Design and investigation of a cycloid helical gear drive

In this paper, an original analysis of the geometric design of a parallel-axis cycloid helical gear drive and an investigation on its basic meshing characteristics are presented. This type of gear drive consists of a pinion with one tooth and a cycloid-helix gear in continuous line contact along the whole length of the tooth. Firstly, mathematical formulations of their tooth surfaces are derived based on the envelope theory and homogeneous coordinate transformation. Secondly, the undercutting analysis is applied to determine the design constraint to avoid the undercutting on the cycloid-helix gear tooth surface. Then, the meshing characteristics including the contact lines, surface of action, induced normal curvature are analyzed. Numerical example is presented to demonstrate the influence of design parameters on the contact stress distribution. Finally, the loaded tooth contact analysis is performed to simulate the tooth contact condition and to validate the stress distribution by the finite element method.