双圆弧谐波传动柔轮齿形参数多目标优化设计
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摘要
根据刚轮和柔轮空载下连续不断啮合和"双共轭"现象能有效提高双圆弧谐波齿轮装置的啮合性能,提出了一种圆弧柔轮齿形参数的多目标优化设计方法。针对无公切线双圆弧齿廓,采用改进运动学法和精确转角关系进行共轭齿廓设计,以缩小共轭空白区间与共轭齿廓差异为优化目标,考虑共轭齿廓的存在条件,建立谐波传动多目标优化模型,进行单目标分析及多目标优化。结果表明:该优化方法可实现柔轮齿形参数的合理选择,使空载状态刚轮与柔轮啮合空白区域小于1.2°,共轭齿廓间差异在0.83μm左右,能满足工程应用要求,保证空载连续啮合及"双共轭"传动精度。
The continuous meshing zone and "double conjugate" phenomenon of the circular spline and flexspline under no-load conditions can effectively improve the meshing performance of the double-arc harmonic gear device. For this reason,a multi-objective optimization design method of the tooth profile parameters of the double-circle flexspline is proposed. For the non-public tangential double-arc tooth profile,the conjugate tooth profile was designed by using the relationship between the improved kinematics method and the precise rotation angle. To reduce the difference between the conjugate blank area and the conjugate tooth profile as the optimization goal,a harmonic drive multi-objective optimization model was established. Considering the existence conditions of conjugate tooth profiles,single target analysis and multi-objective optimization are performed. The results show that the two objective functions increase with the increase of the radial deformation coefficient and the double circular arc inclination,and decrease with the increase of the tooth thickness ratio;Radial deformation coefficient and double circular arc inclination have the greatest influence on the two objective functions,and tooth thickness ratio has less influence on the difference of minimum conjugate tooth profile. Convex arc radius coefficient and concave arc radius coefficient have almost no effect on the minimum blank conjugate area;this optimization method can achieve a reasonable selection of parameters of the soft tooth profile,and make the freewheeling state between the circular spline and the flexspline is less than 1.2°,and the difference between the conjugate profiles is about 0.83 μm,which can meet the requirements of engineering applications. Guaranteed no-load continuous meshing interval and "double conjugate" transmission accuracy.
The continuous meshing zone and "double conjugate" phenomenon of the circular spline and flexspline under no-load conditions can effectively improve the meshing performance of the double-arc harmonic gear device. For this reason,a multi-objective optimization design method of the tooth profile parameters of the double-circle flexspline is proposed. For the non-public tangential double-arc tooth profile,the conjugate tooth profile was designed by using the relationship between the improved kinematics method and the precise rotation angle. To reduce the difference between the conjugate blank area and the conjugate tooth profile as the optimization goal,a harmonic drive multi-objective optimization model was established. Considering the existence conditions of conjugate tooth profiles,single target analysis and multi-objective optimization are performed. The results show that the two objective functions increase with the increase of the radial deformation coefficient and the double circular arc inclination,and decrease with the increase of the tooth thickness ratio;Radial deformation coefficient and double circular arc inclination have the greatest influence on the two objective functions,and tooth thickness ratio has less influence on the difference of minimum conjugate tooth profile. Convex arc radius coefficient and concave arc radius coefficient have almost no effect on the minimum blank conjugate area;this optimization method can achieve a reasonable selection of parameters of the soft tooth profile,and make the freewheeling state between the circular spline and the flexspline is less than 1.2°,and the difference between the conjugate profiles is about 0.83 μm,which can meet the requirements of engineering applications. Guaranteed no-load continuous meshing interval and "double conjugate" transmission accuracy.
引文
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[9]Chen Xiaoxia,Liu Yusheng,Xing Jingzhong,et al.The parametric design of doublecirculararc tooth profile and its influence on the functional backlash of harmonic drive[J].Mechanism and Machine Theory,2014,73(2):124.
[10]Chen Xiaoxia,Lin Shuzhong,Xing Jingzhong,et al.Simulation on gear backlash and interference check of harmonic drive with circulararc teeth profile[J].Computer Integrated Manufacturing Systems,2011,17(3):643648.
