渐开线谐波齿轮传动齿廓参数优化及动态仿真
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摘要
本文基于谐波齿轮传动的弹性共轭理论对刚柔轮齿的渐开线齿廓参数进行了优化,并在分析柔轮理论空间共轭齿廓的基础上,修正了柔轮的渐开线齿廓。进一步利用有限元方法,仿真了谐波齿轮传动的动态工作过程,并研究了优化齿廓的啮合性能。
文中首先通过对谐波齿轮的传动原理的研究,建立了基于柔轮变形函数的刚柔轮齿空间弹性共轭运动模型,并结合平面刚性运动瞬心线理论,导出了共轭齿廓的求解方程。基于上述方程,建立了以柔轮渐开线齿廓尽可能逼近理论共轭齿廓为优化目标的齿廓参数优化模型,并求解出刚柔轮渐开线齿廓的最优变位系数。进而反求柔轮轴向所有横截面内的共轭齿廓,研究各共轭齿廓的空间关系,并对柔轮齿廓进一步修正。
针对重复有限元建模的繁琐性及动态仿真求解对有限元模型质量的要求,本文手动编程实现了参数化有限元模型的建立,并提出了一种能方便程序实现的节点编号方法和网格生成算法。建立了方便参数修改及网格控制的程序界面,并能直接生成适合ABAQUS有限元求解器计算的求解文件。
对波发生器装入柔轮的过程进行了模拟,分析了柔轮初始装配状态下的变形函数及应力分布。以初始装配下柔轮的应力及变形为预载荷,仿真了谐波齿轮负载下的动态工作过程,研究柔轮杯体各处应力在额定载荷下的时变特性和载荷对柔轮的变形函数的影响,分析了谐波齿轮动态啮合接触力的齿向分布及周向分布特征,并比较了优化齿廓与未优化齿廓的啮合性能。
本文的研究结果对改善了谐波齿轮传动的啮合特性具有实际意义,对进一步设计适合动态载荷传动的齿形具有参考价值。
The paper optimizes the involute tooth profile parameters of flexspline and circular spline based on the elastic conjugation theory of harmonic gear drive. The involute tooth profile of flexspine is revised after analyzing the characteristic of the theoretical spatial conjugation tooth profile of flexspline. Then, the dynamic working process of harmonic gear is simulated with finite element method, and the meshing performance of optimal tooth profile is studied.
The spatial elastic conjugation motion model that based on the deformation function of flexspline is set up after researching the transmission principle of harmonic gear. The solution equation of conjugation tooth profile is deduced according to the centrode theory of planar rigid-body motion. Thus, the optimization model of tooth profile parameters is established and its objective is to make the involute profile approaching the theoretical conjugation profile as much as possible. Then the optimal modification coefficient of flexspline tooth and circular spline tooth can be obtained. The tooth profile of flexspline is revised by reversing all conjugation profiles in different cross-section of flexspline and studying their spatial characteristics.
The parameterized finite element model is constructed by manual programming aiming at the tedious repeater modeling and the mesh quality requirement of dynamic simulation solution. A new node numbering algorithm and mesh generation algorithm are presented, and the program interface is set up easy to modify parameters and control mesh quality. The program can generate the solution file for the solver of ABAQUS to compute.
The assembly process of wave generator is simulated. The deformation function and stress distribution of flexspline in the state of assembly are analyzed. Furthermore, the simulation of dynamic working process of harmonic gear under loads condition is conducted taking the deformation and stress of flexspline as preload. The time-variant characteristics of flexspline stress and the influence of loads on deformation function of flexspline are investigated, and the contact forces of harmonic gear drive on tooth direction and circumferential direction are studied. A comparison of meshing performance is made between optimal tooth profile and un-optimized tooth profile.
The research results have practical significance on improving the meshing performance of harmonic gear drive and reference value for the tooth shape which is suitable for dynamic transmission with loads.
文中首先通过对谐波齿轮的传动原理的研究,建立了基于柔轮变形函数的刚柔轮齿空间弹性共轭运动模型,并结合平面刚性运动瞬心线理论,导出了共轭齿廓的求解方程。基于上述方程,建立了以柔轮渐开线齿廓尽可能逼近理论共轭齿廓为优化目标的齿廓参数优化模型,并求解出刚柔轮渐开线齿廓的最优变位系数。进而反求柔轮轴向所有横截面内的共轭齿廓,研究各共轭齿廓的空间关系,并对柔轮齿廓进一步修正。
针对重复有限元建模的繁琐性及动态仿真求解对有限元模型质量的要求,本文手动编程实现了参数化有限元模型的建立,并提出了一种能方便程序实现的节点编号方法和网格生成算法。建立了方便参数修改及网格控制的程序界面,并能直接生成适合ABAQUS有限元求解器计算的求解文件。
对波发生器装入柔轮的过程进行了模拟,分析了柔轮初始装配状态下的变形函数及应力分布。以初始装配下柔轮的应力及变形为预载荷,仿真了谐波齿轮负载下的动态工作过程,研究柔轮杯体各处应力在额定载荷下的时变特性和载荷对柔轮的变形函数的影响,分析了谐波齿轮动态啮合接触力的齿向分布及周向分布特征,并比较了优化齿廓与未优化齿廓的啮合性能。
本文的研究结果对改善了谐波齿轮传动的啮合特性具有实际意义,对进一步设计适合动态载荷传动的齿形具有参考价值。
The paper optimizes the involute tooth profile parameters of flexspline and circular spline based on the elastic conjugation theory of harmonic gear drive. The involute tooth profile of flexspine is revised after analyzing the characteristic of the theoretical spatial conjugation tooth profile of flexspline. Then, the dynamic working process of harmonic gear is simulated with finite element method, and the meshing performance of optimal tooth profile is studied.
