Geometric design, meshing simulation, and stress analysis of pure rolling cylindrical helical gear drives

Abstract

The geometric design, meshing performance, and mechanical behavior of pure rolling helical gear drives are presented. Parametric equations for contact curves on the pinion and gear are determined by coordinate transformation of the active designed pure rolling meshing line for the whole cycle of meshing. Moreover, parametric equations for the tooth surfaces of helical gears with convex-to-convex meshing type are derived according to the motion of generatrices in the transverse section along the calculated contact curves. Then, the basic design parameters are analyzed and formulas for calculation of the geometric size are given. The meshing performance and mechanical behavior, including contact patterns, loaded function of transmission errors, and variation of stresses for two pitch angles of meshing are compared with those of a reference design of micro-geometry modified involute helical gears. Besides, the influence of basic design parameters on tooth contact analysis and stress analysis is studied. The analysis of the results shows that the proposed pure rolling helical gears have the advantage of reducing the relative sliding between tooth surfaces and the possibility of designing pure rolling helical gears with a small number of teeth, though the contact strength of the surfaces is impaired. However, if the appropriate design parameters and Hermite curve parameters for the fillets are properly evaluated as proposed here, the mechanical behavior of the proposed pure rolling helical gear drive, in terms of contact patterns and variation of bending stresses can be superior to that of the micro-geometry modified involute helical gear drives.

Computerized Design, Simulation of Meshing and Stress Analysis of External Helical Gear Drives Based on Critical Control Points

“…The driving and driven tooth profiles contact at the point M, which is the meshing point, and when these two gears rotate, M forms the meshing line K-K in the fixed coordinate system as well as the contact curves C 1 and C 2 on the cylindrical axodes of the gear pair, respectively. In this study, the traditional design method of gear tooth surfaces based on the generation by a cutting tool is replaced by the active design method of the meshing line function [21][22][23][24][25][26], where the tooth profiles are designed by the position of their critical control points. The entire transverse tooth profile is formed by several control points, as illustrated in Figure 2, which is divided into different parts including the active tooth profile and the fillet by control points.…”

“…The meshing point M moves along the meshing lines K-K with the rotation of the gear pair. According to [23][24][25], the law of motion of the meshing point M along K-K providing a uniform velocity along the fixed axis z k is defined as…”

“…Besides this, Yu et al [20] introduced the master-slave concept for conjugate surface modeling and established the first free-form conjugation design in gearing, based on splines controlled by a set of control points that form a control polygon. Meanwhile, an alternative and convenient way to design pure rolling gears based on the active design of the meshing line function has been proposed recently [21][22][23][24][25][26], which was applied for transmissions between parallel shafts, intersecting shafts and rack and pinion. This new design method can be used for the free design of nongenerated gear tooth surfaces by setting a pair of transverse curves such as circular arcs in a mesh at the pitch point to form the active tooth profile according to the chosen meshing line function.…”

“…This new design method can be used for the free design of nongenerated gear tooth surfaces by setting a pair of transverse curves such as circular arcs in a mesh at the pitch point to form the active tooth profile according to the chosen meshing line function. Thus, the meshing type of parallel shaft transmissions is changed from line contact in non-modified involute gears to point contact for non-generated external gears [23,25]. Meanwhile, the recent development of additive manufacturing allows for the free design of gear tooth surfaces including non-generated gear tooth surfaces as proposed in this work.…”

Operating Performance of External Non-Involute Spur˝and Helical Gears: A Review

“…The gears have a large backlash which is harmful to the forward and reverse drives. Chen et al [66] and [67] also developed pure rolling helical gears with convex-to-convex meshing type and pure rolling rack and pinion mechanism. Geometric design, meshing performance, and mechanical behaviour were presented.…”