变厚齿轮的锥形蜗杆砂轮磨削方法
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摘要
为实现变厚齿轮的精密高效磨削,提出锥形蜗杆砂轮连续展成磨削工艺。根据变厚齿轮的特性建立锥形蜗杆砂轮模型,分析锥形蜗杆砂轮磨削变厚齿轮的运动几何学原理;推导锥形蜗杆砂轮主要参数的计算公式,给出金刚滚轮单面修整方法,并运用解析计算法计算滚轮和砂轮接触线,从而求解锥形蜗杆砂轮齿面方程;基于软件MATLAB数字计算方法计算共轭齿面接触线,将其螺旋投影,获得啮合齿轮齿面端面廓形点坐标;通过与理论廓形对比得到量化的齿面廓形误差结果,分析结果验证了该磨削工艺的实际准确性,其对实现变厚齿轮的高效低成本精密磨削有重要意义。
For realizing the precision and high efficiency grinding of beveloid gears,the grinding method with conical worm wheel was put forward.Based on the geometry feature of beveloid gears,the mathematical model of conical worm wheel was established and the gear generating geometric motion principle was analyzed.The calculation formulas of conical worm's main parameters were conducted,and the diamond roller dressing method was discussed.To solve worm tooth surface equation,the analytic method was used to calculate the contact line between diamond roller tooth surface and worm wheel tooth surface and gear.According to functional software,the contact line in conjugate tooth surfaces was calculated,which was projected to a flat surface as to acquire the shape point coordinates in gear end face.Compared with the theoretical standard shape point coordinates,the numerical errors value was computed,and the results showed that the grinding method was effective and accurate,and the proposed method had a important meaning to beveloid gear's high efficiency and low cost precision grinding.
For realizing the precision and high efficiency grinding of beveloid gears,the grinding method with conical worm wheel was put forward.Based on the geometry feature of beveloid gears,the mathematical model of conical worm wheel was established and the gear generating geometric motion principle was analyzed.The calculation formulas of conical worm's main parameters were conducted,and the diamond roller dressing method was discussed.To solve worm tooth surface equation,the analytic method was used to calculate the contact line between diamond roller tooth surface and worm wheel tooth surface and gear.According to functional software,the contact line in conjugate tooth surfaces was calculated,which was projected to a flat surface as to acquire the shape point coordinates in gear end face.Compared with the theoretical standard shape point coordinates,the numerical errors value was computed,and the results showed that the grinding method was effective and accurate,and the proposed method had a important meaning to beveloid gear's high efficiency and low cost precision grinding.
引文
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[13]NI Gaoxiang,ZHU Caichao,SONG Chaosheng,et al.Geametric design and meshing characteristics analysis of beveloid gear transmission with parallel axes[J].Journal of Xi'an Jiaotong University,2016,50(5):57-64(in Chinese).[倪高翔,朱才朝,宋朝省,等.平行轴渐开线变厚齿轮传动的几何设计与啮合特性分析[J].西安交通大学学报,2016,50(5):57-64.]
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[15]AMANI A,SPITAS C,SPITAS V.Generalised non-dimensional multi-parametric involute spur gear design model considering manufacturability and geometrical compatibility[J].Mechanism&Machine Theory,2017,109:250-277.
[16]LITVIN F L.Gear geometry and applied theory[M].Shanghai:Shanghai Science and Technology Press,2008(in Chinese).[F.L.李特文.齿轮几何学与应用理论[M].上海:上海科学技术出版社,2008.]
[17]LIN Chao,WEI Peitang,ZHU Caichao,et al.Study on the tooth surface generation of helical beveloid gear[J].Journal of Mechanical Transmission,2010,34(4):1-5(in Chinese).[林超,魏沛堂,朱才朝,等.变齿厚斜齿轮的齿面生成研究[J].机械传动,2010,34(4):1-5.]
[2]MITOME K I.Table sliding taper hobbing of conical gear using cylindrical hob.Part1:theoretical analysis of table sliding taper hobbing[J].Transactions of the ASME,1981,103(4):452-456.
[3]MITOME K I.Infeed Grinding of straight conical involute gear[J].Japan Society of Mechanical Engineers International Journal,1993,36(543):3656-3661.
