螺旋运动及刀具参数对双重螺旋法加工齿面特征的影响规律
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摘要
双重螺旋法具有高效率、低成本、可干切削等特点是取代"五刀法"的弧齿锥齿轮未来主流加工方法。为了揭示弧齿锥齿轮双重螺旋法的切齿原理,在分析五刀法切齿原理的基础上,研究了刀倾角和齿形角分别在五刀法和双重螺旋法中的不同作用原理,揭示了双重螺旋法切齿原理的本质;分析了螺旋运动在切齿加工中的作用及对齿面几何形貌的影响规律,推导了小轮齿面参考点处的曲率参数计算公式,揭示了螺旋运动系数与参考处曲率的关联规律,并利用轮齿接触分析方法研究了螺旋运动对齿轮副啮合性能的影响规律;利用数值方法研究了刀具齿形角、刀盘半径分别对轮齿接触椭圆长、短半轴半径的影响,建立了刀具参数与轮齿接触特征之间的作用规律。研究工作为优化双重螺旋法的切齿加工参数提供了理论依据。
Duplex helical method will be an advanced and primary manufacturing method of Gleason spiral bevel and hypoid gears and replace five-cut process for its characteristics of higher efficiency, lower cost and power dry cutting. In order to reveal the universal theory of spiral bevel and hypoid gears generated by the duplex helical method, the different working mechanisms of blade angle and tilt angle in the five-cut process and duplex helical method is researched and the major idea in the completing theory is revealed based on the analysis of cutting principle for the five-cut process; In addition, the roles and characteristics of the helical motion are analyzed during machining, the correlation rules between the curvature at the reference points and the helical motion velocity coefficient are revealed by deriving the curvature equations at the reference points of pinion surfaces, and the influence rules between the helical motion velocity coefficient and the meshing performance are discussed by using tooth contact analysis(TCA); Finally, the impacts of blade pressure angle and cutter radius on the major and minor axis semi-diameter of the tooth contact ellipse are studied by using the numerical method, the influence mechanisms between cutter parameters and tooth contact characteristics are established. The research work provides a theoretical basis for optimizing its machining parameters.
Duplex helical method will be an advanced and primary manufacturing method of Gleason spiral bevel and hypoid gears and replace five-cut process for its characteristics of higher efficiency, lower cost and power dry cutting. In order to reveal the universal theory of spiral bevel and hypoid gears generated by the duplex helical method, the different working mechanisms of blade angle and tilt angle in the five-cut process and duplex helical method is researched and the major idea in the completing theory is revealed based on the analysis of cutting principle for the five-cut process; In addition, the roles and characteristics of the helical motion are analyzed during machining, the correlation rules between the curvature at the reference points and the helical motion velocity coefficient are revealed by deriving the curvature equations at the reference points of pinion surfaces, and the influence rules between the helical motion velocity coefficient and the meshing performance are discussed by using tooth contact analysis(TCA); Finally, the impacts of blade pressure angle and cutter radius on the major and minor axis semi-diameter of the tooth contact ellipse are studied by using the numerical method, the influence mechanisms between cutter parameters and tooth contact characteristics are established. The research work provides a theoretical basis for optimizing its machining parameters.
引文
[1]GLEASON W.Applied gear engineering-CAGEWin software customer/dealer tranining center[M].Rochester:The Gleason Works,2004.
[2]STADTFELD H J.Gleason bevel gear technology[M].Rochester:The Gleason Works,2014.
[3]STADTFELD H J.Practical gear characteristics process characteristics of the most popular cutting methods[J].Gear Technology,2016(2):62-70.
[4]STADTFELD H J.Tribology aspects in angular transmission systems part IV:Spiral bevel gears[J].Gear Technology,2011(1):66-72.
[5]STADTFELD H J.Tribology aspects in angular transmission systems part VII:hypoid gears[J].Gear Technology,2011(4):66-72.
[6]爱·维尔德哈泊.锥齿轮及准双曲面齿轮传动啮合原理[M].北京:机械工业出版社,1958.WILDHABER E.Principle of gearing of bevel and hypoid gears[M].Beijing:China Machine Press,1958.
