渐开线圆柱齿轮修形及动力接触特性研究
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摘要
齿轮传动因具有传动效率高、恒功率等特点,广泛应用于机械、电子、化工、冶金、交通等诸多领域。随着近代工业技术的高速发展,对齿轮传动的减振降噪提出了更高的要求。通过齿轮热弹接触分析、齿轮修形、冲击动力仿真以提高齿轮传动的动力学性能已成为当前高性能齿轮设计的热点。
论文课题来源于国家科技支撑计划项目及重庆市自然科学基金项目。将齿轮啮合原理、传热学、接触力学、结构动力学等相结合,对运转过程中的齿轮副进行热弹变形分析及啮合冲击特性研究。本文的主要研究工作如下:
①运用齿轮啮合原理的运动学法,推导了渐开线齿轮齿廓方程,并对不同几何参数的渐开线齿轮副进行了接触有限元建模。
②基于赫兹接触理论,分析了齿轮副齿面接触压力的变化规律;应用ANSYS软件对运转过程中的齿轮副进行了接触有限元分析,得出了轮齿接触力、接触变形及啮合刚度的变化规律。
③分析了齿轮啮合过程中主、被动轮轮齿相对滑动速度,计算了轮齿边界对流换热系数及齿面摩擦热流量,并以多齿对模型分析了齿轮的本体温度场;将温度场、位移场及应力场耦合分析,计算齿轮副的热弹变形,得出齿轮副热弹变形量要比冷态时变形量略小,接触应力较冷态时稍大。
④在轮齿接触有限元分析的基础上,进行了轮齿的修形研究,得到了齿轮副在没有考虑温度影响与考虑温度影响时的修形曲线;利用ANSYS软件对啮入、啮出位置时标准渐开线齿轮副和修形齿轮副进行了接触分析,修形后轮齿接触应力明显减小。
⑤建立了标准渐开线齿轮和修形齿轮的动力接触有限元分析模型,利用ANSYS/LS-DYNA软件仿真,得到了啮合过程中齿轮副动态接触力及动态应力变化规律,修形后的齿轮接触特性明显改善。
⑥通过Visual Basic及ANSYS/APDL语言开发了齿轮热弹接触分析及动力接触有限元分析程序;程序能建立任何模数、齿数、螺旋角及变位系数的齿轮副有限元模型;可以方便地借助ANSYS软件的二次开发实现齿轮副的静力接触、动力接触以及齿轮本体温度场分析。
Gear transmission is widely applied in machines, electronic, chemical, metallurgy, traffic and so on because of its high transmission efficiency and constant power. Along with the rapid development of modern industrial technology, the requirement of vibration and noise reduction is becoming even higher. The design method based on thermo-elastic contact analysis, gear modification, and impact dynamic simulation is widely used to improve the dynamic performance of gear transmission.
The thesis subject is supported by National Project of Scientific and Technical Supporting Programs and Chongqing Natural Science Foundation. Combining with principle of gear engagement, theory of heatl transfer, contact mechanics, and structural dynamics, the thermo-elastic deformation and meshing impact characteristics in meshing process are studied.
The research work presented in this thesis can be summarized as follows:
1) Using the kinematics of gear engagement principle, the tooth profile equation of involute gear is derived, and contact finite element models of involute gear pair with different geometric parameters are established.
2) Based on Hertz theory, the contact pressure on tooth surface is analyzed. The software of ANSYS is used to analyze the contact performance of gear transmission, and then the changes along the contact path of gear tooth contact force, contact deformation and engagement stiffness are obtained.
3) The relative sliding velocity between the tooth flanks is analyzed, then the convection heat transfer coefficient and tooth surface heat flux are calculated. Using above results, the body temperature of gear is studied based on multi-tooth pair model. Coupled with the temperature field, displacement field and stress field, the thermo-elastic deformation of gear pair is obtained. The results indicate the value of gear thermo-elastic deformation is a little smaller than the value of deformation in the cold state and the contact stress is a little larger than the cold state.
4) Based on finite element analysis of tooth contact problem, the gear modification is studied, and the curves of gear modification which without temperature effect and with temperature effect are obtained. The contact finite element analysis of standard involute gear pair and modified gear pair in the meshing in and meshing out position is compared by the software of ANSYS. It shows the contact stress of modification gear pair is significantly reduced.
5) The dynamic contact finite element model of standard involute gear pair and modified gear pair are established. By using the software of ANSYS/LS-DYNA, the dynamic contact force and dynamic stress of gear pair in meshing process are calculated, the contact characteristics of modified gear pair are improved significantly.
