Geometric design and simulation of tooth profile using elliptical segments as its line of action

Abstract

A mathematical model of gear tooth profiles using the ellipse curve, whose curvature is convenient to control by changing the mathematical parameters as its line of action, was built based on the meshing theory. The equation of undercutting condition was derived from the model. A special epicycloidal tooth profile was also presented. An example gear drive with variation of the ellipse parameters was taken to illustrate the proposed method. The contact ratio of the gear drive designed by the proposed method was analyzed. A comparison of the property of the gear drive designed with the involute gear drive was also carried out. The results confirm that the proposed gear drive has higher contact ratio in comparison with the involute gear drive.

Keywords

gear transmission / tooth profile / elliptical segment / epicycloidal / contact ratio

References

[1] LUOS-m, WUY, WANGJian. The generation principle and mathematical models of a novel gear drive [J]. Mechanism and Machine Theory, 2008, 43(12): 1543-1556

[2] CHENX-x, LIUY-s, XINGJ-z, LINS-z, XUWei. The parameter design of double-circular-arc tooth profile and its influence on the functional backlash of harmonic drive [J]. Mechanism and Machine Theory, 2014, 73(3): 1-24

[3] FUENTESA, RUIZ-ORZAEZR, GONZALEZ-PEREZI. Computerized design, simulation of meshing, and finite element analysis of two types of geometry of curvilinear cylindrical gears [J]. Computer Methods in Applied Mechanics and Engineering, 2014, 272(15): 321-339

[4] BAIRB W, SUNGM H, WANGJ S, CHENC F. Tooth profile generation and analysis of oval gears with circular-arc teeth [J]. Mechanism and Machine Theory, 2009, 44(6): 1306-1317

[5] CHENB-k, ZHONGH, LIUJ-y, LIC-y, FANGT-ting. Generation and investigation of a new cycloid drive with double contact [J]. Mechanism and Machine Theory, 2012, 49(3): 270-283

[6] TSAIM H, TSAIY C. Design of high-contact-ratio spur gear using quadratic parametric tooth profiles [J]. Mechanism and Machine Theory, 1998, 33(5): 551-564

[7] WANGJ, LUOS-m, WUYue. A method for the preliminary geometric design of gear tooth profiles with small sliding coefficients [J]. ASME, Journal of Mechanical Design, 2010, 132(5): 1-8

[8] DANIELIG A, MUNDOD. New developments in variable radius gears using constant pressure angle teeth [J]. Mechanism and Machine Theory, 2005, 40(2): 203-217

[9] WANGP Y, FONGZ H. Fourth-order kinematic synthesis for face-milling spiral bevel gears with modified radial motion (MRM) correction [J]. ASME Journal of Mechanical Design, 2006, 128(2): 457-467

[10] LEEC K. Manufacturing process for a cylindrical crown gear drive with a controllable fourth order polynomial function of transmission error [J]. Journal of Materials Processing Technology, 2009, 209(1): 3-13

[11] CAOX-m, FANGZ-d, XUH, SUJ-zhan. Design of pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors [J]. Chinese Journal of Aeronautics, 2008, 21(2): 179-186

[12] TSAIY C, HSUW Y. The study on the design of spiral bevel gear sets with circular-arc contact paths and tooth profiles [J]. Mechanism and Machine Theory, 2008, 43(9): 1158-1174

[13] FONGZ H, CHIANGT W, TSAIC W. Mathematical model for parametric tooth profile of spur gear using line of action [J]. Mathematical and Computer Modelling, 2002, 36(4/5): 603-614

[14] WANGJ, HOUL, LUOS-m, WUYue. Active design of tooth profiles using parabolic curve as the line of action [J]. Mechanism and Machine Theory, 2013, 67(9): 47-63

[15] LITVINF L, FUENTESAGear geometry and applied theory [M], 20042nd edNew YorkCambridge University Press