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Analytical design of a special whirling cutter for a flawless cutting of the concave cycloid profile in whirling milling for various types of vacuum pump screw rotor

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Abstract

A vacuum pump mainly consists of intermeshing screw rotors, which apply a cycloid profile to enhance the operating performance. However, it yields a concave rotor profile, increases the machining difficulty, and requires precision accuracy in the manufacturing process. This study proposes an analytical design of a particular whirling cutter and the rotor cutting method considering double tilt angles and assembly offset setting. The cutting simulation is demonstrated in analytical methods and virtual machining for various vacuum pump screw rotors. The analytical cutting result indicates that the overall lengthwise rotor profile deviation is identical. Besides, the virtual machining result indicates that the tooth surface topology is smooth and uniform, and the maximum profile deviation is still much more undersized than the grinding allowance. Moreover, the proposed method is still reliable for various vacuum pump rotors of Kashiyama type, Quimby type, Hanbell Precise Machinery P series, and Hanbell Precise Machinery P series with clearance design, where their delta deviations consistently tinier than 0.1 mm. Finally, it verifies that the proposed analytical design of the whirling cutter design, utilization of double tilt angles, and assembly offset setting are reliable for various vacuum pump rotors applying whirling milling machining.

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Data availability

All data generated or analyzed during this study are included in the manuscript.

Abbreviations

A c :

center distance between rotor axes (mm)

C :

axial displacement of each machine

E :

assembly offset (mm)

E d :

center distance between the vacuum pump rotor and the cutter (mm)

N :

normal vector

n :

unit normal vector

r :

position vector

r p :

pitch radius of the rotor (mm)

s p :

screw parameter of the rotor

α h :

end-relief angle of the cutter (degree)

β f :

back-rake angle of the cutter (degree)

β s :

side-rake angle of the cutter (degree)

γ 1 :

inclination angle of the cutter (degree)

γ 2 :

twist angle of the cutter (degree)

Δ :

assembly offset (mm)

δ n :

normal deviation (μm)

ε :

geometrical parameter for rotation direction of the rotor

θ :

geometrical parameter for axial direction of the rotor

ϑ :

geometrical parameter for rotation direction of the cutter

ψ :

wrap angle of the rotor (degree)

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Acknowledgements

The authors are grateful to the Ministry of Science and Technology in Taiwan for its financial support under project number MOST 109-2221-E-008-004-MY2 and to Hanbell Precise Machinery Co., Ltd., in Taiwan, for their technical and financial support.

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Not applicable.

Funding

This research was supported by the Ministry of Science and Technology in Taiwan, project number MOST 109-2221-E-008-004-MY2.

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Authors and Affiliations

  1. Department of Mechanical Engineering Education, Universitas Negeri Yogyakarta, 01, Colombo Rd, Karangmalang, Yogyakarta, 55281, Indonesia

    Achmad Arifin

  2. Department of Mechanical Engineering, National Central University, 300, Zhongda Rd., Zhongli District, Taoyuan City, 320317, Taiwan (R.O.C.)

    Yu-Ren Wu & Yu-Hsien Tseng

  3. Research Center for Appropriate Technology, National Research and Innovation Agency (BRIN), Subang, 41213, Indonesia

    Moeso Andrianto

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Contributions

Achmad Arifin constructed the research design and composed the manuscript. Yu-Ren Wu earned the funding and directed the research accomplishment. Moeso Andrianto verified the research result. Yu-Hsien Tseng demonstrated the research implementation by accomplishing the analytical simulation and validating the result. All authors worked concurrently to proofread and structure the submission.

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Correspondence to Yu-Ren Wu.

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Arifin, A., Wu, YR., Tseng, YH. et al. Analytical design of a special whirling cutter for a flawless cutting of the concave cycloid profile in whirling milling for various types of vacuum pump screw rotor. Int J Adv Manuf Technol 129, 5403–5420 (2023). https://doi.org/10.1007/s00170-023-12632-2

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