【作者】 谭昕；

【导师】 张仲甫；

【作者基本信息】 武汉理工大学 ， 机械设计及理论， 2003， 博士

【摘要】 平面二次包络环面蜗杆副作为一种优良的传动形式，具有多齿同时啮合、瞬时双线接触、啮合中易形成弹流动压润滑等优点，是完全符合机械传动领域发展趋势的产品。但是，由于目前加工该型蜗杆副的方法为对偶法，必须专门加工蜗杆和专用蜗轮滚刀，对于不同参数的蜗杆副蜗轮滚刀不能通用并且在加工中需多次对刀，导致平面二包蜗杆副加工成本高而精度低。本文作为“平面二次包络环面蜗杆副智能加工的建模与仿真”研究项目的一个组成部分，主要以在计算机中对平面二包蜗杆副进行三维建模和数字化造型为目标，在严格推导共轭齿面的基础上对平面二包蜗杆副齿面的组成进行了TCA分析，并运用适当的数学方法对蜗杆副型面进行重构，获得了适合于计算机表达的平面二包蜗杆副三维数字化模型。本文的主要创新点和成果如下： 基于经典共轭啮合理论，对平面二包蜗杆副的运动关系进行了严密分析，获得了蜗杆副齿面方程、蜗杆齿面一界曲线方程、蜗轮齿面二界曲线方程等一系列齿面分析所必须的数学公式，并深入研究了蜗杆副齿面接触线的算法，为蜗杆副的三维数字化造型打下了坚实的数学基础。 深入研究了传统平面二包蜗杆副的参数设计方案，指出传统设计方案没有充分考虑平面二包蜗杆副易于形成弹流动压润滑的优势。因此，提出以润滑性能为优化目标、以蜗杆强度、刚度、重量等为约束条件进行该型蜗杆副几何参数优化设计的方案，仿真结果表明该方案有明显效果。 运用推导获得的蜗杆理论齿面方程，精确描述蜗杆齿面的实际接触线，将蜗杆型面沿接触线进行离散，获得蜗杆实体的三维离散模型。在此基础上，在OpenGL编程环境下，以四边形网格构造蜗杆理论型面，以边界表示法中的半边数据结构表达蜗杆实体，获得蜗杆的三维实体模型及其型面数据。 在计算机虚拟环境下，运用实体交、并、差技术，模拟实际加工中的对偶范成法，虚拟包络出蜗杆型面。在虚拟加工过程中，又应用科学计算可视化技术的最新成果—驾驭式计算，对整个虚拟计算过程进行实时跟踪，并可对虚拟加工过程中蜗杆实体的齿厚数据进行驾驭。 为了获得蜗轮轮齿齿面的准确描述，按共轭理论计算了蜗轮齿面的实际接武汉理工大学博士学位论文触线，通过考虑蜗轮齿面的实际几何约束，确定了蜗轮齿面的实际啮合区，并运用数值方法精确计算了蜗轮齿面的边界线。在此基础上计算了实际接触线的长度并分析接触线总长随转角的变化规律，实现蜗轮齿面的计算机辅助TCA分析。 根据TCA分析的结果，运用截面法对蜗轮齿面进行离散处理。用一系列通过蜗轮轴线的截平面与蜗轮齿面求交，用数值计算常用的对分法求解交线上的一系列交点，从而将蜗轮齿面离散成型值点云。然后，运用三角Bemstai~B己zie:三角片对上述离散型值点云进行插值，获得近似Gl连续的构造齿面，为干涉检验、有限元分析、快速原形制造和数控加工等后续工作提供了合适于计算机表达的齿面模型。 最后，提出以球头刀为加工刀具、以五轴三联动的加工方式逐齿铣削完成蜗轮数控加工的理论加工方案。在这一方案下，提出以截交线上的型值点作为刀触点制定走刀轨迹的方法，以Y35J2型滚齿机为实践平台提出加工平面二包蜗杆副的数控改造方案，对这一方案进行了计算机仿真。仿真结果表明了蜗轮造型方法的正确性和蜗轮数控加工的可行性。更多还原

【Abstract】 Planar double-enveloping toroid worm gear drive is an excellent way to transmit torque and movement through two axes that are not parallel. It has many advantages such as several couples of teeth meshsing simultaneously, double touching lines on each interacting surface, high transmission ratio and heavy load, etc. And it’s easy to form elastohydrodynamics lubricant film between two interacting surfaces. But this kind worm gear drive is not used widely in China. The reason is that its manufacturing method-dual generating method-is outdated. In order to manufacture this type of worm gear drive precisely and cheaply, we should explore a whole new dis- dual generating method. As a part of the project "the modeling and simulation of Planar double- enveloping toroid worm gear drive’s intelligent manufacturing method", this dissertation focuses on the 3D modeling of Planar double-enveloping toroid worm gear in Computer. The author of this dissertation has completed lots of studies and researches in this field and has found some new methods for the 3D modeling of worm gear drive. Creative points and all tasks having be finished are briefly shown below:According to the classical space meshing theory, we have strictly deduced a series of formulae such as the equation of contacting line of worm, the equation of the second limiting curve of worm gear, and the equation of working surface and non-working surface, etc. And we have deeply studied the algorism of the actual contacting lines of worm gear drive.We have deeply studied the old design mode and point out that the lubricating advantages of this type of worm gear drive is not fully used. We put forward a new way which optimizes the lubricating property. The result of simulation proves our assumption.Based on the algorithm of contacting lines of worm, this dissertation uses 3D discrete contacting lines to depict a worm surface. Under OpenGL environment, we use four-side grids to reconstruct a worm surface and gain a solid modeling of worm.Under the computer virtual reality environment, we simulate the manufacturing process of dual generating method. Using "union", "subtract" and "interference" methods, a solid worm is formed in computer. Steering computation is used in this virtual manufacturing process.This dissertation strictly analyzes the worm gear surface. With regard to the restrains of geometries boundaries of the surface, we have finished the tooth contact analyses (TCA) and precisely drawn the actual contacting area on the surface. The relations between the total length of the actual contacting lines and the rotating angle of worm gear are also revealed in this dissertation.According to the TCA results, we use a series of planes which include the axis of worm gear to intersect with the worm gear surface, and calculate the intersecting points which belong to both plane and surface. Under this way, the surfaces are separated into lots of discrete points. Then we use Bernstain-Bezier triangles to interpolate these points and reconstruct the wormgear surface. A new digital model of worm gear is provided. We can use this digital model to CNC, RP&RM, Interference-detecting, etc.Finally, we refit a Y35J2 nobbing machine into a five- coordinate CNC machine. The simulation results show that the modeling method is correct and the CNC manufacturing scheme is feasible.更多还原