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Research Papers: Design of Direct Contact Systems

A Designing and Generating Method for Grinding Relief Surfaces of a Dual-Cone Double-Enveloping Hourglass Worm Gear Hob

[+] Author and Article Information
Chengjie Rui

College of Engineering,
China Agricultural University,
Beijing 100083, China
e-mail: ruichengjie@126.com

Haitao Li

Key Laboratory of Optimal Design of Modern
Agricultural Equipment in Beijing,
China Agricultural University,
Beijing 100083, China
e-mail: h89533@cau.edu.cn

Jie Yang

College of Engineering,
China Agricultural University,
Beijing 100083, China
e-mail: yj2511@cau.edu.cn

Wenjun Wei

Professor
College of Engineering,
China Agricultural University,
Beijing 100083, China
e-mail: mech01@cau.edu.cn

Xuezhu Dong

Professor
College of Engineering,
China Agricultural University,
Beijing 100083, China
e-mail: h.li@cau.edu.cn

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 14, 2018; final manuscript received July 27, 2018; published online September 18, 2018. Assoc. Editor: Hai Xu.

J. Mech. Des 140(12), 123301 (Sep 18, 2018) (12 pages) Paper No: MD-18-1215; doi: 10.1115/1.4041053 History: Received March 14, 2018; Revised July 27, 2018

Land widths and relief angles of a dual-cone double-enveloping hourglass worm gear hob are important factors that influence the life and the hobbing performance of the hob. Both of them are obtained by generating relief surfaces of the hob. Due to the reason that all teeth of this type of hob have different profiles with each other, all of the relief surfaces are difficult to generate for keeping all cutting teeth with uniformed relief angles and uniformed land widths. For the purpose that land widths and relief angles could be machined precisely, this paper puts forward a designing and generating method for grinding the relief surfaces. The relief surfaces are ground using the same double-cone grinding wheel as grinding the helical surfaces of the worm. Based on the theory of gearing, the mathematical model for grinding relief surfaces is built. Motion parameters when grinding the different points of the land edges on different teeth of the hob are solved. A generating simulation is built by putting those motion parameters into a four-axis hourglass worm-grinding machine. The results of the simulation show that the relief surfaces can be ground continuously and the land widths and the relief angles meet the requirements.

Copyright © 2018 by ASME
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References

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Figures

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Fig. 1

An hourglass worm gear hob hobs a worm gear

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Fig. 2

A hob tooth geometry

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Fig. 3

Flow chart of designing the relief surfaces

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Fig. 4

Coordinate systems

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Fig. 5

Position between the grinding wheel and the worm

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Fig. 6

A double-cone grinding wheel

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Fig. 7

A cylindrical generating surface generates the rake face

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Fig. 8

A cylindrical generating surface

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Fig. 9

Position between the cylindrical generating surface and the hob

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Fig. 10

The rake face and the cutting edge

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Fig. 11

The offset surface and the land edge

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Fig. 12

The vectors of P1 on different surfaces

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Fig. 13

Flow chart for calculating the grinding motion parameters

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Fig. 14

Schematic of relief grinding by a double-cone-generating surface

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Fig. 15

Contraction of the generating wheel and the hob

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Fig. 16

Schematic of a four-axis hourglass worm-grinding machine

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Fig. 17

The helical surfaces after grinding

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Fig. 18

Schematic of a four-axis computer numerical control milling machine

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Fig. 19

The Rake face with spiral flute

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Fig. 20

Position of the hob and the double-cone grinding wheel

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Fig. 21

Process for grinding a relief surface

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Fig. 22

The hob with completed relief grinding

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Fig. 23

The no. 4 tooth with completed relief grinding

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Fig. 24

The measurement of the relief angle

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Fig. 25

Curves of the relief angles

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Fig. 26

Curves of the relief angles on the pitch circle

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Fig. 27

The measurement of the land width

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Fig. 28

Curves of the land widths

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Fig. 29

Curves of the land widths on the pitch circle

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