渐开线圆柱齿轮的参数化建模与接触等几何分析
Parametric Modeling and Isogeometric Contact Analysis of Cylindrical Involute Gear
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摘要: 渐开线圆柱齿轮的齿面接触力学性能是保障齿轮传动稳定性和可靠性的关键, 针对传统有限元方法设计仿真割裂带来的接触计算流程复杂和精度较低等问题, 提出一种基于NURBS表达的渐开线圆柱齿轮参数化建模及单齿啮合等几何接触仿真方法. 首先根据齿轮几何设计参数采用最小二乘法拟合方法重构齿轮轮廓曲线, 再分片构造齿轮平面模型, 对平面模型进行偏置创建面向等几何分析的NURBS实体参数化模型; 然后基于点面法详细推导二维齿轮平面模型和三维齿轮实体模型的无摩擦等几何接触计算相关公式; 最后通过数值仿真算例, 将等几何计算结果与商业软件计算结果进行对比, 验证了所提方法在齿轮接触计算中的有效性. 结果表明, 该方法在齿轮接触数值计算方面展现出了更优的收敛效果, 为齿轮的接触分析和设计仿真一体化提供了一种有效的解决方案.Abstract: 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.