基于热流耦合的齿轮对流换热及温度场分析
|
摘要
齿轮啮合过程中由于轮齿啮合面相对滑动将产生大量热量,若产生的热量不能及时散去则会导致齿轮的温度上升,引起齿轮的承载能力和工作性能的下降,甚至直接导致齿轮失效。齿轮箱的润滑冷却效果是决定齿轮温度的主要原因,而齿轮箱内润滑油的流动特性对其性能有较大的影响。因此,开展基于热流耦合的齿轮对流换热及温度场数值仿真分析,对改善齿轮副传热特性具有重要的理论意义及工程应用价值。
本文课题来源于重庆市科技攻关计划项目。基于齿轮啮合原理、流体动力学和传热学理论,运用数值仿真方法,研究油浴润滑的齿轮箱内部流场、齿轮对流换热及齿轮温度场。本文的主要研究工作如下:
①将UG建立的渐开线齿轮副参数化模型导入Gambit中,建立齿轮箱内流体的计算模型;采用动网格及UDF技术,在Fluent中对齿轮箱油浴润滑的内部气液两相流场进行了瞬态特性数值模拟,得出瞬时油液分布、流体压力和速度。
②对不同齿轮转速和浸油深度的齿轮箱内部流场进行流体动力学仿真,计算其瞬时油液分布以及压力、速度时间历程,对比分析了不同转速和浸油深度对齿轮箱内部流场特性的影响规律。
③构建了包括流体与固体的齿轮箱三维瞬态传热有限元模型,计算了啮合齿面的平均热流量,利用Fluent软件对齿轮箱的传热模型进行热流耦合仿真分析,得出了齿轮对流换热系数的等值线。
④对运转过程中齿轮的瞬态温度场进行了流体动力学仿真,得出不同时刻齿轮副的温度等值线以及轮齿啮合区附近节点的温度时间历程,并研究了转速对齿轮温度分布的影响。
Because of the relative sliding of tooth meshing surface, a large amount of heat will be produced in the process of gear meshing. If the produced heat cannot be dissipated timely, the excess heat would lead to gear temperature rising, which will decrease bearing capacity of gears and reduce their working performance, and even cause gear failures directly. Cooling effect of lubrication of gearbox is the main factor of gear temperature determination, which can be influenced greatly by the flow characteristics of lubricant in gearbox. Therefore, a numerical simulation analysis of gear convective heat transfer and temperature field based on heat-fluid coupled method has important theoretical significance and great engineering value for improving heat transfer characteristics of gear pair.
The topic of this thesis is supported by scientific and technological project of Chongqing. Based on principles of gear engagement, hydrodynamics and the theory of heat transfer, the flow field in the gearbox with oil-bath lubrication, the convective heat transfer and temperature field of gears are studied by numerical simulation method. The main content of this paper can be summarized as follows:
①Parametric model of involute gears are constructed with UG, which can be imported into Gambit to establish the fluid calculation model of gearbox. Using the moving mesh technology and user-defined function (UDF), the transient flow field of gas?liquid two?phase oil-bath lubrication of gearbox was analyzed by the software of Fluent. As a result, the transient fluid distribution, oil pressure and velocity in the gearbox are obtained.
②After hydrodynamic simulation of flow field with different gear velocities and oil depths in the gearbox, transient fluid distribution and time history curves of pressure and velocity in the gearbox are discussed. Thus the influence law of the flow field characteristics can be concluded after comparison.
③The 3D transient heat transfer finite element model of gearbox including fluid and solid is constructed, and then the average heat flux on the meshing gear surface is calculated, based on which the heat?fluid coupled simulation analysis of the thermal model of gearbox is carried on by Fluent, and the contour of convective heat transfer coefficient of gears is obtained.
④The temperature contour of gears and temperature time history curves of nodes in the meshing zone of gear tooth in difference time are obtained after the transient hydrodynamic simulation of gearbox in rotation has been carried out, and the influence of different gear velocities on gear temperature distribution is analyzed.