6) By the language of Visual Basic and ANSYS/APDL, a finite element anlysis program is compiled to analyze the thermo-elastic contact and dynamic contact problem of gears. Using this program, the finite element model of gear pair with different module, teeth number, helical angle and modification coefficient can be built quickly, and the static/dynamic contact analysis and body temperature calculation can be completed conveniently by the help of the secondary development of ANSYS.
论文课题来源于国家科技支撑计划项目及重庆市自然科学基金项目。将齿轮啮合原理、传热学、接触力学、结构动力学等相结合,对运转过程中的齿轮副进行热弹变形分析及啮合冲击特性研究。本文的主要研究工作如下:
①运用齿轮啮合原理的运动学法,推导了渐开线齿轮齿廓方程,并对不同几何参数的渐开线齿轮副进行了接触有限元建模。
②基于赫兹接触理论,分析了齿轮副齿面接触压力的变化规律;应用ANSYS软件对运转过程中的齿轮副进行了接触有限元分析,得出了轮齿接触力、接触变形及啮合刚度的变化规律。
③分析了齿轮啮合过程中主、被动轮轮齿相对滑动速度,计算了轮齿边界对流换热系数及齿面摩擦热流量,并以多齿对模型分析了齿轮的本体温度场;将温度场、位移场及应力场耦合分析,计算齿轮副的热弹变形,得出齿轮副热弹变形量要比冷态时变形量略小,接触应力较冷态时稍大。
④在轮齿接触有限元分析的基础上,进行了轮齿的修形研究,得到了齿轮副在没有考虑温度影响与考虑温度影响时的修形曲线;利用ANSYS软件对啮入、啮出位置时标准渐开线齿轮副和修形齿轮副进行了接触分析,修形后轮齿接触应力明显减小。
⑤建立了标准渐开线齿轮和修形齿轮的动力接触有限元分析模型,利用ANSYS/LS-DYNA软件仿真,得到了啮合过程中齿轮副动态接触力及动态应力变化规律,修形后的齿轮接触特性明显改善。
⑥通过Visual Basic及ANSYS/APDL语言开发了齿轮热弹接触分析及动力接触有限元分析程序;程序能建立任何模数、齿数、螺旋角及变位系数的齿轮副有限元模型;可以方便地借助ANSYS软件的二次开发实现齿轮副的静力接触、动力接触以及齿轮本体温度场分析。
Gear transmission is widely applied in machines, electronic, chemical, metallurgy, traffic and so on because of its high transmission efficiency and constant power. Along with the rapid development of modern industrial technology, the requirement of vibration and noise reduction is becoming even higher. The design method based on thermo-elastic contact analysis, gear modification, and impact dynamic simulation is widely used to improve the dynamic performance of gear transmission.
The thesis subject is supported by National Project of Scientific and Technical Supporting Programs and Chongqing Natural Science Foundation. Combining with principle of gear engagement, theory of heatl transfer, contact mechanics, and structural dynamics, the thermo-elastic deformation and meshing impact characteristics in meshing process are studied.
The research work presented in this thesis can be summarized as follows:
1) Using the kinematics of gear engagement principle, the tooth profile equation of involute gear is derived, and contact finite element models of involute gear pair with different geometric parameters are established.
2) Based on Hertz theory, the contact pressure on tooth surface is analyzed. The software of ANSYS is used to analyze the contact performance of gear transmission, and then the changes along the contact path of gear tooth contact force, contact deformation and engagement stiffness are obtained.
3) The relative sliding velocity between the tooth flanks is analyzed, then the convection heat transfer coefficient and tooth surface heat flux are calculated. Using above results, the body temperature of gear is studied based on multi-tooth pair model. Coupled with the temperature field, displacement field and stress field, the thermo-elastic deformation of gear pair is obtained. The results indicate the value of gear thermo-elastic deformation is a little smaller than the value of deformation in the cold state and the contact stress is a little larger than the cold state.
4) Based on finite element analysis of tooth contact problem, the gear modification is studied, and the curves of gear modification which without temperature effect and with temperature effect are obtained. The contact finite element analysis of standard involute gear pair and modified gear pair in the meshing in and meshing out position is compared by the software of ANSYS. It shows the contact stress of modification gear pair is significantly reduced.
5) The dynamic contact finite element model of standard involute gear pair and modified gear pair are established. By using the software of ANSYS/LS-DYNA, the dynamic contact force and dynamic stress of gear pair in meshing process are calculated, the contact characteristics of modified gear pair are improved significantly.
