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Research Papers: Design of Direct Contact Systems

A Method to Generate the Spiral Flutes of an Hourglass Worm Gear Hob

[+] Author and Article Information
Jie Yang

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

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

Chengjie Rui

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

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 August 19, 2017; final manuscript received March 21, 2018; published online April 17, 2018. Assoc. Editor: Hai Xu.

J. Mech. Des 140(6), 063301 (Apr 17, 2018) (12 pages) Paper No: MD-17-1571; doi: 10.1115/1.4039769 History: Received August 19, 2017; Revised March 21, 2018

All of the cutting edges on an hourglass worm gear hob have different shapes and spiral angles. If the spiral angles are small, straight flutes are typically adopted. However, for hobs with multiple threads, the absolute values of the negative rake angles on one side of the cutting teeth will greatly affect the cutting performance of the hob if straight flutes are still used. Therefore, spiral flutes are typically adopted to solve this problem. However, no method to determine the spiral flute of an hourglass worm gear hob has been proposed until now. Based on the curved surface generating theory and the hourglass worm forming principle, a method for generating the spiral flute of the planar double enveloping hourglass worm gear hob is proposed in this paper. A mathematical model was built to generate the spiral flute. The rake angles of all cutting teeth of the hob are calculated. The laws of the rake angles of the cutting teeth for four hobs with different threads from one to four threads were analyzed when straight flutes and spiral flutes are adopted. The laws between the value of the negative rake angles of the hob with four threads and the transmission ratio were studied. The most appropriate transmission ratio for generating the spiral flute was obtained. The machining of the spiral flutes was simulated using a virtual manufacturing system, and the results verify the correctness of the method.

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Figures

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Fig. 1

The hourglass worm gear driving and the hob

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Fig. 2

Coordinate systems of helical surface machining

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Fig. 3

Machining the helical surface using a flat grinding wheel

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Fig. 4

Coordinate systems of rake face machining

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Fig. 5

Schematic diagram of the flute machining

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Fig. 6

Cylindrical generating surface

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Fig. 7

The rake angle at an arbitrary point P on the side cutting edge: (a) the side cutting edge and (b) the rake angle on point P

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Fig. 8

The laws of the rake angles of the hob with one thread

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Fig. 9

The laws of the rake angles of the hob with two threads

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Fig. 10

The laws of the rake angles of the hob with three threads

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Fig. 11

The laws of the rake angles of the hob with four threads

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Fig. 12

The law of the rake angles on the left side of the hob

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Fig. 13

The laws of the rake angles on the right side of the hob

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Fig. 14

The laws of the rake angles for teeth no. 3 and no. 5

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Fig. 15

The laws of the rake angles when iq1 = −0.0105

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Fig. 16

The laws of the left side rake angles of the straight flute hob

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Fig. 17

The laws of the right side rake angles of the straight flute hob

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Fig. 18

The laws of the left side rake angles of the spiral flute hob

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Fig. 19

The laws of the right side rake angles of the spiral flute hob

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Fig. 20

Machining the helical surfaces of the basic worm: (a) the left side helical surface and (b) the right side helical surface

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Fig. 21

Machining the spiral flutes of the hob

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Fig. 22

Simulation results: (a) the helical surface of the basic worm and (b) the spiral flute of the hourglass worm gear hob

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Fig. 23

Measuring the angle: (a) the normal vector at the rake face and the helical surface of the basic worm and (b) the result of the angle measurement

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