Geometry design and mathematical model of a new kind of gear transmission with circular arc tooth profiles based on curve contact analysis

A new meshing relationship for gear drive to characterize the conjugation geometry is studied in this paper based on conjugate curves. Conjugate curves are described as two smooth curves always keep continuous and tangent contact with each other in given contact direction under motion law. The general principle of curve meshing is developed for the given spatial or plane curve. The meshing equation along arbitrary direction of contact angle is derived. The properties of geometric and motion of the contact of conjugate curves are discussed. According to the equidistance-enveloping method, tubular meshing surfaces are proposed to build up circular arc tooth profiles, which inherit all properties of conjugate curves. The geometry design and mathematical model of the gears are established. Three types of contact pattern of tooth profiles are generated: convex-to-convex, convex-to-plane and convex-to-concave. A calculation example for convex-to-concave tooth profiles of gears is provided. Theoretical and numerical results demonstrate the feasibility and correctness of proposed conjugate curves theory and it lays the foundation for the design of high performance gear transmission.

[1]  E. Buckingham.  Analytical mechanics of gears , 1949 .

[2]  Daren Wu,et al.  A Geometric Theory of Conjugate Tooth Surfaces , 1992 .

[3]  F. Litvin,et al.  Gear geometry and applied theory , 1994 .

[4]  Faydor L. Litvin,et al.  New developments in the design and generation of gear drives , 2001 .

[5]  S. Barone.  Gear Geometric Design by B-Spline Curve Fitting and Sweep Surface Modelling , 2001, Engineering with Computers.

[6]  Shih-Hsi Tong,et al.  Design of new tooth profiles for high-load capacity gears , 2001 .

[7]  Jack Phillips.  General Spatial Involute Gearing , 2003 .

[8]  Feng Xianying,et al.  Study on the design principle of the LogiX gear tooth profile and the selection of its inherent basic parameters , 2004 .

[9]  Christos Spitas,et al.  Optimizing involute gear design for maximum bending strength and equivalent pitting resistance , 2007 .

[10]  Derek G. Chetwynd,et al.  Investigation of a novel elastic-mechanical wheel transmission under light duty conditions , 2008 .

[11]  David B. Dooner,et al.  Kinematic Geometry of Gearing: Dooner/Kinematic Geometry of Gearing , 2012 .

[12]  Stephen P. Radzevich.  Theory of Gearing: Kinematics, Geometry, and Synthesis , 2012 .

[13]  David B. Dooner,et al.  Kinematic Geometry of Gearing , 2012 .

[14]  K. Ting,et al.  Conjugate Curve Design with Spline Contact Path , 2012 .

[15]  Renping Shao,et al.  Dynamic characteristics of cracked gear and three-dimensional crack propagation analysis , 2013 .

[16]  Zihni B. Saribay.  Tooth geometry and bending stress analysis of conjugate meshing face-gear pairs , 2013 .

[17]  Yangzhi Chen,et al.  A generalized space curve meshing equation for arbitrary intersecting gear , 2013 .

[18]  Hou Liang,et al.  Active design of tooth profiles using parabolic curve as the line of action , 2013 .

[19]  Dong Liang,et al.  The generation principle and mathematical model of a new involute-helix gear drive , 2013 .

[20]  Jiqiang Xia,et al.  Design of noncircular bevel gear with concave pitch curve , 2013 .