基于动凝聚和线性互补的齿轮动态接触分析  

Gear Dynamic Contact Analysis Method Based on Dynamic Condensation and Linear Complementarity

作　　者：董昭荣 张楚 董惠敏[1] DONG Zhaorong;ZHANG Chu;DONG Huimin(School of Mechanical Engineering,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学机械工程学院,大连116024

出　　处：《组合机床与自动化加工技术》2023年第12期174-177,182,共5页Modular Machine Tool & Automatic Manufacturing Technique

基　　金：国家重点研发计划项目(2018YFB2001504)。

摘　　要：有限元方法是研究齿轮传动性能的主要方法,但是其求解过程中大量非线性运算使其分析过程需要耗费大量的计算机资源与时间。因此对三级近似递推缩减公式进行迭代推导得出新的动凝聚公式,提高凝聚方法的计算精度。并且针对齿轮三维动态啮合条件下的接触分析提出一种点面线性互补动态接触分析有限元方法,结合新推导的动凝聚公式将整体计算维度凝聚到主自由度。以Bozzak-Newmark方法将微分方程转变为代数方程,建立主从动齿轮接触的线性互补关系并进行求解。分别利用所提出的方法与ANSYS瞬态动力学计算结果对比,验证线性互补齿轮动态接触分析的计算精度,提高齿轮动态接触分析的计算效率。For dynamic contact analysis of strongly nonlinear gear transmission caused by the large computation time consuming problem.This article first was based on the level 3 approximate recursive reduction formula for iteration.The new dynamic condensation formula is deduced,and combined with linear complementary aspects and the finite element method proposed contact analysis method based on dynamic condensation and linear complementary gear dynamic.The reduction matrix was used to converge the whole calculation dimension to the principal degree of freedom,and the contact linear complementary relationship was established between the points and surfaces of the meshing tooth surfaces of the principal and slave gear.The differential equation was transformed into an algebraic equation by using the Bozzak-Newmark method,so that the dynamic contact analysis and solution of gear could be achieved with high precision and fast speed.

关 键 词：动凝聚 点面接触分析 线性互补 有限元方法 

分 类 号：TH16[机械工程—机械制造及自动化] TG502[金属学及工艺—金属切削加工及机床]