基于双参数点矢量族包络的异形螺旋曲面宽行磨削方法研究

The five-axis form grinding for special shaped helicoid has great engineering application value in the area of automobile, aviation and aerospace, national defense and energy. Due to the lack of support on pointed principal and method, its grinding precision and application area are restricted. This project will conduct the research based on the envelope to a two-parametric family of point vectors and learn from the theory of helicoid form grinding and research achievements of surface five-axis machining. Firstly, research on the digital approaching method of wheel profile calculating, establish the eliminating model of wheel interference or undercutting, and the optimization model of wheel profile; secondly, research on the cross product imprint method and its geometry feature, establish the combination expression model of the swept surface of a wheel. Afterwards, research on the method of determining the initial path and profile of wheel, and the global optimization of wheel based on least squares fitting of wheel envelope surface, optimize wheel profile to eliminate the undercuttin error that cannot be deal with by global optimization of tool path, thus establish a global optimization model of wheel path which profile and path can optimize together. At last, conduct the simulation analysis and experimental verification. This research will provide principle support on kinematic geometry method for the five-axis form grinding of helicoids with special shape, and has wide range application prospects in the precision manufacturing of precision transmission parts, complex cutting tools and high level CNC equipments.

异形螺旋曲面宽行磨削在汽车、航空航天、国防及能源等行业有着极高的工程应用价值，但因缺乏针对性的原理与方法支撑，致其加工精度与实际应用范围受限。本项目基于双参数点矢量族包络原理，借鉴螺旋曲面成形加工理论以及直纹面宽行铣削研究成果进行研究。首先，研究成形砂轮廓形设计的数字逼近法，建立砂轮干涉或过切消除模型、砂轮廓形优化模型；其次，研究矢积特征法及其几何特性，建立砂轮扫掠体包络面的组合表达模型；接着，进行砂轮初始路径及廓形确定方法、基于最小二乘法曲面拟合的砂轮路径整体优化方法研究，并优化砂轮廓形以消除路径整体优化方法不能处理的过切误差，从而建立廓形联变的砂轮路径整体优化模型；最后，进行仿真分析及磨削实验验证。项目研究可为异形螺旋曲面宽行磨削提供运动几何学原理与方法支撑，并在精密传动零件、复杂刀具精密制造以及高档数控装备中具有广阔的应用前景。

本项目针对拓扑修形齿轮的精密加工难题，提出了双参数点矢量族包络理论，开展拓扑修形齿轮的成形砂轮和蜗杆砂轮磨削关键技术研究。首先，提出双参数点矢量族包络方法，建立拓扑修形齿面的数字模型。其次，针对拓扑修形齿轮成形砂轮磨削，建立点矢量族一次包络模型，规划成形砂轮运动轨迹，通过砂轮包络面仿真，显化成形磨削原理性误差，提出成形误差减小方法，并通过成形磨齿实验验证了方法的正确性。接着，针对拓扑修形齿轮的蜗杆砂轮磨削，建立了点矢量二次包络模型，规划了蜗杆砂轮运动轨迹，通过实例验证了点矢量二次包络方法的正确性，并基于齿面扭曲产生原因分析，提出了齿面扭曲补偿方法。最后，将所提理论应用于拓扑修形齿轮成形磨削实验，以及蜗杆砂轮磨齿机功能软件开发中，实现了研究成果的转化。.项目经权威专家鉴定为达到国际先进水平，获得2016年重庆市科技进步一等奖，发表SCI/EI论文6篇，授权发明专利6项，软件著作权3项。项目成果为异形螺旋曲面精密磨削提供了理论基础与方法支撑，应用前景广阔。