齿轮三维误差表征与分解  

Characterization and Decomposition of Gear 3-D Deviation

作　　者：石照耀[1] 赵保亚 于渤[1] 郭晓忠[1] SHI Zhaoyao;ZHAO Baoya;YU Bo;GUO Xiaozhong(Beijing Engineering Research Center of Precision Measurement Technology and Instruments,Beijing University of Technology,Beijing 100124;School of Mechatronics Engineering,North China Institute of Aerospace Engineering,Langfang 065000)

机构地区：[1]北京工业大学北京市精密测控技术与仪器工程技术研究中心,北京100124 [2]北华航天工业学院机电学院,廊坊065000

出　　处：《机械工程学报》2022年第6期1-9,共9页Journal of Mechanical Engineering

基　　金：国家自然科学基金重点(51635001);国家重点研发计划“制造基础技术与关键部件”(2018YFB2001400);国家自然科学青年基金(51805011)资助项目。

摘　　要：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.

关 键 词：齿轮误差 三维误差表征 齿轮修形 齿轮测量 LEGENDRE多项式 

分 类 号：TH132.41[机械工程—机械制造及自动化]