Deformation Discipline of the Flexspline in Harmonic Drives with Engagement Output

Dong, Honggang; Zhi, Chen; Chunmao, Zhang; Wang, Delun

doi:10.1007/978-1-4471-4141-9_19

Cited by 4 publications

(5 citation statements)

References 3 publications

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“…According to the geometric equations Dong et al, 2009), in Fig. 14b, the circumferential displacement v(φ) is shown in Eq.…”

Section: Circumferential Displacement Vmentioning

confidence: 99%

Circumferential spatial tooth profile modification of flexspline for strain wave gear (A novel method and a case study)

HUANG,

QIAN,

WEI

et al. 2023

JAMDSM

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Strain wave gear, also known as "harmonic drive" is widely used in the industrial robotics field due to the excellent deceleration performance. The tooth modification of the flexspline faces the requirements of high accuracy and service life. In this paper, a novel spatial tooth profile modification method along the circumferential direction of flexspline for strain wave gear is proposed. The circumferential modification method has a small change of meshing point position and working pressure angle, which is beneficial to maintain the transmission accuracy and improve the service life. In addition, the relation model of spatial motion between hob and flexspline, and the relation between tooth profile and modification quantity are study in the view of engineering application aim to reveal that the principle of circumferential modification is the rotation of the tooth profile along the center of the tooth apex circle. And the feasibility of circumferential modification is verified by a actual machining. Then, two main factors, circumferential modification quantity and radius of flexspline indexing circle are analyzed. Afterward, the novel stepwise modification of the circumferential spatial tooth profile of flexspline is introduced. Finally, a case study of circumferential spatial tooth profile modification of flexspline for strain wave gear is conducted. The case study shows that the maximum distance offset value in circumferential modification is 7.8 μm, which is smaller than the traditional modification value (13.2 μm), and the maximum working pressure angle value is 2.24 °, which is smaller than the minimum value (3.93 °) in traditional modification. And the FEM results and the cross-section tooth pairs comparing with the theoretical model also show the possibility of the proposed modification method.

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“…According to the geometric equations Dong et al, 2009), in Fig. 14b, the circumferential displacement v(φ) is shown in Eq.…”

Section: Circumferential Displacement Vmentioning

confidence: 99%

Circumferential spatial tooth profile modification of flexspline for strain wave gear (A novel method and a case study)

HUANG,

QIAN,

WEI

et al. 2023

JAMDSM

View full text Add to dashboard Cite

show abstract

“…If the uniform correction is adopted for each section of the axial direction, the profile of FS and CS will be interfered. In the past, the main section was selected properly to avoid the interference of tooth profile (Zhou, 2016; Dong, 2008); thus, the tooth profile is fully engaged in the main section, and the rest of the sections along the axial direction are partially engaged.…”

Section: Case Studymentioning

confidence: 99%

“…To truly describe the deformation of FS under two-disk wave generator, Chen et al (2014) researched a calculation method to describe the deformation, and the internal forces of neutral surface of FS is presented based on the force equilibrium equations and continuous conditions with geometric constraints. Under the load condition, the deformation of the FS will be different; Dong et al (2012) established a kinematic simulation analysis model of ABAQUS for HD to deals with the deformation function of FS, by modified tooth profile under load condition; the conjugate region increases, and the deformation function varies a little. Adams et al (2016) developed a model for calculating vibration of elliptically deformed wave generator (WG).…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional tooth profile design method of harmonic drive considering the deformation difference of the flexspline

Zhang

2021

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Purpose This paper aims to improve the meshing effect of the gear teeth. It is recommended to analyze the deformation difference between the inner and outer surfaces of the flexspline. The purpose of this paper is to modify the profile of the flexspline based on the deformation difference to improve the transmission accuracy and operating life of the harmonic drive. Design/methodology/approach In this paper, ring theory is used to calculate the deformation difference of the inner and outer surfaces of the flexspline, and the actual tooth profile of the flexspline is corrected based on the deformation difference. Then, the flexspline is divided into multiple sections along the axial direction, so that the three-dimensional tooth profile of the flexspline is modified to improve the gear tooth meshing effect. Findings This paper proves the effect of the deformation difference between the inner and outer surfaces of the flexspline on the tooth backlash, which affects the transmission accuracy and life of the harmonic drive. It is recommended to modify the tooth profile of the flexspline based on the deformation difference, so as to ensure the tooth meshing effect. Originality/value This paper provides a new way for the optimization of the three-dimensional tooth profile design of the harmonic drive.

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“…Based on this, Ivanov [7] and Shen [10] conducted a more detailed study on the FS deformation under the action of various WGs such as four-rollers WG, double-discs WG, and cam WG. Dong et al [12] calculated the assembly deformation of a cupshaped FS and fitted the loaded deformation results with cubic spline curves. Ma et al [13] developed an experimental apparatus that integrates a special-fabricated micro-displacement platform and a pair of laser sensors to measure the radial displacement of the FS and investigated the effect of the driving speed on the deformation characteristics of the FS.…”

Section: Introductionmentioning

confidence: 99%

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

Yao

Chen

Xing

et al. 2021

Chin. J. Mech. Eng.

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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.

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Deformation Discipline of the Flexspline in Harmonic Drives with Engagement Output

Cited by 4 publications

References 3 publications

Circumferential spatial tooth profile modification of flexspline for strain wave gear (A novel method and a case study)

Circumferential spatial tooth profile modification of flexspline for strain wave gear (A novel method and a case study)

Three-dimensional tooth profile design method of harmonic drive considering the deformation difference of the flexspline

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

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