Calculation of Tooth Thickness Errors and Its Adjustment on Meshing Backlash of Harmonic Drive

Yang, Congbin; Ma, Honglie; Zhang, Tao; Zheng, Jian; Liu, Zhifeng; Cheng, Qiang

doi:10.1007/s12541-022-00738-8

Cited by 4 publications

(3 citation statements)

References 28 publications

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“…Note that α 4 / 175 + 6α 2 / 5 is much less than 3 for α near 0 rad. Omitting these two terms in equation (5) gives…”

Section: The First Initial Approximationmentioning

confidence: 99%

“…an important tool to monitor and control the quality of gear manufacturing [1][2][3][4][5]. This measurement is closely related to the calculation of the inverse involute function.…”

Section: Introductionmentioning

confidence: 99%

“…the IIF α = inv −1 (θ) is to be found. This problem arises quite often in gear tooth geometry calculations, such as in the determination of non-standard center distances, offsets for cutting unconventional gears with teeth of consistent strength, non-standard pin dimensions, and maximum profile heights of spur gears [4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

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Calculation of the inverse involute function and application to measurement over pins

Zhou,

Wu,

Chen

et al. 2024

Meas. Sci. Technol.

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Measurement over pins plays a crucial role in ensuring the quality in gear manufacturing, which requires the evolution of the inverse involute function. In this paper, an efficient algorithm for calculating the inverse involute function is proposed. Firstly, the initial approximate solution of the pressure angle near 0 rad is established by using Padé approximation and one step of Schröder iteration. Then the involute equation is transformed into another form by introducing a variable transformation, and the initial approximate solution of the pressure angle near π/2 rad is constructed by using the same method. The piecewise initial approximate solution over the entire interval of expanded angle is obtained by combining these solutions. The accuracy of the initial approximate solution can be significantly improved by using one step of Schröder iteration again. A numerical example of two-pin measurement is presented to show the superiority of our method over traditional iterative approach. The algorithm has high efficiency and accuracy, and is a useful tool for designers to accurately calculate the gear system.

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“…Note that α 4 / 175 + 6α 2 / 5 is much less than 3 for α near 0 rad. Omitting these two terms in equation (5) gives…”

Section: The First Initial Approximationmentioning

confidence: 99%

“…an important tool to monitor and control the quality of gear manufacturing [1][2][3][4][5]. This measurement is closely related to the calculation of the inverse involute function.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Calculation of the inverse involute function and application to measurement over pins

Zhou,

Wu,

Chen

et al. 2024

Meas. Sci. Technol.

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show abstract

Rapid non-contact measurement of distance between two pins of flexspline in harmonic reducers based on standard/actual parts comparison

Liu,

Cui,

Liang

et al. 2024

Precision Engineering

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A novel harmonic drive with the full conjugate tooth profile

Xie,

Yang,

Zhou

et al. 2024

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper presents an approach for designing a novel tooth profile of harmonic drives, which is composed of two pieces of curves, hypocycloid and epicycloid, generated by the rolling circles with appropriate radii. Compared with the conventional double-circular-arc or cycloidal tooth profile of harmonic drives, the tooth profile is characterized by full conjugation, more number of engaged teeth, and can be expressed analytically, etc. Firstly, the generation of the cycloids are briefly described, and then their conjugate criterion is investigated systematically based on Camus’s theorem. Secondly, the tooth profile equations for the circular spline and flexspline are established and the deformed neutral curve equation is derived. Next, the contact properties among the tooth profiles, including the line of action, meshing angle, etc., are studied systematically. Finally, a finite element model and a physical prototype for the harmonic drive with the tooth profile are developed, respectively. The effectiveness of the design method is verified by the contact performances simulation. The research may provide a new thought for the innovative design of harmonic drives with full conjugate tooth profile.

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Calculation of Tooth Thickness Errors and Its Adjustment on Meshing Backlash of Harmonic Drive

Cited by 4 publications

References 28 publications

Calculation of the inverse involute function and application to measurement over pins

Calculation of the inverse involute function and application to measurement over pins

Rapid non-contact measurement of distance between two pins of flexspline in harmonic reducers based on standard/actual parts comparison

A novel harmonic drive with the full conjugate tooth profile

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