包络锥蜗杆传动的啮合理论与失配技术研究

The main content of this research project is to study the meshing geometry of the enveloping spiroid gearing and its mismatched technique. The generating flank of the helicoidal surface of the spiroid involves the plane, the conical surface, the toroidal surface, etc. The global meshing characteristics of an enveloping spiroid drive with line contact are investigated, such as the working length of the spiroid, the scope of the conjugate zone on the tooth surface of the spiroid gear, and the distribution of the instantaneous contact lines. Meanwhile the local meshing characteristics of the drive are investigated, including the induced principal curvature, the angle of slide and so on. The undercutting mechanisms of the enveloping spiroid and the mating spiroid gear are proclaimed, and the related shunning measures are proposed. Finally the geometric design method for an enveloping spiroid gear set is advised. In order to simplify the manufacturing technology and reduce the sensitivity to the assembly errors, the ease-off enveloping spiroid drive is proposed. Two mismatched strategies are put forward. One is to make differences between the generating flank of the conical hob and the helicoid of the spiroid deliberately, and the other is to replace the spiroid gear by some gear with simple fabrication process, for example a Gleason hypoid gear, under some certain modified conditions. The spiroid gear pair obtained according to the later mismatched strategy may be called the pseudo spiroid gear drive. The momentary contact point in a mismatched enveloping spiroid pair is worked out by means of solving the nonlinear equations, and then to determine the contact zone on the tooth surface of the spiroid gear and to acquire the transmission error of the mismatched drive by employing the improved local synthesis approach. On the basis of a sufficient numerical simulation research, the preferred ease-off way is recommended and a feasible geometrical design method is summed up for a mismatched enveloping spiroid drive. The enveloping spiroid gear pair with typical parameters is trial-manufactured to verify the theoretical conclusions after experimental tests.

本项目研究包络锥蜗杆传动的啮合原理与失配技术。涉及的锥蜗杆螺旋面产形面有平面、锥面和圆环面等。对于线接触包络锥蜗杆副，研究锥蜗杆工作长度、锥蜗轮齿面共轭区范围与瞬时接触线分布等全局啮合特性，及诱导主曲率和滑动角等局部啮合特性；揭示锥蜗杆和锥蜗轮根切的机理，给出避免措施；提出合理的几何设计方法。为了简化制造工艺、降低对装配误差的敏感性，提出失配啮合制包络锥蜗杆传动。失配策略大致有两种：合理人为设置锥蜗杆螺旋面和锥滚刀产形面的差异，实现失配点接触；在适宜修形条件下，以Gleason准双曲面齿轮等制造工艺相对简单的齿轮，代替锥蜗轮，形成伪锥蜗杆传动。通过求解非线性方程组，得到失配包络锥蜗杆副瞬时接触点，进而利用改进的局部综合法，确定齿面接触区及传动误差。在充分数值仿真研究基础上，推荐首选失配方案，总结出失配传动的几何设计方法。试制具有典型参数的包络锥蜗杆副，进行试验测试，验证理论分析的结论。

建立了各种包络锥蜗杆传动的啮合理论，包括：锥面包络锥蜗杆传动的啮合理论，圆环面包络锥蜗杆传动的啮合理论和平面包络锥蜗杆传动的啮合理论。系统研究了包络锥蜗杆传动的各种类型，包括：锥面包络锥蜗杆传动，圆环面包络锥蜗杆传动和平面包络锥蜗杆传动。其中，每种传动类型又各被细分为正交型和非正交型两类。大量数值算例研究表明各种类型的包络锥蜗杆传动均具有优良的啮合性能，例如：锥蜗轮齿面啮合区宽阔，锥蜗杆有效工作螺纹足够长，瞬时接触线分布均匀，齿面接触强度分布均匀，齿面间润滑条件优良。提出了锥面包络锥蜗杆传动的失配技术原理。数值算例研究表明失配型锥面包络锥蜗杆传动的啮合性能优良，同时对误差和变形的敏感性低。改进了基于参考点的啮合理论，提出了新的确定参考点的方法和计算齿面压力角的方法，拓展了该理论的应用范围。