[11]Xin Hongbing.Design for basic rack of harmonic drive with doublecirculararc tooth profile[J].China Mechanical Engineering,2011,22(6):656662.
[12]杨勇,王家序,周青华,等.双圆弧谐波齿轮传动柔轮齿廓参数的优化设计[J].四川大学学报:工程科学版,2016,48(1):186193.Yang Yong,Wang Jiaxu,Zhou Qinghua,et al.Optimization design for flexspline tooth profile parameters of doublecirculararc harmonic drives[J].Journal of Sichuan University(Engineering Science Edition),2016,48(1):186193.
[13]翟永.谐波齿轮传动双圆弧齿形设计与分析[D].大连:大连海事大学轮机工程学院,2015.Zhai Yong.Doublearc tooth profile design and analysis of harmonic drive[D].Dalian:School of Marine Engineering,Dalian Maritime University,2015.
[2]Timofeev G A.Drives with harmonic gears for servo systems[J].Russian Engineering Research,2016,36(3):187193.
[3]董惠敏.基于柔轮变形函数的谐波齿轮传动运动几何学及其啮合性能研究[D].大连:大连理工大学机械工程学院,2008.Dong Huimin.Study of kinematics and meshing characteristic of harmonic drive based on the deformation function of the flexspline[D].Dalian:School of Mechanical Engineering,Dalian University of Technology,2008.
[4]刘邓辉,邢静忠,陈晓霞.渐开线谐波齿轮的空间齿廓设计及啮合特性分析[J].机械设计,2016,33(3):2429.Liu Denghui,Xing Jingzhong,Chen Xiaoxia.Spatial tooth profile design and engagement analysis of harmonic gear with involute profile[J].Journal of Machine Design,2016,33(3):2429.
[5]Ishikawa S,Takizawa N.Wave gear drive having negative deflection meshing tooth profile[P].US Patent:7735396,20100615.
[6]Ishikaua S.Wave gear device having threedimensionally contactable shifted tooth profile[P].US Patent:8776638,20140715.
[7]王家序,周祥祥,李俊阳,等.不同共轭原理的双圆弧齿廓谐波齿轮传动分析[J].四川大学学报:工程科学版,2015,47(5):160166.Wang Jiaxu,Zhou Xiangxiang,Li Junyang,et al.Doublecirculararc tooth profile of harmonic drive analysis based on different conjugate principle[J].Journal of Sichuan University(Engineering Science Edition),2015,47(5):160166.
[8]王家序,周祥祥,李俊阳,等.公切线式双圆弧齿廓谐波齿轮传动设计[J].湖南大学学报:自然科学版,2016,43(2):5663.Wang Jiaxu,Zhou Xiangxiang,Li Junyang,et al.Design of doublecirculararc and common tangent tooth profile of harmonic drive[J].Journal of Hunan University(Natural Sciences),2016,43(2):5663.
[9]Chen Xiaoxia,Liu Yusheng,Xing Jingzhong,et al.The parametric design of doublecirculararc tooth profile and its influence on the functional backlash of harmonic drive[J].Mechanism and Machine Theory,2014,73(2):124.
[10]Chen Xiaoxia,Lin Shuzhong,Xing Jingzhong,et al.Simulation on gear backlash and interference check of harmonic drive with circulararc teeth profile[J].Computer Integrated Manufacturing Systems,2011,17(3):643648.
[11]Xin Hongbing.Design for basic rack of harmonic drive with doublecirculararc tooth profile[J].China Mechanical Engineering,2011,22(6):656662.
[12]杨勇,王家序,周青华,等.双圆弧谐波齿轮传动柔轮齿廓参数的优化设计[J].四川大学学报:工程科学版,2016,48(1):186193.Yang Yong,Wang Jiaxu,Zhou Qinghua,et al.Optimization design for flexspline tooth profile parameters of doublecirculararc harmonic drives[J].Journal of Sichuan University(Engineering Science Edition),2016,48(1):186193.
[13]翟永.谐波齿轮传动双圆弧齿形设计与分析[D].大连:大连海事大学轮机工程学院,2015.Zhai Yong.Doublearc tooth profile design and analysis of harmonic drive[D].Dalian:School of Marine Engineering,Dalian Maritime University,2015.