Mathematical Model of a Vertical Six-Axis Cartesian CNC Machine for Producing Face Milled and Face Hobbed Bevel Gears

[+] Author and Article Information
Ruei-Hung Hsu

No. 100, Wenhwa Road, Seatwen Taichung, 407 Taiwan rhhsu@fcuoa.fcu.edu.tw

Yi-Pei Shih

No. 43, Keeling Road, Section 4 Taipei, 10607 Taiwan shihyipei@mail.ntust.edu.tw

Zhang-Hua Fong

160, Sanhsing Village Minhsiung Chiayi, Taiwan 621 Taiwan imezhf@ccu.edu.tw

Chin-Lung Huang

No. 64, Wunhua Rd., Huwei Yunlin, 63201 Taiwan clhuang@nfu.edu.tw

Szu-Hung Chen

No.101, Renhua Rd., Dali Dist. Taichung, 412 Taiwan chen.lioness@gmail.com

Shih-Sheng Chen

No. 250, Kuo-Kuang Road Taichung, 40227 Taiwan aprilxsteel@gmail.com

Yi-Hui Lee

No.168, Sec. 1, University Rd., Minhsiung, Chiayi, 62102, Taiwan, R.O.C. Chiayi, 62102 Taiwan yhlee@alum.ccu.edu.tw

Kuan-Hung Chen

No.168, Sec. 1, University Road, Minxiong Township, Chiayi County 621, Taiwan (R.O.C.) Chiayi, 62102 Taiwan mr.taroz@gmail.com

Tzu-Ping Hsu

No.168, Sec. 1, University Rd. Chiayi, 62102 Taiwan szp0520@gmail.com

Wei-Jen Chen

No.168, Sec. 1, University Rd. Chiayi, 62102 Taiwan avril50535@gmail.com

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received May 2, 2019; final manuscript received July 14, 2019; published online xx xx, xxxx. Assoc. Editor: Hai Xu.

ASME doi:10.1115/1.4044433 History: Received May 02, 2019; Accepted July 20, 2019


Prior to the development of sophisticated computer numerical control (CNC), both face milling (FM) and face hobbing (FH), the two most popular technologies for bevel gear production, required cradle-type machines with diverse and complicated mechanisms. In the last two decades, however, the gear industry has replaced these traditional machines with six-axis CNC bevel gear cutting machines that have superior efficiency and accuracy. One such machine is a vertical six-axis machine with a vertical spindle arrangement, which offers two industrially proven advantages: compact design and maximum machine stiffness. The technical details of this machine, however, remain undisclosed, so this paper proposes a mathematical model that uses inverse kinematics to derive the vertical machine's nonlinear six-axis coordinates from those of a traditional machine. The model also reduces manufacturing errors by applying an effective flank correction method based on a sensitivity analysis of how slight variations in the individual machine setting coefficients affects tooth geometry. We prove the model's efficacy by first using the proposed equations to derive the nonlinear coordinates for pinion and gear production and then conducting several cutting experiments on the gear and its correction. Although the numerical illustration used for this verification is based only on FM bevel gears produced by an SGDH cutting system, the model is in fact applicable in the production of both FM and FH bevel gears.

Copyright © 2019 by ASME
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