汽车减振器动态特性仿真技术研究
|
摘要
减振器动态特性仿真技术是推动减振器技术发展的重要手段,也是车辆动力学特性仿真分析技术的重要内容。本文针对传统的减振器仿真模型普遍存在的困难和问题,对建立和求解不依赖于实验测试的减振器分布参数模型进行了系统研究。
对减振器动态特性仿真数值方法进行系统研究。内容包括:非线性有限元方法、计算流体动力学数值方法以及流-固耦合数值方法。针对减振器这一复杂的流-固耦合系统,提出了基于多求解器的流-固耦合仿真方法,即采用有限体积法求解流场,而固体结构仍采用有限元法进行求解,求解器之间通过流-固耦合面传递数据。这种联合仿真的方法为建立和求解减振器分布参数模型奠定了基础。
对减振器阻尼阀低速特性进行CFD仿真分析及实验验证。对减振器的结构特点、工作原理及阻尼特性进行了详细分析,研究了流场网格密度与求解精度之间的关系,建立了精度较高的阻尼阀流场网格模型,并分别采用层流、SST、层流-SST混合模型对其进行了CFD仿真分析,获取了减振器的低速特性,揭示了减振器内部的流场规律。实验测试验证了CFD仿真分析的准确性。
推导减振器环形阀片大挠度变形通用解析式。基于钱氏摄动法,导出了减振器单阀片刚度曲线方程,进一步推导了叠加阀片大挠度解析式,并将其推广到一般情形。解析式的待定系数采用有限元和曲线拟合方法求得。数值计算验证表明:该解析式不仅适用于阀片(单个阀片和叠加阀片)大挠度计算,还适用于阀片小挠度计算,且具有
较高的计算精度。对减振器的流-固耦合建模和求解技术进行研究。研究了不同网格形式的阀片有限元模型的求解精度,建立了精度较高的叠加阀片有限元接触模型,对减振器的流-固耦合求解关键技术进行了分析,对减振器的流-固耦合动态特性进行了仿真分析和研究,对减振器阻尼特性、内部流场规律以及叠加阀片非线性动力学响应特征进行了详细分析。减振器的性能实验验证了建模和求解方法的正确性。
The simulation techniques for dynamic characteristics of automobile shock absorber are important means toward the development of shock absorber technology. They are also the main content of vehicle dynamic characteristics simulation techniques. Facing on the difficulties and problems of traditional shock absorber simulation models, the systemic research on building the distribution parameter model of shock absorber and solving it without the experiment tests was carried out in this thesis.
The systemic research on the numerical simulation method of dynamic characteristics of shock absorber was carried out in this thesis. The content includes: nonlinear finite element method, computational fluid dynamics numerical method and fluid-structure interaction numerical method. For the complex fluid-structure interaction system of shock absorber, the fluid-structure interaction simulation method basing on multi-solvers was proposed, that is, the fluid filed is solved by finite volume method, but the solid structure is solved by finite element method, and the data transmission between solvers is passed through coupling surface. This combined simulation method lays the foundation of shock absorber’s distribution parameter model building and solving.
The CFD simulation analysis and experimental verification for the low speed characteristics of shock absorber’s valve were carried out. The structure characteristic, work principle and damping characteristic of shock absorber were analyzed in detail. The relationship between the element density of fluid filed and the calculation accuracy was studied. Then, the fluid field grid model of damper valve with higher accuracy was established, and used for CFD simulation based on laminar model, SST turbulence model and laminar-SST mixed model respectively. The low speed characteristics of shock absorber were obtained. Meanwhile, the internal fluid field rule of shock absorber was revealed. The experiment tests verify that the CFD simulation analysis is satisfactory accurate.
The general analytical formula of large deflection for annular throttle-slices in shock absorber was deduced. Chien-perturbation method was used to derive the stiffness curve equation of single throttle-slice in shock absorber. Furthermore, the analytical formula of large deflection for superposition throttle-slices was deduced directly and then generalized. The undetermined coefficients of analytical formula were obtained by finite element method and curve fitting. Numerical results show that the general analytical formula can be used not only for the large deflection calculation (including single throttle-slice and superposition ones), but also for small deflection calculation, and has satisfactory accuracy.
