwhile, the wrapping angle is solved according to the boundary conditions. The assembly forces are derived to investigate the circumferential elongation and strain. Then, considering the tooth effects on the neutral layer of flexspline, the tooth is positioned on the equivalent neutral layer, which is the non-elongation layer within one gear pitch but offset from the geometric mid-layer. The equivalent neutral layer is positioned by the empirical formula of the offset ratio, which is summarized by the orthogonal simulation on finite element models of racks. Finally, finite element models of a ring-shaped and a cup-shaped flexspline assembled with elliptical cam are established to verify the effectiveness and accuracy of the piecewise method. The results show that, compared with the geometric method, the tooth positioning deviation calculated by the piecewise method can be reduced by about 70% with a more accurate deformation description from the geometric condition and mechanic condition inside and outside the wrapping angle.Yunpeng YaoXiaoxia ChenJingzhong XingLiteng ShiYuqi WangSpringerOpenarticleHarmonic driveDeformation calculationCam wave generatorForce analysisEquivalent neutral layerOcean engineeringTC1501-1800Mechanical engineering and machineryTJ1-1570ENChinese Journal of Mechanical Engineering, Vol 34, Iss 1, Pp 1-20 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Harmonic drive Deformation calculation Cam wave generator Force analysis Equivalent neutral layer Ocean engineering TC1501-1800 Mechanical engineering and machinery TJ1-1570
spellingShingle	Harmonic drive Deformation calculation Cam wave generator Force analysis Equivalent neutral layer Ocean engineering TC1501-1800 Mechanical engineering and machinery TJ1-1570 Yunpeng Yao Xiaoxia Chen Jingzhong Xing Liteng Shi Yuqi Wang Tooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis
description	Abstract Deformation of the flexspline is the basis of analyzing tooth trajectory and designing tooth profile. Considering the tooth influence on the position of equivalent neutral layer, a piecewise method for calculating the deformation of flexspline assembled with a cam wave generator is presented in this paper. Firstly, a mechanic model of a ring of uniform thickness in contact with a rigid cam is established. The displacements of the ring inside and outside an unknown wrapping angle are determined by the geometric constraints of the cam profile and the equilibrium relationship, respectively. Meanwhile, the wrapping angle is solved according to the boundary conditions. The assembly forces are derived to investigate the circumferential elongation and strain. Then, considering the tooth effects on the neutral layer of flexspline, the tooth is positioned on the equivalent neutral layer, which is the non-elongation layer within one gear pitch but offset from the geometric mid-layer. The equivalent neutral layer is positioned by the empirical formula of the offset ratio, which is summarized by the orthogonal simulation on finite element models of racks. Finally, finite element models of a ring-shaped and a cup-shaped flexspline assembled with elliptical cam are established to verify the effectiveness and accuracy of the piecewise method. The results show that, compared with the geometric method, the tooth positioning deviation calculated by the piecewise method can be reduced by about 70% with a more accurate deformation description from the geometric condition and mechanic condition inside and outside the wrapping angle.
format	article
author	Yunpeng Yao Xiaoxia Chen Jingzhong Xing Liteng Shi Yuqi Wang
author_facet	Yunpeng Yao Xiaoxia Chen Jingzhong Xing Liteng Shi Yuqi Wang
author_sort	Yunpeng Yao
title	Tooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis
title_short	Tooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis
title_full	Tooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis
title_fullStr	Tooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis
title_full_unstemmed	Tooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis
title_sort	tooth position and deformation of flexspline assembled with cam in harmonic drive based on force analysis
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/86408e4046ee4b2385d759ac6a387f3e
work_keys_str_mv	AT yunpengyao toothpositionanddeformationofflexsplineassembledwithcaminharmonicdrivebasedonforceanalysis AT xiaoxiachen toothpositionanddeformationofflexsplineassembledwithcaminharmonicdrivebasedonforceanalysis AT jingzhongxing toothpositionanddeformationofflexsplineassembledwithcaminharmonicdrivebasedonforceanalysis AT litengshi toothpositionanddeformationofflexsplineassembledwithcaminharmonicdrivebasedonforceanalysis AT yuqiwang toothpositionanddeformationofflexsplineassembledwithcaminharmonicdrivebasedonforceanalysis
_version_	1718429473839251456

Tooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis

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