Research on Hobbing Process Principles and Linkage Models for Higher-Order Elliptic Gear

Liu, You Yu; Han, Jiang; Zhang, Gou Zheng

doi:10.4028/www.scientific.net/amr.479-481.2343

Cited by 5 publications

(11 citation statements)

References 6 publications

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“…High-order elliptic helical gear is a typical noncircular helical gear, 21 and shares the essential characteristics of non-circular helical gear with free pitch curve. Taking an external high-order elliptic left-handed gear as an example in this paper, the performances of eight practical linkage-models above are analyzed by shaping virtually using Matlab, respectively.…”

Section: Practical Linkage-modelsmentioning

confidence: 99%

Study of optimal strategy and linkage-model for external non-circular helical gears shaping

Liu

2014

Proceedings of the Institution of Mechanical Engineers, Part C:

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As an efficient manufacturing method for gears, shaping technology developed for non-circular helical gears will greatly break through the dilemma of their applications; especially for those gears with part of pitch curves being concave, being not able to be hobbed. Two fundamental linkage-models for external non-circular helical gears were built based on the meshing theory of non-circular gears in this article. According to four linkage methods in plane and two kinds of additional rotation in vertical direction, eight shaping strategies and their practical linkage-models (1)-(8) were developed. Taking a three-order elliptic helical gear as an example, the kinematic characteristics of the eight practical linkagemodels were analyzed, which reveals that equal arc-length of gear billet (models (3) and (4)) have the highest accuracy under a given efficiency. The dynamic characteristics of models (3) and (4) were analyzed, which shows that model (4) (equal arc-length of gear billet and additional rotation on shaper cutter) is better in performance, and is an optimal one. The optimal linkage-model was demonstrated to be valid by a virtual shaping, and be able to shape those non-circular helical gears with part of pitch curves being concave. Moreover, the accuracy among every gear tooth is uniform. The theory developed and the results of the virtual shaping were illustrated with a shaping experiment. The train of thought and the results will be useful for any external non-circular helical gears with free pitch curves.

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Section: Practical Linkage-modelsmentioning

confidence: 99%

Study of optimal strategy and linkage-model for external non-circular helical gears shaping

Liu

2014

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…As for the first part of the pitch curve during a period, equations (28) can be inferred according to 2 …”

Section: Inspection Of the Curvature Radius And The Convexity Of Pitcmentioning

confidence: 99%

“…Equations (1) are the polar equation of the pitch curve of a high-order and two-stage modified ellipse, which is offered in literature 4 based on the high-order ellipse 2 and the modified ellipse. 3 …”

Section: Formation Mechanism Of High-order Multistage Modified Ellipsementioning

confidence: 99%

“…Elliptic gears 1 are the most widely applied ones. High-order elliptical gears 2 can evolve from elliptical gears with the polar radius keeping the same, and the polar angle being reduced integer times, which can implement a periodic transmission ratio. Modified elliptical gears 3 have closed curves that can evolve from two elliptical gears with different order, and their order cannot be integer.…”

Section: Introductionmentioning

confidence: 99%

“…order of the ellipse of driving gear n 2 order of the ellipse of driven gear N number of stage r 1ij polar radius of driving gear for stage j of period i (mm) r 2ij polar radius of driven gear for stage j of period i (mm) z 0 teeth number of shaper z 0 min minimum teeth number of shaper z 1 teeth number of driving gear z 2 teeth number of driven gear t tooth profile angle of tool skew rack in end face (rad) n tooth profile angle of tool skew rack in normal plane (rad), usually n ¼ 20 12 pressure angle (rad) 2 angular acceleration of the driven gear (radÁs À2 ) c helical angle (rad) " contact ratio, " 5 1 1 polar angle of driving gear (rad) 2 polar angle of driven gear (rad) 1 diameter-tangent angle (rad) 1 curvature radius of driving gear (mm) 2 curvature radius of driven gear (mm) ! 1 angular speed of the driving gear (radÁs À1 ) !…”

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confidence: 99%

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External high-order multistage modified elliptical helical gears and design procedure of their gear pairs

Han

Liu

et al. 2016

Proceedings of the Institution of Mechanical Engineers, Part C:

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In view of the limited quantity of modified segments for high-order and two-stage modified elliptical helical gears, and poor adjustment capacity for transmission ratio, the formation mechanism of a high-order multistage modified ellipse was studied, and a unified mathematical expression of the family of ellipses was derived. Thus, a design procedure for the helical gear pairs of the high-order multistage modified ellipse was suggested, and then their transmission characteristics were discussed exhaustively. Moreover, some checking methods such as curvature radius of pitch curve, convexity, pressure angle, undercutting, and contact ratio were offered. Finally, two design cases, including two-order and threestage modified elliptical helical gear pair and two-order and four-stage one, were implemented. The cases indicate that a high-order multistage modified elliptical helical gear can be utilized in practice.

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A linkage model and applications of hobbing non-circular helical gears with axial shift of hob

Xia

Liu

et al. 2013

Mechanism and Machine Theory

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Research on Hobbing Process Principles and Linkage Models for Higher-Order Elliptic Gear

Cited by 5 publications

References 6 publications

Study of optimal strategy and linkage-model for external non-circular helical gears shaping

Study of optimal strategy and linkage-model for external non-circular helical gears shaping

External high-order multistage modified elliptical helical gears and design procedure of their gear pairs

A linkage model and applications of hobbing non-circular helical gears with axial shift of hob

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