Tooth contact analysis of a curvilinear gear set with modified pinion tooth geometry

Abstract

This article investigated the contact behaviours of a modified curvilinear gear set for parallel-axis transmission, which exhibits a pre-designed parabolic transmission error (TE) and localized bearing contact. The proposed gear set is composed of a modified pinion with curvilinear teeth and an involute gear with curvilinear teeth. Tooth contact analysis enabled the authors to explore the influences of assembly errors and design parameters on TEs and contact ellipses of this gear set. It is observed that TEs were continuous and the contact ellipses were localized in the middle of the tooth flanks, even under assembly errors. Finite-element contact analysis was performed to study stress distributions under different design parameters. In addition, numerical examples are presented to demonstrate the contact characteristics of the modified curvilinear gear set.

Contact stress and transmission errors under load of a modified curvilinear gear set based on finite element analysis

“…Mathematical models of the modified curvilinear gears have been developed according to the theory of gearing 9,10 and the generation mechanism. 11,31 Modified curvilinear pinion and gear tooth surface…”

“…The application of cutters with a circular-arc instead of a straight edge in their normal sections introduced a pre-designed parabolic TE when the modified curvilinear gear set was under an ideal meshing condition. 11,31 Moreover, the proposed modified curvilinear gear set was insensitive to axial misalignments and would provide continuous parabolic TE even when axial misalignments were present. Figure 3 shows the formation of the 3D imaginary rack cutter AE i (i ¼ P and G for pinion and gear, respectively) to generate the pinion/gear by moving its normal section along a curve of radius E i (i ¼ P and G for pinion and gear, respectively).…”

“…Based on the theory of gearing, the tooth surfaces of the modified curvilinear pinion can be represented in the S 1 ðX 1 , Y 1 , Z 1 Þ coordinate system using the following equations 11,31 x and f 1 ð 1 , P , P Þ ¼ R P ðcos P À cos n Þ À S P 2 Â cos P sin P AE E P ð1 À cos P Þ sin P À R P ðsin P À sin n Þ cos P cos P Ç r 1 1 sin P ¼ 0…”

“…However, center distance variation of the gear set results in unfavorable discontinuous TEs. 6 A recent study 11 proposed a modified curvilinear gear set comprising a modified pinion with curvilinear teeth and an involute gear with curvilinear teeth. TCA results show that a pre-designed parabolic TE and localized bearing contact can be obtained under axial misalignments or center distance misalignment.…”

“…The proposed gear set is expected to exhibit point contact and parabolic TE under an ideal meshing condition. Based on the mathematical models of the pinion and the gear, 11 a mesh generation program was developed to establish the finite element (FE) model of the gear tooth surface. This study focused on the mesh density of possible contact areas predicted using TCA.…”