弧齿锥齿轮的向量式有限元静态啮合分析

Static Meshing Analysis of Spiral Bevel Gears Based on Vector Form Intrinsic Finite Element Method

针对目前向量式有限元的类型和应用范围,根据向量式有限元的基本理论推导了八节点六面体实体单元的基本理论计算式,阐述了逆向运动和单元内力的求解过程,将向量式有限元的应用范围拓展到空间和工程应用领域。对于空间实体结构的接触行为,采用主从面算法和内外算法分别进行了全局搜索和局部搜索,以实现碰撞检测,并通过罚函数法来处理接触问题。以一对弧齿锥齿轮为例,建立了向量式有限元模型,利用该模型进行了分析和计算,并将计算结果与传统有限元计算结果进行了对比,结果表明:通过向量式有限元计算得到的接触力、接触应力以及齿面印痕等与传统有限元方法计算的结果吻合程度较高,并且可以在网格单元较少的情况下得到较为精确的结果。

According to the basic theory of the vector form intrinsic finite element （VFIFE） and its element type and current applications, basic theoretic formulas of the hexahedral entity element are derived by calculating reverse movement and element inner forces, which extends VFIFE application to complex solid structures and engineering fields. For the collision-contact behavior of solid surfaces, the master-slave algorithm and inside-outside algorithm are used to perform global search and local search between the particie and hexahedral mesh surface of the outer entity surface, and a penalty method based on the central differential formula is presented for the analysis of collision response. Taking a pair of spiral bevel：gears： for example, its model is established and analyzed by VFIFE, and the results are compared with that of finite element method （FEM）. COmparison shows that the stress, contact force and contact pattern agree well with the FEM results, and the VFIFE method is efficient for analyzing solid structures with a relatively sparse grid.