大型立式行星齿轮减速器传动系统的优化设计
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摘要
行星齿轮传动系统是大型立式减速器的核心部件,其性能直接影响到整个系统的运作,设计过程中既要保证其传动的安全性,又要尽量的减小它的体积。因此如何合理的确定传动系统中各项参数的配置,一直是困扰设计人员的主要问题。现代的机械优化设计得益于其设计周期短,人力物力耗费较少等优点,已经被广泛应用在这项设计之中。
但是现行常用的优化设计往往考虑的设计变量和边界条件不够全面,如:漏掉了很多影响传动的因素,且将应力、强度等视为固定不变的值。这样无论在经济上还是在实用上都不会得到问题的最优解。鉴于以上因素,本文首先引入可靠性方面的理论重新构建了更为完整的多目标的优化数学模型,随后利用两种数学软件Matlab、Lingo,三种方法分别编程对模型进行求解,并将得到的轮系参数组合的新系统进行静态特性的对比分析,以确定最为合理的优化结果。
为确保系统有良好的动态性能,本文利用pro/e结合adams软件,建立实际的齿轮啮合模型进行运动学仿真,用以观察传动系统运行时齿轮的啮合,对比分析优化前后系统的动态啮合力特性。随后将整个传动系统等效为平移-扭转的弹簧-阻尼集中质量模型,并通过对其进行的模态分析,最终得到模型的固有频率和模态振型,以验证优化后的模型是否会发生共振。
行星传动需要行星架组件结构来支持,为保证行星架在优化后系统中的安全性,对其进行受力分析。在获得了行星架整体结构的应力场和位移场的情况下,观察到其结构设计趋于保守,所以利用Ansys建立其参数化有限元模型,并对其进行相应的优化设计,使得新的行星架组件即可以配合优化后的齿轮传动,又可以在满足自身的强度要求的前提下适当减重。
本文最终通过对齿轮系统参数和行星架组件参数的优化设计达到了在安全范围内降低整个传动系统成本的效果。
Planetary gear reducer drive system is the core of large vertical components, its performance has a direct impact on the operation of the whole system, the design process should not only ensure the security of its transmission, but also decrease its volume as much as possible. For this problem the traditional spreadsheet method has been replaced by the modern machinery optimization design because of the long design cycle and the cost of a large human and material.
But the optimal design of the traditional transmission system, one part it doesn’t consider the variables and the boundary conditions comprehensive, the other part it treats the will stress and strength as an fixed value, it ignores more influence factors of transmission, so it won’t get the optimal solution on both economy and applicability. Given all these problems, this paper has restructured the optimum target function, design variables and constraints with reliability factors, then it has used three software and two methods to solute the program, finaly the results has compared of the static characteristics to find the best solvtion.
In order to make sure of the system dynamic performance, this paper has used pro/e combining with adams to establish the actual gear meshing model for observing the transmission gear meshing, then it has compared the dynamics characteristics of the original and the optimized transmission system. It has confirmed that the resonance won’t occur in the system through the natural frequency.
Considering that the particularity of planetary gear planetary drive needs planets frame structure to support, so it needs statics analysis to guarantee planet shelf stability after the optimization. While obtained structure of the stress and displacement field, this paper has used Ansys to implement parametric finite element modeling for the planet shelf components, and then it has optimized on the model, the optimization must make sure that the new components can be gear transmission with and satisfy the strength requirement of itself.
Finaly it has reduced the effect of the transmission system cost through the gear parameters and planet shelf the optimization design.
