【摘要】 介绍了螺旋翅片管的结构特点,用空间解析几何的方法分析了螺旋翅片管结构的本质特征,用螺旋面和螺旋线的基本性质解析了螺旋翅片管的几何性质.给出了翅片表面任意点的切线和次法线向量表达公式.为了研究轧辊与轧件的空间几何关系,推导了轧辊与轧件的坐标变换公式,以此为基础给出了轧片与轧件的切点坐标公式以及轧片半径的求解公式.更多还原

【Abstract】 Spatial analytic geometry is introduced to analyze the essentially geometric characters of integral helical finned tubes and the spatial relationship between rollers and rolled pieces in the rotary rolling process. A mathematical model is constructed for helical finned tubes based on the concept of helicoidal surfaces and cylindrical helixes. The binormal vector and tangential vector of any point on the helix,corresponding to the roller’s axial vector on the point of the tube surface,are achieved by an expression with the main structural parameters of helical finned tubes. In order to research the spatial relationship between rollers and rolled pieces,two coordinate systems are established to set rollers and rolled pieces respectively,and a coordinate transformation expression between the two coordinate systems is deduced. Based on coordinate transformation,the process is introduced to deduce the value of roller radius and the coordinate values of contact points between rollers and rolled pieces.更多还原