Study of optimal strategy and linkage-model for external non-circular helical gears shaping

Abstract

As an efficient manufacturing method for gears, shaping technology developed for non-circular helical gears will greatly break through the dilemma of their applications; especially for those gears with part of pitch curves being concave, being not able to be hobbed. Two fundamental linkage-models for external non-circular helical gears were built based on the meshing theory of non-circular gears in this article. According to four linkage methods in plane and two kinds of additional rotation in vertical direction, eight shaping strategies and their practical linkage-models (1)–(8) were developed. Taking a three-order elliptic helical gear as an example, the kinematic characteristics of the eight practical linkage-models were analyzed, which reveals that equal arc-length of gear billet (models (3) and (4)) have the highest accuracy under a given efficiency. The dynamic characteristics of models (3) and (4) were analyzed, which shows that model (4) (equal arc-length of gear billet and additional rotation on shaper cutter) is better in performance, and is an optimal one. The optimal linkage-model was demonstrated to be valid by a virtual shaping, and be able to shape those non-circular helical gears with part of pitch curves being concave. Moreover, the accuracy among every gear tooth is uniform. The theory developed and the results of the virtual shaping were illustrated with a shaping experiment. The train of thought and the results will be useful for any external non-circular helical gears with free pitch curves.

Keywords

Non-circular helical gears external gears gear shaping optimal strategy accuracy of gear tooth

Get full access to this article

View all access options for this article.

References

Liu

Nagamura

Ikejo

. Simulation on the vibration characteristics of elliptical gears. Proc IMechE, Part C: J Mechanical Engineering Science 2013; 227(4): 819–830.

Litvin

Gonzalez-Perez

Fuentes

. Design and investigation of gear drives with non-circular gears applied for speed variation and generation of functions. Comput Methods Appl Mech Eng 2008; 197(45–48): 3783–3802.

Chen

. Study on a new non-uniform and intermittent mechanism. China Mech Eng 2012; 23(23): 2778–2782.

Luo

. Parameters optimization of pick-up mechanism of planetary gear train with ellipse gears and incomplete non-circular gear. Trans Chin Soc Agric Machinery 2013; 44(6): 62–68.

Lin

Hou

Gong

. Flow characteristics of high-order ellipse bevel gear pump. J Drainage Irrigat Machinery Eng 2011; 29(05): 379–385.

Alexandru

Macaveiu

Alexandru

. Design and simulation of a steering gearbox with variable transmission ratio. Proc IMechE, Part C: J Mechanical Engineering Science 2012; 226(10): 2538–2548.

Wang

Lim

Ding

. Multi-tooth contact behavior of helical gear applying modified meshing equation. Proc IMechE, Part C: J Mechanical Engineering Science 2013; 227(1): 146–160.

Litvin

Fuentes

. Gear geometry and applied theory, 2nd edition. New York, NY: Cambridge University Press, 2004.

Brinksmeier

Lübben

Fritsching

. Distortion minimization of disks for gear manufacture. Int J Machine Tools Manuf 2011; 51(4): 331–338.

10.

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(12): 701–708.

11.

Zhao

Gao

Chen

. Design and parameters optimization of deformed eccentric non-circular gears transplanting mechanism. Trans Chin Soc Agric Machinery 2011; 42(12): 74–77.

12.

Xia

Liu

. A linkage model and applications of hobbing non-circular helical gears with axial shift of hob. Mech Machine Theory 2013; 70(12): 32–44.

13.

Liu

Zhang

Han

. Graphic simulation of hobbing process for higher-order elliptic gear. Adv Mater Res 2012; 482–484: 466–469.

14.

Cheng

Ding

. CAD/CAM and machining simulation of non-circular gear. Machinery Des Manuf 2010; 229(03): 66–68.

15.

Rajurkar

Sundaram

Malshe

. Review of electrochemical and electrodischarge machining. Procedia CIRP 2013; 6: 13–26.

16.

Guan

Liao

Meng

. Study of cutting precision gear wheel with fiber laser. Appl Laser 2005; 25(06): 365–368.

17.

Hsu

. A study on precision forging of spur gear forms and spline by the upper bound method. Int J Mech Sci 2002; 44(8): 1543–1558.

18.

Cesarettia

Dinib

De Kestelierc

. Building components for an outpost on the Lunar soil by means of a novel 3D printing technology. Acta Astronaut 2014; 93(2): 430–450.

19.

Yao

. Design of non-circular gears, Beijing: China Machine Press, 2012.

20.

Blinder

. Guide to essential math, 2nd ed. London: Academic Press, 2013.

21.

Liu

Han

Zhang

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

22.

Liu

. Study on some common close convex pitch curves of noncircular gear pair. Trans Chin Soc Agric Machinery 2007; 38(06): 143–146.

23.

Liu

Han

. Research on hobbing process strategy for non-circular helical gears and performance analyses for the functional models. Trans Chin Soc Agric Machinery 2013; 44(5): 281–287.

24.

Fei

Deng

Zhang

. Research on embedded CNC device based on ARM and FPGA. Procedia Eng 2011, pp. 818–824.

25.

Bloemen

MCT

van Gerven

van der Wal

MBA

. An objective device for measuring surface roughness of skin and scars. J Am Acad Dermatol 2011; 64(4): 706–715.

26.

Chen

Zhang

. Investigation of error separation for three dimensional profile rotary measuring system. Measurement 2014; 47(2): 627–632.