The fluid-structure interaction modeling and solving techniques of shock absorber were studied. The calculation accuracy of finite element model of throttle-slice with different mesh styles was studied. The finite element contact model of superposition throttle-slices with higher accuracy was established. The fluid-structure interaction key techniques of shock absorber were analyzed. The fluid-structure interaction dynamic characteristics of shock absorber were simulated and studied. Then, the damping characteristic, the internal fluid field rule and the nonlinear dynamic response characteristic of superposition throttle-slices of shock absorber were analyzed in detail. The performance experiment tests of shock absorber verify that the modeling and solving methods are correct and satisfactory accurate.
对减振器动态特性仿真数值方法进行系统研究。内容包括:非线性有限元方法、计算流体动力学数值方法以及流-固耦合数值方法。针对减振器这一复杂的流-固耦合系统,提出了基于多求解器的流-固耦合仿真方法,即采用有限体积法求解流场,而固体结构仍采用有限元法进行求解,求解器之间通过流-固耦合面传递数据。这种联合仿真的方法为建立和求解减振器分布参数模型奠定了基础。
对减振器阻尼阀低速特性进行CFD仿真分析及实验验证。对减振器的结构特点、工作原理及阻尼特性进行了详细分析,研究了流场网格密度与求解精度之间的关系,建立了精度较高的阻尼阀流场网格模型,并分别采用层流、SST、层流-SST混合模型对其进行了CFD仿真分析,获取了减振器的低速特性,揭示了减振器内部的流场规律。实验测试验证了CFD仿真分析的准确性。
推导减振器环形阀片大挠度变形通用解析式。基于钱氏摄动法,导出了减振器单阀片刚度曲线方程,进一步推导了叠加阀片大挠度解析式,并将其推广到一般情形。解析式的待定系数采用有限元和曲线拟合方法求得。数值计算验证表明:该解析式不仅适用于阀片(单个阀片和叠加阀片)大挠度计算,还适用于阀片小挠度计算,且具有
较高的计算精度。对减振器的流-固耦合建模和求解技术进行研究。研究了不同网格形式的阀片有限元模型的求解精度,建立了精度较高的叠加阀片有限元接触模型,对减振器的流-固耦合求解关键技术进行了分析,对减振器的流-固耦合动态特性进行了仿真分析和研究,对减振器阻尼特性、内部流场规律以及叠加阀片非线性动力学响应特征进行了详细分析。减振器的性能实验验证了建模和求解方法的正确性。
The simulation techniques for dynamic characteristics of automobile shock absorber are important means toward the development of shock absorber technology. They are also the main content of vehicle dynamic characteristics simulation techniques. Facing on the difficulties and problems of traditional shock absorber simulation models, the systemic research on building the distribution parameter model of shock absorber and solving it without the experiment tests was carried out in this thesis.
The systemic research on the numerical simulation method of dynamic characteristics of shock absorber was carried out in this thesis. The content includes: nonlinear finite element method, computational fluid dynamics numerical method and fluid-structure interaction numerical method. For the complex fluid-structure interaction system of shock absorber, the fluid-structure interaction simulation method basing on multi-solvers was proposed, that is, the fluid filed is solved by finite volume method, but the solid structure is solved by finite element method, and the data transmission between solvers is passed through coupling surface. This combined simulation method lays the foundation of shock absorber’s distribution parameter model building and solving.
The CFD simulation analysis and experimental verification for the low speed characteristics of shock absorber’s valve were carried out. The structure characteristic, work principle and damping characteristic of shock absorber were analyzed in detail. The relationship between the element density of fluid filed and the calculation accuracy was studied. Then, the fluid field grid model of damper valve with higher accuracy was established, and used for CFD simulation based on laminar model, SST turbulence model and laminar-SST mixed model respectively. The low speed characteristics of shock absorber were obtained. Meanwhile, the internal fluid field rule of shock absorber was revealed. The experiment tests verify that the CFD simulation analysis is satisfactory accurate.
The general analytical formula of large deflection for annular throttle-slices in shock absorber was deduced. Chien-perturbation method was used to derive the stiffness curve equation of single throttle-slice in shock absorber. Furthermore, the analytical formula of large deflection for superposition throttle-slices was deduced directly and then generalized. The undetermined coefficients of analytical formula were obtained by finite element method and curve fitting. Numerical results show that the general analytical formula can be used not only for the large deflection calculation (including single throttle-slice and superposition ones), but also for small deflection calculation, and has satisfactory accuracy.