The spatial elastic conjugation motion model that based on the deformation function of flexspline is set up after researching the transmission principle of harmonic gear. The solution equation of conjugation tooth profile is deduced according to the centrode theory of planar rigid-body motion. Thus, the optimization model of tooth profile parameters is established and its objective is to make the involute profile approaching the theoretical conjugation profile as much as possible. Then the optimal modification coefficient of flexspline tooth and circular spline tooth can be obtained. The tooth profile of flexspline is revised by reversing all conjugation profiles in different cross-section of flexspline and studying their spatial characteristics.
The parameterized finite element model is constructed by manual programming aiming at the tedious repeater modeling and the mesh quality requirement of dynamic simulation solution. A new node numbering algorithm and mesh generation algorithm are presented, and the program interface is set up easy to modify parameters and control mesh quality. The program can generate the solution file for the solver of ABAQUS to compute.
The assembly process of wave generator is simulated. The deformation function and stress distribution of flexspline in the state of assembly are analyzed. Furthermore, the simulation of dynamic working process of harmonic gear under loads condition is conducted taking the deformation and stress of flexspline as preload. The time-variant characteristics of flexspline stress and the influence of loads on deformation function of flexspline are investigated, and the contact forces of harmonic gear drive on tooth direction and circumferential direction are studied. A comparison of meshing performance is made between optimal tooth profile and un-optimized tooth profile.
The research results have practical significance on improving the meshing performance of harmonic gear drive and reference value for the tooth shape which is suitable for dynamic transmission with loads.
引文
[1]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.
[2]沃尔阔夫,克拉伊聂夫著.谐波齿轮传动[M].北京:电子工业出版社,1985.
[3]Huimin Dong,Delun Wang,Kwun Lon Ting.Elastic Kinematic and Geometric Model of Harmonic Gear Drives[C].ASME Design Engineering Technical Conferences & Computers and Information in Engineering Conference,2008.
[4]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,2000.
[5]M.H.伊万诺夫。沈允文等译.谐波齿轮传动[M].北京:国防工业出版社,1987.
[6]刘书海.基于运动几何学的谐波齿轮传动齿形的研究[D].大连:大连理工大学,2003.
[7]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,第34卷第5期,10月,2002.
[8]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,2003.
[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]刘文芝,张乃仁,张春林等.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.
[12]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.
[13]付军锋,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.
[14]崔博文,沈允文.用有限元法研究谐波齿轮传动齿间啮合力的分布规律[J].机械传动,1997,21(1):7-9.
[15]王文静,辛洪兵,徐正兴.谐波齿轮传动小长径比柔轮有限元应力分析[J].北京工商大学学报(自然科学版),2007,25(4):26-29.
[16]Musser,C.W.Strain Wave Gearing.U.S.Pat.Nos.2,906,143,SEPT.29,1959.
[17]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.
[18]H.Kazerooni.Dynamics and Control of Instrumented Harmonic Drives[J].Journal of Dynamic Systems,Measurement,and Control,1995,Vol.117:15-19
[19]M.H.伊万诺夫.沈允文等译.谐波齿轮传动[M].北京:国防工业出版社,1987.
[20]K.Kondo.J.Takada.Study on Tooth Profiles of the Harmonic Drive[J].Transaction of the ASME,1990,Vol.112:131-137.
[21]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.
[22]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.
[23]阳培,张立勇等.谐波齿轮传动技术发展概述[J].机械传动,2005,29(3):69-72.
[24]范又功.谐波齿轮渐开线工作齿廓的位移系数的选择[J].机床,1993,5:30-32.
[25]王廷风,李功书等.谐波齿轮传动柔轮有限元分析及结构参数改进[J].光学精密工程,2005,13(Supp):86-90.
[26]吴序堂.齿轮啮合原理[M].北京:机械工业出版社,1982.
[27]王勖成.有限单元法[M].北京:清华大学出版社,2003.
