基于齿面自然活动标架的点啮合齿面数字化设计和制造技术研究

The idea of curved surface moving frame based on differential geometry is proposed to study design and CNC manufacture technology for point-contact tooth surface to achieve CNC manufacture technology for point-contact tooth surface oriented directly to the multi-axis CNC machine tools. The proposed research works can improve the nowaday CNC manufacture technology for point-contact tooth surface, which still follows the traditional technology based on the cradle machine tools, to adequately utilize the universal manufacture capability of the multi-axis CNC machine tools and machine the point-contact tooth surface in according to the predesigned meshing characteristics. The proposed research works are an improvement or a development of the traditional manufacture technology for the point-contact tooth surfaces, which will effectively improve the transmission technology of the point-contact gears. Thus, the proposed research works are useful to society and innovative in theory..The contents of the proposed research works cover: (i)a geometric nonlinearity elastic-kinetics theory for the point-contact tooth surfaces based on modern mathematical ideas, e.g., manifold, exterior differentiation and moving frame, etc, which will accurately compute stress and strain in the contact area and predict the gear pair noise characteristics, (ii)a control strategy of the related motion between the cutter and the workpiece based on the multi-axis CNC machine tools to generate the point-contact tooth surfaces provided with predesigned meshing characteristics, (iii)a head-cutter surface design method with which the predesigned head-cutter surfaces generate the various point-contact tooth surfaces in according to the predesigned precision. The above-mentioned reveals that the proposed research works are academically important and possessed of good application outlooks.

将微分几何的曲面自然活动标架理论引入点啮合齿面的设计和CNC制造研究领域，研究直接面向多轴联动数控机床的点啮合齿面的数字化制造技术；改变当前在多轴联动数控齿轮加工机床上沿用基于摇台式齿轮加工机床的点啮合齿面的设计和展成技术的状况，充分发挥多轴联动数控机床的万能成形功能，使点啮合齿面的加工完全按设计所预定的齿面啮合性能进行。本研究是传统点啮合齿面设计和展成技术在数控技术条件下的发展和完善，将有效提高点啮合齿面传动技术水平，具有重要的社会意义和理论创新性。.运用微分流形、外微分法和曲面活动标架等现代数学工具，研究能精确分析啮合区应力、应变分布和预测齿面啮合噪音的点啮合齿面几何非线性弹性动力学理论；研究在多轴联动数控机床上按预定的齿面啮合特性展成点啮合齿面的刀具相对工件运动的控制方法；研究针对不同齿面结构、满足预定齿面加工精度的盘铣刀曲面设计方法。本项目具有重要的学术意义和良好的应用前景。

当前点啮合齿面数字化设计和制造技术依赖和受限于特定的加工机床，其齿面设计理论无法对点啮合齿面进行大范围整体拓扑结构设计以满足预定的重载啮合特性要求；其齿面加工理论无法充分利用多轴联动数控加工机床的万能运动功能，完全按点啮合齿面大范围整体拓扑结构设计要求加工齿面。针对当前点啮合齿面设计和制造技术的缺陷，基于微分几何学的曲面活动标架理论，提出了一种以包络特征曲线为样条曲线的复杂曲面的重构方法——曲面包络逼近理论。以此为基础，构建了全新的点啮合齿面数字化设计和制造技术理论。与以往点啮合齿面的数字化设计和制造方法相比，此方法的理论创新和工程价值在于：（1）以点啮合齿面活动标架作为齿面设计和加工的坐标系，以给定的第一齿面及其点接触迹线和刀具曲面的内蕴运动不变量作为设计第二齿面和齿面加工运动控制的参数，形成了具有通用性的，可对齿面啮合特性进行全局优化的点啮合齿面设计和加工方法，保证齿面设计与齿面加工的无缝对接。（2）齿面设计以无载啮合时两齿面间隙作为预测和控制重载情况下的接触区的设计目标参数，建立了点啮合齿面整体优化设计的泛函极值模型；相应地，齿面加工以刀具包络面与设计齿面之间的间隙作为加工运动优化的控制目标，建立了点啮合齿面多轴联动数控加工运动泛函极值模型，实现了齿面大范围整体加工精度控制与齿面重载啮合特性要求的统一。（3）以满足预定的重载啮合特性或齿面加工精度要求为目标，建立了旋转刀具曲面优化设计的泛函极值模型，进一步保证所研究点啮合齿面设计和加工理论的可行性和精确性。研究和实验表明：（1）基于曲面包络逼近理论的点啮合齿面的数字化设计和制造理论充分利用了多轴联动数控加工机床的万能运动功能，提高了齿面设计和加工的精度。（2）曲面包络逼近理论同样适用于解决大型平坦敞口复杂曲面的非球面刀具宽行加工的刀具运动规划问题和以功能为导向的空间运动机构的设计问题。