本文课题来源于重庆市科技攻关计划项目。基于齿轮啮合原理、流体动力学和传热学理论,运用数值仿真方法,研究油浴润滑的齿轮箱内部流场、齿轮对流换热及齿轮温度场。本文的主要研究工作如下:
①将UG建立的渐开线齿轮副参数化模型导入Gambit中,建立齿轮箱内流体的计算模型;采用动网格及UDF技术,在Fluent中对齿轮箱油浴润滑的内部气液两相流场进行了瞬态特性数值模拟,得出瞬时油液分布、流体压力和速度。
②对不同齿轮转速和浸油深度的齿轮箱内部流场进行流体动力学仿真,计算其瞬时油液分布以及压力、速度时间历程,对比分析了不同转速和浸油深度对齿轮箱内部流场特性的影响规律。
③构建了包括流体与固体的齿轮箱三维瞬态传热有限元模型,计算了啮合齿面的平均热流量,利用Fluent软件对齿轮箱的传热模型进行热流耦合仿真分析,得出了齿轮对流换热系数的等值线。
④对运转过程中齿轮的瞬态温度场进行了流体动力学仿真,得出不同时刻齿轮副的温度等值线以及轮齿啮合区附近节点的温度时间历程,并研究了转速对齿轮温度分布的影响。
Because of the relative sliding of tooth meshing surface, a large amount of heat will be produced in the process of gear meshing. If the produced heat cannot be dissipated timely, the excess heat would lead to gear temperature rising, which will decrease bearing capacity of gears and reduce their working performance, and even cause gear failures directly. Cooling effect of lubrication of gearbox is the main factor of gear temperature determination, which can be influenced greatly by the flow characteristics of lubricant in gearbox. Therefore, a numerical simulation analysis of gear convective heat transfer and temperature field based on heat-fluid coupled method has important theoretical significance and great engineering value for improving heat transfer characteristics of gear pair.
The topic of this thesis is supported by scientific and technological project of Chongqing. Based on principles of gear engagement, hydrodynamics and the theory of heat transfer, the flow field in the gearbox with oil-bath lubrication, the convective heat transfer and temperature field of gears are studied by numerical simulation method. The main content of this paper can be summarized as follows:
①Parametric model of involute gears are constructed with UG, which can be imported into Gambit to establish the fluid calculation model of gearbox. Using the moving mesh technology and user-defined function (UDF), the transient flow field of gas?liquid two?phase oil-bath lubrication of gearbox was analyzed by the software of Fluent. As a result, the transient fluid distribution, oil pressure and velocity in the gearbox are obtained.
②After hydrodynamic simulation of flow field with different gear velocities and oil depths in the gearbox, transient fluid distribution and time history curves of pressure and velocity in the gearbox are discussed. Thus the influence law of the flow field characteristics can be concluded after comparison.
③The 3D transient heat transfer finite element model of gearbox including fluid and solid is constructed, and then the average heat flux on the meshing gear surface is calculated, based on which the heat?fluid coupled simulation analysis of the thermal model of gearbox is carried on by Fluent, and the contour of convective heat transfer coefficient of gears is obtained.
④The temperature contour of gears and temperature time history curves of nodes in the meshing zone of gear tooth in difference time are obtained after the transient hydrodynamic simulation of gearbox in rotation has been carried out, and the influence of different gear velocities on gear temperature distribution is analyzed.
引文
[1] Blok H. Theoretical Study on Temperature Rise at Surface of Actual Contact under Oiliness Lubrication Conditions[J]. Proc. Gen. Discussion on Lubrication, 1937, 2: 222-235.
[2] Townsend D P, Akin L S. Analytical and experimental spur gear tooth temperature as affected by operating variables[J]. Journal of Mechanical Design, Transactions of the ASME, 1981, 103(1): 219-226.
[3] Anifantis N, Dimarogonas A. D. Flash and bulk temperatures of gear teeth due to friction[J]. Department of Mechanical Engineering, Washington University, 1993, 28(1): 159-164.
