Hobbing Strategy and Performance Analyses of Linkage Models for Non-Circular Helical Gears Based on Four-Axis Linkage

Liu, Youyu; Han, Jiang; Xia, Lian; Tian, Xiaoqing

doi:10.5545/sv-jme.2012.524

Cited by 16 publications

(11 citation statements)

References 14 publications

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“…A high-order multistage modified elliptical helical gear can be hobbed while it meets with equation (24). 13 The minimum curvature radius ρ1min of the driving gear is as follows from equation (19). …”

Section: Design Of Helical Gear Pairs Of High-order Multistage Modifimentioning

confidence: 99%

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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Section: Design Of Helical Gear Pairs Of High-order Multistage Modifimentioning

confidence: 99%

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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“…According to Eqs. (13), (16) and 18, a six-axis linkage model based on diagonal hobbing is built by use of a method of equal arc-length for the gear billet such that the velocity of the hob remains constant [12]. ω b , v d and v z are three independent fundamental frequencies, and the other axes move with them in a strict transmission ratio.…”

Section: Linkage Models Based On Diagonal Hobbingmentioning

confidence: 99%

“…Tian et al [11] have built some basic mathematical models for hobbing non-circular helical gears, with helical teeth, by a generating method of helical tooling rack based on non-diagonal hobbing, but provided no processing program for them. We have constructed some hobbing schemes and linkage models based on a four-axis linkage [12] and a five-axis linkage [13], and have singled out two excellent strategies with their linkage models. All in all, those works make hobbing noncircular (spur or helical) gears possible and greatly improve the production efficiency in contrast to the classic wire electric discharge machining [14] that is used to machine non-circular spur gears.…”

Section: Introductionmentioning

confidence: 99%

Six-Axis Linkage Strategy and Its Models for Non-Circular Helical Gears Based on Diagonal Hobbing

Liu

Diao

2015

SV-JME

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Among cutter teeth of the hob when hobbing non-circular helical gears, there are some issues such as uneven load and wear. To solve those problems, a simultaneous six-axis hobbing model had been developed based on diagonal hobbing. Four probable working conditions were provided. Linkage models corresponding to the four conditions were verified by virtual hobbing, in which the profile accuracies were compared and analyzed. The four working conditions were analyzed including linear (or angular) velocities and linear (or angular) accelerations. Consequently, two implementation strategies including repeating axial shift and reciprocating axial shift were offered. The linkage models and their strategies have been verified by hobbing testing. Experimental results show that diagonal hobbing is superior to non-diagonal hobbing in that the hob life of the former is 3.68 longer than that of the latter, and the micro-topography in the teeth surface of the former is more stable during transmission.

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“…Recently, Hao et al [18] proposed methods to design an *Corresponding Author Email: thai.nguyenhongr@hust.edu.vn (N. H. Thai) NCGs pair based on an arbitrary centrode. However, those NCGs pairs could only be used for low-load application because the effect of undercutting and interference was not taken into the design process; (4) Methods for manufacturing the NCGs spur and the NCGs helical were the research object of other researchers [19][20][21]. Among those four trends, NCGs tooth profile design has drawn the most interest.…”

Section: Introductionmentioning

confidence: 99%

A Novel Curve for the Generation of the Non-circular Gear Tooth Profile

2022

IJE

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This paper presents a novel curve generated by a point attached to an ellipse as it rolls without slipping along a datum line of rack cutter. A mathematical model of the non-circular gear profile has been developed based on the theory of gearing. The effect of an axial ratio  (the ratio of the lengths of the major and minor axes of the ellipse) and the position of the point KR, at which the novel curve starts to generate on the tooth shape and the undercut of the non-circular gear pair is also taken into consideration. A numerical program developed from the mathematical model has been proposed for the calculation and design of the non-circular gears (NCGs). Case studies are presented to show the steps of tooth shape design and to examine the geometrical profile of the NCGs in relation to design parameters of the rack cutter etc. From that, the axial ration  and position of the point KR on the generating ellipse ƩE can be selected for each specific case in order to design the appropriate profiles of the NCGs. On that basis, an experiment to determine the gear ratio of the NCGs pair based on the meshing between gears has manufactured.

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Hobbing Strategy and Performance Analyses of Linkage Models for Non-Circular Helical Gears Based on Four-Axis Linkage

Cited by 16 publications

References 14 publications

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

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

Six-Axis Linkage Strategy and Its Models for Non-Circular Helical Gears Based on Diagonal Hobbing

A Novel Curve for the Generation of the Non-circular Gear Tooth Profile

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