但是现行常用的优化设计往往考虑的设计变量和边界条件不够全面,如:漏掉了很多影响传动的因素,且将应力、强度等视为固定不变的值。这样无论在经济上还是在实用上都不会得到问题的最优解。鉴于以上因素,本文首先引入可靠性方面的理论重新构建了更为完整的多目标的优化数学模型,随后利用两种数学软件Matlab、Lingo,三种方法分别编程对模型进行求解,并将得到的轮系参数组合的新系统进行静态特性的对比分析,以确定最为合理的优化结果。
为确保系统有良好的动态性能,本文利用pro/e结合adams软件,建立实际的齿轮啮合模型进行运动学仿真,用以观察传动系统运行时齿轮的啮合,对比分析优化前后系统的动态啮合力特性。随后将整个传动系统等效为平移-扭转的弹簧-阻尼集中质量模型,并通过对其进行的模态分析,最终得到模型的固有频率和模态振型,以验证优化后的模型是否会发生共振。
行星传动需要行星架组件结构来支持,为保证行星架在优化后系统中的安全性,对其进行受力分析。在获得了行星架整体结构的应力场和位移场的情况下,观察到其结构设计趋于保守,所以利用Ansys建立其参数化有限元模型,并对其进行相应的优化设计,使得新的行星架组件即可以配合优化后的齿轮传动,又可以在满足自身的强度要求的前提下适当减重。
本文最终通过对齿轮系统参数和行星架组件参数的优化设计达到了在安全范围内降低整个传动系统成本的效果。
Planetary gear reducer drive system is the core of large vertical components, its performance has a direct impact on the operation of the whole system, the design process should not only ensure the security of its transmission, but also decrease its volume as much as possible. For this problem the traditional spreadsheet method has been replaced by the modern machinery optimization design because of the long design cycle and the cost of a large human and material.
But the optimal design of the traditional transmission system, one part it doesn’t consider the variables and the boundary conditions comprehensive, the other part it treats the will stress and strength as an fixed value, it ignores more influence factors of transmission, so it won’t get the optimal solution on both economy and applicability. Given all these problems, this paper has restructured the optimum target function, design variables and constraints with reliability factors, then it has used three software and two methods to solute the program, finaly the results has compared of the static characteristics to find the best solvtion.
In order to make sure of the system dynamic performance, this paper has used pro/e combining with adams to establish the actual gear meshing model for observing the transmission gear meshing, then it has compared the dynamics characteristics of the original and the optimized transmission system. It has confirmed that the resonance won’t occur in the system through the natural frequency.
Considering that the particularity of planetary gear planetary drive needs planets frame structure to support, so it needs statics analysis to guarantee planet shelf stability after the optimization. While obtained structure of the stress and displacement field, this paper has used Ansys to implement parametric finite element modeling for the planet shelf components, and then it has optimized on the model, the optimization must make sure that the new components can be gear transmission with and satisfy the strength requirement of itself.
Finaly it has reduced the effect of the transmission system cost through the gear parameters and planet shelf the optimization design.
引文
[1]渐开线齿轮行星传动的设计与制造委员会.渐开线齿轮行星传动的设计与制造[M].第一版.机械工业出版社,2002:5-6.
[2]郝竹叶.德国RENK公司简介[J].大型铸锻件,2007,3(2):47-48.
[3]杨小明.西马克德马克公司SMSDEMAG简介[J].大型铸锻件,2007,1(1):48-49.
[4]邓小林.为5000t/d生产线配套的大型原料立磨的技术现状[J].中国水泥,2006,(9):58-62.
[5]赖京丽.科技创新铸造辉煌[J].传动技术(四川),1998,(1):42-43.
[6]成吉昌.江苏泰隆逆风飞扬[J].装备制造,2009,(7):67-69.
[7]陈梁,周升友.我国首台高科技智能型大功率船用齿轮箱试航成功[J].中国船舶报,2004,4(3):28-29.
[8]张运节.机械优化设计综述与展望[J].科技信息,2006(4):703-704.
[9]彭文生.齿轮技术新面貌[J].国际学术动态,1990(3):11-14.
[10]侯曦暘，王世杰. 2K-H型行星齿轮减速器优化设计[J].机械工程与自动化,2010(1):108-112.
[11] Giorgio Bonori, Marco Barbieri. Optimum Profile Modifications of Spur Gears by Means of Genetic Algorithms[J]. Journal of Sound and Vibration. 2008(313): 603-616.
[12] Shuting Li. Effect of Addendum on Contact Strength, Bending Strength and Basic Performance Parameters of a Pair of Spur Gears[J]. Mechanism and Machine Theory. 2008 (43):1557-1584.
[13] Grzegorz Litak,Michael I.Friswell. Vibration in Gear Systems[J]. Chaos, Solitons and Fractals. 2003 (43):795-800.