[28]齿轮手册编委会.齿轮手册(第二版上册)[M].北京:机械工业出版社,2000.
[29]Rathindranath Maiti,A Novel Harmonic Drive with Pure Involute Tooth Gear Pair[J].Transaction of the ASME,2004,Vol.126:178-182.
[30]辛洪兵,何惠阳.谐波齿轮传动共扼齿廓的研究.长春光学精密机械学院学报[J],1996,19(1):22-26.
[31]乐可锡,沈允文.谐波齿轮传动的空间接触特性及齿面最佳修整[J].机械科学与技术,1991,2:29-33.
[32]辛洪兵.研究谐波齿轮传动啮合原理的种新方法[J].中国机械王程,2002,13(3):7-9.
[33]向国齐.谐波齿轮传动柔轮有限元分析研究[D].成都:四川大学,2005.
[35]董惠敏.谐波齿轮传动的齿形研究和对渐开线齿形的修形[D].大连:大连理工大学,1983.
[34]唐焕文,秦学志.实用最优化方法.大连:大连理工大学出版社,2000.
[36]张志涌.精通Matlab6.5版[M].北京:北京航空航天大学出版社,2003.
[37]庄茁,张帆等.ABAQUS非线性有限元分析与实例[M].北京:科学出版社,2005.
[2]沃尔阔夫,克拉伊聂夫著.谐波齿轮传动[M].北京:电子工业出版社,1985.
[3]Huimin Dong,Delun Wang,Kwun Lon Ting.Elastic Kinematic and Geometric Model of Harmonic Gear Drives[C].ASME Design Engineering Technical Conferences & Computers and Information in Engineering Conference,2008.
[4]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,2000.
[5]M.H.伊万诺夫。沈允文等译.谐波齿轮传动[M].北京:国防工业出版社,1987.
[6]刘书海.基于运动几何学的谐波齿轮传动齿形的研究[D].大连:大连理工大学,2003.
[7]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,第34卷第5期,10月,2002.
[8]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,2003.
[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]刘文芝,张乃仁,张春林等.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.
[12]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.
[13]付军锋,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.
[14]崔博文,沈允文.用有限元法研究谐波齿轮传动齿间啮合力的分布规律[J].机械传动,1997,21(1):7-9.
[15]王文静,辛洪兵,徐正兴.谐波齿轮传动小长径比柔轮有限元应力分析[J].北京工商大学学报(自然科学版),2007,25(4):26-29.
[16]Musser,C.W.Strain Wave Gearing.U.S.Pat.Nos.2,906,143,SEPT.29,1959.
[17]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.
[18]H.Kazerooni.Dynamics and Control of Instrumented Harmonic Drives[J].Journal of Dynamic Systems,Measurement,and Control,1995,Vol.117:15-19
[19]M.H.伊万诺夫.沈允文等译.谐波齿轮传动[M].北京:国防工业出版社,1987.
[20]K.Kondo.J.Takada.Study on Tooth Profiles of the Harmonic Drive[J].Transaction of the ASME,1990,Vol.112:131-137.
[21]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.
[22]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.
[23]阳培,张立勇等.谐波齿轮传动技术发展概述[J].机械传动,2005,29(3):69-72.
[24]范又功.谐波齿轮渐开线工作齿廓的位移系数的选择[J].机床,1993,5:30-32.
[25]王廷风,李功书等.谐波齿轮传动柔轮有限元分析及结构参数改进[J].光学精密工程,2005,13(Supp):86-90.
[26]吴序堂.齿轮啮合原理[M].北京:机械工业出版社,1982.
[27]王勖成.有限单元法[M].北京:清华大学出版社,2003.
[28]齿轮手册编委会.齿轮手册(第二版上册)[M].北京:机械工业出版社,2000.
[29]Rathindranath Maiti,A Novel Harmonic Drive with Pure Involute Tooth Gear Pair[J].Transaction of the ASME,2004,Vol.126:178-182.
[30]辛洪兵,何惠阳.谐波齿轮传动共扼齿廓的研究.长春光学精密机械学院学报[J],1996,19(1):22-26.
[31]乐可锡,沈允文.谐波齿轮传动的空间接触特性及齿面最佳修整[J].机械科学与技术,1991,2:29-33.
[32]辛洪兵.研究谐波齿轮传动啮合原理的种新方法[J].中国机械王程,2002,13(3):7-9.
[33]向国齐.谐波齿轮传动柔轮有限元分析研究[D].成都:四川大学,2005.
[35]董惠敏.谐波齿轮传动的齿形研究和对渐开线齿形的修形[D].大连:大连理工大学,1983.
[34]唐焕文,秦学志.实用最优化方法.大连:大连理工大学出版社,2000.
[36]张志涌.精通Matlab6.5版[M].北京:北京航空航天大学出版社,2003.
[37]庄茁,张帆等.ABAQUS非线性有限元分析与实例[M].北京:科学出版社,2005.