6) By the language of Visual Basic and ANSYS/APDL, a finite element anlysis program is compiled to analyze the thermo-elastic contact and dynamic contact problem of gears. Using this program, the finite element model of gear pair with different module, teeth number, helical angle and modification coefficient can be built quickly, and the static/dynamic contact analysis and body temperature calculation can be completed conveniently by the help of the secondary development of ANSYS.
引文
[1]张晋西,郭学琴.齿轮三维参数化建模与加工运动仿真[J].机械设计, 2002, 19(3):33-35.
[2]林昌华.实现齿轮参数化实体建模的编程方法[J].现代制造工程, 2002, (9):34-35.
[3]李燕.基于Pro/E的齿轮三维参数化特征造型设计[J].制造技术与机床, 2003, (7):30-32.
[4]廖俐. Pro/E在参数化齿轮建模中的应用及操作技巧[J].机械工程师, 2004, (7):16-18.
[5]肖石林,鲍务均.渐开线齿轮在CATIA中的三维参数化建模与应用[J].起重运输机械,2004, (10):19-21.
[6]王波.基于CATIA环境下的斜齿轮三维参数建模及参数化应用[J].机械, 2004, (6):33-35.
[7]周学良,阮景奎.基于UG/Open的齿轮参数化建模[J].湖北汽车工业学院学报, 2004, 18(2): 23-25.
[8]曲艳峰,杨小兵.利用UG/NX的二次开发技术实现齿轮参数化设计[J].上海电力学院学报, 2006, 22(1):93-96.
[9]李常义,潘存云,姚齐水,李伟建.基于ANSYS的渐开线圆柱齿轮参数化几何造型技术研究[J].机电工程, 2004, 21(9):35-38.
[10]包家汉,张玉华,薛家国.基于ANSYS的齿轮参数化建模及其应用[J].安徽工业大学学报(自然科学版), 2005, 22(1):35-38.
[11]刘志柱,刘曜.二次开发在ANSYS参数化建模中的应用[J],机电产品开发与创新, 2006,19(5):117-118.
[12]李润方,王建军.平面二包蜗杆传动弹性接触有限元分析[J].计算结构力学及其应用,1984, (1):85-90.
[13]杨生华,王统.齿轮轮齿变形中的接触有限元仿真分析[J].煤矿机械, 1999, (8):9-11.
[14]朱坚民,周福章,雷静桃.渐开线斜齿圆柱齿轮弹性变形的三维有限元分析[J].农业机械学报, 1998, 29(4):113-117.
[15] Barlarn D, Zahavi E. The reliability of solutions in contact problems[J]. Comp & Struct, 1999,(7):35-45.
[16] Tengjiao Lin, H. Ou, Runfang Li. A finite element method for 3D static and dynamic contact/impact analysis of gear drives[J]. Comput. Methods Appl. Mech. Engrg. 2007, 196:1716-1728.
[17]吴序堂.齿轮啮合原理[M].北京:机械工业出版社, 1982.
[18] K.L. Wang, H.S. Cheng. A Numerical Solution to the Dynamic Load, Film Thickness and Surface Temperatures in Spur Gears, Part I Analysis. Transactions of the ASME[J]. Journal ofMechanical Design, 1981, 103:112-115.
[19] K.L. Wang, H.S. Cheng. A Numerical Solution to the Dynamic Load, Film Thickness and Surface Temperatures in Spur Gears, Part II Analysis. Transactions of the ASME[J]. Journal of Mechanical Design, 1981, 103:121-124.
[20] N.Patir,H.S. Cheng.Prediction of the Bulk Temperature in Spur Gears Based on Finite Element Temperature Analysis.The ASLE/ASME Lubrication Conference,1977,103:126-129.
[21] D.P.Townsend, L.S. Akin. Analytical and Experimental Spur gear Tooth Temperature as Affected by Operating Variables[J]. Transactions of the ASME, Journal of Mechanical Design, 1981, 103:114-118.
[22] N. Anifantis, A.D. Dimarogonas. Flash and Bulk temperatures of Gear Teeth Due to Friction[J]. Journal of Mechanical Machine Theory, 1993, 28(1):232-235.
[23] Simon V. Thermo-EHD Analysis of Lubrication of Helical Gears[J]. Tran. ASME. J. Mech. Transm. And Auto. In Design, 1988, 111:331-333.
[24] Anifantis N. Flash and Bulk Temperature of a Spur Gear Tooth due to Friction[J]. Mech Mach Theory, 1993, 28(1):159-164.
[25] Blok H. Thermal Network for Predicting Bulk Temperature in Gear Transmissions[J]. Proc. 7th Round Table Discussion, Marin Reduction Gears, Fins pong, Sweden,1995: 3-25.