[14]于玲,贾春强. Matlab遗传算法工具箱函数及应用实例[J].机械工程师,2004(11):27-28.
[15]张金标.基于遗传算法的减速器混合离散变量优化设计[J].机械工程师,2008(5):138-140.
[16]梅占国,李必文.轮式工程机械轮边减速器优化模型与方法[J].现代机械,2008(4):47-48.
[17] V.Senthil Kumar, D.V.Muni, G.Muthuveerappan. Optimization of Asymmetric Spur Gear Drives to Improve the Bending Load Capacity[J]. Mechanism and Machine Theory,2008 (43):829-858.
[18]李必文,张春良.轮边减速器优化设计存在的问题及对策[J].中国工程机械学报,2008,6(1):53-56.
[19]王世杰,刘玉春,张剑. NGW型潜油行星减速器可靠性优化设计[J].机械传动,2003,27(1):23-29.
[20]叶秉良,赵匀,俞高红等.拖拉机NGW型行星式最终传动多目标可靠性优化[J].农业工程学报,2008,24(11):89-93.
[21]吴敏.机械减速器齿轮传动的优化设计[J].装备制造技术,2007(1):1-2.
[22] F.L.Litvin. Gear Geometry and Applied Theory [M]. Prentice Hall Englewood Cliffs.1994: 22-98.
[23] A.Kahraman. Natural Modes of Planetary Gear Trains[J]. Journal of Sound Vibration. 2009 (173):125-130.
[24]王建维,张建明,魏小鹏.基于模拟退火算法的减速器多目标优化设计[J].农业机械学报,2006,37(10):120-123.
[25] Faydor L.Litvin, Alfonso Fuentes, Kenichi Hayasaka. Design, Manufacture, Stress Analysis and Experimental Tests of Low-noise High Endurance Spiral Bevel Gears[J]. Mechanism and Machine Theory. 2006 (41):83-118.
[26]张涵,关德娟.行星齿轮减速器多目标优化设计研究[J].电子机械工程,2006,22(3):1-4.
[27]王克琦,赵风雷.二级行星减速器多目标优化设计研究[J].通用机械,2006(6):93-95.
[28] Lin. J,R.G. Parker. Structured Vibration Characteristics of Planetary Gears with Unequally Spaced Planets[J]. Journal of Sound and Vibration. 2000 (233):921-928.
[29] Parker R. G. Mesh Phasing for Epicyclic Gear Vibration Reduction[C]. Proceedings of the International Conference on Mechanical Transmissions. Chongqing, 2001.
[30]张可村,李换琴.工程优化方法及应用[M].西安交通大学,2007:202-207.
[31] Djamel Berkoune a, Khaled Mesghouni. Resolution Approach for Multi-objective Problems with Uncertain Demands[J]. European Journal of Operational Research . 2008 (187): 403-414.
[32]刘亚磊,郭登明,易先忠等.基于MATLAB优化工具箱的机械优化设计[J].现代机械,2006(6):32-33.
[33] V.Savsani, R.V.Rao, D.P.Vakharia. Optimal Weight Design of a Gear Train Using Particle Swarm Optimization and Simulated Annealing Algorithms[J]. Mechanism and Machine Theory. 2010 (45):531-541.
[34] Cevdet Gologlu, Metin Zeyveli. A genetic Approach to Automate Preliminary Design of Gear Drives[J]. Computers&Industrial Engineering. 2009 (57):1043- 1051.
[35]柳敏飞.基于MATLAB遗传算法的齿轮减速器的优化设计[J].组装机床与自动化加工技术,2009(8):36-39.
[36]赵升吨,申亚京,尚万峰.轧机机架参数敏感性分析及顺序优化的研究[J].西安交通大学学报,2008,42(1):1-4.
[37]朱振荣.渐开线行星齿轮传动技术的发展[J].热能动力工程,2007,4:40-42
[38]叶秉良,赵匀,俞高红等.拖拉机NGW型行星式最终传动多目标可靠性优化[J].农业工程学报,2008,24(11):89-93.
[39]朱文予.机械可靠性设计[M].第二版.上海交通大学出版社,1997:233-235.
