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An accurate calculation method of side mill profile from the coordinates of discrete points of helicoid section curve

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Abstract

According to the gearing principle, the side mill for machining the helicoid (cylindrical helical surfaces of constant pitch) can be calculated from the parametric equation of the helicoid section curve. However, in practice, only a series of discrete point coordinates on the work-piece section curve were measured, which lead to the low calculation accuracy, especially when the section curve is composed of multi-segments, the calculation accuracy at the connection point (cusp) is lower. To improve the calculation accuracy, this paper first deduced the contact condition formula, and pointed out that the first derivation of discrete points had a great impact on the calculation accuracy. Then, an improved curve fitting method was proposed to calculate the first derivation of discrete points. In order to further improve the calculation accuracy at the cusp, a method of piecewise solving the cutter profile was proposed. Finally, calculation examples of the side mill profile of the main screw of a three screw pump, as well as a screw pump rotor, were carried out. The results show that the calculation accuracy of the improved curve fitting method is high, and the method of piecewise solving the cutter profile of discrete points is feasible.

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Data availability

The data used to support the findings of this study are available from the corresponding author upon request.

Code availability

The code used to support the findings of this study is available from the corresponding author upon request.

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Acknowledgements

The authors thank Dr. Wu Fan for drawing some CAD drawings for this paper.

Funding

This research is supported by “the Fundamental Research Funds for the Central Universities of China (Grant No. PA2021GDSK0096).”

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Authors and Affiliations

  1. Anhui Province Key Lab of Aerospace Structural Parts Forming Technology and Equipment, Institute of Industry & Equipment Technology, School of Mechanical Engineering, HeFei University of Technology, Hefei, 230009, People’s Republic of China

    Lihua Zhou, Suping Fang & Kangkang Ding

  2. State Key Laboratory for Manufacturing System Engineering, School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, People’s Republic of China

    Suping Fang

  3. Gear PE(Japan) Office, Setagaya-ku, Tokyo, 155-0031, Japan

    Yoshiki Kawasaki

Authors
  1. Lihua Zhou
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  2. Suping Fang
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  3. Kangkang Ding
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  4. Yoshiki Kawasaki
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Contributions

Zhou Lihua is mainly responsible for methodology, software, and writing; Fang Suping is mainly responsible for supervision, resources, and project administration; Ding Kangkang is mainly responsible for original draft preparation; Yoshiki Kawasaki is mainly responsible for investigation and validation.

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Correspondence to Suping Fang.

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Zhou, L., Fang, S., Ding, K. et al. An accurate calculation method of side mill profile from the coordinates of discrete points of helicoid section curve. Int J Adv Manuf Technol 120, 4849–4861 (2022). https://doi.org/10.1007/s00170-022-08932-8

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