External high-order multistage modified elliptical helical gears and design procedure of their gear pairs

Abstract

In view of the limited quantity of modified segments for high-order and two-stage modified elliptical helical gears, and poor adjustment capacity for transmission ratio, the formation mechanism of a high-order multistage modified ellipse was studied, and a unified mathematical expression of the family of ellipses was derived. Thus, a design procedure for the helical gear pairs of the high-order multistage modified ellipse was suggested, and then their transmission characteristics were discussed exhaustively. Moreover, some checking methods such as curvature radius of pitch curve, convexity, pressure angle, undercutting, and contact ratio were offered. Finally, two design cases, including two-order and three-stage modified elliptical helical gear pair and two-order and four-stage one, were implemented. The cases indicate that a high-order multistage modified elliptical helical gear can be utilized in practice.

Keywords

Non-circular gears external gears high-order multistage modified ellipse helical gears gear pairs

Get full access to this article

View all access options for this article.

References

Liu

Zhao

. Kinematic principle analysis of transplanting mechanism with planetary elliptic gears in automatic vegetable transplanter. Transact Chinese Soc Agri Mach 2011; 42: 53–57. in Chinese).

Liu

Han

Zhang

. Research on hobbing process principles and linkage models for higher-order elliptic gear. Adv Mater Res 2012; 479–481: 2343–2346.

Zhao

Chen

. Kinematics modeling and analysis of deformed elliptic geared seven-bar linkage plant setting mechanism. China Mech Eng 2013; 24: 1001–1007.

Zhang

Nie

. Study and design on high-order deformed elliptic gears. J Xi'an Jiaotong Univ 2005; 39: 726–730. in Chinese).

Zhang

Nie

. Investigation on CAD system of the ellipse species gears. Transact Chinese Soc Agric Mach 2006; 3: 138–141. in Chinese).

Yao

. Design of non-circular gears, Beijing: China Machine Press, 2012. chap. 2. (in Chinese).

Litvin

Fuentes

. Gear geometry and applied theory, 2nd ed. New York: Cambridge University Press, 2004. chap. 12.

Mathworks. “quadl,” Documentation Center, http://www.mathworks.cn/cn/help/matlab/ref/quadl.html (2014, accessed 21 June 2014).

Gao

. Optimization of part -building orientation based on mixed genetic algorithm for layered manufacturing. China Mech Eng 2003; 14: 1645–1648. in Chinese).

10.

Mathworks. “trapz,” Documentation Center, http://www.mathworks.cn/cn/help/matlab/ref/trapz.html (2014, accessed 21 June 2014).

11.

Tsai

Kolibal

. The golden section search algorithm for finding a good shape parameter for meshless collocation methods. Eng Anal Boundary Element 2010; 34: 738–746.

12.

Ding

Hong

Sun

. Approach to accuracy improvement and uncertainty determination of radius of curvature measurement on standard spheres. Measurement 2013; 46: 3220–3227.

13.

Liu

Han

Xia

. Hobbing strategy and performance analyses of linkage models for non-circular helical gears based on four-axis linkage. Strojniski Vestnik-J Mech Eng 2012; 58: 701–708.

14.

Xia

Liu

. A linkage model and applications of hobbing non-circular helical gears with axial shift of hob. Mech Mach Theor 2013; 70: 32–44.

15.

Zhang

Huang

Han

. Research of flexible beam impact dynamics based on space probe-cone docking mechanism. Adv Space Res 2012; 49: 1053–1061.