高速列车头型共形映射建模理论研究

Conformal mapping-based analytical modeling on head shape of high-speed train

高速列车头部外形趋向流线化 ,其数学模型建立难度大 ,限制了头型几何参数优化求解及工程设计研究。本文应用近代复变三角插值共形映射理论和法线迭代收敛方法及三次样条插值 ,求解复杂高速列车三维头型与轴对称二维模型的相互转换函数及头型解析数学模型 ,使头型建模优化及其快速 CAD/ CAM一体化成为可能 。

With the fast development of high speed train, the streamline train head is adopted to satisfy its aerodynamic characteristics. It is especially difficult to model the irregular geometry by one continuous formula. Traditional train head surface is often divided into a number of parts described by spline and put together after manufacture. So it is difficult to optimize its geometry parameters and realize the exact machining. Complex conformal mapping theory with triangle interpolation iterative method, normal convergence and spline longitudinal interpolation are presented in this paper to transform the train head into axis symmetric model. By this method, the continuous analytical model is solved, which makes CAD/CAM possible. This also helps its finite element modeling and parameters optimizing. At last, this method is verified by an example of streamline train head.