Dynamic Analysis of Line Gear Pair Based on Numerical Manifold Method

As a kind of tiny gear based on space curve meshing theory, the line gear is very suitable for miniaturized machines due to its compact size and low weight. However, the line gear usually suffers from serious vibration problems since its line teeth are designed as twisted three-dimensional cantilevers to provide conjugated meshing curves. A dynamic model of the line gear pair is established in this paper using the numerical manifold method (NMM) to alleviate its vibration conditions, which can simultaneously provide mathematical and physical covers. The displacement function is first derived for the line teeth, and the dynamic equations of the manifold element are acquired. After inspecting the reasons that cause meshing excitation, the dynamic response of the line teeth is attained in all three orthogonal directions. The attained dynamic response shows that the vibration in the axial gear direction is more significant than that in the curvature direction. Furthermore, the vibration differential equations of the line teeth are solved through a detailed example, and the relationship between the design parameters and the natural frequency is revealed. The vibration characteristics of the first four order of the line gear are revealed through the method of NMM and compared with the result that is carried out through the commercial finite element method (FEM). The comparison shows that NMM can efficiently relieve the vibration problems of the line gear.