谐波传动柔轮结构参数优化与整机动态仿真
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摘要
柔轮作为谐波传动中的关键部件,其疲劳强度大小、轮齿啮合性能直接影响谐波传动的使用寿命与承载能力,因此选择合理的柔轮结构参数非常重要。本文以D120谐波传动为研究对象,基于有限元方法分析柔轮的应力与弹性变形,并通过对柔轮杯体及齿形参数的优化,改善了传动性能。
本文在对谐波传动原理研究的基础上,首先采用壳体单元建立参数化柔轮接触分析模型,通过求解空负载情况下柔轮的应力场与弹性变形,确定柔轮容易发生疲劳破坏的位置。
其次,将壳体有限元接触分析模型与正交试验法相结合,运用批处理方式进行求解,分析柔轮杯体各结构参数对最大应力的影响。以此为依据,把柔轮应力最小作为目标函数,采用零阶方法优化得到最佳柔轮杯体参数。
然后,基于谐波齿轮传动运动几何学,推导出共轭齿廓计算模型,为后续的齿形优化奠定了基础。同时,根据柔轮弹性变形的空间分布,对轮齿运动的接触状态进行了分析,所得接触线分布在后续仿真中得到验证。
最后,建立谐波传动实体参数化有限元模型,结合谐波传动运动几何学,分析空负载轮齿瞬心线及共轭齿廓。在柔杯最佳结构参数的基础上,保持渐开线基本齿形不变,通过逼近理论共轭齿廓的方式对其变位系数进行空负载循环修正,求解出最优的齿形参数,从而获得以D120为原型的新结构参数谐波传动,并仿真对比分析新模型相对原始模型在柔轮应力与轮齿啮合性能方面的改善情况。
本文的研究方法与结果不仅为谐波齿轮传动的结构设计改进提供了新思路,而且为进一步研究柔轮结构与弹性变形函数的关系提供了参考。
The flexspline, as a critical component of harmonic drive, of which the fatigue strength and meshing performance directly affect the service life and bearing capacity of harmonic drive. Therefore, a reasonable choice of the flexspline structure parameters is very important. This paper takes D120 harmonic drive as the research object. The stress and elastic deformation of flexspline are analyzed based on the finite element method. The transmission performance of harmonic drive is improved by optimizing the cup and tooth profile parameters of flexspline.
Firstly, the parameterized model of flexspline contact analysis is established using the shell elements on the basis of harmonic drive theory. The easily fatigue damage location of flexspline is determined by solving the stress field and elastic deformation under load and no-load.
Secondly, orthogonal test is applied to study the impact of structural parameters on the maximum stress of flexspline. Further, an optimization model is built to minimize the maximum stress and the optimum parameters of flexspline cup are obtained using zero-order method.
Thirdly, the computation model of conjugate tooth profile is derived based on the kinematics of harmonic gear drive, which sets a foundation for the subsequent tooth profile optimization. Meanwhile, the contact state of gear tooth is analyzed according to the spatial distribution of flexspline elastic deformation. The contact line distribution obtained is proved in dynamic simulation.
Finally, the entity parametric finite element model of harmonic gear drive is set up, and the gear tooth centrodes and conjugate tooth profile under load and no-load are analyzed by combining with the kinematics of harmonic gear drive. Keep the basic involute profile unchanged on the basis of the optimum structural parameter of flexspline cup. The best parameters of tooth profile are got by amending the addendum coefficient in the manner of approaching the theory conjugate tooth profile. Thus, a new structural model is obtained according to D120 harmonic gear drive. The comparative analysis of new model and original model in flexspline stress and meshing performance is done.
The research methods and results not only provide new ideas for structure improvement of harmonic gear drive but also provide reference for further studies on the relationship between flexspline structure and elastic deformation.