[4]HE Jingliang,WU Xutang.On the hobbing principle of conical involute gears[J].Mechanical Science and Technology for Aerospace Engineering,2003,22(5):751-753(in Chinese).[贺敬良,吴序堂.渐开线锥形齿轮滚削原理[J].机械科学与技术,2003,22(5):751-753.]
[5]HE Jingliang,WU Xutang.The grinding principle of conical involute gears on NC conical wheel gear grinding machine[J].Heavy Machinery,2003(3):15-18(in Chinese).[贺敬良,吴序堂.数控锥面砂轮磨齿机磨削锥形齿轮原理[J].重型机械,2003(3):15-18.]
[6]WANG Guangjian,CHU Zhigang.Research on the modification coefficient calculation of conical involute planetary gear with few tooth difference[J].China Mechanical Engineering,2009,20(4):481-484(in Chinese).[王光建,褚志刚.变齿厚齿轮少齿差传动变位系数计算研究[J].中国机械工程,2009,20(4):481-484.]
[7]BRECHER C,BRUMM M,HBNER F,et al.Influence of the manufacturing method on the running behavior of beveloid gears[J].Production Engineering,2013,7(2):265-274.
[8]BRECHER C,LPENHAUS C,GRESCHERT R.Influence of the metal working fluid on the running behavior of gear analogy test parts[J].Production Engineering,2015,9(3):425-431.
[9]BRECHER C,LPENHAUS C,BRIMMERS J.Function-oriented tolerancing of tooth flank modifications of beveloid gears[J].Procedia Cirp,2016,43:124-129.
[10]HUANG Jinli.Research on machining method of space beveloid gear pairs[D].Harbin:Joural of Harbin Engineering University,2014(in Chinese).[黄金利.空间变厚齿轮副加工方法的研究[D].哈尔滨:哈尔滨工业大学,2014.]
[11]ZIMMER M,OTTO M,STAHL K.Homogeneous geometry calculation of arbitrary tooth shapes-mathesmatical approach and practical applications[C]//Proceedings of American Gear Manufacturers Association Fall Technical Meeting.New York,N.Y.,USA:Curran Associates,Inc,2015:196-212.
[12]ZHU Caichao,LIU Libin,LIU Mingyong,et al.Geometry design and tooth contact analysis of intersected beveloid gears[J].Journal of Mechanical Engineering,2012,48(23):135-142(in Chinese).[朱才朝,刘立斌,刘明勇,等.相交轴渐开线变厚齿轮几何设计与啮合特性分析[J].机械工程学报,2012,48(23):135-142.]
[13]NI Gaoxiang,ZHU Caichao,SONG Chaosheng,et al.Geametric design and meshing characteristics analysis of beveloid gear transmission with parallel axes[J].Journal of Xi'an Jiaotong University,2016,50(5):57-64(in Chinese).[倪高翔,朱才朝,宋朝省,等.平行轴渐开线变厚齿轮传动的几何设计与啮合特性分析[J].西安交通大学学报,2016,50(5):57-64.]
[14]NI Gaoxiang,ZHU Caichao,SONG Chaosheng,et al.Tooth contact analysis of crossed beveloid gear transmission with parabolic modification[J].Mechanism&Machine Theory,2017,113:40-52.DOI:10.1016/J.mechmachtheory.2017.03.004.
[15]AMANI A,SPITAS C,SPITAS V.Generalised non-dimensional multi-parametric involute spur gear design model considering manufacturability and geometrical compatibility[J].Mechanism&Machine Theory,2017,109:250-277.
[16]LITVIN F L.Gear geometry and applied theory[M].Shanghai:Shanghai Science and Technology Press,2008(in Chinese).[F.L.李特文.齿轮几何学与应用理论[M].上海:上海科学技术出版社,2008.]
[17]LIN Chao,WEI Peitang,ZHU Caichao,et al.Study on the tooth surface generation of helical beveloid gear[J].Journal of Mechanical Transmission,2010,34(4):1-5(in Chinese).[林超,魏沛堂,朱才朝,等.变齿厚斜齿轮的齿面生成研究[J].机械传动,2010,34(4):1-5.]