渐开线蜗轮的精确建模与修形
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摘要
为了适应单件、小批量生产模式,文章提出了一种新的渐开线蜗轮修形建模技术。根据微分几何与齿轮啮合原理依次推导得出蜗杆齿面方程、蜗轮副啮合方程,进而得出蜗轮齿面方程。将蜗轮齿面方程计算出的齿面点云沿齿面法向偏移,得出修形后的齿面。对蜗杆与修形蜗轮的动态啮合进行有限元分析,得出接触区与传动误差。分析结果表明,文中的修形建模方法精度高、啮合性能良好、调整方便。这种修形建模方法还可以用于其它类型的圆柱蜗轮副。
In order to adapt to single piece and small batch production model,a new modeling technique of involute worm gear modification is proposed in this paper.According to the differential geometry and the gear meshing principle,the equation of the tooth surface of the worm and the meshing equation of the worm gear pair are derived,and then the equation of the tooth surface of the worm gear is obtained.The points of worm gear surface,which are calculated by worm gear tooth surface equation,are deviated in normal direction so that the modified tooth surface is obtained.The dynamic meshing of the worm and the worm gear is analyzed by finite element method,then the contact area and the transmission error are obtained.The analysis results show that the modeling method of this paper is of high accuracy,good meshing performance and convenient adjustment.This method can also be used for other types of cylindrical worm gear pair.
In order to adapt to single piece and small batch production model,a new modeling technique of involute worm gear modification is proposed in this paper.According to the differential geometry and the gear meshing principle,the equation of the tooth surface of the worm and the meshing equation of the worm gear pair are derived,and then the equation of the tooth surface of the worm gear is obtained.The points of worm gear surface,which are calculated by worm gear tooth surface equation,are deviated in normal direction so that the modified tooth surface is obtained.The dynamic meshing of the worm and the worm gear is analyzed by finite element method,then the contact area and the transmission error are obtained.The analysis results show that the modeling method of this paper is of high accuracy,good meshing performance and convenient adjustment.This method can also be used for other types of cylindrical worm gear pair.
引文
[1]杨兰春.蜗杆传动手册[M].上海:华东化工学院出版社,1990.
[2]Fang Hong-Sheng,Chung-Biau Tsay.Mathematical Model and Bearing Contacts of the ZK-Type Worm Gear Set Cut by Oversize Hob Cutters[J].Mechanism&Machine Theory,2000,31(12):1689-1708.
[3]李艳玲,李巧玲,宁振武.数控加工技术在机械制造业中的重要性[J].中国科技信息,2005(18):76.
[4]黄卫.数控机床及故障诊断技术[M].北京:机械工业出版社,2004.
[5]刘鹄然,赵东福,宋德玉.现代啮合理论[M].杭州:浙江大学出版社,2008.
[6]F Klocke,E Brinksmeier,K Weinert.Capability Profile of Hard Cutting and Grinding Processes[J].CIRP AnnalsManufacturing Technology,2005,54(2):22-45.
[7]周济,周艳红.数控加工技术[M].北京:国防工业出版社,2002.
[8]江磊,王玉兰.基于Solidworks的阿基米德蜗杆蜗轮建模方法探讨[J].机械与电子,2007(3):67-70.
[9]李书平.基于UG的渐开线蜗轮参数化设计[J].机械设计与制造,2009(5):222-223.
[10]李俊源.基于Solidworks的蜗轮蜗杆三维参数化设计[J].长春理工大学学报(自然科学版),2006,29(1):98-100.
[11]蔡磊,罗良清,李志明.阿基米德蜗杆零件实体建模研究[J].湖北工业大学学报,2006,21(3):152-153.
[12]阮锦,刘强,阮锋.蜗轮蜗杆的三维参数化设计及其运动仿真分析[J].机械设计与制造,2007(11):74-76.
[13]曾峰,牛鸣岐,赵先锋,等.蜗轮齿面的三维仿真造型[J].水利电力机械,2007,29(6):12-15.
[14]刘广武,侯洪生,唐扬扬.ZA蜗轮蜗杆的主动参数化精确3D数模设计[J].机械传动,2015(3):56-61.
[15]杨富卿,李寅森.点接触阿基米德蜗杆传动啮合分析[J].焦作矿业学院学报,1994,13(6):71-75.
[16]沈谦.点接触圆柱蜗杆传动的设计原理[J].南京航空学院学报,1991,23(2):48-54.
[17]万飞,王勇勤,张光辉.大型轧机压下装置ZC1蜗轮齿面可控啮合修形的研究与应用[J].钢铁,2007,42(3):76-78.
[2]Fang Hong-Sheng,Chung-Biau Tsay.Mathematical Model and Bearing Contacts of the ZK-Type Worm Gear Set Cut by Oversize Hob Cutters[J].Mechanism&Machine Theory,2000,31(12):1689-1708.
[3]李艳玲,李巧玲,宁振武.数控加工技术在机械制造业中的重要性[J].中国科技信息,2005(18):76.
[4]黄卫.数控机床及故障诊断技术[M].北京:机械工业出版社,2004.
[5]刘鹄然,赵东福,宋德玉.现代啮合理论[M].杭州:浙江大学出版社,2008.
[6]F Klocke,E Brinksmeier,K Weinert.Capability Profile of Hard Cutting and Grinding Processes[J].CIRP AnnalsManufacturing Technology,2005,54(2):22-45.
[7]周济,周艳红.数控加工技术[M].北京:国防工业出版社,2002.
[8]江磊,王玉兰.基于Solidworks的阿基米德蜗杆蜗轮建模方法探讨[J].机械与电子,2007(3):67-70.
[9]李书平.基于UG的渐开线蜗轮参数化设计[J].机械设计与制造,2009(5):222-223.
[10]李俊源.基于Solidworks的蜗轮蜗杆三维参数化设计[J].长春理工大学学报(自然科学版),2006,29(1):98-100.
[11]蔡磊,罗良清,李志明.阿基米德蜗杆零件实体建模研究[J].湖北工业大学学报,2006,21(3):152-153.
[12]阮锦,刘强,阮锋.蜗轮蜗杆的三维参数化设计及其运动仿真分析[J].机械设计与制造,2007(11):74-76.
[13]曾峰,牛鸣岐,赵先锋,等.蜗轮齿面的三维仿真造型[J].水利电力机械,2007,29(6):12-15.
[14]刘广武,侯洪生,唐扬扬.ZA蜗轮蜗杆的主动参数化精确3D数模设计[J].机械传动,2015(3):56-61.
[15]杨富卿,李寅森.点接触阿基米德蜗杆传动啮合分析[J].焦作矿业学院学报,1994,13(6):71-75.
[16]沈谦.点接触圆柱蜗杆传动的设计原理[J].南京航空学院学报,1991,23(2):48-54.
[17]万飞,王勇勤,张光辉.大型轧机压下装置ZC1蜗轮齿面可控啮合修形的研究与应用[J].钢铁,2007,42(3):76-78.