本文在对谐波传动原理研究的基础上,首先采用壳体单元建立参数化柔轮接触分析模型,通过求解空负载情况下柔轮的应力场与弹性变形,确定柔轮容易发生疲劳破坏的位置。
其次,将壳体有限元接触分析模型与正交试验法相结合,运用批处理方式进行求解,分析柔轮杯体各结构参数对最大应力的影响。以此为依据,把柔轮应力最小作为目标函数,采用零阶方法优化得到最佳柔轮杯体参数。
然后,基于谐波齿轮传动运动几何学,推导出共轭齿廓计算模型,为后续的齿形优化奠定了基础。同时,根据柔轮弹性变形的空间分布,对轮齿运动的接触状态进行了分析,所得接触线分布在后续仿真中得到验证。
最后,建立谐波传动实体参数化有限元模型,结合谐波传动运动几何学,分析空负载轮齿瞬心线及共轭齿廓。在柔杯最佳结构参数的基础上,保持渐开线基本齿形不变,通过逼近理论共轭齿廓的方式对其变位系数进行空负载循环修正,求解出最优的齿形参数,从而获得以D120为原型的新结构参数谐波传动,并仿真对比分析新模型相对原始模型在柔轮应力与轮齿啮合性能方面的改善情况。
本文的研究方法与结果不仅为谐波齿轮传动的结构设计改进提供了新思路,而且为进一步研究柔轮结构与弹性变形函数的关系提供了参考。
The flexspline, as a critical component of harmonic drive, of which the fatigue strength and meshing performance directly affect the service life and bearing capacity of harmonic drive. Therefore, a reasonable choice of the flexspline structure parameters is very important. This paper takes D120 harmonic drive as the research object. The stress and elastic deformation of flexspline are analyzed based on the finite element method. The transmission performance of harmonic drive is improved by optimizing the cup and tooth profile parameters of flexspline.
Firstly, the parameterized model of flexspline contact analysis is established using the shell elements on the basis of harmonic drive theory. The easily fatigue damage location of flexspline is determined by solving the stress field and elastic deformation under load and no-load.
Secondly, orthogonal test is applied to study the impact of structural parameters on the maximum stress of flexspline. Further, an optimization model is built to minimize the maximum stress and the optimum parameters of flexspline cup are obtained using zero-order method.
Thirdly, the computation model of conjugate tooth profile is derived based on the kinematics of harmonic gear drive, which sets a foundation for the subsequent tooth profile optimization. Meanwhile, the contact state of gear tooth is analyzed according to the spatial distribution of flexspline elastic deformation. The contact line distribution obtained is proved in dynamic simulation.
Finally, the entity parametric finite element model of harmonic gear drive is set up, and the gear tooth centrodes and conjugate tooth profile under load and no-load are analyzed by combining with the kinematics of harmonic gear drive. Keep the basic involute profile unchanged on the basis of the optimum structural parameter of flexspline cup. The best parameters of tooth profile are got by amending the addendum coefficient in the manner of approaching the theory conjugate tooth profile. Thus, a new structural model is obtained according to D120 harmonic gear drive. The comparative analysis of new model and original model in flexspline stress and meshing performance is done.
The research methods and results not only provide new ideas for structure improvement of harmonic gear drive but also provide reference for further studies on the relationship between flexspline structure and elastic deformation.
引文
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[23]K.Kondo,J.Takada.Study on tooth profiles of the harmonic drive[J].Journal of Mechanical Design,1990,112(3):131-137.
[24]范元勋,王华坤,宋德锋.谐波传动共轭齿廓的运动学仿真研究[J].南京航空航天大学学报,2002,34(5):447-450.
[25]范元勋,王华坤,宋德锋.谐波齿轮传动共轭齿廓的计算机数值模拟研究[J].南京理工大学学报,2002,26(4):389-392.
[26]阳培,张立勇,王长路,王建敏.谐波齿轮传动技术发展概述[J].机械传动,2005,29(3):69-72.
[27]毛彬彬,王克武.谐波齿轮的齿形研究和发展[J].煤矿机械,2008,29(7):6-8.
[28]Rathindranath Maiti.A Novel Harmonic Drive with Pure Involute Tooth Gear Pair[J].Journal of Mechanical Design,2004,126:178-182.
[29]辛洪兵,何惠阳,谢金瑞.精密谐波齿轮传动采用圆弧齿廓的合理性证明[J].长春光学精密机械学院学报,1997,20(3):47-50.
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[31]曾世强,杨家军,王宣福.双圆弧齿形谐波齿轮传动的运动特性分析[J].华中理工大学学报,2000,28(1):12-14.
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[2]沈允文,叶庆泰.谐波齿轮传动的理论和设计[M].北京:机械工业出版社,1985.
[3]王长明,阳培,张立勇.谐波齿轮传动概述[J].机械传动,2006,30(4):86-88.
[4]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:大连理工大学机械学院,2008.
[5]辛洪兵.谐波传动技术及其研究动向[J].北京轻工业学院学报,1999,17(1):30-36.
[6]周卫东.渐开线谐波齿轮传动齿廓参数优化及动态仿真[D].大连:大连理工大学机械学院,2008.
[7]付军峰,董海军,沈允文.谐波齿轮传动中柔轮应力的有限元分析[J].中国机械工程,2007,18(18):2210-2214.
[8]机械设计手册编委会.机械设计手册(新版第三卷)[M].北京:机械工业出版社,2004.