[4] Atan Ebubekir, Ozdemir Serhan. Intelligence modeling of the transient asperity temperatures in meshing spur gears[J] Mechanism and Machine Theory, 2005, 40(1): 119-127.
[5] H?hn Bernd-Robert, Klaus Michaelis. Influence of immersion depth of dip lubricated gear on power loss, bulk temperature and scuffing load carrying capacity[J]. International Journal of Mechanics and Materials in Design, 2008, 4(2): 145-156.
[6]江亲瑜,王松年,阵谌橱.油池润滑齿轮本体温度计算新公式[J].机械, 1996, 23(6): 16-19.
[7]陈国定,李剑新,刘志全,斜齿轮非定常温度场的计算[J].西北工业大学学报, 2000, 18(1): 11-14.
[8]张永红,苏华,刘志全,沈允文.行星齿轮传动系统的稳态热分析[J].航空学报, 2000, 21(5): 431-433.
[9]龙慧,张光辉,罗文军.旋转齿轮瞬时接触应力和温度的分析模拟[J].机械工程学报, 2004, 40(08): 24-29.
[10]赵宁,孙晓玲,陈国定.双圆弧齿轮传动的有限元热分析[J].现代制造工程, 2006, (04): 50-52.
[11]李桂华,王春霞,费业泰.啮合齿轮轮齿温度场的解析法[J].组合机床与自动化加工技术, 2008, (07): 9-12.
[12] Ip K C W, Day B, Richardson D. Fluid flow and heat transfer in pipe work systems[J]. Building Serv Eng Res Technol. 1989, 10(4): 143-149.
[13] Karim Kiared, Fa??al Larachi, Jamal Chaouki. Mean and Turbulent Particle Velocity in the Fully Developed Region of a Three-Phase Fluidized Bed[J]. Chemical Engineering & Technology, 1999, 22(8): 683-689.
[14] Riemslagh K, Vierendeels J, Dick E. An arbitrary Lagrangian-Eulerian finite-volume method for the simulation of rotary displacement pump flow[J]. Applied Numerical Mathematics, 2000,32(4): 419-433.
[15] Vande V J, Vierendeels J, Dick E. Flow simulations in rotary volumetric pumps and compressors with the fictitious domain method[J]. Journal of Computational and Applied Mathematics, 2004, 168(1-2): 491-499.
[16]徐尚龙,李涤尘,卢秉恒.基于细胞沉积的人工骨微管设计及三维流场分析[J].机械工程学报, 2005, 41(4): 154-157.
[17] Ghorai Subhashini, Nigam K D P. CFD modeling of ?ow profiles and interfacial phenomenon two-phase ?ow in pipes[J]. Chemical Engineering and Processing, 2006, 45(1): 55–65.
[18]宋月兰,高正明,李志鹏.多层新型桨搅拌槽内气-液两相流动的实验与数值模拟[J].过程工程学报, 2007, (1).
[19]江帆,陈维平,李元元,等.润滑用齿轮泵内部流场的动态模拟[J].现代制造工程, 2007, (6): 116-118.
[20]江帆,陈维平,王一军,等.基于动网格的离心泵内部流场数值模拟[J].流体机械, 2007, 35(7): 20-24.
[21]孙丽,黄少青,仲峻峰.基于Fluent的多回路泵流场数值模拟[J].制造技术与机床, 2010, (1): 72-73, 78.
[22] Zhang Xiaobin, Gan Zhihua, Qiu Limin. Computational fluid dynamic simulation of an inter-phasing pulse tube cooler[J]. Journal of Zhejiang University SCIENCE A, 2008, 9(1): 93-98.
[23] Tien C L, Tsuji J. Heat transfer by laminar forced flow against a non-isothermal rotating disk[J]. International Journal of Heat and Mass Transfer, 1964, 7(2): 247-252.
[24] Dorfman L A. Hydrodynamic resistance and the heat loss of rotating solids[J]. Oliver and Boyd Ltd. Translated, 1963, 18(2): 77-101.
[25] Fischer S, Obermeier E, Siegen. Convective heat transfer in a rotating annulus device[J]. Warme- und Stofffibertragung, 1986, 20: 43-46.
