基于齿面参数化表示的准双曲面齿轮的设计

Design of Hypoid Gear Tooth Surface Represented by Non-Uniform Rational B-Spline Polynomial

为了能将拟合齿面模型用于准双曲面齿轮的设计,采用加工仿真方法获得了齿面上离散型值点坐标数据,完成了齿面非均匀有理B样条的曲面拟合.依据准双曲面齿轮的主动设计原理,解决了在已知齿面的NURBS表示、齿面接触迹线和传动比函数的条件下来设计未知齿面的关键技术,给出了基于离散化齿坯模型的加工仿真算法,将齿面的接触分析问题转化成一个优化问题,从而构建了齿面接触分析模型,并在其中采用啮合点法线与啮合点间连线之间的夹角趋于0的条件替代了法线重合条件.研究结果表明,齿面的NURBS表示模型可以作为面向准双曲面齿轮设计与制造过程的统一模型,以该模型为基础,可以完成齿面设计、数控机床刀位数据生成和坐标测量路径规划等一系列重要工作.

In order that the digital tooth surface model can be used in design of hypoid gear, based on the discrete tooth surface points obtained by computerized simulation, a mathematical model is established by non-uniform rational B-spline(NURBS) polynomial and it can be employed in the processes of designing,manufacturing and measuring. This digital model and the function-oriented active design technique have been combined to form a new designing method for hypoid gears. According to the theory of the function-oriented design of hypoid gear, the mathematical models and algorithms of machining process simulation, design and analysis meshing and contact have been proposed for the tooth surface represented by NURBS surface. The new theory and method have a good adaptability to computerized numerical control(CNC) bevel gear cutting machines and coordinate measurement machine(CMM) and can be used to create the initial machine tool cutting location data or measurement path planning. An actual example is provided to verify its correctness. .