基于切齿高阶运动的螺旋锥齿轮齿面修缘方法
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摘要
提出了一种利用机床柔性使用常规直刃刀具进行螺旋锥齿轮修缘的方法。根据不同刀具建立了螺旋锥齿轮修缘齿面的求解方程,并以此建立了螺旋锥齿轮啮合分析有限元模型分析对比了不同刀具修形对应修缘齿面的传动性能。根据对比结果选取圆弧刃刀具作为切齿高阶运动齿面修缘的优化目标,在齿面方程引入高阶运动系数并建立了基于高阶切齿运动的修缘齿面逼近优化计算模型,求解获得新的切齿调整参数得到近似修缘齿面。采用有限元分析和滚动检查实验对优化获得的修缘齿面和未修缘齿面进行了传动性能验证,其结果表明:切齿高阶运动逼近的修缘齿面啮合时的1阶振动幅值减小约16.6%,可以有效提高齿轮副的传动性能。
A method of approximate tooth surface relief in use of standard cutting tool was proposed with the advantage of machine flexibility.The tooth surface equation was established according to different types of modified cutting tool,the relived tooth surface was solved and the meshing FEA model was established.According to the gear meshing simula-tion of the FEA method,the transmission performances of different relived tooth surfaces were compared,and the arc-edged cutting tool was chosen as the optimization target according to the result.The higher order cutting motion was introduced,and the optimization model of tooth surface approaching was established according to the optimization target.The transmission performances of optimal tooth surface and unrelieved tooth surface were compared.Results showed that the first-order vibration amplitude decreased approximately16.6% when optimal tooth surface was meshed,and the gear transmission performance was effectively improved.
A method of approximate tooth surface relief in use of standard cutting tool was proposed with the advantage of machine flexibility.The tooth surface equation was established according to different types of modified cutting tool,the relived tooth surface was solved and the meshing FEA model was established.According to the gear meshing simula-tion of the FEA method,the transmission performances of different relived tooth surfaces were compared,and the arc-edged cutting tool was chosen as the optimization target according to the result.The higher order cutting motion was introduced,and the optimization model of tooth surface approaching was established according to the optimization target.The transmission performances of optimal tooth surface and unrelieved tooth surface were compared.Results showed that the first-order vibration amplitude decreased approximately16.6% when optimal tooth surface was meshed,and the gear transmission performance was effectively improved.
引文
[1] 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].Journal of Mechanical Design,2002,124(5):441-459.
[2] 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.
[3] FUENTES A,LITVIN F L,MULLINS B R.Design and stress analysis of low-noise adjusted bearing contact spiral bevel gears[J].Journal of Mechanical Design,2002,124(3):524-532.
[4] ASTOUL J,MERMOZ E,SARTOR M,et al.New methodology to reduce the transmission error of the spiral bevel gears[J].Manufacturing Technology,2014,63(1):165-168.
[5] SU J Z,FANG Z D,CAI X W.Design and analysis of spiral bevel gears with seventh-order function of transmission error[J].Chinese Journal of Aeronautics,2013,26(5):1310-1316.
[6]方宗德,刘涛,邓效忠.基于传动误差设计的弧齿锥齿轮啮合分析[J].航空学报,2002,13(3):226-230.FANG Zongde,LIU Tao,DENG Xiaozhong.Tooth contact analysis of spiral bevel gears based on the design of transmission error[J].Acta Aeronautica et Astronautica Sinica,2002,13(3):226-230.(in Chinese)
[7] GHOSH S S,CHAKRABORTY G.On optimal tooth profile modification for reduction of vibration and noise in spur gear pairs[J].Mechanism and Machine Theory,2016,105(11):145-163.
[8]马辉,逄旭,宋溶泽,等.考虑齿轮-转子系统振动响应的最佳修形曲线研究[J].振动与冲击,2015,34(11):17-22.MA Hui,FENG Xu,SONG Rongze,et al.Optimal profile modification curves for spur gears considering vibration responses of a gear-rotor system[J].Journal of Vibration and Shock,2015,34(11):17-22.(in Chinese)
[9]马辉,逄旭,宋溶泽,等.考虑齿顶修缘的齿轮-转子系统振动响应分析[J].机械工程学报,2014,50(7):39-45.MA Hui,FENG Xu,SONG Rongze,et al.Vibration response analysis of a geared rotor system considering the tip relief[J].Journal of Mechanical Engineering,2014,50(7):39-45.(in Chinese)
[10]吴序堂.齿轮啮合原理[M].北京:机械工业出版社,1982.
[11] LITVIN F L.Gear geometry and applied theory[M].2nd ed.New York:Cambridge University Press,2004.
[12]汪中厚,王杰,王巧玲,等.基于有限元法的螺旋锥齿轮传动误差研究[J].振动与冲击,2014,33(14):165-170.WANG Zhonghou,WANG Jie,WANG Qiaoling,et al.Transmission error of spiral bevel gear based on finite element method[J].Journal of Vibration and Shock,2014,33(14):165-170.(in Chinese)
[13] GONZALEZ I P,FUENTES A.Implementation of a finite element model for stress analysis of gear drives based on multi-point constraints[J].Mechanism and Machine Theory,2017,117(11):35-47.
[14]张卫青,张明德,郭晓东,等.全数控锥齿轮铣齿机运动控制方法及切齿实验研究[J].中国机械工程,2009,20(22):2733-2737.ZHANG Weiqing,ZHANG Mingde,GUO Xiaodong,et al.Research on the kinematic control method of CNC hypoid cutting machine and the cutting experiments[J].China Mechanical Engineering,2009,20(22):2733-2737.(in Chinese)
[15]郑昌启.弧齿锥齿轮和准双曲面齿轮[M].北京:机械工业出版社,1988.