[26] Cardone G, Astarita T, Carlomagno G M. Heat transfer measurements on a rotating disk[J]. Optical Diagnostics in Engineering, 1997, 3(1): 1-9.
[27]刘志全,沈允文,陈国定,张永红.某直升机齿轮传动系统的稳态热分析[J].中国机械工程, 1999, 10(6): 607-610.
[28]龙慧.高速齿轮传动轮齿的温度模拟及过程参数的敏感性分析[D].重庆:重庆大学博士论文, 2001.
[29] Mahmud S, Fraser R A. Thermodynamic Analysis of Flow and Heat Transfer Inside Channel with Two Parallel Plates[J]. Int. J. Exergy, 2002, 2: 140-146.
[30] Mahmud S, Fraser R A. The Second Law Analysis in Fundamental Convective Heat TransferProblems[J]. Int. J. Thermal Science, 2003, 42: 177-186.
[31]吴双应.对流换热过程的热力学分析及应用[D].重庆:重庆大学博士论文, 2004.
[32]王延忠,虞顺磊.基于无油润滑的弧齿锥齿轮的三维瞬态温度场仿真分析[J].机械工程师, 2008, 1: 65-68.
[33] Awad M M. Heat transfer from a rotating disk to fluids for a wide range of prandtl numbers using the asymptotic model[J]. Journal of Heat Transfer, J. Heat Transfer, 2008, 130(1): 1-4.
[34]赵宁,魏方,程昌,曹蕾蕾.船用齿轮箱稳态热分析[J].机械设计与制造, 2009, (10): 141-143.
[35] Lemfeld F, Fraňa K, Unger J. Numerical simulations of unsteady oil flows in the gear-boxes[J]. Journal of applied science in the thermodynamics and fluid mechanics, 2007, 1(1): 1-5.
[36]王福军.计算流体动力学分析—CFD软件原理与应用[M].北京:清华大学出版社, 2004.
[37]王敬,邵朋礼,魏来生,郭刘洋.车辆传动系统热平衡计算与仿真研究[J].工程设计学报, 2003, 10(6): 315-320, 336.
[38] Patir N, Cheng H S. Prediction of the Bulk Temperature in Spur Gears Based on Finite Element Temperature Analysis[J]. ASLE Transactions, 1979, 22(1): 25-36.
[39]汝艳.低速重载齿轮本体温度场的研究[D].合肥:合肥工业大学硕士论文, 2007.
[40] Heijningen G J J, Blok H. Continuous as against intermittent fling-off cooling of gear teeth[J]. Journal of Lubrication Technology, Transactions of the ASME. 1974(10): 529-538.
[41]杜平安,甘娥忠,于亚婷.有限元法-原理、建模及应用[M].北京:国防工业出版社, 2004.
[42]高忠信,陆力. CFD技术在水力机械研究中的应用[J].中国水利, 2008, (21): 76-78, 82.
[43]张言羊,刘正平.直齿圆柱齿轮三维本体温度场和热变形的研究[J].西安交通大学学报, 1990, 24(4): 25-50.
[44]李绍彬,李润方,林腾蛟.行星齿轮传动装置内齿轮轮齿热有限元分析[J].机械传动, 2003, 27(1): 1-2.
[45]肖望强;李威,韩建友.非对称齿廓渐开线齿轮传动的热分析[J].农业机械学报, 2006, 37(12): 164-167.
[46]明兴祖,严宏志,钟掘.基于温度场的螺旋锥齿轮啮合热特性分析[J].机械传动, 2007, 31(5): 1-5.
[47]沈胜强,张志千,朱铁柱.缸内对流换热与气体流动的计算分析[J].内燃机学报, 1993, 11(2): 103-108.
[48]邓策.机械式变速箱热平衡分析与仿真[D].吉林:吉林大学硕士论文, 2009.
[49]王瑞金,张凯,王刚. Fluent技术基础与应用[M].北京:清华大学出版社, 2007.