[7]BAXTER M L.Second–order surface generation[J].Industrial Mathematics,1973,23(2):85-106.
[8]SHTIPELMAN B A.Design and manufacture of hypoid gears[M].New York:John Wiley&Sons,Inc.,1978.
[9]LITVIN F L,FUENTES A.Gear geometry and applied theory[M].2nd ed.New York:Cambridge University Press,2004.
[10]曾韬.螺旋锥齿轮设计与加工[M].哈尔滨:哈尔滨工业大学出版社,1989.ZENG Tao.Design and manufacture of spial bevel and hypoid gears[M].Harbin:Harbin Institute of Technology Press,1989.
[11]魏冰阳,邓效忠,仝昂鑫,等.曲面综合法弧齿锥齿轮加工参数计算[J].机械工程学报,2016,52(1):20-25.WEI Bingyang,DENG Xiaozhong,TONG Angxin,et al.Surface synthesis method on generating parameters computation of spiral bevel-gears[J].Journal of Mechanical Engineering,2016,52(1):20-25.
[12]江平,刘光磊,张瑞庭,等.航空弧齿锥齿轮接触印痕高度的一种控制方法[J].机械工程学报,2015,51(5):64-70.JIANG Ping,LIU Guanglei,ZHANG Ruiting,et al.A method to control the contact pattern height of spiral bevel gears in aviation[J].Journal of Mechanical Engineering,2015,51(5):64-70.
[13]GLEASON W.Calculation instructions generated hypoid gears duplex helical method[M].New York:The Gleason Works,1971.
[14]TSAY C B,LIN J Y.A mathematical model for the tooth geometry of hypoid gears[J].Mathematical and Computer Modelling,1993,18(2):23-34.
[15]GONZALEZ-PEREZ I,FUENTES A,HAYASAKA K.Computerized design and tooth contact analysis of spiral bevel gears generated by the duplex helical method[C]//American Society of Mechanical Engineers,2011:149-158.
[16]王哲,刘庆民,孙万才.加工弧齿锥齿轮的精确双重螺旋法(V)[J].吉林林学院学报,1995,11(4):210-216.WANG Zhe,LIU Qingmin,SUN Wancai.The exact duplex helical method in generation of spiral bevel gears(V)[J].Journal of Jilin Forestry University,1995,11(4):210-216.
[17]张宇,严宏志,曾韬.弧齿锥齿轮双重螺旋法切齿原理及齿面接触分析研究[J].机械工程学报,2015,51(21):15-23.ZHANG Yu,YANG Hongzhi,ZENG Tao.Cutting principle and tooth contact analysis of spiral bevel and hypoid gears generated by duplex helical method[J].Chinese Journal of Mechanical Engineering,2015,51(21):15-23.
[18]ZHANG Yu,YANG Hongzhi.New methodology for determining basic machine settings of spiral bevel and hypoid gears manufactured by duplex helical method[J].Mechanism and Machine Theory,2016,100(6):283-295.
[19]天津齿轮机床研究所.格里森锥齿轮技术资料译文集第五分册——格里森锥齿轮加工方法及齿轮接触分析[M].北京:机械工业出版社,1982.Tianjin Gear Machine Tool Research Institute.A collection of technical materials of Gleason system bevel gears-the fifth volume-cutting methods and tooth contact analysis for Gleason system bevel gears[M].Beijing:China Machine Press,1982.
[20]吴序堂.齿轮啮合原理[M].2版.西安:西安交通大学出版社,2009.WU Xutang.Principle of gearing[M].2nd ed.Xi’an:Xi’an Jiaotong University Press,2009.
[2]STADTFELD H J.Gleason bevel gear technology[M].Rochester:The Gleason Works,2014.
[3]STADTFELD H J.Practical gear characteristics process characteristics of the most popular cutting methods[J].Gear Technology,2016(2):62-70.
[4]STADTFELD H J.Tribology aspects in angular transmission systems part IV:Spiral bevel gears[J].Gear Technology,2011(1):66-72.
