齿轮三维误差表征与分解

Characterization and Decomposition of Gear 3-D Deviation

复杂曲面测量技术的发展使得快速获取齿轮齿面三维拓扑误差成为现实。为挖掘齿轮三维误差信息,实现齿轮精度的全面评价和测量结果的充分利用,齿轮三维误差的表征与分解成为了一个基础问题。在建立齿面法向偏差计算模型的基础上,将齿面法向偏差映射至齿轮啮合面坐标系,通过降维处理,实现齿面三维误差的二维化,以此构建基于Legendre正交多项式的齿面三维误差表征方法;建立Legendre多项式的展开系数与齿轮齿面各项特征误差之间的关系,实现齿面三维误差中各项特征误差的解耦;试验结果验证齿面三维误差Legendre多项式表征与分解的有效性,为齿轮三维测量大数据分析、齿轮精度全面评定、工艺误差溯源和齿轮性能预报提供理论依据。

The breakthrough of complex surface measurement technology makes the rapid acquisition of gear topology error a reality.For deeply digging into the 3-D information,the characterization and decomposition of 3-D deviations become basic problems of overall evaluating the gear accuracy and taking full advantage of measurements.The normal deviations of gear are mapped to the coordinate system of the plane of action.This manuscript completes the two-dimensionalization of the 3-D tooth flank basing on dimensional reduction technology and Legendre polynomials for building up the 3-D deviation characterization of the tooth flank.The relationship between the expansion coefficients of Legendre polynomials and the characteristic deviations of the tooth flanks has been illustrated to realize the decouple of characteristic errors.The experiment shows the effectiveness of Legendre polynomials in characterizing and decomposing the 3-D deviations,which provides theoretical foundation for gear 3-D big data analysis,overall evaluation of the gear accuracy,machining error traceability and performance prediction of gear pairs.