Pitch Line Synthesis of Noncircular Planetary Gears
Main Article Content
Abstract
During process of designing noncircular planetary gearing system, one of the most important tasks is synthesis of pitch lines of the gears with condition of preserving correct transmission function. In this work, the authors present a method for synthesizing pitch lines of the noncircular planetary gearing system based on given pitch line of the planetary gear. In comparison with previous experience-based methods, this work also sets the condition for the pitch line of the second sun gear, which will cover all the inside planetary gears. Moreover, the authors propose a synthesizing process of the pitch lines of the noncircular planetary gearing system.
Keywords
noncircular gears, noncircular planetary gears, planetary gear train, pitch lines
Article Details
References
[1] Emmanuel Poulle; Équatoires et horlogerie planétaire du XIIIe au XVIe siècle, Vols 2, Droz, Geneva and Champion, Paris (1980) pp. 1162.
[2] Leonardo da Vinci, Codex Madrid (1493).
[3] W.W. Boyd; Elliptical gears provide feed control, Mach. Des. 12 (1940).
[4] D. Dooner, H-D Yoon and A Seireg; Kinematic considerations for reducing the circulating power effects in gear-type continuously variable transmissions; Proc Instn Mech Engrs Vol 212, Part D (1998) 463 – 478, Doi: 10.1243/0954407981526118
[5] Fang Yan Zheng, Ai Hua Ren, Chuan Qiong Sun, Guo Xing Sun; The Optimization and Simulation of New Type Non-Circular Gears in CVT; Advanced Machanics and Materials, Vol 86 (2011) 684-687, Doi: 10.4028/www.scientific.net/AMM.86.684
[6] Takashi Emura, Akira Arakawa, A New Steering Mechanism Using Noncircular Gears (1992) 604-610, Doi: 10.1299/kikaic.57.154
[7] Dooner, D.B, Function generation utilizing an 8-Bar linkage and optimized noncircular gear elements with application to automotive steering, Institution of Mechanical Engineers, Part C (2001) 847-857, Doi: 10.1243/0954406011524090
[8] David B. Dooner, Kinematic geometry of gearing, Wiley, (2012)
[9] Fangyan Zheng, Lin Hua, Xinghui Han, Bo Li and Dingfang Chen, Synthesis of Shaped Noncircular Gear Using a Three-Linkage Computer Numerical Control Shaping Machine, Journal of Manufacturing Science and Engineering Vol 139 (2017), Doi: 10.1115/1.4035794
[10] Giorgio Figliolini, Jorge Angeles, The synthesis of elliptical gears generated by shaper – cutters, Journal of Mechanical Design, ASME, Vol. 125 (2003) 793-801, Doi: 10.1115/1.1631573
[11] Fangyan Zheng, Lin Hua, Xinghui Han, Bo Li, Dingfang Chen, Synthesis of indexing mechanisms with non-circular gears, Mechanism and Machine Theory 105 (2016) 108-128, Doi: 10.1016/j.mechmachtheory.2016.06.019
[12] Faydor L. Litvin, Ignacio Gonzalez-Perez, Alfonso Fuentes, Kenichi Hayasaka, Design and investigation of gear drives with non-circular gears applied for speed variation and generation of functions, Comput. Methods Appl. Mech. Engrg, 197 (2008) 3783–3802, Doi: 10.1016/j.cma.2008.03.001
[13] Faydor L. Litvin, Alfonso Fuentes-Azna, Ignacio Gonzalez-Perez, Kenichi Hayasaka, Noncircular Gears Design and Generation, Published in the United States of America by Cambridge University Press, New York (2009).
[14] D. Mundo, Geometric design of a planetary gear train with non-circular gears, Mechanism and Machine Theory 41 (2006) 456–472, Doi: 10.1016/j.mechmachtheory.2005.06.003
[15] Nguyễn Xuân Lạc, Nguyên lý máy chuyên nghiệp, Bách khoa 1969.
[16] Dazhu Li, Lian Xia, Youyu Liu, Jiang Han, Research on Non-circular Gear Hobbing Simulation Based on Piecewise Cubic Spline Fitting, Engineering Materials Vol 620 (2014) 357-362, Doi: 10.4028/www.scientific.net/KEM.620.357
[2] Leonardo da Vinci, Codex Madrid (1493).
[3] W.W. Boyd; Elliptical gears provide feed control, Mach. Des. 12 (1940).
[4] D. Dooner, H-D Yoon and A Seireg; Kinematic considerations for reducing the circulating power effects in gear-type continuously variable transmissions; Proc Instn Mech Engrs Vol 212, Part D (1998) 463 – 478, Doi: 10.1243/0954407981526118
[5] Fang Yan Zheng, Ai Hua Ren, Chuan Qiong Sun, Guo Xing Sun; The Optimization and Simulation of New Type Non-Circular Gears in CVT; Advanced Machanics and Materials, Vol 86 (2011) 684-687, Doi: 10.4028/www.scientific.net/AMM.86.684
[6] Takashi Emura, Akira Arakawa, A New Steering Mechanism Using Noncircular Gears (1992) 604-610, Doi: 10.1299/kikaic.57.154
[7] Dooner, D.B, Function generation utilizing an 8-Bar linkage and optimized noncircular gear elements with application to automotive steering, Institution of Mechanical Engineers, Part C (2001) 847-857, Doi: 10.1243/0954406011524090
[8] David B. Dooner, Kinematic geometry of gearing, Wiley, (2012)
[9] Fangyan Zheng, Lin Hua, Xinghui Han, Bo Li and Dingfang Chen, Synthesis of Shaped Noncircular Gear Using a Three-Linkage Computer Numerical Control Shaping Machine, Journal of Manufacturing Science and Engineering Vol 139 (2017), Doi: 10.1115/1.4035794
[10] Giorgio Figliolini, Jorge Angeles, The synthesis of elliptical gears generated by shaper – cutters, Journal of Mechanical Design, ASME, Vol. 125 (2003) 793-801, Doi: 10.1115/1.1631573
[11] Fangyan Zheng, Lin Hua, Xinghui Han, Bo Li, Dingfang Chen, Synthesis of indexing mechanisms with non-circular gears, Mechanism and Machine Theory 105 (2016) 108-128, Doi: 10.1016/j.mechmachtheory.2016.06.019
[12] Faydor L. Litvin, Ignacio Gonzalez-Perez, Alfonso Fuentes, Kenichi Hayasaka, Design and investigation of gear drives with non-circular gears applied for speed variation and generation of functions, Comput. Methods Appl. Mech. Engrg, 197 (2008) 3783–3802, Doi: 10.1016/j.cma.2008.03.001
[13] Faydor L. Litvin, Alfonso Fuentes-Azna, Ignacio Gonzalez-Perez, Kenichi Hayasaka, Noncircular Gears Design and Generation, Published in the United States of America by Cambridge University Press, New York (2009).
[14] D. Mundo, Geometric design of a planetary gear train with non-circular gears, Mechanism and Machine Theory 41 (2006) 456–472, Doi: 10.1016/j.mechmachtheory.2005.06.003
[15] Nguyễn Xuân Lạc, Nguyên lý máy chuyên nghiệp, Bách khoa 1969.
[16] Dazhu Li, Lian Xia, Youyu Liu, Jiang Han, Research on Non-circular Gear Hobbing Simulation Based on Piecewise Cubic Spline Fitting, Engineering Materials Vol 620 (2014) 357-362, Doi: 10.4028/www.scientific.net/KEM.620.357