[26]邱良恒,辛一行,王统,蒋松.齿轮本体温度场和热变形修形计算[J].上海交通大学学报, 1995, 29(2):79-86.
[27]刘辉,吴昌林.全工况下斜齿轮轮齿动态温度场的研究[J].华中理工大学学报, 1998,26(3):41-43.
[28]吴昌林.基于热网络的汽车变速箱热分布的有限元分析[J].华中理工大学学报, 1998,26(6):84-86.
[29]钱作勤,厉海祥,陆瑞松. ANSYS在求解点线啮合齿轮稳态温度场中的应用[J].武汉造船, 1999, (4):23-26.
[30]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.
[31]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.
[32]马旋,李建华,陈国定.减速器齿轮传动系统的稳态热分析及试验研究[J].西北工业大学学报, 2002, 20(1):32-35.
[33]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(8):24-29.
[34]李润方,汤庆平.运转过程中轮齿耦合热弹性接触有限元分析[J].齿轮, 1989, 13(1):23-28.
[35]李润方,龚剑霞.接触问题数值方法及其在机械设计中的应用[M].重庆:重庆大学出版社, 1991.
[36]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.
[37]屈文涛,沈允文,徐建宁,赵宁.双圆弧齿轮传动的温度场和热变形分析[J].石油机械,2006, 34(3):13-15.
[38]杨廷力,叶新,王玉璞.渐开线高速齿轮的齿高修形[J].齿轮, 1982, 6(3):14-24.
[39]詹东安,王树人,唐树为.高速齿轮齿部修形技术研究[J].机械设计, 2000, 17(8):8-10.
[40]王朝晋,丁玉成.关于齿廓修形的研究[J].齿轮, 1987, 11(6):4-11.
[41]仙波正庄,任宏达等译.高强度齿轮设计[M].北京:机械工业出版社, 1981, 105-205.
[42]薛家国,彭文生.具有误差齿轮的弹性啮合特性及修形[J].齿轮, 1986, 10(3):22-28.
[43]李绍彬,李润方,林腾蛟.基于热弹变形的圆柱齿轮理想修形曲线[J].中国机械工程,2003, 14(14):1175-1179.
[44]宋乐民.渐开线鼓形齿的鼓形量[J].齿轮, 1981, 5(2):63-67.
[45]陶燕光,黎上威,马宪本.高速齿轮热变形修形的试验研究[J].齿轮, 1988, 12(2):25-28.
[46]李绍彬.渐开线高速齿轮的修形设计[J].现代制造工程, 2003, (3):71-74.
[47]成国玉.高速齿轮的修形[J].江苏冶金, 2004, 32(4):37-40.
[48] T. J. Hughes, R. L. Taylor, J. L. Sackman, A. Cumier,W. Kanoknukulchai. A Finite Element Method a class of Contact Impact Problems[J]. Comput. Meth. Appl. Mech. Engng, 1976, 8:49-276.
[49]浅野直辉,刘崇德译.用有限元素法分析动态接触应力的兹辛古法[J].重庆大学科技,1981, (1):154-162.
[50]土肥修,浅野直辉,李润方译.动态弹性接触问题的有限元分析法[J].重庆大学科技,1981, (1):163-175.
[51] J. O. Hallquist, G. L. Goudreau, D. J. Benson. Sliding Interfaces with Contact-Impact In Large-scale Lagrangian Computations[J]. Comput. Meth. Appl. Mech. Engrg, 1985, 51:107-137.
[52] A. B. Chaudhary, K. J. Bathe. A Solution Method for Static and Dynamic Analysis of Three-dimensional Contact Problems with Friction[J]. Computer and Structure, 1986, 24(6):855-873.
[53] W. H. Chen, J. T. Yen. Three-dimensional Finite Element Analysis of Static and DynamicContact Problems with Friction[J]. Computer and Structures, 1990, 25(5):541-552.
[54] F. F. Mahmoud, M. M. Hassan, N. J. Salamon. Dynamic Contact of Deformable Bodies[J]. Computer and Structures, 1990,36(1):169-181.
[55] Y Kanto, G.Yagawa. A Dynamic Contact Bucking Analysis by The Penalty Finite Element Method[J]. Int.J. Numer. Meth. Engrg, 1990, 29:755-774.
[56] Robert L. Taylor, P. Papadopoulos. On a Finite Element Method for Dynamic Contact/Impact Problems[J]. Int. J. Numer. Meth. Engrg, 1993, 36:2123-2140.
