齿轮变摩擦三维接触问题有限元混合法求解及程序设计

【作者】 周炜；

【导师】 唐进元； 李国顺；

【作者基本信息】 中南大学 ， 机械设计及理论， 2011， 硕士

【摘要】 本文以齿轮接触模型-接触算法-接触特性仿真为主线展开。首先对齿轮静态、准静态和冲击-动力接触模型进行研究,基于有限元法和接触理论给出不同接触模型的适用场合和计算方法。借用Fortran语言编制求解齿轮接触问题的有限元程序包,对二维平面应力和三维条件下齿轮接触进行模拟。本文主要工作和创新点如下：1.针对齿轮静态接触模型,介绍其力学描述、适用场合和优缺点；研究有限元静力算法,利用自制程序包分别计算平面应力和三维条件下给定接触力时的轮齿变形；2.针对齿轮准静态接触模型,介绍其力学描述、适用场合和优缺点；研究准静态接触问题的有限元混合法,并针对三维圆柱齿轮接触轴向摩擦力较小的特点,提出用摩擦合力作为迭代变量应用于接触求解,以此加快收敛速度；利用自制程序包分别对Stribeck摩擦平面应力和三维条件下的齿轮接触进行计算,探讨接触合力、节点接触分力和节点接触状态随相对滑动速度的变化规律,并与Coulomb摩擦条件下的计算结果进行对比；3.针对齿轮冲击-动力接触模型,介绍其力学描述、适用场合和优缺点；针对齿轮正常啮合过程中由于速度突变导致的冲击现象,提出齿轮传动啮合接触冲击概念；研究冲击-动力接触问题的有限元混合算法,利用自制程序包对Stribeck摩擦平面应力下齿轮啮合接触冲击进行计算,讨论不同初始冲击速度下各接触点对法向冲击力、摩擦力以及法向冲击合力和摩擦合力的变化规律,并与Coulomb摩擦条件下的结果作对比分析；4.应用LS-DYNA程序包对三维齿轮传动啮合接触冲击进行计算,研究初始冲击速度、冲击位置对冲击合力、冲击应力和冲击时间的影响,并利用最大冲击力解析解对所得结果进行对比验证,最后给出不同冲击条件下齿面最大接触应力点在整个冲击过程中的分布规律。本文针对不同齿轮接触模型,给出相应处理算法,利用自制程序包着重探讨Stribeck摩擦条件下齿轮啮合接触-冲击问题。通过商用软件和试验的对比验证,表明本文工作是有效的。更多还原

【Abstract】 The thesis is developed with the main thread:gear contact model-contact algorithm-contact characteristic simulation. The employment is first devoted to study of static, quasi-static and dynamic contact model of gear device, aiming at which applicable situations and calculating methods are presented based on finite element method along with contact theory. The program packages for gear contact problem are worked out by Fortran language, and are imposed to simulate gear engagement under two dimensional plane stress and three dimensional conditions respectively. The main parts and innovation points are:1. The mechanical description, applicable occasions, advantages and shortcomings for gear static contact model are illustrated. The finite element static algorithm is proposed. The deformations under given contact forces in plane stress and three dimensional conditions are computed respectively by the designed program package.2. The mechanical description, applicable occasions, advantages and shortcomings for gear quasi-static contact model are illustrated. The mixed finite element method for quasi-static contact problem is studied. The technique for three dimensional spur gear contact is put forward for the sake of increasing convergence speed on the basis of convenience to identify axial friction, where resultant friction force is treated as iterative variable to attain solution. The designed program package is employed to analyze gear contact problem with Stribeck friction model under plane stress and three dimensional conditions, where the changing rules of resultant contact forces, nodal contact components and nodal contact states with relative sliding velocity are discussed, and are compared with those gained in Coulomb friction model.3. The mechanical description, applicable occasions, advantages and shortcomings for gear dynamic contact model are illustrated. The concept of contact-impact for gear transmission is introduced in view of the impact phenomenon as a result of a sudden change in velocity during the natural meshing process. The mixed finite element method for dynamic contact problem is researched. The designed program package is used to calculate the gear impact question under plane stress condition with Stribeck friction model, where the nonal normal contact forces, nonal friction, the resultant normal contact forces and friction under different initial impact velocities are computed, and are compared with those obtained with Coulomb friction model.4. Three dimensional gear contact-impact analysis is implemented by LS-DYNA code, in which the relationship between initial impact velocity, impact position with resultant contact force, contact stress, impact time is inquired into. The achieved results are inspected by analytical solution of maximal contact force. The distribution law of maximal stress points on tooth surface during the entire impact process under diverse impact conditions is also offered.The thesis commits itself to providing corresponding processing algorithms for different gear contact model, and probing into gear contact problem with Stribeck friction model by designed program package. The validity of work in this paper is acquired by the contrastive analysis with commercial software together with experiment.更多还原