Evaluating lightweight gear transmission error: a novel nonlinear finite element approach using direct constraint contact algorithm

With the growing demand for lightweight gear transmission systems, composite materials have emerged as a promising solution due to their high specific properties. However, the complexity of designing gear pairs with composite materials necessitates the development of reliable numerical procedures. This study presents a robust numerical approach using a flexible multibody method through the MSC MARC solver to accurately estimate static transmission error (STE) in lightweight gears, considering the nonlinear behavior caused by gear contact. The Finite Element (FE) model uses the Multi-Point Constraint equations (MPCs) to ensure the non-penetration condition considering a node-to-surface contact detection. The proposed method is compared against commercial software for standard gear pair cases, demonstrating its effectiveness in addressing complex structures based on composite materials. The numerical procedure is further applied to analyze hybrid metal-composite gear pairs and compared to a holed one. The results provide insights into the time evolution and harmonic components of STE, highlighting the advantages of hybrid gears in terms of reduced vibrations and noise for the same mass reduction compared to holed gears. Additionally, ply arrangements resulting in quasi-isotropic properties of the composite disc are compared to unidirectional laminates to highlight the fiber orientation effect on the STE results.