[50]温诗铸,黄平.摩擦学原理[M].北京:清华大学出版社, 2002..
[51]陶文铨.计算传热学[M].北京:科学出版社, 2000.
[52]林子光,徐大耐.齿轮传动的润滑[M].北京:机械工业出版社, 1980.
[53]苏欣,孟继安,程新广,过增元.圆筒内层流对流换热的最佳速度场及工程应用[J].清华大学学报, 2005, 45(5): 677-680.
[54] Seleznev V. Numerical Simulation of a Gas Pipeline Network Using Computational Fluid Dynamics Simulators[J]. Zhejiang Univ Sci A, 2007, 8(5): 755-765.
[55]俞佐平,陆煜.传热学[M].北京:高等教育出版社, 1995.
[56]淮良贵.机械设计[M].北京:高等教育出版社, 1988.
[57]罗爱辉,张旭强,张延松,陈关龙.电阻点焊电极头冷却对流换热数值模拟与分析[J].焊接学报, 2007, 28(1): 13-20.
[58]罗志国,倪冰.利用FLUENT模拟连铸结晶器内的气液两相流动[J].工业加热, 2008, 37(1): 6-7.
[59]王补宣.工程传热传质学[M].北京:科学出版社, 1998.
[60]过增元.热流体学[M].北京:清华大学出版社, 1986.
[61]王优强,黄丙习,佟景伟,杨沛然.渐开线直齿轮时变热弹流润滑模拟[J].机械强度, 2006, 28(3): 363-368.
[62]赵宁,陶福星双.双圆弧齿轮传动系统失油润滑瞬态热分析[J].计算机仿真, 2008, 25(1): 77-81.
[63]黄智勇.高速列车传动齿轮箱的热平衡计算分析[D].上海:上海交通大学硕士论文, 2007.
[2] Townsend D P, Akin L S. Analytical and experimental spur gear tooth temperature as affected by operating variables[J]. Journal of Mechanical Design, Transactions of the ASME, 1981, 103(1): 219-226.
[3] Anifantis N, Dimarogonas A. D. Flash and bulk temperatures of gear teeth due to friction[J]. Department of Mechanical Engineering, Washington University, 1993, 28(1): 159-164.
[4] Atan Ebubekir, Ozdemir Serhan. Intelligence modeling of the transient asperity temperatures in meshing spur gears[J] Mechanism and Machine Theory, 2005, 40(1): 119-127.
[5] H?hn Bernd-Robert, Klaus Michaelis. Influence of immersion depth of dip lubricated gear on power loss, bulk temperature and scuffing load carrying capacity[J]. International Journal of Mechanics and Materials in Design, 2008, 4(2): 145-156.
[6]江亲瑜,王松年,阵谌橱.油池润滑齿轮本体温度计算新公式[J].机械, 1996, 23(6): 16-19.
[7]陈国定,李剑新,刘志全,斜齿轮非定常温度场的计算[J].西北工业大学学报, 2000, 18(1): 11-14.
[8]张永红,苏华,刘志全,沈允文.行星齿轮传动系统的稳态热分析[J].航空学报, 2000, 21(5): 431-433.
[9]龙慧,张光辉,罗文军.旋转齿轮瞬时接触应力和温度的分析模拟[J].机械工程学报, 2004, 40(08): 24-29.
[10]赵宁,孙晓玲,陈国定.双圆弧齿轮传动的有限元热分析[J].现代制造工程, 2006, (04): 50-52.
[11]李桂华,王春霞,费业泰.啮合齿轮轮齿温度场的解析法[J].组合机床与自动化加工技术, 2008, (07): 9-12.
[12] Ip K C W, Day B, Richardson D. Fluid flow and heat transfer in pipe work systems[J]. Building Serv Eng Res Technol. 1989, 10(4): 143-149.
[13] Karim Kiared, Fa??al Larachi, Jamal Chaouki. Mean and Turbulent Particle Velocity in the Fully Developed Region of a Three-Phase Fluidized Bed[J]. Chemical Engineering & Technology, 1999, 22(8): 683-689.