[40]杨文,顾保磊,戴光耀.一种避免早熟收敛的改进遗传算法[J].软件导刊,2009,8(3):53-55.
[41]田会芳,林喜镇,赵恒.基于Pro/E和ADAMS齿轮啮合的动力学仿真[J].机械传动,2006,30(6):66-69.
[42]孙中平.基于ADAMS的齿轮减速器动力学仿真[J].交通科技与经济,2007,9(4):77-79.
[43] J. L.Frater, R.Augm, VB.Oswald. Vibration in Planetary Gear System with Unequal Planet Stiffness[J]. NASA Technical Memorandum. 1983 (8):28-34.
[44] Marcello Faggioni, Farhad S.Samani, Gabriele Bertacchi. Dynamic Optimization of Spur Gears[J]. Mechanism and Machine Theory. 2010 (46):544-557.
[45] Ales Belsak. Jurij Prezelj. Visualisation and Analysis of Noise Sources of a Gear Unit[J]. Engineering Failure Analysis. 2009 (16):1570-1578.
[46]刘欣.基于虚拟样机技术的直齿行星传动动力学研究[D].天津:天津大学,2007:3-4.
[47]张文斌.某型雷达天线座方位减速器箱体有限元分析和优化设计[D].沈阳:东南大学,2006:40-60.
[2]郝竹叶.德国RENK公司简介[J].大型铸锻件,2007,3(2):47-48.
[3]杨小明.西马克德马克公司SMSDEMAG简介[J].大型铸锻件,2007,1(1):48-49.
[4]邓小林.为5000t/d生产线配套的大型原料立磨的技术现状[J].中国水泥,2006,(9):58-62.
[5]赖京丽.科技创新铸造辉煌[J].传动技术(四川),1998,(1):42-43.
[6]成吉昌.江苏泰隆逆风飞扬[J].装备制造,2009,(7):67-69.
[7]陈梁,周升友.我国首台高科技智能型大功率船用齿轮箱试航成功[J].中国船舶报,2004,4(3):28-29.
[8]张运节.机械优化设计综述与展望[J].科技信息,2006(4):703-704.
[9]彭文生.齿轮技术新面貌[J].国际学术动态,1990(3):11-14.
[10]侯曦暘，王世杰. 2K-H型行星齿轮减速器优化设计[J].机械工程与自动化,2010(1):108-112.
[11] Giorgio Bonori, Marco Barbieri. Optimum Profile Modifications of Spur Gears by Means of Genetic Algorithms[J]. Journal of Sound and Vibration. 2008(313): 603-616.
[12] Shuting Li. Effect of Addendum on Contact Strength, Bending Strength and Basic Performance Parameters of a Pair of Spur Gears[J]. Mechanism and Machine Theory. 2008 (43):1557-1584.
[13] Grzegorz Litak,Michael I.Friswell. Vibration in Gear Systems[J]. Chaos, Solitons and Fractals. 2003 (43):795-800.
[14]于玲,贾春强. Matlab遗传算法工具箱函数及应用实例[J].机械工程师,2004(11):27-28.
[15]张金标.基于遗传算法的减速器混合离散变量优化设计[J].机械工程师,2008(5):138-140.
[16]梅占国,李必文.轮式工程机械轮边减速器优化模型与方法[J].现代机械,2008(4):47-48.
[17] V.Senthil Kumar, D.V.Muni, G.Muthuveerappan. Optimization of Asymmetric Spur Gear Drives to Improve the Bending Load Capacity[J]. Mechanism and Machine Theory,2008 (43):829-858.
[18]李必文,张春良.轮边减速器优化设计存在的问题及对策[J].中国工程机械学报,2008,6(1):53-56.
[19]王世杰,刘玉春,张剑. NGW型潜油行星减速器可靠性优化设计[J].机械传动,2003,27(1):23-29.
[20]叶秉良,赵匀,俞高红等.拖拉机NGW型行星式最终传动多目标可靠性优化[J].农业工程学报,2008,24(11):89-93.
[21]吴敏.机械减速器齿轮传动的优化设计[J].装备制造技术,2007(1):1-2.
[22] F.L.Litvin. Gear Geometry and Applied Theory [M]. Prentice Hall Englewood Cliffs.1994: 22-98.