[5]STADTFELD H J.Tribology aspects in angular transmission systems part VII:hypoid gears[J].Gear Technology,2011(4):66-72.
[6]爱·维尔德哈泊.锥齿轮及准双曲面齿轮传动啮合原理[M].北京:机械工业出版社,1958.WILDHABER E.Principle of gearing of bevel and hypoid gears[M].Beijing:China Machine Press,1958.
[7]BAXTER M L.Second–order surface generation[J].Industrial Mathematics,1973,23(2):85-106.
[8]SHTIPELMAN B A.Design and manufacture of hypoid gears[M].New York:John Wiley&Sons,Inc.,1978.
[9]LITVIN F L,FUENTES A.Gear geometry and applied theory[M].2nd ed.New York:Cambridge University Press,2004.
[10]曾韬.螺旋锥齿轮设计与加工[M].哈尔滨:哈尔滨工业大学出版社,1989.ZENG Tao.Design and manufacture of spial bevel and hypoid gears[M].Harbin:Harbin Institute of Technology Press,1989.
[11]魏冰阳,邓效忠,仝昂鑫,等.曲面综合法弧齿锥齿轮加工参数计算[J].机械工程学报,2016,52(1):20-25.WEI Bingyang,DENG Xiaozhong,TONG Angxin,et al.Surface synthesis method on generating parameters computation of spiral bevel-gears[J].Journal of Mechanical Engineering,2016,52(1):20-25.
[12]江平,刘光磊,张瑞庭,等.航空弧齿锥齿轮接触印痕高度的一种控制方法[J].机械工程学报,2015,51(5):64-70.JIANG Ping,LIU Guanglei,ZHANG Ruiting,et al.A method to control the contact pattern height of spiral bevel gears in aviation[J].Journal of Mechanical Engineering,2015,51(5):64-70.
[13]GLEASON W.Calculation instructions generated hypoid gears duplex helical method[M].New York:The Gleason Works,1971.
[14]TSAY C B,LIN J Y.A mathematical model for the tooth geometry of hypoid gears[J].Mathematical and Computer Modelling,1993,18(2):23-34.
[15]GONZALEZ-PEREZ I,FUENTES A,HAYASAKA K.Computerized design and tooth contact analysis of spiral bevel gears generated by the duplex helical method[C]//American Society of Mechanical Engineers,2011:149-158.
[16]王哲,刘庆民,孙万才.加工弧齿锥齿轮的精确双重螺旋法(V)[J].吉林林学院学报,1995,11(4):210-216.WANG Zhe,LIU Qingmin,SUN Wancai.The exact duplex helical method in generation of spiral bevel gears(V)[J].Journal of Jilin Forestry University,1995,11(4):210-216.
[17]张宇,严宏志,曾韬.弧齿锥齿轮双重螺旋法切齿原理及齿面接触分析研究[J].机械工程学报,2015,51(21):15-23.ZHANG Yu,YANG Hongzhi,ZENG Tao.Cutting principle and tooth contact analysis of spiral bevel and hypoid gears generated by duplex helical method[J].Chinese Journal of Mechanical Engineering,2015,51(21):15-23.
[18]ZHANG Yu,YANG Hongzhi.New methodology for determining basic machine settings of spiral bevel and hypoid gears manufactured by duplex helical method[J].Mechanism and Machine Theory,2016,100(6):283-295.
[19]天津齿轮机床研究所.格里森锥齿轮技术资料译文集第五分册——格里森锥齿轮加工方法及齿轮接触分析[M].北京:机械工业出版社,1982.Tianjin Gear Machine Tool Research Institute.A collection of technical materials of Gleason system bevel gears-the fifth volume-cutting methods and tooth contact analysis for Gleason system bevel gears[M].Beijing:China Machine Press,1982.
[20]吴序堂.齿轮啮合原理[M].2版.西安:西安交通大学出版社,2009.WU Xutang.Principle of gearing[M].2nd ed.Xi’an:Xi’an Jiaotong University Press,2009.