摘要
随着能源短缺和环境污染问题的日益加剧,风能作为一种清洁的可再生能源,已被世界各国高度重视。近年来,虽然我国风电产业得到快速发展,但风电机组的总体设计制造水平与国际先进水平相比还有很大差距。
风电齿轮箱是风电机组中最重要的部件之一。目前,我国已安装的风力发电机组,特别是大型风电机组的故障率居高不下,其中齿轮箱故障占了很大的比重。对大型风电齿轮箱进行系统的研究,降低风电机组中齿轮箱的故障率,提高风电机组的性能和可靠性对推动我国风电产业的发展有重要意义。
大型风电齿轮箱中通常包括行星齿轮传动。均载性能直接决定着行星齿轮传动的可靠性等工作性能。本文主要对大型风电齿轮箱的均载性能及关键部件进行了研究,完成的主要工作和得出的结论包括以下几个方面。
(1)建立了大型风电齿轮箱的静力学均载分析模型,进行了误差分析,得到了静力学载荷分布不均匀系数的计算方法和太阳轮浮动量。结果表明,系统的静力学载荷分布不均匀系数随各误差的增大而增大,内齿圈偏心误差对载荷分布不均匀系数的影响最大。在其他条件不变的情况下,载荷分布不均匀系数随太阳轮支撑刚度的增大而增大。
(2)采用集中参数法建立了大型风电齿轮箱的动力学均载分析模型,得到了其运动微分方程。采用傅立叶法求解得到了系统的动载系数和动力学载荷分布不均匀系数。分析了各齿轮偏心误差和转速对动力学均载性能的影响。结果显示,太阳轮偏心误差对动力学均载性能的影响最大,其次是内齿圈,行星轮偏心误差的影响最小;系统的动力学载荷分布不均匀系数随转速的升高而增大。
(3)以各级接触疲劳强度近似相等为目标函数,建立了大型风电齿轮箱传动参数优化设计模型,采用遗传算法完成了大型风电齿轮箱参数的优化设计。与传统设计方法相比较,本优化设计能够更好的实现系统的整体性能最优。
(4)建立了行星架的刚度模糊可靠性模型,对行星架进行了刚度模糊可靠性优化设计,得到了行星架侧壁厚度的最优值。进一步通过有限元结构分析,优化了行星架侧壁连接板的结构。与初始设计的计算结果相比较,改进后结构的重量降低了32kg。优化前结构中最大位移为0.85mm,最大应力为211MPa;优化后的改进模型的最大位移为0.55mm,最大应力为91.70MPa。通过对行星架的优化及结构改进,很大程度上降低了结构的变形和应力,提高了行星架刚度,降低了行星架变形对轮齿啮合状态的影响。
(5)在对某大型风电齿轮箱箱体受力进行系统分析的基础上,采用有限元法分析了各箱体组成部分在不同组合情况下的应力、变形情况。算例箱体的最大综合位移为1.169mm,出现在箱体背面区域,特别是左爪及轴承2受力的区域变形较大;最大应力为99.68MPa,满足设计要求。分析了整个箱体装配体的模态特性,结果表明其固有频率较高,前十阶固有频率在233.19Hz～526.8Hz范围内,其固有频率满足风电齿轮箱设计标准要求。
(6)应用齿廓法线法推导出了插齿加工的渐开线直齿内齿圈的精确齿廓曲线方程,并通过Solidworks中的宏功能采用Visual Basic语言编程实现了内齿圈齿廓渐开线以及齿根过渡曲线的自动生成,建立了内齿圈的精确三维实体模型,研究了内齿圈的轮齿变形及齿根应力。结果表明,内齿圈的最大变形出现在齿顶的中间部位,而最大应力出现在受载齿的齿根部位;内齿圈的最大变形和齿根最大应力随着齿根过渡圆角半径的增大而减小。在螺栓孔及销孔不变的情况下,内齿圈的轮齿最大变形和齿根最大应力随轮缘厚度的增大而减小,螺栓孔及销孔对轮齿最大变形影响不大,但对齿根最大应力的影响比较显著。
The energy shortage and environment pollution become increasingly serious. Wind power, as a clean and renewable energy, is paid great attention by the countries all over the world. In recently years, wind power of our country developed rapidly. But compared with the advanced level in the world, there's still great disparity on the design and manufacturing technology of large scale wind turbine.