[57] J.G.Malone, N.L.Johnson. A Parallel Finite Element Contact/Impact Algorithm for Non-Linear Explicit Transient Anlysis:Part I-The search Algorithm and Contact Mechanics[J]. Int.J.Numer.Meth.Engrg, 1994, 37:559-590.
[58] J.G.Malone, N.L.Johnson. A Parallel Finite Element Contact/Impact Algorithm for Non-Linear Explicit Transient Anlysis:Part II-The search Algorithm and Contact Mechanics[J]. Int.J.Numer.Meth.Engrg, 1994, 37:591-603.
[59] N. J. Carpenter, R. L. Taylor, M. G. Katona. Lagrange Constraints for Transient Finite Element Surface Contact[J]. Int. J. Num. Meth. Engrg, 1991, 32:103-128.
[60] M. L. Ayari, V E. Saouma. Static and Dynamic ContarUttnpact Problems Using Frictitious Forces[J]. Int. J. Num. Meth. Engrg, 1991, 32:623-643.
[61] Seung HwanKo, Byung Man Kwak. Frictional Dynamic Contact Analysis Using Finite Element Nodal Displacement Description[J]. Computer and Structure, 1992, 42(5):797-807.
[62] Seok-Soon Lee. A Computational Method for Frictional Contact Problem Using Finite Element Method[J]. Int.J.Num.Meth Engrg, 1994, 37:217-228.
[63] B.P.Gautham, N.Ganesan. Finite Element Analysis of Contact-ImPact Betweena Shell of Revolutton and a rigid wall[J]. Int .J.Num.Meth. Engrg, 1994, 37:3251-3262.
[64]欧恒安,李润方,龚剑霞.三维冲击-动力接触问题有限元混合算法[J].重庆大学学报,1994, 17(2):52-57.
[65]陈兵奎,李润方.冲击-动力接触问题有限元方法的几点注记[J].计算结构力学及其应用,1996, 13(2):48-52.
[66]邢誉峰,诸得超.两杆纵向非线性弹性碰撞的瞬间响应[J].北京航空航天大学学报, 1998, 24(1):39-42.
[67]姚文席,魏任之.渐开线直齿轮的啮合冲击研究[J].振动与冲击, 1990, 9(4):57-61.
[68]王玉芳,童忠舫.齿轮的误差对啮合冲击的影响[J].振动与冲击, 1994, 13(2):14-18.
[69]唐进元,肖利民.齿轮齿顶修缘时啮合冲击速度的计算[J].长沙铁道学院学报, 1995, 13(l): 26-30.
[70]李润方,陈兵奎.冲击/动力接触问题有限元混合方法及其应用[J].非线性力学学报,1997, (3):236-242.
[71]林腾蛟,李润方,陶泽光.齿轮传动三维间隙非线性冲击-动力接触特性数值仿真[J].机械工程学报, 2000, 36(6):55-58.
[72]林腾蛟,李润方,郭晓东,王立华.准双曲面齿轮三维间隙非线性冲击特性分析[J].中国机械工程, 2003, 14(9):727-730.
[73] A.Bajer, L.Demkowicz. Dynamic contact/impact problems, energy conservation, and planetary gear trains[J]. Computer Methods in Applied Mechanics and Engineering, 2002, 191(37-38):4159-4191.
[74]谢海东,周照耀,夏伟,邱诚,张文.斜齿轮传动中啮合冲击数值研究[J].机械传动,2005, 29(3):6-9.
[75]马雪洁,谢刚,王小林.基于ANSYS/LS-DYNA的准双曲面齿轮动力学接触仿真分析[J].机械传动, 2005,29(6):51-53.
[76]盛云,武宝林.齿轮传动中啮合冲击的计算分析[J].机械设计, 2005,22(7):41-43.
[77]许泽银.基节误差对齿轮啮合冲击影响的分析与计算[J].合肥学院学报, 2005, 15(2):81-84.
[78]吴大任,骆家舜.齿轮啮合原理[M].北京:科学出版社, 1985.
[79]吴继泽,王统.齿根过渡曲线与齿根应力[M].北京:国防工业出版社, 1989.
[80]刘相新,孟宪颐. ANSYS基础与应用教程[M].北京:科学出版社, 2006.
[81]张朝晖. ANSYS8.0热分析教程与实例解析[M].北京:中国铁道出版社, 2005.
[82]李绍彬.高速重载齿轮传动热弹变形及非线性耦合动力学研究[D].重庆:重庆大学, 2003.
[83]李润方.齿轮传动的刚度分析和修形方法[M].重庆:重庆大学出版社,1998.
[84]唐增宝,陈久荣.齿轮动态性能最佳的齿廓修形曲线和参数[J].华中理工大学学报, 1995, 23(11):52-55.
