机床几何位姿误差对强力刮齿加工精度的影响及修正
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摘要
为减小机床几何位姿误差对强力刮齿加工精度的影响,分析了刮齿法向轮廓误差对各项几何位姿误差的敏感性,并给出了误差修正方法。基于齐次坐标变换理论,根据机床结构建立含误差的机床运动传递链。由刮齿加工成形原理,建立含误差的齿面方程及几何位姿误差与齿面法向轮廓误差的映射关系,分析法向轮廓误差对各项几何位姿误差的敏感性,得到敏感误差项。提出一种实际逆向运动学方法求解刮齿加工成形函数,从而获得误差修正后的数控代码解析表达式。以圆柱内齿轮刮削为例,仿真切削并分析了几何位姿误差修正前后的法向轮廓精度,结果表明所提方法可有效修正机床几何位姿误差导致的加工误差,提高刮齿加工精度。
To reduce the influence of machine tool's geometric location errors on gear accuracy in the process of power skiving, the sensitivity of profile normal error to each geometric location error was analyzed and an error correction method was proposed. Based on the homogeneous coordinate transformation, the error kinematic chain of machine tool was reconstructed according to machine tool structure. The tooth surface equation with errors and the mapping relationship between geometric location error and profile normal error were established based on the skiving theory. The sensitive error terms could be obtained by analyzing the sensitivity of profile normal error to location errors. An actual inverse kinematics method was proposed to solve the skiving forming function, and then the analytical expression of the corrected numerical control machining code was derived. By taking cylinder internal gear skiving as an example, the profile normal precision before and after correction were simulated and analyzed for a comparison. The simulation showed that the proposed method could correct the machining error caused by geometric location errors and improve the skiving precision effectively.
To reduce the influence of machine tool's geometric location errors on gear accuracy in the process of power skiving, the sensitivity of profile normal error to each geometric location error was analyzed and an error correction method was proposed. Based on the homogeneous coordinate transformation, the error kinematic chain of machine tool was reconstructed according to machine tool structure. The tooth surface equation with errors and the mapping relationship between geometric location error and profile normal error were established based on the skiving theory. The sensitive error terms could be obtained by analyzing the sensitivity of profile normal error to location errors. An actual inverse kinematics method was proposed to solve the skiving forming function, and then the analytical expression of the corrected numerical control machining code was derived. By taking cylinder internal gear skiving as an example, the profile normal precision before and after correction were simulated and analyzed for a comparison. The simulation showed that the proposed method could correct the machining error caused by geometric location errors and improve the skiving precision effectively.
引文
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[17] CHEN Xinchun.Fundamental research on the design and manufacture of the theoretical error-free slice cutter[D].Tianjin:Tianjin University,2013(in Chinese).[陈新春.无理论刃形误差剐齿刀设计与制造基础研究[D].天津:天津大学,2013.]
[2] LI Jia,CHEN Xinchun,ZHANG Hongyuan.Slicing technology for cylindrical gears[J].Journal of Mechanical Engineering,2011,47(19):193-198(in Chinese).[李佳,陈新春,张鸿源.圆柱齿轮剐齿技术[J].机械工程学报,2011,47(19):193-198.]
[3] SCHULZE V,KüHLEWEIN C,AUTENRIETH H.3D-FEM modeling of gear skiving to investigate kinematics and chip formation mechanisms[J].Advanced Materials Research,2011,223:46-55.
[4] CHEN Xinchun,LI Jia,LOU Benchao.A study on the design of error-free spur slice cutter[J].International Journal of Advanced Manufacturing Technology,2013,68(1/2/3/4):727-738.
[5] TSAI C Y.Mathematical model for design and analysis of power skiving tool for involute gear cutting[J].Mechanism & Machine Theory,2016,101:195-208.
[6] GUO Zheng,MAO Shimin,LI Xiaoe,et al.Research on the theoretical tooth profile errors of gears machined by skiving[J].Mechanism & Machine Theory,2016,97:1-11.
[7] GUOZheng,MAO Shimin,DU Xiaofeng,et al.Influences of tool setting errors on gear skiving accuracy[J].International Journal of Advanced Manufacturing Technology,2017,91(9/10/11/12):1-9.
[8] GUO Erkuo,HONG Rongjing,HUANG Xiaodiao,et al.Research on the cutting mechanism of cylindrical gear power skiving[J].International Journal of Advanced Manufacturing Technology,2015,79(1/2/3/4):541-550.
[9] GUOErkuo,HONG Rongjing,HUANG Xiaodiao,et al.A novel power skiving method using the common shaper cutter[J].International Journal of Advanced Manufacturing Technology,2015,83(1):1-9.
[10] FANG Chenggang,GONG Jianming,GUO Erkuo,et al.Influence and compensation for cylindrical gear accuracy with eccentricity in form grinding[J].Computer Integrated Manufacturing Systems,2015,21(3):716-723(in Chinese).[方成刚,巩建鸣,郭二廓,等.圆柱齿轮偏心对成形磨齿精度的影响及补偿[J].计算机集成制造系统,2015,21(3):716-723.]
[11] CHEN Jianxiong,LIN Shuwen,HE Bingwei.Geometric error compensation for multi-axis CNC machines based on differential transformation[J].International Journal of Advanced Manufacturing Technology,2014,71(1/2/3/4):635-642.
[12] HUANG Nuodi,JIN Yongqiao,BI Qingzhen,et al.Integrated post-processor for 5-axis machine tools with geometric errors compensation[J].International Journal of Machine Tools & Manufacture,2015,94:65-73.
[13] ZHOU Xiangdong,JIANG Zhouxiang,SONG Bao,et al.A compensation method for the geometric errors of five-axis machine tools based on the topology relation between axes[J].International Journal of Advanced Manufacturing Technology,2017,88(5/6/7/8):1993-2007.
[14] YANG Jixiang,MAYER J R R,ALTINTAS Y.A position independent geometric errors identification and correction method for five-axis serial machines based on screw theory[J].International Journal of Machine Tools & Manufacture,2015,95:52-66.
[15] DING Shuang,HUANG Xiaodiao,YU Chunjian,et al.Novel method for position-independent geometric error compensation of five-axis orthogonal machine tool based on error motion[J].International Journal of Advanced Manufacturing Technology,2016,83(5/6/7/8):1069-1078.
[16] DING Shuang,HUANG Xiaodiao,YU Chunjian,et al.Actual inverse kinematics for location error compensation of five-axis machine tool[J].Computer Integrated Manufacturing Systems,2017,23(10):2156-2163(in Chinese).[丁爽,黄筱调,于春建,等.5轴数控机床装配误差补偿的实际逆向运动学[J].计算机集成制造系统,2017,23(10):2156-2163.]
[17] CHEN Xinchun.Fundamental research on the design and manufacture of the theoretical error-free slice cutter[D].Tianjin:Tianjin University,2013(in Chinese).[陈新春.无理论刃形误差剐齿刀设计与制造基础研究[D].天津:天津大学,2013.]