Wind turbine gearbox is an important component in the wind turbine. At present, the failure rate of wind turbine, especially the large-scale wind turbine which has been installed in our country is high. And the failure of the gearbox takes a large proportion. Therefore, systematic study on the large scale wind turbine gearbox can help reduce the failure rate of the gearbox, improve the performance and reliability of wind turbine. This has important significance for promoting the development of the wind power industry in our country.
The large scale wind turbine gearbox generally includes planetary transmission. The load sharing properties directly affect the operating performance, reliability and life of the planetary transmission. So the load sharing properties and the key parts in the large scale wind turbine gearbox are studied. The main work and conclusions are as following.
1. The static load sharing analysis model of large scale wind turbine gearbox is built, and the transmission errors are analyzed. The calculation method of static load sharing coefficient and the floating quantity of sun gear is acquired. The results indicate that the load sharing coefficient increase when the eccentric errors increasing. And the gear ring eccentric error has the maxmum influence on the load sharing properties. When equal parameters, the load sharing coefficient increase as the sun gear supporting rigidity rising.
2. The dynamic load sharing property model is built, and the motion differential equation is derived. The dynamic load coefficient and dynamic load sharing coefficient is got after solve the motion differential equation with Fourier method. The result indicate that the sun gear ecentric error has the most remarkable effect on dynamic load sharing coefficient, the secondly is gear ring eccentric error, the planet gear eccentric error has the smallest influence.
3. The optimal design model of large scale wind turbine is built to reach the objection of contact-fatigue strength of different stage approximately equal. The optimization of transimission parameters is implemented through genetic algorithm program. Compared with traditional design, the optimal design provides a method to obtain integral reasonable transmission parameters of large scale wind turbine gearbox.
4. The fuzzy reliability model of planetary carrier is built, and the fuzzy reliability optimal design for planet carrier is carried out. Through the optimum design, the optimum solution of side wall thickness is got. The structure of the connection board between the two side walls is further optimized by finite element method. Compared with the original design, the weight of planet carrier reduced 32Kg. The largest displacement on original design is 0.845mm, the largest stress is 211MPa. After the optimum design, the biggest displacement decrease to 0.55mm, and the maximum stress reduced to 91.7MPa. By the structural optimum design, the deformation and stress is reduced, the rigidity is enhanced, and the influence on tooth engagement state from the deforming of planet carrier is reduced.
5. Analyzed the load that acted on the gearbox of large scale wind turbine. The stress and deformation of different assembled gearbox are studied by finite element method. The results indicate that the biggest complex displacement on gearbox reaches 1.17mm, and it appears on the back district of the gearbox, especially near the left supporting hole and the bearing two. The largest stress on the gearbox is 99.68MPa, satisfy the design requirement. Mode analysis of the entire assembled gearbox is carried out, the first ten step natural frequency and corresponding vibrate mode are got. The results indicate that the first ten step natural frequency range from 233.2Hz to 526.8Hz, the natural frequency is higher than the value specified by the standard.
6. The profile equations of shaping gear ring are deduced out by profile normal line method. The involute and transition curves are automatically generated through the macro function in Solidworks. And the three-dimension model is built. Based on the three-dimension model, the deformation and dedendum stress is studied. The results indicate that the largest deformation appear on the middle region of the addendum, the position of largest stress appears at the dedendum region of loaded tooth. As the curvature radius of transition curve rising, both the largest deformation and the largest dedendum stress reduce. With unchanged hole structure, the largest displacement and largest stress reduce as the rim thickness increase. And the influence of hole structure to the displacement of the ring gear is small, but the hole structure has significant influence on the largest stress of ring gear.
引文
[1]Global Wind 2008 Report[R],Global Wind Energy Council,2008:6.
[2]J.F.Manwell,J.G.McGowan and A.L.Rogers.Wind Energy Explained Theory,Desingn and Application[M],University of Massachusetts,Amherst,2002.
[3]阿瑟劳斯·泽尔沃斯.全球风电发展现状及展望[J].中国能源,2008(4):22-28
[4]Global Wind Energy Outlook 2008[R],Global Wind Energy Council,2008:10.
[5]施鹏飞.中国风电装机容量迅猛增加及存在的问题[J].可再生能源,2007,25(3):4-5.
[6]李俊峰,高虎,施鹏飞,等.2007中国风电发展报告[M].北京:中国环境科学出版社.