[85]尚晓江,苏建宇. ANSYS/LS-DYNA动力分析方法与工程实例[M].北京:中国水利水电出版社, 2006.
[2]林昌华.实现齿轮参数化实体建模的编程方法[J].现代制造工程, 2002, (9):34-35.
[3]李燕.基于Pro/E的齿轮三维参数化特征造型设计[J].制造技术与机床, 2003, (7):30-32.
[4]廖俐. Pro/E在参数化齿轮建模中的应用及操作技巧[J].机械工程师, 2004, (7):16-18.
[5]肖石林,鲍务均.渐开线齿轮在CATIA中的三维参数化建模与应用[J].起重运输机械,2004, (10):19-21.
[6]王波.基于CATIA环境下的斜齿轮三维参数建模及参数化应用[J].机械, 2004, (6):33-35.
[7]周学良,阮景奎.基于UG/Open的齿轮参数化建模[J].湖北汽车工业学院学报, 2004, 18(2): 23-25.
[8]曲艳峰,杨小兵.利用UG/NX的二次开发技术实现齿轮参数化设计[J].上海电力学院学报, 2006, 22(1):93-96.
[9]李常义,潘存云,姚齐水,李伟建.基于ANSYS的渐开线圆柱齿轮参数化几何造型技术研究[J].机电工程, 2004, 21(9):35-38.
[10]包家汉,张玉华,薛家国.基于ANSYS的齿轮参数化建模及其应用[J].安徽工业大学学报(自然科学版), 2005, 22(1):35-38.
[11]刘志柱,刘曜.二次开发在ANSYS参数化建模中的应用[J],机电产品开发与创新, 2006,19(5):117-118.
[12]李润方,王建军.平面二包蜗杆传动弹性接触有限元分析[J].计算结构力学及其应用,1984, (1):85-90.
[13]杨生华,王统.齿轮轮齿变形中的接触有限元仿真分析[J].煤矿机械, 1999, (8):9-11.
[14]朱坚民,周福章,雷静桃.渐开线斜齿圆柱齿轮弹性变形的三维有限元分析[J].农业机械学报, 1998, 29(4):113-117.
[15] Barlarn D, Zahavi E. The reliability of solutions in contact problems[J]. Comp & Struct, 1999,(7):35-45.
[16] Tengjiao Lin, H. Ou, Runfang Li. A finite element method for 3D static and dynamic contact/impact analysis of gear drives[J]. Comput. Methods Appl. Mech. Engrg. 2007, 196:1716-1728.
[17]吴序堂.齿轮啮合原理[M].北京:机械工业出版社, 1982.
[18] K.L. Wang, H.S. Cheng. A Numerical Solution to the Dynamic Load, Film Thickness and Surface Temperatures in Spur Gears, Part I Analysis. Transactions of the ASME[J]. Journal ofMechanical Design, 1981, 103:112-115.
[19] K.L. Wang, H.S. Cheng. A Numerical Solution to the Dynamic Load, Film Thickness and Surface Temperatures in Spur Gears, Part II Analysis. Transactions of the ASME[J]. Journal of Mechanical Design, 1981, 103:121-124.
[20] N.Patir,H.S. Cheng.Prediction of the Bulk Temperature in Spur Gears Based on Finite Element Temperature Analysis.The ASLE/ASME Lubrication Conference,1977,103:126-129.
[21] D.P.Townsend, L.S. Akin. Analytical and Experimental Spur gear Tooth Temperature as Affected by Operating Variables[J]. Transactions of the ASME, Journal of Mechanical Design, 1981, 103:114-118.
[22] N. Anifantis, A.D. Dimarogonas. Flash and Bulk temperatures of Gear Teeth Due to Friction[J]. Journal of Mechanical Machine Theory, 1993, 28(1):232-235.
[23] Simon V. Thermo-EHD Analysis of Lubrication of Helical Gears[J]. Tran. ASME. J. Mech. Transm. And Auto. In Design, 1988, 111:331-333.
[24] Anifantis N. Flash and Bulk Temperature of a Spur Gear Tooth due to Friction[J]. Mech Mach Theory, 1993, 28(1):159-164.
[25] Blok H. Thermal Network for Predicting Bulk Temperature in Gear Transmissions[J]. Proc. 7th Round Table Discussion, Marin Reduction Gears, Fins pong, Sweden,1995: 3-25.
[26]邱良恒,辛一行,王统,蒋松.齿轮本体温度场和热变形修形计算[J].上海交通大学学报, 1995, 29(2):79-86.
