基于刀具齿廓修形的弧齿锥齿轮齿面设计
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摘要
为避免表面研磨弧齿锥齿轮在重载情况下发生边缘接触,改善齿面应力分布,用弧线刃刀具替换展成齿轮齿面的直线刃刀具.首先,基于刀具的几何结构建立新型刀具的数学模型,并建立了切削刃锥面;然后,基于非齐次坐标变换建立弧齿锥齿轮在数控机床上的加工方法并获得理想齿面;最后,以face-milled弧齿锥齿轮工作面为例,对基于直线刃刀具和新型弧线刃刀具加工所得的齿轮副进行几何齿接触分析(TCA)和有限元分析(FEA).研究结果表明,提出的刀具齿廓修形方法能够明显改善face-milled弧齿锥齿轮的啮合性能.
To avoid tooth edge contact and improve the contact stress distribution of face-milled spiral bevel gears in the case of heavy load and misalignment,the cutter blade profile design is one of the most effective solutions.Generally,a circular arc blade was used to substitute the straight blade to get a desired theoretical tooth surface.First,based on the structure of cutter head,the mathematical model of the new cutter blade profile was built,and the cutting cone was set up based on the profile of the cutter blade.Then,the gear tooth surface was obtained based on the homogeneous coordinate transformation.Finally,a numerical simulation example between the original cutter and new optimal cutter,including tooth contact analysis(TCA),loaded tooth contact analysis,and finite element analysis(FEA),was carried out for face-milled spiral bevel gears to verify effectiveness.Research results show that the proposed optimization method of the cutter blade profile can obviously improve the meshing performance of face-milled spiral bevel gears.
To avoid tooth edge contact and improve the contact stress distribution of face-milled spiral bevel gears in the case of heavy load and misalignment,the cutter blade profile design is one of the most effective solutions.Generally,a circular arc blade was used to substitute the straight blade to get a desired theoretical tooth surface.First,based on the structure of cutter head,the mathematical model of the new cutter blade profile was built,and the cutting cone was set up based on the profile of the cutter blade.Then,the gear tooth surface was obtained based on the homogeneous coordinate transformation.Finally,a numerical simulation example between the original cutter and new optimal cutter,including tooth contact analysis(TCA),loaded tooth contact analysis,and finite element analysis(FEA),was carried out for face-milled spiral bevel gears to verify effectiveness.Research results show that the proposed optimization method of the cutter blade profile can obviously improve the meshing performance of face-milled spiral bevel gears.
引文
[1]LITIVIN F L,CHAING W S,KUAN C,et al.Generation and geometry of hypoid gear-member with face-hobbed teeth of uniform depth[J].International Journal of Machine Tools and Manufacture,1991,31(2):167-181.
[2]郑昌启.弧齿锥齿轮和准双曲面齿轮:啮合原理、齿坯设计、加工调整和齿面分析计算原理[M].北京:机械工业出版社,1988.
[3]LITVIN F L,WANG A G,HANDSCHUH R F.Computerized generation and simulation of meshing and contact of spiral bevel gears with improved geometry[J].Computer Methods in Applied Mechanics and Engineering,1998,158(1/2):35-64
[4]LITVIN F L,FUENTES A,FAN Q,et al.Computerized design,simulation of meshing and contact and stress analysis of face-milled formate generated spiral bevel gears[J].Mechanism and Machine Theory,2002,37(5):441-459
[5]LITVIN F L,FUENTES A,HAYASAKA K.Design,manufacture,stress analysis,and experimental tests of low-noise high endurance spiral bevel gears[J].Mechanism and Machine Theory,2006,41(1):83-118
[6]WANG P Y,FONG Z H.Mathematical model of face-milling spiral bevel gear with modified radial motion(MRM)correction[J].Mathematical&Computer Modelling,2005,41(11):1307-1323.
[7]WANG P Y,FONG Z H.Adjustability improvement of face-milling spiral bevel gears by modified radial motion(MRM)method[J].Mechanism&Machine Theory,2005,40(1):69-89.
[8]GUO W,MAO S,YANG Y,et al.Optimization of cutter blade profile for face-hobbed spiral bevel gears[J].International Journal of Advanced Manufacturing Technology,2016,85(1/4):1-8.
[9]刘万春,刘光磊.基于抛物线刀刃的弧齿锥齿轮齿面啮合分析[J].机械与电子,2008(7):13-15.
[10]蔡香伟.航空弧齿锥齿轮的啮合特性分析及齿面设计研究[D].西安:西北工业大学图书馆,2015.
[2]郑昌启.弧齿锥齿轮和准双曲面齿轮:啮合原理、齿坯设计、加工调整和齿面分析计算原理[M].北京:机械工业出版社,1988.
[3]LITVIN F L,WANG A G,HANDSCHUH R F.Computerized generation and simulation of meshing and contact of spiral bevel gears with improved geometry[J].Computer Methods in Applied Mechanics and Engineering,1998,158(1/2):35-64
[4]LITVIN F L,FUENTES A,FAN Q,et al.Computerized design,simulation of meshing and contact and stress analysis of face-milled formate generated spiral bevel gears[J].Mechanism and Machine Theory,2002,37(5):441-459
[5]LITVIN F L,FUENTES A,HAYASAKA K.Design,manufacture,stress analysis,and experimental tests of low-noise high endurance spiral bevel gears[J].Mechanism and Machine Theory,2006,41(1):83-118
[6]WANG P Y,FONG Z H.Mathematical model of face-milling spiral bevel gear with modified radial motion(MRM)correction[J].Mathematical&Computer Modelling,2005,41(11):1307-1323.
[7]WANG P Y,FONG Z H.Adjustability improvement of face-milling spiral bevel gears by modified radial motion(MRM)method[J].Mechanism&Machine Theory,2005,40(1):69-89.
[8]GUO W,MAO S,YANG Y,et al.Optimization of cutter blade profile for face-hobbed spiral bevel gears[J].International Journal of Advanced Manufacturing Technology,2016,85(1/4):1-8.
[9]刘万春,刘光磊.基于抛物线刀刃的弧齿锥齿轮齿面啮合分析[J].机械与电子,2008(7):13-15.
[10]蔡香伟.航空弧齿锥齿轮的啮合特性分析及齿面设计研究[D].西安:西北工业大学图书馆,2015.