The fluid-structure interaction modeling and solving techniques of shock absorber were studied. The calculation accuracy of finite element model of throttle-slice with different mesh styles was studied. The finite element contact model of superposition throttle-slices with higher accuracy was established. The fluid-structure interaction key techniques of shock absorber were analyzed. The fluid-structure interaction dynamic characteristics of shock absorber were simulated and studied. Then, the damping characteristic, the internal fluid field rule and the nonlinear dynamic response characteristic of superposition throttle-slices of shock absorber were analyzed in detail. The performance experiment tests of shock absorber verify that the modeling and solving methods are correct and satisfactory accurate.
引文
[1] Duym S. Simulation tools, modelling and identification, for an automotive shock absorber in the context of vehicle dynamics[J]. Vehicle System Dynamics. 2000, 33: 261-285.
[2] Lee K. Numerical modelling for the hydraulic performance prediction of automotive monotube dampers[J]. Vehicle System Dynamics. 1997, 28: 25-39.
[3]李世民,吕振华.汽车筒式液阻减振器技术的发展[J].汽车技术. 2001(8): 10-16.
[4]张德庆.汽车减振器的建模及仿真设计[D].镇江:江苏大学, 2003.
[5]袁长颂.液压减振器特性仿真及其参数化设计[D].安徽:安徽理工大学, 2005.
[6]俞德孚,马彪.悬架减振器外特性畸变及其对车辆运行的有害影响[J].兵工学报坦克装甲车与发动机分册. 1990(1): 32-39.
[7]俞德孚,刘晓璞,李晓雷.车辆悬架减振器外特性的高频畸变与高频设计[J].北京工业学院学报. 1988, 8(3(Ⅱ)): 82-89.
[8]高晓芳,苏德胜,邵敏.电流变液减振器技术的研究现状及发展方向[J].机械工程师. 2007(1): 21-23.
[9]姚喆赫,梅德庆.用于汽车悬架的磁流变减振器研究综述[J].机电工程. 2006, 23(1): 58-62.
[10] Duym S, Stiens R, Reybrouck K. Evaluation of shock absorber models[J]. Vehicle System Dynamics. 1997, 27: 109-127.
[11] Lang H H. A study of the characteristics of automotive hydraulic dampers at high stroking frequencies[D]. Michigan: The University of Michigan, 1977.
[12] Duym S W, Stiens R, Baron G V, et al. Physical modeling of the hysteretic behaviour of automotive shock absorbers[R]. SAE Paper, 970101.
[13] Yeh E C, Lu S H, Yang T W, et al. Dynamic analysis of a double-tube shock absorber for robust design[J]. JSME International Journal, Series C. 1997, 40: 335-345.
[14] Karadayi R, Masada G Y. Nonlinear Shock Absorber model[J]. ASME. 1989: 149-165.
[15] Besinger F H, Cebon D, Cole D J. Damper model for Heavy vehicle Ridedynamics[J]. Vehicle System Dynamics. 1995(24): 35-64.
[16] Worden K. Data processing and experiment design for the restoring force surface method, part I: Integration and differentiation of measured time data[J]. Mechanical Systems and Signal Processing. 1990, 4(4): 295-319.
[17] Audenino A, Belingardi G, Garibaldi L. An application of the restoring force mapping method for the diagnostic of vehicular shock absorbers dynamic simulation behaviour[C]. Italy: Dipartimento di Meccanica del Politecnico di Torino: 1990.
[18] Cafferty S, Worden K, Tomlinson G. Characterization of automotive shock absorbers using random excitation[J]. Proceedings of IMechE, Part D: Journal of Automobile Engineering. 1995, 209: 239-248.
[19] Schiehlen W, Hu B. Spectral simulation and shock absorber identification[J]. International Journal of Non-Linear Mechanics. 2003, 38: 161-171.
[20] Herr F, Mallin T, Lane J, et al. A shock absorber model using cfd analysis and Easy5[R]. SAE Paper, 1999011322.