[27]刘辉,吴昌林.全工况下斜齿轮轮齿动态温度场的研究[J].华中理工大学学报, 1998,26(3):41-43.
[28]吴昌林.基于热网络的汽车变速箱热分布的有限元分析[J].华中理工大学学报, 1998,26(6):84-86.
[29]钱作勤,厉海祥,陆瑞松. ANSYS在求解点线啮合齿轮稳态温度场中的应用[J].武汉造船, 1999, (4):23-26.
[30]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.
[31]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.
[32]马旋,李建华,陈国定.减速器齿轮传动系统的稳态热分析及试验研究[J].西北工业大学学报, 2002, 20(1):32-35.
[33]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(8):24-29.
[34]李润方,汤庆平.运转过程中轮齿耦合热弹性接触有限元分析[J].齿轮, 1989, 13(1):23-28.
[35]李润方,龚剑霞.接触问题数值方法及其在机械设计中的应用[M].重庆:重庆大学出版社, 1991.
[36]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.
[37]屈文涛,沈允文,徐建宁,赵宁.双圆弧齿轮传动的温度场和热变形分析[J].石油机械,2006, 34(3):13-15.
[38]杨廷力,叶新,王玉璞.渐开线高速齿轮的齿高修形[J].齿轮, 1982, 6(3):14-24.
[39]詹东安,王树人,唐树为.高速齿轮齿部修形技术研究[J].机械设计, 2000, 17(8):8-10.
[40]王朝晋,丁玉成.关于齿廓修形的研究[J].齿轮, 1987, 11(6):4-11.
[41]仙波正庄,任宏达等译.高强度齿轮设计[M].北京:机械工业出版社, 1981, 105-205.
[42]薛家国,彭文生.具有误差齿轮的弹性啮合特性及修形[J].齿轮, 1986, 10(3):22-28.
[43]李绍彬,李润方,林腾蛟.基于热弹变形的圆柱齿轮理想修形曲线[J].中国机械工程,2003, 14(14):1175-1179.
[44]宋乐民.渐开线鼓形齿的鼓形量[J].齿轮, 1981, 5(2):63-67.
[45]陶燕光,黎上威,马宪本.高速齿轮热变形修形的试验研究[J].齿轮, 1988, 12(2):25-28.
[46]李绍彬.渐开线高速齿轮的修形设计[J].现代制造工程, 2003, (3):71-74.
[47]成国玉.高速齿轮的修形[J].江苏冶金, 2004, 32(4):37-40.
[48] T. J. Hughes, R. L. Taylor, J. L. Sackman, A. Cumier,W. Kanoknukulchai. A Finite Element Method a class of Contact Impact Problems[J]. Comput. Meth. Appl. Mech. Engng, 1976, 8:49-276.
[49]浅野直辉,刘崇德译.用有限元素法分析动态接触应力的兹辛古法[J].重庆大学科技,1981, (1):154-162.
[50]土肥修,浅野直辉,李润方译.动态弹性接触问题的有限元分析法[J].重庆大学科技,1981, (1):163-175.
[51] J. O. Hallquist, G. L. Goudreau, D. J. Benson. Sliding Interfaces with Contact-Impact In Large-scale Lagrangian Computations[J]. Comput. Meth. Appl. Mech. Engrg, 1985, 51:107-137.
[52] A. B. Chaudhary, K. J. Bathe. A Solution Method for Static and Dynamic Analysis of Three-dimensional Contact Problems with Friction[J]. Computer and Structure, 1986, 24(6):855-873.
[53] W. H. Chen, J. T. Yen. Three-dimensional Finite Element Analysis of Static and DynamicContact Problems with Friction[J]. Computer and Structures, 1990, 25(5):541-552.
[54] F. F. Mahmoud, M. M. Hassan, N. J. Salamon. Dynamic Contact of Deformable Bodies[J]. Computer and Structures, 1990,36(1):169-181.
[55] Y Kanto, G.Yagawa. A Dynamic Contact Bucking Analysis by The Penalty Finite Element Method[J]. Int.J. Numer. Meth. Engrg, 1990, 29:755-774.
[56] Robert L. Taylor, P. Papadopoulos. On a Finite Element Method for Dynamic Contact/Impact Problems[J]. Int. J. Numer. Meth. Engrg, 1993, 36:2123-2140.
[57] J.G.Malone, N.L.Johnson. A Parallel Finite Element Contact/Impact Algorithm for Non-Linear Explicit Transient Anlysis:Part I-The search Algorithm and Contact Mechanics[J]. Int.J.Numer.Meth.Engrg, 1994, 37:559-590.
