基于整体误差的非圆柱齿轮齿面三维拓扑测量与精度评价方法研究

Aiming at the problem of complex tooth profile shape, the lack of precision standard, the difficulty of error measuring process, a method of the three-dimensional topology measurement and precision evaluation for noncircular gear tooth surface based on integrated error theory is proposed. According to the gear error geometry theory, the error type and precision index which can describe the transmission error of noncircular gear will be analyzed, it will provide the theoretical foundation for error measurement technology. Based on the coordinate measuring method, the theoretical model of digital gear tooth surface and the three dimensional topological error measurement model of the real tooth surface on noncircular gears will be established, through complete analysis on the coordinate transformations, the trace planning method and the probe radius compensation in the process of error measurement, the optimal algorithm of measurement data analysis will be obtained. Based on the multi-degrees of freedom theory for gear error, the integrated error of noncircular gear tooth surface can be described with deviation surface, which is the difference between real tooth surface and theoretical tooth surface at the same points, the corresponding relation and variation law between various order error of tooth surface and individual error of gear will be studied by means of error decomposition method, the Error evaluation and the measurement uncertainty evaluation process will also be analyzed respectively. Through the above research, An effective method for accurate measurement of noncircular gear error can be obtained, the new method can provide complete data for the transmission quality evaluation and the error source analysis of noncircular gears, and then which can provide the theoretical basis for improving the manufacturing precision of noncircular gears.

针对非圆柱齿轮齿廓形状复杂、缺少精度标准以及误差测量困难等问题，提出基于整体误差的非圆柱齿轮齿面三维拓扑测量与精度评价方法。根据齿轮误差几何学理论，分析能够表征非圆柱齿轮传动误差的误差类型和精度指标，为其误差测量提供理论依据；基于坐标测量法，分别建立非圆柱齿轮数字化齿面理论模型和真实齿面三维拓扑误差测量模型，通过对测量过程的坐标变换、路径规划、测头半径补偿等问题的系统分析，研究测量数据处理的最优算法；基于齿轮误差多自由度理论，研究采用真实齿面和理论齿面之间的差值构成的差曲面来表征非圆柱齿轮齿面整体误差，通过误差分解来分析齿面各阶误差与齿轮单项误差的对应关系及变化规律，并进行误差评定和测量不确定度评价。通过上述研究，可获得一种非圆柱齿轮误差精确测量的有效方法，为非圆柱齿轮传动质量的评定和误差来源分析提供较完整的数据，进而为提高非圆柱齿轮的制造精度提供理论依据。

本项目以非圆柱齿轮为研究对象，开展其齿面误差三维拓扑测量与精度评价方法研究。根据非圆柱齿轮齿廓形成原理和齿形分布规律，建立了能够表征直齿、斜齿非圆柱齿轮传动误差的项目和精度评定指标；推导了各项误差计算公式，分析了非圆柱齿轮节曲线的向径、极角、弧长等参数与各精度指标之间的几何关系；通过引入特征系数来表征不同结构参数的非圆柱齿轮误差，分析了非圆柱齿轮误差与其结构参数之间的变化规律，确定了非圆柱齿轮精度标准及公差数值。根据齿轮啮合原理及非圆柱齿轮齿面方程，建立了精确的三维数值齿面模型，并基于节曲面方程，建立了不同测量方法下的非圆柱齿轮的坐标测量模型。推导了测量机坐标系、工作台坐标系及工件坐标系之间的变换矩阵；获取了测量机坐标系统与工件坐标系统的匹配关系，并建立了坐标系统之间偏离量的数据处理模型，在此基础上推导了齿面待测点理论坐标处法矢量的计算公式。根据齿轮加工方法以及三维形貌特征，推导了非圆柱齿轮的结构参数与测球半径的对应关系，分析测头半径对坐标测量值的影响规律，确定测头半径补偿算法；根据被测非圆柱齿轮的几何拓扑关系定义三维扫描的边界，依据不同的约束条件，获取了最优的无干涉扫描路径以及测量系统的误差补偿方法；结合边界条件下非圆柱齿轮三维齿面误差数据的曲面拟合算法。通过实验测量非圆柱齿轮的齿面数据，利用测量点云数据重构了非圆柱齿轮整体误差曲面，根据实际齿面与理论齿面之间的偏差进行误差曲面拟合，获得非圆柱齿轮三维齿面拓扑误差曲面；通过齿轮误差多自由度分解，分析了实际齿面各阶误差与齿轮单项误差的对应关系及变化规律；建立了齿形误差、齿向误差评定模型，进行非圆柱齿轮拓扑误差评定算法研究，通过不同测量方式的非圆柱齿轮三维齿面误差测量实验，研究误差补偿策略并进行测量不确定度评价，最终建立了一套可以用于指导非圆柱齿轮齿面误差测量评定的分析方法。.本项目在国内外学术期刊及国际会议发表论文24篇，其中SCI/EI收录12篇，授权发明专利2项；培养毕业研究生16人。