[21] Tallec P L, Mouro J. Fluid structure interaction with large structural displacements[J]. Computer methods in applied mechanics and engineering. 2001, 190: 3039-3067.
[22]陈耀钧.轿车液阻减振器阻力特性模拟计算及分析[J].汽车技术. 1995(10): 7-13.
[23]黄志刚,郑慕侨,于立萍.阀片型减振器的外特性仿真[J].计算机仿真. 1996, 13(1): 36-44.
[24]李双义,毕凤荣,邹立明.双筒减振器阀片的大挠曲变形及特性分析[J].汽车技术. 1999(11): 22-25.
[25]李希文.液压减震器动态特性的计算机仿真[J].航空学报. 1999(2): 75-79.
[26]黄恒,程广伟,邓楚南.车用减振器的外特性建模与仿真[J].汽车技术. 2005(11): 4-7.
[27]李幼德,李静,宋大凤等.汽车减振器弹簧阀片变形模型的研究[J].汽车工程. 2003, 25(3): 287-290.
[28]任卫群,赵峰,张杰.汽车减振器阻尼特性的仿真分析[J].系统仿真学报. 2006, 18(增刊2): 957-960.
[29]周长城.汽车减振器阀系解析计算与特性综合仿真[D].北京:北京理工大学,2006.
[30] ZHOU Changcheng, ZHENG Zhiyun, GU Liang, et al. Study on the availability opening size of throttle and affection to the velocity characteristic of shock absorber[J]. Beijing Institute of Technology. 2007, 16(1): 23-27.
[31]周长城,赵力航,顾亮.减振器叠加节流阀片的研究[J].北京理工大学学报. 2006, 26(8): 681-684.
[32]陈轶杰.油气弹簧阻尼阀参数解析计算与系统设计研究[D].北京:北京理工大学, 2008.
[33]陈轶杰,顾亮.油气弹簧环形节流阀片大挠曲变形分析与试验[J].吉林大学学报(工学版). 2009, 39(2): 388-392.
[34]陈勇,何辉.夏利轿车液力减振器簧片的变形分析[J].汽车技术. 2000(8): 10-16.
[35]贺李平,顾亮,辛国国等.减振器环形阀片大挠曲变形的高精度解析式[J].北京理工大学学报. 2009, 29(6): 510-514.
[36]江浩斌,杨如泉,陈龙等.麦弗逊式前悬架液力减振器阻尼特性仿真与试验[J].汽车工程. 2007, 29(11): 970-974.
[37]袁长颂.有限元法在减振器建模中的应用[J].客车技术与研究. 2007(2): 20-21.
[38]檀润华,陈鹰,赵凡等.汽车减震器新型数学模型的研究[J].汽车工程. 1998, 20(2): 113-117.
[39]吕振华,高源,王望予等.汽车转向系减振器原理及其阻尼特性的试验分析[J].汽车技术. 1997(7): 26-30.
[40]冯雪梅,刘佐民.减振器内部油压行为分布特征有限元分析[J].武汉理工大学学报. 2002, 24(5): 121-124.
[41]冯雪梅,刘佐民,魏东.减振器双节流孔闭式油路稳态行为特征有限元分析[J].机械设计与研究. 2003, 19(1): 66-69.
[42]单春贤.摩托车减震器阻尼特性热力学模型的建立与流场模拟分析[D].江苏大学, 2007.
[43]吕振华,伍卓安,李世民.减振器节流阀非线性特性的有限元模拟分析[J].机械强度. 2003, 25(6): 614-620.
[44]李世民.筒式液阻减振器液-固耦合动力学特性仿真技术研究[D].北京:清华大学, 2004.
[45]李世民,吕振华.汽车减振器液-固耦合动力学特性的分步间接耦合模拟分析[J].汽车技术. 2005(2): 12-16.
[46]吕振华,姜利泉.基于液-固耦合有限元分析方法的气-液型减振器补偿阀性能研究[J].工程力学. 2006, 23(11): 163-169.
[47]吕振华,李世民.筒式液阻减振器动态特性模拟分析技术的发展[J].清华大学学报. 2002, 42(11): 1532-1536.
[48] Johansen, Stein T. Multi-phase flow modeling applied to metallurgical processes.[J]. Modeling, Identification and Control. 2002, 23: 77-92.