[7]施鹏飞.2007年中国风电场装机容量统计[J].中国风能,2008(1).
[8]施鹏飞.2008中国风电场装机容量统计[R].2009.
[9]王徽,黄成力.海上风力发电技术.上海节能,2007(1):23-26.
[10]Eize Vries.Developments and Trends in Wind Turbines[J].Renewable Energy World,2002,5(4):62-71.
[11]王超,张怀宇,王新慧,等.风力发电技术及其发展方向[J].电站系统工程,2006(2):11-13.
[12]周燕莉.风力发电的现状与发展趋势[J].甘肃科技,2008,24(3):9-11.
[13]张方军.风电发电技术及其发展方向[J].电气时代,2005(11):22-25.
[14]Facing up to the Gearbox Challenge:A survey of gearbox failure and collected industry Knowledge[J],Windpower Monthly,2005,21,(11).
[15]J.Antoni and R.B.Randall.Differential diagnosis of gear and bearing faults[J].Journal of Vibration and Acoustics-Transactions of the Asme,2002,124(2):165-171.
[16]Summary of Wind turbine Accident data to 31 December 2008[EB/OL].Caithness Windfarm Information Forum 2008.2008,31.Http://www.caithnesswindfarms.co.uk.
[17]T.Larsen,K.Thomsen,and F.Rasmussen Dynamics of a Wind Turbine Planetary Gear Stage[J].Proceedings of the European Wind Energy Conference (EWEC2003),Madrid,Spain,June 16-19,2003.
[18]D.Lin,M.Wiseman,D.Banjevic,etc.An approach to signal processing and condition-based maintenance for gearboxes subject to tooth failure[J].Mechanical Systems and Signal Processing,2004,18:993-1007.
[19]F.Krull.Vibrations and dynamic behavior of gearboxes in drive trains of wind turbines[J].Proceedings of the 7th German Wind Energy Conference(DEWEK 2004),Wilhelmshaven,Germany,2004,10:20-21.
[20]A.Fernandez,F.Viadero,J.Pascual,etc.Vibration Behaviour Modelling for a Low-Speed Gearbox[J].Proceedings of the International Conference on Noise and Vibration Engineering(ISMA 2002),2002,9:16-18.
[21]ANSI/AGMA/AWEA 6006-A03,Standard for Design and Specification of Gearbox fox Wind Turbine[S],2003,10.
[22]张和平,张志宏,刘忠明.大型风力发电齿轮箱设计技术及软件开发[J].2005年中国机械工程学会年会论文集,北京:机械工业出版社,2005:42.
[23]Niff B,Musiai W D,Developing A Wind Turbine Gearbox Load Description[J],Presented at Global Windpower Conference and Exhibition,Chicago,Ill,March 2004.
[24]Shanmugam KN.Wind power project development-some key issues[J].Windpro J 2004(79):6.
[25]龙泽强,肖劲松.风力发电研究和开发的现状与展望[J].世界科技研究与发展,2003,25(4):26-30.
[26]李树吉,陈雷,杨树人.风力机齿轮箱的优化设计[J].广州:中国新能源期刊,2000,12.
[27]刘贤焕,叶仲和.大型风力发电机组用齿轮箱优化设计及方案分析[J].机械设计与研究,2006(1):29-32.
[28]冯键,陈雪华.基于有限元的大型风电齿圈制造技术的研究[J].机械设计,2007,31(1):81-83.
[29]August A,Kasuba R.Torsional Vibration and Dynamic Loads in a Basic Planetary Gear System[J].Journal of Acoustics,Stress,and Reliability in Design. Transaction of the ASME1986,108:348-253.
[30]Jarchow F,Vonderschmidt R.Gearing Power Transm.Proc.Int.Symp.1981,327.
[31]日高照晃,山本信行,石田武.行星齿轮装置均载机构中的各种误差和载荷分配的关系[A].日本机械学会论文集(C编)52卷480号,1986,2200-2206.
[32]Timothy L K,Irebert R D.A Method to Analyze and Optimize the Load Sharing of Split Path Transmissions,NASA Technical Memorandum 107201,1996.
[33]Timothy L K,Irebert R D.Experimental Study of Split-Path Transmission Load Sharing.NASA Technical Memorandum 107202,1996.
[34]Kahraman A,Singh R.Nonlinear Dynamics of a Spur Gear Pair[J].Journal of Sound andVibration,1990,142(1):49-75.