[14] Riemslagh K, Vierendeels J, Dick E. An arbitrary Lagrangian-Eulerian finite-volume method for the simulation of rotary displacement pump flow[J]. Applied Numerical Mathematics, 2000,32(4): 419-433.
[15] Vande V J, Vierendeels J, Dick E. Flow simulations in rotary volumetric pumps and compressors with the fictitious domain method[J]. Journal of Computational and Applied Mathematics, 2004, 168(1-2): 491-499.
[16]徐尚龙,李涤尘,卢秉恒.基于细胞沉积的人工骨微管设计及三维流场分析[J].机械工程学报, 2005, 41(4): 154-157.
[17] Ghorai Subhashini, Nigam K D P. CFD modeling of ?ow profiles and interfacial phenomenon two-phase ?ow in pipes[J]. Chemical Engineering and Processing, 2006, 45(1): 55–65.
[18]宋月兰,高正明,李志鹏.多层新型桨搅拌槽内气-液两相流动的实验与数值模拟[J].过程工程学报, 2007, (1).
[19]江帆,陈维平,李元元,等.润滑用齿轮泵内部流场的动态模拟[J].现代制造工程, 2007, (6): 116-118.
[20]江帆,陈维平,王一军,等.基于动网格的离心泵内部流场数值模拟[J].流体机械, 2007, 35(7): 20-24.
[21]孙丽,黄少青,仲峻峰.基于Fluent的多回路泵流场数值模拟[J].制造技术与机床, 2010, (1): 72-73, 78.
[22] Zhang Xiaobin, Gan Zhihua, Qiu Limin. Computational fluid dynamic simulation of an inter-phasing pulse tube cooler[J]. Journal of Zhejiang University SCIENCE A, 2008, 9(1): 93-98.
[23] Tien C L, Tsuji J. Heat transfer by laminar forced flow against a non-isothermal rotating disk[J]. International Journal of Heat and Mass Transfer, 1964, 7(2): 247-252.
[24] Dorfman L A. Hydrodynamic resistance and the heat loss of rotating solids[J]. Oliver and Boyd Ltd. Translated, 1963, 18(2): 77-101.
[25] Fischer S, Obermeier E, Siegen. Convective heat transfer in a rotating annulus device[J]. Warme- und Stofffibertragung, 1986, 20: 43-46.
[26] Cardone G, Astarita T, Carlomagno G M. Heat transfer measurements on a rotating disk[J]. Optical Diagnostics in Engineering, 1997, 3(1): 1-9.
[27]刘志全,沈允文,陈国定,张永红.某直升机齿轮传动系统的稳态热分析[J].中国机械工程, 1999, 10(6): 607-610.
[28]龙慧.高速齿轮传动轮齿的温度模拟及过程参数的敏感性分析[D].重庆:重庆大学博士论文, 2001.
[29] Mahmud S, Fraser R A. Thermodynamic Analysis of Flow and Heat Transfer Inside Channel with Two Parallel Plates[J]. Int. J. Exergy, 2002, 2: 140-146.
[30] Mahmud S, Fraser R A. The Second Law Analysis in Fundamental Convective Heat TransferProblems[J]. Int. J. Thermal Science, 2003, 42: 177-186.
[31]吴双应.对流换热过程的热力学分析及应用[D].重庆:重庆大学博士论文, 2004.
[32]王延忠,虞顺磊.基于无油润滑的弧齿锥齿轮的三维瞬态温度场仿真分析[J].机械工程师, 2008, 1: 65-68.
[33] Awad M M. Heat transfer from a rotating disk to fluids for a wide range of prandtl numbers using the asymptotic model[J]. Journal of Heat Transfer, J. Heat Transfer, 2008, 130(1): 1-4.
[34]赵宁,魏方,程昌,曹蕾蕾.船用齿轮箱稳态热分析[J].机械设计与制造, 2009, (10): 141-143.
[35] Lemfeld F, Fraňa K, Unger J. Numerical simulations of unsteady oil flows in the gear-boxes[J]. Journal of applied science in the thermodynamics and fluid mechanics, 2007, 1(1): 1-5.
