Geometry and parameter design of novel circular arc helical gears for parallel-axis transmission

Zhen Chen,Bo Li,Liang Zhang,Jing Yang,Huafeng Ding,Linbo Luo

doi:10.1177/1687814017690957

Zhen Chen, Bo Li + Show 4 more

Open Access

https://doi.org/10.1177/1687814017690957

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Abstract

Based on the space curve meshing equation, in this article, a geometry design of a novel circular arc helical gear mechanism with pure rolling for parallel transmission was presented. Different from conventional circular arc gears, the meshing points of circular arc helical gears were limited at the instantaneous centre of rotation. The parameter equations describing the contact curves for both the driving gear and the driven gear were deduced from the space curve meshing equation, and parameter equations of the concave–convex circular arc profiles were established both for internal meshing and external meshing. Furthermore, a formula for the contact ratio was presented, and the impact factors influencing the contact ratio were discussed. Then, the parameter design was presented for the geometry parameters of tooth profiles, such as normal pitch, tooth height and tooth thickness. Using the deduced equations, several numerical examples were then considered, and prototype samples were produced to experimentally validate the contact ratio equation and the theoretical kinematic performance. The circular arc helical gear mechanism investigated in this study showed a high gear transmission performance such as a pure rolling meshing, a high contact ratio and a large comprehensive strength, when considering engineering applications.

Highlights

The meshing of conventional gears is usually based on the principle of conjugate surface meshing.[1,2,3] The basic kinematic relations proposed by Litvin and Fuentes[4] relate to the velocities of the contact point to the contact normal for a pair of gears that are in mesh
The results showed that the minimum tooth number of the circular arc helical gear mechanism (CAHGM) which can ensure a contact ratio larger than one is one, when the value range of the parameter Dt is sufficiently large
The geometry design of the CAHGM used for parallel axes transmission with concave–convex circular arc profile is presented in this article

Summary

Introduction

The meshing of conventional gears is usually based on the principle of conjugate surface meshing.[1,2,3] The basic kinematic relations proposed by Litvin and Fuentes[4] relate to the velocities of the contact point to the contact normal for a pair of gears that are in mesh. For a left-handed helical motion in the coordinate system S1, the parameter equations for the left-handed circular helicoid S1 can be written as Calculation of sliding ratios for CAHGM. Equation (23) indicates that if helix angle b remains constant, the contact ratio e of a CAHGM system depends on the tooth number and the variable parameter t of the helix, but not on u, R, a or r. The results indicate that when the parameter value range of cylindrical helix is fixed, the contact ratio increases with the tooth number. The concave–convex tooth profile of CAHGM has large synthetic curvature radius which could greatly reduce the contacting stress like the circular arc gears.

Experimental setup and kinematic performance tests

Experimental results and analysis

Conclusion