[35]Kahraman A,Singh R.Nonlinear Dynamics of a Geared Rotor-bearing System with MultipleClearances[J].Journal of Sound and Vibration,1991,144(3):469-06.
[36]Kahraman A,Singh R.Interactions Between Time-varying Mesh Stiffness and ClearanceNon-linearities in a Geared system[J].Journal of Sound and Vibration,1991,146(1):135-156.
[37]Kahraman A.Load Sharing Characteristics of Planetary Transmissions[J].Mech.Mach.Theory,1994,29(8):1151-1165.
[38]Kahraman A.Static Load Sharing Characteristics of Transmission Planetary Gear Sets:Model and Experiment[J].Society of Automotive Engineers,1999:1954-1963.
[39]Al Shyyab and A.Kahraman.Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method:period-one motions[J].Journal of Sound and Vibration,2005,284(1-2):151-172.
[40]邵晓荣.齿轮制造及安装误差对行星齿轮均载系数的影响[J].东北重型机械学院院报,1994,18(4):306-309.
[41]张淳,张锁怀,梁兆兰.内齿行星齿轮传动原理性载荷不均匀性问题的探讨[J].机械科学与技术,1995(3):54-57.
[42]李平林,刘伟强,吴宗泽.采用油膜均载的实验研究[J].机械设计,1996(5): 29-34.
[43]陈纯.行星齿轮传动均载构件位移量的计算[J].机械设计与制造,2001(3):52-53.
[44]肖铁英,袁盛治,陆卫杰.行星齿轮机构均载系数的计算方法[J].东北重型机械学院学报,1994,16(4):290-295.
[45]袁茹,王三民,沈允文.行星齿轮传动的功率分流动态均衡优化设计[J].航空学报,2000,15(4):410-412.
[46]袁擎宇,朱如鹏,朱自冰,等.两级星型齿轮传动静力学均载分析[J].机械科学与技术,2004,23(7):789-792.
[47]方宗德,沈允文.斜齿轮传动动态性的理论与实验研究[J].中国机械工程学会第二届齿轮传动力学会议论文集,1991:52-59.
[48]方宗德,沈允文,黄镇东.三路功率分流恒星式减速器的动态特性[J].航空学报,1990,11(7):341-350.
[49]张涛.行星齿轮油膜均载机构动力学分析[J].起重运输机械,2006(8):76-79.
[50]鲍和云,朱如鹏.两级星型齿轮传动动态均载特性分析[J].航空动力学报,2005,20(6):937-943.
[51]鲍和云,朱如鹏.两级星型齿轮传动动力学系统基本构件浮动量分析[J].机械科学与技术,2006,25(6)708-711.
[52]李润方,王建军.齿轮系统动力学-振动、冲击、噪声[M].北京:科学出版社,1997.
[53]王建军,李其汉,李润方.齿轮系统非线性振动研究进展[J].力学进展,2005,5(1):47-51.
[54]G.V.Tordio,R.Gouvin.Dynamic Stability of a Two-Stage Gear Train under the Influenee of Variable Meshing Stiffness[J].ASME Journal of Engineering for Industry,1997,(99):785-791.
[55]P.Velex,M.Matar.A Mathematical Model for Analyzing the Influence of Shape Deviation and Mounting Errors on Gear Behavior.Journal of Sound and Vibration,1996,(191):629-660.
[56]W.A.Tuplin.Gear Tooth Stresses at High Speed[J],Proceedings of the Institution of Mechanical Engineers,1950,16:162-167.
[57]L.D.Mitchell and J.W.Daws.Proposed solution methodology for the dynamically coupled nonlinear gear rotor mechanics equation[J].ASME Vib.Acous.Stress Reliab.Des,1985,(107):112-116.
[58]K.Umezawa.Vibration of power transmission helical gear with narrow face width[J].ASME Paper,1984,84-159.
[59]Lin J,Parker R G.Analytical Characterization of the Unique Properties of Planetary Gear Free Vibration[J].Transactions of the ASME,Journal of Vibration and Acoustics,1999,121:316-321.
[60]Parker R G,Agashe V,Vijayakar S M.Dynamic Response of a Planetary Gear System Using a Finite Element/Contact Mechanics Model[J].ASME,Journal of Mechanical Design,2000,122:304-310.