[16]聂少武,邓静,邓效忠,等.弧齿锥齿轮齿面拓扑修形及加工参数计算[J].航空动力学报,2017,32(8):2009-2016.NIE Shaowu,DENG Jing,DENG Xiaozhong,et al.Tooth surface topology modification and processing parameters calculation for spiral bevel gears[J].Journal of Aerospace Power,2017,32(8):2009-2016.(in Chinese)
[17]苏进展,郭晓东,刘永生,等.刀倾法准双曲面小轮粗切优化及验证[J].华南理工大学学报,2016,44(11):84-89.SU Jinzhan,GUO Xiaodong,LIU Yongsheng,et al.Optimization and validation of hypoid pinion roughing summary based on tilted method[J].Journal of South China University of Technology,2016,44(11):84-89.(in Chinese)
[18]周建星,刘更,马尚君.内激励作用下齿轮箱动态响应与振动噪声分析[J].振动与冲击,2011,30(6):234-238.ZHOU Jianxing,LIU Geng,MA Shangjun.Vibration and noise analysis of gear transmission system[J].Journal of Vibration and Shock,2011,30(6):234-238.(in Chinese)
[2] 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.
[3] FUENTES A,LITVIN F L,MULLINS B R.Design and stress analysis of low-noise adjusted bearing contact spiral bevel gears[J].Journal of Mechanical Design,2002,124(3):524-532.
[4] ASTOUL J,MERMOZ E,SARTOR M,et al.New methodology to reduce the transmission error of the spiral bevel gears[J].Manufacturing Technology,2014,63(1):165-168.
[5] SU J Z,FANG Z D,CAI X W.Design and analysis of spiral bevel gears with seventh-order function of transmission error[J].Chinese Journal of Aeronautics,2013,26(5):1310-1316.
[6]方宗德,刘涛,邓效忠.基于传动误差设计的弧齿锥齿轮啮合分析[J].航空学报,2002,13(3):226-230.FANG Zongde,LIU Tao,DENG Xiaozhong.Tooth contact analysis of spiral bevel gears based on the design of transmission error[J].Acta Aeronautica et Astronautica Sinica,2002,13(3):226-230.(in Chinese)
[7] GHOSH S S,CHAKRABORTY G.On optimal tooth profile modification for reduction of vibration and noise in spur gear pairs[J].Mechanism and Machine Theory,2016,105(11):145-163.
[8]马辉,逄旭,宋溶泽,等.考虑齿轮-转子系统振动响应的最佳修形曲线研究[J].振动与冲击,2015,34(11):17-22.MA Hui,FENG Xu,SONG Rongze,et al.Optimal profile modification curves for spur gears considering vibration responses of a gear-rotor system[J].Journal of Vibration and Shock,2015,34(11):17-22.(in Chinese)
[9]马辉,逄旭,宋溶泽,等.考虑齿顶修缘的齿轮-转子系统振动响应分析[J].机械工程学报,2014,50(7):39-45.MA Hui,FENG Xu,SONG Rongze,et al.Vibration response analysis of a geared rotor system considering the tip relief[J].Journal of Mechanical Engineering,2014,50(7):39-45.(in Chinese)
[10]吴序堂.齿轮啮合原理[M].北京:机械工业出版社,1982.
[11] LITVIN F L.Gear geometry and applied theory[M].2nd ed.New York:Cambridge University Press,2004.
[12]汪中厚,王杰,王巧玲,等.基于有限元法的螺旋锥齿轮传动误差研究[J].振动与冲击,2014,33(14):165-170.WANG Zhonghou,WANG Jie,WANG Qiaoling,et al.Transmission error of spiral bevel gear based on finite element method[J].Journal of Vibration and Shock,2014,33(14):165-170.(in Chinese)
[13] GONZALEZ I P,FUENTES A.Implementation of a finite element model for stress analysis of gear drives based on multi-point constraints[J].Mechanism and Machine Theory,2017,117(11):35-47.
[14]张卫青,张明德,郭晓东,等.全数控锥齿轮铣齿机运动控制方法及切齿实验研究[J].中国机械工程,2009,20(22):2733-2737.ZHANG Weiqing,ZHANG Mingde,GUO Xiaodong,et al.Research on the kinematic control method of CNC hypoid cutting machine and the cutting experiments[J].China Mechanical Engineering,2009,20(22):2733-2737.(in Chinese)
[15]郑昌启.弧齿锥齿轮和准双曲面齿轮[M].北京:机械工业出版社,1988.
[16]聂少武,邓静,邓效忠,等.弧齿锥齿轮齿面拓扑修形及加工参数计算[J].航空动力学报,2017,32(8):2009-2016.NIE Shaowu,DENG Jing,DENG Xiaozhong,et al.Tooth surface topology modification and processing parameters calculation for spiral bevel gears[J].Journal of Aerospace Power,2017,32(8):2009-2016.(in Chinese)
[17]苏进展,郭晓东,刘永生,等.刀倾法准双曲面小轮粗切优化及验证[J].华南理工大学学报,2016,44(11):84-89.SU Jinzhan,GUO Xiaodong,LIU Yongsheng,et al.Optimization and validation of hypoid pinion roughing summary based on tilted method[J].Journal of South China University of Technology,2016,44(11):84-89.(in Chinese)
[18]周建星,刘更,马尚君.内激励作用下齿轮箱动态响应与振动噪声分析[J].振动与冲击,2011,30(6):234-238.ZHOU Jianxing,LIU Geng,MA Shangjun.Vibration and noise analysis of gear transmission system[J].Journal of Vibration and Shock,2011,30(6):234-238.(in Chinese)