内啮合斜齿轮高精度三维有限元自动建模方法

Research on The Automatic Modelling Method for High Precision Finite Element Model of Internal Helical Gear

为提高内啮合斜齿轮有限元接触分析的建模速度和模型精度,提出了一种齿轮高精度三维有限元模型的自动建模方法。基于齿轮插刀齿廓方程,利用齿廓法线法,得到包括齿根过渡曲线的内、外斜齿轮端面齿廓,建立了内、外齿轮参数化粗网格有限元模型。开发了表层六面体网格剖分方法,自动识别齿面接触带单元,进行分级剖分细化,保证了有限元模型的建模精度和网格密度。进行了齿面接触分析,得到了内啮合斜齿轮的弯曲应力、接触应力、接触印痕、传动误差、时变啮合刚度和载荷分配率。粗细网格有限元模型计算结果对比分析表明,该方法提高了内啮合斜齿轮有限元建模效率和计算精度,缩短了计算时间,为快速准确的齿轮接触分析奠定了基础。

In order to improve the accuracy and efficiency of tooth contact analysis of internal helical gears,an automatic modeling method of high-precision three-dimensional finite element model of internal helical gear is proposed.The dentiform normal method is applied to derive the tooth profile equations of the internal and external helical gear on the basis of the accurate description of the gear cutter.The parameterized coarse mesh finite element model of internal and external gears are established.Local multi-level refinement method of the hexahedral element has been developed to identify the element on the tooth surface in the contact region automatically to ensure the accuracy and mesh density of the gear finite element model.The tooth contact analysis was carried out,to obtain the bending stress,contact stress,contact stress distribution,transmission error,time-varying meshing stiffness as well as load sharing ratio of the helical internal gears.Comparison of the coarse mesh model with the refined mesh model indicate that the methodology proposed in this paper improves the modeling speed and calculation accuracy of the internal gears,but greatly shorten the computing time,which lays the foundation for fast and accurate internal gear tooth contact analysis.