[61]J.Lin and R.G.Parker.Planetary gear parametric instability caused by mesh stiffness variation[J].Journal of Sound and Vibration,2002,249(1):129-145.
[62]R.G Parker,J.Lin.Mesh Stiffness Variation Instabilities in Two-Stage Gear Systems[J].Journal of Vibration and Acoustics,2002,124(1):68-76.
[63]Parker R G,Vijayakar S M,Imajo T.Non-linear dynamic response of a spur gear pair:modelling and experimental comparisons[J].Journal of Sound and Vibration,2000,237(3):435-455.
[64]沈允文等.齿轮系统减振设计的结构灵敏度分析[J],机械工程学报,1996,32(5).
[65]沈允文,邵长健.利用行星架附加阻尼的行星齿轮系统减振研究[J].机械传动,1999,23(4):29-32.
[66]王三民,沈允文,董海军.含间隙和时变啮合刚度的弧齿锥齿轮传动系统非线性振动特性研究[J].机械工程学报,2003,39(2):28-32.
[67]汤和等.理想齿轮噪声与振动谱的计算机仿真[J],齿轮,14(4).
[68]孙涛,沈允义,孙智民,等.行星齿轮传动非线性动力学方程求解与动态特性分析[J].机械工程学报,2002,38(3):10-15.
[69]孙涛,沈允文.行星齿轮传动非线性动力学模型与方程[J].机械工程学报, 2002,38(3):6-9.
[70]孙智民,沈允文,王三民,等.星型齿轮传动非线性动力学建模与动载荷研究[J].航空动力学报,200l,16(4):402-407.
[71]孙智民,季红林,沈允文.2K-H行星齿轮传动非线性动力学[J].清华大学学报(自然科学版),2003,43(5):636-639.
[72]朱才朝,秦大同,李润方.内齿行星齿轮传动动态特性的研究[J].重庆大学学报(自然科学版),1997(5):26-32.
[73]朱才朝,黄泽好,唐倩.风力发电齿轮箱系统耦合非线性动态特性的研究[J].机械工程学报,2005(8):203-207.
[74]Joris Peeters.Simulation of Dynamic Drive Train Loads In a Wind Turbine[D].Ph.D.dissertation,2006.
[75]R Hbaieb,F Chaari,T Fakhfakh et al.Dynamic stability of a planetary gear train under influence of variable meshing stiffnesses[J].Automobile Engineering 2006,(8):1171-1725.
[76]Wrigth AD,Balas MJ.Design of control to alternate loads in the controls advanced research turbine[J].Sol energy Eng 2003;125(4):396-401.
[77]张文忠.NTK300/31风电机齿轮箱的故障分析与预防[J].内蒙古电力技术,2001(5):46-47.
[78]郁明山,李奇,韩歌山,等.渐开线齿轮行星传动的设计与制造[M].北京:机械工业出版社,2002.
[79]雷先明.高速星形减速器齿轮系均载分析[J].机械,2000,27(6):8-9.
[80]齿轮手册编委会.齿轮手册(上册)[M].北京:机械工业出版社,1994.
[81]陈纯.行星齿轮传动均载构件移量的计算[J].机械设计与制造 2001,(3):52-53.
[82]甘永生.几何量公差与检测[M].上海:上海科技大学出版社,1997.
[83]S.Barone,L.Borgianni,and P.Forte.Evaluation of the effect of misalignment and profile modification in face gear drive by a finite element meshing simulation[J].Journal of Mechanical Design,2004,126(5):916-924.
[84]C.Braccesi,L.Landi,and R.Scaletta.New dual meshless flexible body methodology for multi-body dynamics:simulation of generalized moving loads[J].Proceedings of the Institution of Mechanical Engineers Part K-Journal of Multi-Body Dynamics,2004,218(1):51-62.
[85]I.Howard,S.X.Jia,and J.D.Wang.The dynamic modelling of a spur gear in mesh including friction and a crack[J].Mechanical Systems and Signal Processing,2001,15(5):831-853.
[86]Yi Cheng Chen,Chung Biau Tsay.Stress analysis of a helical gear set with localized bearing contact[J].Finite Elements in Analysis and Design,2002,(38):707-723.
[87]朱孝录.齿轮承载能力分析[M].北京高等教育出版社:1992.
[88]Gerald R.数值方法和MATLAB实现与应用[M].伍卫国,万群,张辉译.北京:机械工业出版社,2004.
