成形磨齿齿向修形扭曲误差分析及补偿
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摘要
在斜齿圆柱齿轮的齿向修形磨削加工过程中,采用传统的附加径向运动的修形方式存在着修形扭曲误差。为改善齿向修形扭曲误差,根据空间啮合理论,建立成形磨齿齿向修形的数学模型,求解出砂轮与工件之间的瞬时接触线。通过分析砂轮半径与砂轮安装角对齿向修形接触线的影响规律,提出了3种齿面修形扭曲误差的补偿方法。最后,以一种斜齿鼓形修形齿轮为例,分别通过数值模型和磨齿实验验证了文中所提方法的有效性。
When the tooth lead modification was performed on a helical gear by form grinding method, there are existing the phenomenon of modification twist. In order to improve the twist error of tooth lead modification, a mathematical model of form grinding is established for tooth lead modification to solve the simultaneous contact line between the grinding wheel and gear surface based on gear engagement theory. By analyzing the influence of grinding wheel radius and grinding wheel setting angle on tooth lead modification contact line, the three methods were proposed based on optimizing the grinding wheel profile, the wheel setting angle, both the wheel profile and setting angle. Finally, as an example of helical crowning gear, the proposed methods are validated through the model and experiment separately,which can effectively improve the modification error in form grinding.
When the tooth lead modification was performed on a helical gear by form grinding method, there are existing the phenomenon of modification twist. In order to improve the twist error of tooth lead modification, a mathematical model of form grinding is established for tooth lead modification to solve the simultaneous contact line between the grinding wheel and gear surface based on gear engagement theory. By analyzing the influence of grinding wheel radius and grinding wheel setting angle on tooth lead modification contact line, the three methods were proposed based on optimizing the grinding wheel profile, the wheel setting angle, both the wheel profile and setting angle. Finally, as an example of helical crowning gear, the proposed methods are validated through the model and experiment separately,which can effectively improve the modification error in form grinding.
引文
[1] 秦大同,朱晓冬,刘向阳.修形斜齿轮成形磨削中的砂轮廓形优化方法和齿形误差分析[J].机械传动,2013,37(4):1-5.QIN D T,ZHU X D,LIU X Y.Profile Optimization of Grinding Wheel and Tooth Profile Error Analysis for Form-grinding Modified Helical Gear[J].Journal of Mechanical Transmission,2013,37(4):1-5.
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[3] SHIHY P.Free-Form Flank Correction in Helical Gear Grinding Using a Five-Axis Computer Numerical Control Gear Profile Grinding Machine[J].Journal of Manufacturing Science and Engineering,2012,134:041006.
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[9] HIDEHIRO YOSHINO,KAZUHIRO IKENO.Studies on 3-D Tooth Surface Modification of Helical Gears[J].JSME,1994,60(571):1053-1059.
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[11] HIDEHIRO Y,IKENO K I.Tooth-Trace Crowning in Form Grinding of Helical Gears[J].JSME,1991,57(538):2144-2148.
[12] HIDEHIRO Y,MING S,AKIRA I.Design and Manufacture of Pinion Cutters for Finishing Gears with an Arbitrary Profile[J].JSME International Journal,1992,35(2):313-319.
[13] KOBAYASHI Y,NISHIDA N,OUGIYA Y,et al.Estimation of Grinding Wheel Setting Error in Helical Gear Processing by Form Grinding[C]//Proceedings of Transactions of the Japan Society of Mechanical Engineers Part C,1997,63(612):2852-2858.
[14] SHEN Y B,FANG Z D,ZHAO N,et al.Application of Modified Geometry of Face-gear Drive with Double Crowned Helical Pinion[C]//Proceedings of In ICADAM 2008,Advanced Design and Manufacture to Gain a Competitive Edge,2008:579-588.
[15] TüRICHA.Producing Profile and Lead Modifications in Threaded Wheel and Profile Grinding[S].AGMA 09FTM03,2009-09-01.
[16] LEE C K.Manufacturing Process for a Cylindrical Crown Gear Drive With a Controllable Fourth Order Polynomial Function of Transmission Error[J].Journal of Materials Processing Technology,2009,209(1):3-13.
[17] SHIHY P.Flank Correction for Spiral Bevel and Hypoid Gears on a Six-Axis CNC Hypoid Generator[J].Journal of Mechanical Design,2008,130(6):876-877.