[36]王福军.计算流体动力学分析—CFD软件原理与应用[M].北京:清华大学出版社, 2004.
[37]王敬,邵朋礼,魏来生,郭刘洋.车辆传动系统热平衡计算与仿真研究[J].工程设计学报, 2003, 10(6): 315-320, 336.
[38] Patir N, Cheng H S. Prediction of the Bulk Temperature in Spur Gears Based on Finite Element Temperature Analysis[J]. ASLE Transactions, 1979, 22(1): 25-36.
[39]汝艳.低速重载齿轮本体温度场的研究[D].合肥:合肥工业大学硕士论文, 2007.
[40] Heijningen G J J, Blok H. Continuous as against intermittent fling-off cooling of gear teeth[J]. Journal of Lubrication Technology, Transactions of the ASME. 1974(10): 529-538.
[41]杜平安,甘娥忠,于亚婷.有限元法-原理、建模及应用[M].北京:国防工业出版社, 2004.
[42]高忠信,陆力. CFD技术在水力机械研究中的应用[J].中国水利, 2008, (21): 76-78, 82.
[43]张言羊,刘正平.直齿圆柱齿轮三维本体温度场和热变形的研究[J].西安交通大学学报, 1990, 24(4): 25-50.
[44]李绍彬,李润方,林腾蛟.行星齿轮传动装置内齿轮轮齿热有限元分析[J].机械传动, 2003, 27(1): 1-2.
[45]肖望强;李威,韩建友.非对称齿廓渐开线齿轮传动的热分析[J].农业机械学报, 2006, 37(12): 164-167.
[46]明兴祖,严宏志,钟掘.基于温度场的螺旋锥齿轮啮合热特性分析[J].机械传动, 2007, 31(5): 1-5.
[47]沈胜强,张志千,朱铁柱.缸内对流换热与气体流动的计算分析[J].内燃机学报, 1993, 11(2): 103-108.
[48]邓策.机械式变速箱热平衡分析与仿真[D].吉林:吉林大学硕士论文, 2009.
[49]王瑞金,张凯,王刚. Fluent技术基础与应用[M].北京:清华大学出版社, 2007.
[50]温诗铸,黄平.摩擦学原理[M].北京:清华大学出版社, 2002..
[51]陶文铨.计算传热学[M].北京:科学出版社, 2000.
[52]林子光,徐大耐.齿轮传动的润滑[M].北京:机械工业出版社, 1980.
[53]苏欣,孟继安,程新广,过增元.圆筒内层流对流换热的最佳速度场及工程应用[J].清华大学学报, 2005, 45(5): 677-680.
[54] Seleznev V. Numerical Simulation of a Gas Pipeline Network Using Computational Fluid Dynamics Simulators[J]. Zhejiang Univ Sci A, 2007, 8(5): 755-765.
[55]俞佐平,陆煜.传热学[M].北京:高等教育出版社, 1995.
[56]淮良贵.机械设计[M].北京:高等教育出版社, 1988.
[57]罗爱辉,张旭强,张延松,陈关龙.电阻点焊电极头冷却对流换热数值模拟与分析[J].焊接学报, 2007, 28(1): 13-20.
[58]罗志国,倪冰.利用FLUENT模拟连铸结晶器内的气液两相流动[J].工业加热, 2008, 37(1): 6-7.
[59]王补宣.工程传热传质学[M].北京:科学出版社, 1998.
[60]过增元.热流体学[M].北京:清华大学出版社, 1986.
[61]王优强,黄丙习,佟景伟,杨沛然.渐开线直齿轮时变热弹流润滑模拟[J].机械强度, 2006, 28(3): 363-368.
[62]赵宁,陶福星双.双圆弧齿轮传动系统失油润滑瞬态热分析[J].计算机仿真, 2008, 25(1): 77-81.
[63]黄智勇.高速列车传动齿轮箱的热平衡计算分析[D].上海:上海交通大学硕士论文, 2007.