Parametric Modeling and Isogeometric Contact Analysis of Cylindrical Involute Gear

The mechanical contact properties of tooth surfaces in cylindrical involute gears are critical for ensuring the stability and reliability of gear transmission systems. To address the challenges of complex contact calculations and the limited accuracy caused by the separation of design and simulation in traditional  finite element methods, this paper proposes a parametric modeling approach using NURBS(non-uniform rational B-splines)and an isogeometric contact simulation method for gear meshing behavior. First, the gear profile curve is reconstructed based on geometric design parameters using the least squares fitting method. A multi-patch gear plane model derived from the reconstructed curve is then offset to create a NURBS-based solid parametric model for isogeometric analysis. Detailed formulations for frictionless isogeometric contact calculations of both two-dimensional gear plane models and three-dimensional solid models are developed using the node-to-surface method. Finally, numerical simulations validate the proposed approach by comparing isogeometric results with those obtained from commercial software. The findings highlight the method’s superior convergence in gear contact calculations, offering a robust solution for accurate gear contact analysis and the seamless unification of design and simulation.