[18] SHIHY P,CHEN S D.A Flank Correction Methodology for a Five-axis CNC Gear Profile Grinding Machine[J].Machanism and Machine Theory,2012,47(1):31-45.
[19] 吴序堂.齿轮啮合原理[M].2版,西安:西安交通大学,2009.
[20] 丁汉,朱利民.复杂曲面数字化制造的几何学理论和方法[M].北京:科学出版社,2011.
[2] SHIHY P.A Novel Ease-off Flank Modification Methodology for Spiral Bevel and Hypoid Gears[J].Mechanism and Machine Theory,2010,45(8):1108-1124.
[3] SHIHY P.Free-Form Flank Correction in Helical Gear Grinding Using a Five-Axis Computer Numerical Control Gear Profile Grinding Machine[J].Journal of Manufacturing Science and Engineering,2012,134:041006.
[4] YOSHIKOTO Y,TOSHIFUMI K.Gear Grinding Machine:US 7083496[P].2006-12-14.
[5] 宫虎.五坐标数控加工运动几何学基础及刀位规划原理与方法的研究[D].大连:大连理工大学,2006.
[6] 方成刚,黄筱调,郭二廓,等.基于砂轮姿态优化的修形齿轮成形磨削刀路规划[J].南京工业大学学报(自然科学版),2013,35(5):87-93.FANG C G,HUANG X D,GUO E K,et al.Tool Path Planning for Lead Modification of Form Grinding Based on Wheel Configuration Optimization[J].Journal of Nanjing University of Technology(Natural Science Edition),2013,35(5):87-93.
[7] NISHIDA N,KOBAYASHI Y,OUGIYA Y,et al.Profile Calculation Method for Form Grinding Wheels for Helical Gears and Avoidance of Interferences[J].Journal of the Japan Society for Precision Engineering,1992,58(4):628-634.
[8] 邓兴奕,亢恒.鼓形齿的成形磨削方法及其分析[J].重庆大学学报(自然科学版),1989,12(4):38-45.DENG X Y,KANG H.Analysis on the Profile Grinding process of Drum-Tooth Gear[J].Journal of Chongqing University(Natural Science Edition),1989,12(4):38-45.
[9] HIDEHIRO YOSHINO,KAZUHIRO IKENO.Studies on 3-D Tooth Surface Modification of Helical Gears[J].JSME,1994,60(571):1053-1059.
[10] YOSHINO H,IKENO K.Error Compensation for form Grinding of Gears[J].Transactions of the Japan Society of Mechanical Engineers C,1991,57(543):3652-3655.
[11] HIDEHIRO Y,IKENO K I.Tooth-Trace Crowning in Form Grinding of Helical Gears[J].JSME,1991,57(538):2144-2148.
[12] HIDEHIRO Y,MING S,AKIRA I.Design and Manufacture of Pinion Cutters for Finishing Gears with an Arbitrary Profile[J].JSME International Journal,1992,35(2):313-319.
[13] KOBAYASHI Y,NISHIDA N,OUGIYA Y,et al.Estimation of Grinding Wheel Setting Error in Helical Gear Processing by Form Grinding[C]//Proceedings of Transactions of the Japan Society of Mechanical Engineers Part C,1997,63(612):2852-2858.
[14] SHEN Y B,FANG Z D,ZHAO N,et al.Application of Modified Geometry of Face-gear Drive with Double Crowned Helical Pinion[C]//Proceedings of In ICADAM 2008,Advanced Design and Manufacture to Gain a Competitive Edge,2008:579-588.
[15] TüRICHA.Producing Profile and Lead Modifications in Threaded Wheel and Profile Grinding[S].AGMA 09FTM03,2009-09-01.
[16] LEE C K.Manufacturing Process for a Cylindrical Crown Gear Drive With a Controllable Fourth Order Polynomial Function of Transmission Error[J].Journal of Materials Processing Technology,2009,209(1):3-13.
[17] SHIHY P.Flank Correction for Spiral Bevel and Hypoid Gears on a Six-Axis CNC Hypoid Generator[J].Journal of Mechanical Design,2008,130(6):876-877.
[18] SHIHY P,CHEN S D.A Flank Correction Methodology for a Five-axis CNC Gear Profile Grinding Machine[J].Machanism and Machine Theory,2012,47(1):31-45.
[19] 吴序堂.齿轮啮合原理[M].2版,西安:西安交通大学,2009.
[20] 丁汉,朱利民.复杂曲面数字化制造的几何学理论和方法[M].北京:科学出版社,2011.