[58] J.G.Malone, N.L.Johnson. A Parallel Finite Element Contact/Impact Algorithm for Non-Linear Explicit Transient Anlysis:Part II-The search Algorithm and Contact Mechanics[J]. Int.J.Numer.Meth.Engrg, 1994, 37:591-603.
[59] N. J. Carpenter, R. L. Taylor, M. G. Katona. Lagrange Constraints for Transient Finite Element Surface Contact[J]. Int. J. Num. Meth. Engrg, 1991, 32:103-128.
[60] M. L. Ayari, V E. Saouma. Static and Dynamic ContarUttnpact Problems Using Frictitious Forces[J]. Int. J. Num. Meth. Engrg, 1991, 32:623-643.
[61] Seung HwanKo, Byung Man Kwak. Frictional Dynamic Contact Analysis Using Finite Element Nodal Displacement Description[J]. Computer and Structure, 1992, 42(5):797-807.
[62] Seok-Soon Lee. A Computational Method for Frictional Contact Problem Using Finite Element Method[J]. Int.J.Num.Meth Engrg, 1994, 37:217-228.
[63] B.P.Gautham, N.Ganesan. Finite Element Analysis of Contact-ImPact Betweena Shell of Revolutton and a rigid wall[J]. Int .J.Num.Meth. Engrg, 1994, 37:3251-3262.
[64]欧恒安,李润方,龚剑霞.三维冲击-动力接触问题有限元混合算法[J].重庆大学学报,1994, 17(2):52-57.
[65]陈兵奎,李润方.冲击-动力接触问题有限元方法的几点注记[J].计算结构力学及其应用,1996, 13(2):48-52.
[66]邢誉峰,诸得超.两杆纵向非线性弹性碰撞的瞬间响应[J].北京航空航天大学学报, 1998, 24(1):39-42.
[67]姚文席,魏任之.渐开线直齿轮的啮合冲击研究[J].振动与冲击, 1990, 9(4):57-61.
[68]王玉芳,童忠舫.齿轮的误差对啮合冲击的影响[J].振动与冲击, 1994, 13(2):14-18.
[69]唐进元,肖利民.齿轮齿顶修缘时啮合冲击速度的计算[J].长沙铁道学院学报, 1995, 13(l): 26-30.
[70]李润方,陈兵奎.冲击/动力接触问题有限元混合方法及其应用[J].非线性力学学报,1997, (3):236-242.
[71]林腾蛟,李润方,陶泽光.齿轮传动三维间隙非线性冲击-动力接触特性数值仿真[J].机械工程学报, 2000, 36(6):55-58.
[72]林腾蛟,李润方,郭晓东,王立华.准双曲面齿轮三维间隙非线性冲击特性分析[J].中国机械工程, 2003, 14(9):727-730.
[73] A.Bajer, L.Demkowicz. Dynamic contact/impact problems, energy conservation, and planetary gear trains[J]. Computer Methods in Applied Mechanics and Engineering, 2002, 191(37-38):4159-4191.
[74]谢海东,周照耀,夏伟,邱诚,张文.斜齿轮传动中啮合冲击数值研究[J].机械传动,2005, 29(3):6-9.
[75]马雪洁,谢刚,王小林.基于ANSYS/LS-DYNA的准双曲面齿轮动力学接触仿真分析[J].机械传动, 2005,29(6):51-53.
[76]盛云,武宝林.齿轮传动中啮合冲击的计算分析[J].机械设计, 2005,22(7):41-43.
[77]许泽银.基节误差对齿轮啮合冲击影响的分析与计算[J].合肥学院学报, 2005, 15(2):81-84.
[78]吴大任,骆家舜.齿轮啮合原理[M].北京:科学出版社, 1985.
[79]吴继泽,王统.齿根过渡曲线与齿根应力[M].北京:国防工业出版社, 1989.
[80]刘相新,孟宪颐. ANSYS基础与应用教程[M].北京:科学出版社, 2006.
[81]张朝晖. ANSYS8.0热分析教程与实例解析[M].北京:中国铁道出版社, 2005.
[82]李绍彬.高速重载齿轮传动热弹变形及非线性耦合动力学研究[D].重庆:重庆大学, 2003.
[83]李润方.齿轮传动的刚度分析和修形方法[M].重庆:重庆大学出版社,1998.
[84]唐增宝,陈久荣.齿轮动态性能最佳的齿廓修形曲线和参数[J].华中理工大学学报, 1995, 23(11):52-55.
[85]尚晓江,苏建宇. ANSYS/LS-DYNA动力分析方法与工程实例[M].北京:中国水利水电出版社, 2006.