[9]李玉光,尤竹平.谐波齿轮传动柔轮位移场和应力场的有限元分析[J].大连大学学报,1991,1(4):101-106.
[10]曹庭驹,郑振东.谐波齿轮传动短筒柔轮应力的有限元计算分析[J].华北水利水电学院学报,1992,2:13-26.
[11]乐可锡,全永昕,周桂如,张民杰.谐波齿轮传动中空间动态啮合力的理论计算[J].浙江大学学报,1995,29(2):220-228.
[12]Dong Huimin,You Zhuping,Liu Jian.Spatial Elastic Conjugation Theory in Harmonic Drive,Proceedings of MTM' 97(International Conference on Mechanical Transmission and Mechanisms),China Machine Press,Beijing,1997.
[13]张丽华.基于有限元分析的谐波齿轮传动变形协调研究[D].大连:大连理工大学机械学院,2003.
[14]Se Hoon Oh,Seung Hwan Chang,Dai Gil Lee.Improvement of the dynamic properties of a steel-composite hybrid flexspline of a harmonic drive[J].Composite Structures,1997,38:251-260.
[15]Han Su Jeon,Se Hoon Oh.A study on stress and vibration analysis of a steel and hybrid flexspline for harmonic drive[J].Composite Structures,1999,47:827-833.
[16]董惠敏,张晓青.基于实验建模的谐波齿轮传动柔轮的有限元分析研究[J].机械传动,2001,25(2):16-19.
[17]张晓青.谐波齿轮传动中杯形柔轮的有限元分析研究[D].大连:大连理工大学机械学院,2001.
[18]刘文芝,张乃仁,张春林,赵永忠.谐波齿轮传动中杯形柔轮的有限元计算与分析[J].机械工程学报,2006,42(4):52-57.
[19]王延风,李书功,谢涛.谐波齿轮传动柔轮有限元力学分析及结构参数改进[J].光学精密工程,2005,13:86-90.
[20]付军峰,董海军.柔轮应力的有限元分析及结构参数的合理选择[J].机械科学与技术,2007,26(9):1101-1104.
[21]Musser,C.W.Strain Wave Gearing.U.S.Pat.Nos.2,906,143,SEPT.29,1959.
[22]王淑芬.谐波齿轮传动的运动几何学研究[D].大连:大连理工大学机械学院,2000.
[23]K.Kondo,J.Takada.Study on tooth profiles of the harmonic drive[J].Journal of Mechanical Design,1990,112(3):131-137.
[24]范元勋,王华坤,宋德锋.谐波传动共轭齿廓的运动学仿真研究[J].南京航空航天大学学报,2002,34(5):447-450.
[25]范元勋,王华坤,宋德锋.谐波齿轮传动共轭齿廓的计算机数值模拟研究[J].南京理工大学学报,2002,26(4):389-392.
[26]阳培,张立勇,王长路,王建敏.谐波齿轮传动技术发展概述[J].机械传动,2005,29(3):69-72.
[27]毛彬彬,王克武.谐波齿轮的齿形研究和发展[J].煤矿机械,2008,29(7):6-8.
[28]Rathindranath Maiti.A Novel Harmonic Drive with Pure Involute Tooth Gear Pair[J].Journal of Mechanical Design,2004,126:178-182.
[29]辛洪兵,何惠阳,谢金瑞.精密谐波齿轮传动采用圆弧齿廓的合理性证明[J].长春光学精密机械学院学报,1997,20(3):47-50.
[30]辛洪兵.圆弧齿廓谐波齿轮传动齿形设计中的几个问题[J].机械传动,1999,23(2):11-13.
[31]曾世强,杨家军,王宣福.双圆弧齿形谐波齿轮传动的运动特性分析[J].华中理工大学学报,2000,28(1):12-14.
[32]刘书海,董惠敏,邹开其.基于运动几何学的谐波齿轮传动双圆弧齿形优化设计[J].大连大学学报,2002,23(2):13-16.
[33]毛彬彬,王克武.ANSYS平台上的双圆弧齿廓谐波传动柔轮有限元分析[J].现代制造工程,2008,6:59-62.
[34]Jeong K.S,Lee D.G,Oh S.H.Development of the composite flexslpine for a cycloid-type harmonic drives using net shape manufacturing method[J].Composite Structures,1995,32:557-565.
[35]Yeh Thomas,Yang Daniel C.H,Tong Shih-His.Design of new tooth profiles for high-load capacity gears[J].Mechanism and Machine Theory,2001,36:1105-1120.
[36]Oguz Kayabasi,Fehmi Erzincanli.Shape optimization of tooth profile of a flexspline for a harmonic drive by finite element modelling[J].Materials and Design,2007,28:441-447.
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