[89]Edward B M.MATLAB原理与工程应用[M].高会生,李新叶,胡智奇译.北京:电子工业出版社,2002.
[90]周奇才,李婧,俞敬.减速器行星齿轮传动常规设计和优化设计的比较[J].中国工程机械学报,2007,5(3):308-312.
[91]赵勇,吉鸿涛,查建中.行星齿轮传动系统的可靠性优化设计[J],机械设计与制造.2001(5):5-6.
[92]陈举华,王寿佑.行星齿轮传动多目标模糊可靠性优化设计[J].山东机械,1995(2):23-24.
[93]尹力.行星齿轮传动的可靠性优化设计[J].重庆交通学院院报,1997,16(4):71-76.
[94]周明,孙树栋.遗传算法原理及应用[M].北京:国防工业出版社,1999.
[95]张志宏,刘忠明,张和平等.大型风电齿轮箱行星架结构分析及优化[J].机械设计,2008,25(9):54-56.
[96]王云根,施一萍.侧板式行星架的有限元分析及结构设计[J].机械传动,1999,23(1):7-9.
[97]赵丽娟,陈令国,刘红梅.矿用减速器行星架的有限元分析[J].煤矿机械,2007,28(1):51-52.
[98]王超等.机械可靠性工程[M].北京:冶金工业出版社,1992.
[99]王彩华.工程结构的模糊优化设计[M].北京:中国建筑工业出版社,1986.
[100]吴序堂.齿轮啮合原理[M].北京:机械工业出版社,1986.
[101]Meltzer G,Ivanov Y Y.Fault detection in gear drives with non-stationary rotational speed part Ⅰ:the time-frequency approach[J].Mechanical Systems and Signal Processing,2003,17(5):1033-1047.
[102]B.Schlecht,T.Schulze,and T.H(a|¨)hnel.Today's techniques of the assessment of dynamic loads in drive trains of wind turbines using multibody-system-simulation [J].Proceedings of the 7th German Wind Energy Conference (DEWEK2004),Wilhelmshaven,Germany,2004,Oktober:20-21.
[103]P.Velex and V.Cahouet.Experimental and numerical investigations on the influence of tooth friction in spur and helical gear dynamics[J].Journal of Mechanical Design,2000,122(4):515-522.
[104]X.Zhao,P.Maisser,and P.Tenberge.Stability analysis of a variable speed wind turbine with power splitting transmission using multi-flexible-body methodology [J].VDI-Berichte Nr.1606,Schwingungen in Anlagen und Maschinen,pp.95-112,Veitsh(o|¨)chheim,W(u|¨)rzburg,Germany,May 16-17,2001.
[105]J.D.Wang and I.Howard.The torsional stiffness of involute spur gears[J].Journal of Mechanical Engineering Science,2004,218:131-142.
[106]J.H.Kuang,A.D.Lin.Theoretical aspects of torque responses in spur gearing due to mesh stiffness variation[J].Mechanical Systems and Signal Processing,2003,17(2):255-271.
[107]傅志方.振动模态分析与参数识别[J].北京:机械工业出版社,1990.
[108]冯键,陈雪华.基于有限元的大型风电齿圈制造技术的研究[J].机械设计,2007;31(1):81-83.
[109]郑胜强,马振利.基于Matlab的齿轮传动可靠性优化分析[J].后期工程学院院报,2006(2):84-88.
[110]陈满意,陈定方.基于Matlab的齿轮减速器的可靠性优化设计[J].机械传动,2002(3):34-36.
[111]冯健,陈雪华.基于有限元的大型风电齿圈制造技术的研究[J].电力自动化 设备,2007,31(1):81-83.
[112]梁兆兰,吴春英,王乃信.双轴输入式内齿行星传动的动态受力分析[J].机械科学与技术,1994,51(3):67-71.
[113]张锁怀.内齿行星齿轮传动受力分析[J].机械传动,1994,18(4):32-35.
[114]段明南,李山青,陆军.取料机行星减速器齿轮架断裂失效分析[J].冶金设备,2008(4):35-38.
[115]朱学文,朱国文,何小新.斜齿轮的参数化建模与动力学分析[J].机械传动,2006(2):32-34.
[116]朱诗顺,李玉兰,骆素君等.混合动力牵引车独立悬架变截面板簧的有限元分析[J].起重运输机械,2003(12):43-44.