[23] A.Kahraman. Natural Modes of Planetary Gear Trains[J]. Journal of Sound Vibration. 2009 (173):125-130.
[24]王建维,张建明,魏小鹏.基于模拟退火算法的减速器多目标优化设计[J].农业机械学报,2006,37(10):120-123.
[25] Faydor L.Litvin, Alfonso Fuentes, Kenichi Hayasaka. Design, Manufacture, Stress Analysis and Experimental Tests of Low-noise High Endurance Spiral Bevel Gears[J]. Mechanism and Machine Theory. 2006 (41):83-118.
[26]张涵,关德娟.行星齿轮减速器多目标优化设计研究[J].电子机械工程,2006,22(3):1-4.
[27]王克琦,赵风雷.二级行星减速器多目标优化设计研究[J].通用机械,2006(6):93-95.
[28] Lin. J,R.G. Parker. Structured Vibration Characteristics of Planetary Gears with Unequally Spaced Planets[J]. Journal of Sound and Vibration. 2000 (233):921-928.
[29] Parker R. G. Mesh Phasing for Epicyclic Gear Vibration Reduction[C]. Proceedings of the International Conference on Mechanical Transmissions. Chongqing, 2001.
[30]张可村,李换琴.工程优化方法及应用[M].西安交通大学,2007:202-207.
[31] Djamel Berkoune a, Khaled Mesghouni. Resolution Approach for Multi-objective Problems with Uncertain Demands[J]. European Journal of Operational Research . 2008 (187): 403-414.
[32]刘亚磊,郭登明,易先忠等.基于MATLAB优化工具箱的机械优化设计[J].现代机械,2006(6):32-33.
[33] V.Savsani, R.V.Rao, D.P.Vakharia. Optimal Weight Design of a Gear Train Using Particle Swarm Optimization and Simulated Annealing Algorithms[J]. Mechanism and Machine Theory. 2010 (45):531-541.
[34] Cevdet Gologlu, Metin Zeyveli. A genetic Approach to Automate Preliminary Design of Gear Drives[J]. Computers&Industrial Engineering. 2009 (57):1043- 1051.
[35]柳敏飞.基于MATLAB遗传算法的齿轮减速器的优化设计[J].组装机床与自动化加工技术,2009(8):36-39.
[36]赵升吨,申亚京,尚万峰.轧机机架参数敏感性分析及顺序优化的研究[J].西安交通大学学报,2008,42(1):1-4.
[37]朱振荣.渐开线行星齿轮传动技术的发展[J].热能动力工程,2007,4:40-42
[38]叶秉良,赵匀,俞高红等.拖拉机NGW型行星式最终传动多目标可靠性优化[J].农业工程学报,2008,24(11):89-93.
[39]朱文予.机械可靠性设计[M].第二版.上海交通大学出版社,1997:233-235.
[40]杨文,顾保磊,戴光耀.一种避免早熟收敛的改进遗传算法[J].软件导刊,2009,8(3):53-55.
[41]田会芳,林喜镇,赵恒.基于Pro/E和ADAMS齿轮啮合的动力学仿真[J].机械传动,2006,30(6):66-69.
[42]孙中平.基于ADAMS的齿轮减速器动力学仿真[J].交通科技与经济,2007,9(4):77-79.
[43] J. L.Frater, R.Augm, VB.Oswald. Vibration in Planetary Gear System with Unequal Planet Stiffness[J]. NASA Technical Memorandum. 1983 (8):28-34.
[44] Marcello Faggioni, Farhad S.Samani, Gabriele Bertacchi. Dynamic Optimization of Spur Gears[J]. Mechanism and Machine Theory. 2010 (46):544-557.
[45] Ales Belsak. Jurij Prezelj. Visualisation and Analysis of Noise Sources of a Gear Unit[J]. Engineering Failure Analysis. 2009 (16):1570-1578.
[46]刘欣.基于虚拟样机技术的直齿行星传动动力学研究[D].天津:天津大学,2007:3-4.
[47]张文斌.某型雷达天线座方位减速器箱体有限元分析和优化设计[D].沈阳:东南大学,2006:40-60.
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