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

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.

Nonrelative sliding gear mechanism based on function-oriented design of meshing line functions for parallel axes transmission

“…where T is the variable parameter of helix. The parametric equations of equations (13) and 14indicate that the contact curves for parallel axes transmission with a uniform motion of meshing points have the same expression as reported in Chen et al 21 The driving and driven contact curves are both equal-pitch cylindrical helixes:…”

“…Chen et al 21 reported a design method of conjugated concave-to-convex meshing circular arc helical surfaces according to the equal-pitch cylindrical helical motion of generatrix circles along cylindrical helixes. In the study reported in Chen et al, 21 the generatrix circles were located in the normal plane of cylindrical helix. In this study, the plane generatrix curves are located in a plane passing through the rotation axes and perpendicular to the bottom plane.…”

Nonrelative sliding of spiral bevel gear mechanism based on active design of meshing line

“…A design method of conjugated concave–convex meshing circular arc helical surfaces based on constant pitch cylindrical helical motion of plane generatrix circles along cylindrical helixes was previously proposed, whereby the generatrix circles were located in the normal plane of the cylindrical helix. 19 In this study, the plane generatrix curves are located in a plane that cuts through the axes of rotation.…”

“…According to the parametric equations of the tooth surfaces and parametric equations (25) to (31) and (33), a pair of 3D solid models for a nonrelative sliding gear mechanism with uniformly accelerated motion of meshing points was modeled and the results of the assembly simulation are presented in Figure 8. According to the calculation formula of contact ratio in Chen et al., 19 the value of contact ratio of this pair of nonrelative sliding gears with uniformly accelerated motion of meshing points is 1.33. According to differential geometry, the spiral angle at T=π/3 is 55.45∘.…”

“…Alternatives to traditional spiral bevel gear design arose with the development of space curve meshing theory, [17][18][19][20][21] and new types of gears have been designed for transmission between intersecting axes, such as the space-curve meshing-wheels, 18 and are based on conjugate contact curves and not conjugate surfaces. Chen et al 22 deduced a generalized space curve meshing equation for an arbitrary angle intersecting gear pair, and spatial helix gears were designed for transmission between arbitrary angle intersecting axes.…”