[49] Lion A, Loose S. A thermomechanically coupled model for automotive shock absorbers: theory, experiments and vehicle simulations on test tracks[J]. Vehicle System Dynamics. 2002, 37: 241-261.
[50]余卓平,王欲峰,宁国宝等.汽车液压减振器热-机耦合动力学影响因素分析[J].机械设计. 2007, 24(11): 29-32.
[51]张立军,余卓平.汽车悬架液压减振器热机耦合动力学模型[J].同济大学学报(自然科学版). 2008, 36(12): 1691-1696.
[52]张立军,余卓平,阳鹏.汽车液压减振器热-机耦合特性试验研究[J].汽车技术. 2005(4): 28-31.
[53] Bathe K J, Zhang H, Wang M H. Finite Element Analysis of incompressible and compressible fluid flows with free surfaces and structural interactions[J]. Computers and Structures. 1995, 56: 193-213.
[54] Belytschko T, Flanagan D P, Kennedy J M. Finite element methods with user-controlled meshes for Fluid-Structure Interaction[J]. Computer Methods in Applied Mechanics and Engineering. 1981, 33: 669-688.
[55] Hughes T J R, Liu W K, Zimmermann T K. Lagrangian-Eulerian finite element formulation for incompression viscous flows[J]. Computer Methods in Applied Mechanics and Engineering. 1981, 293: 329-349.
[56] Tezduyar T E. Stabilized finite element formulations for incompressible flow computations[J]. Advances in Applied Mechanics. 1991, 28: 1-44.
[57] Wang X. Analytical and computational approaches for some fluid-structure interaction analyses[J]. Computers and Structures. 1999, 72: 423-433.
[58]郭术义,陈举华.流固耦合应用研究进展[J].济南大学学报. 2004, 18(2): 123-126.
[59] Mitra S, Sinhamahapatra K P. 2D simulation of fluid-structure interaction using finite element method[J]. Finite Elements in Analysis and Design. 2008, 45: 52-59.
[60]钱若军,董石麟,袁行飞.流固耦合理论研究进展[J].空间结构. 2008, 14(1): 3-15.
[61]张潇,王延荣,张小伟等.基于多层动网格技术的流固耦合方法研究[J].船舶工程. 2009, 31(1): 64-67.
[62] Bathe K J, Zhang H, Ji S. Finite element analysis of fluid flows fully coupled with structural interactions[J]. Computers and Structures. 1999, 72: 1-16.
[63] Bathe K J, Zhang H, Zhang X. Some advances in the analysis of fluid flows[J]. Computers and Structures. 1997, 64: 909-930.
[64] Zhang H, Zhang X, Ji S, et al. Recent development of fluid-structure interaction capabilities in the ADINA system[J]. Computers and Structures. 2003, 81: 1071-1085.
[65]骆清国,刘红彬,龚正波, et al.柴油机气缸盖流固耦合传热分析研究[J].兵工学报. 2008, 29(7): 769-773.
[66]汪玉,周璞,刘东岳等.考虑流固耦合作用的舰船抗冲击仿真计算[J].振动与冲击. 2005, 24(1): 73-79.
[67]邬海军,郭鹏程,廖伟丽, et al. ANSYS在水轮机部件流固耦合振动分析中的应用[J].水电能源科学. 2004, 22(4): 64-66.
[68]黄俊,周正东,戴耀东等.腹主动脉瘤的流固耦合分析方法研究[J].现代生物医学进展. 2009, 9(2): 334-336.
[69]弓三伟,邹正平,杨振亚等.汽轮机末级叶片流固耦合数值模拟[J].热能动力工程. 2009, 24(1): 31-38.
[70]陆忠东,吴光强,殷学仙等.液力变矩器流固耦合研究[J].汽车技术. 2009(2): 37-42.
[71] Saeed Moaveni著,王崧,董春敏,金云平等译.有限元分析-ANSYS理论与应用(第二版)[M].北京:电子工业出版社, 2005.
[72] Clough R W. The finite element method in plane stress analysis[J]. Proceedings ofAmerican Society of Civil Engineers. 1960, 23: 345-378.
[73]王勖成.有限单元法[M].北京:清华大学出版社, 2003.
[74]薛守义.有限单元法[M].北京:中国建材工业出版社, 2005.
[75]张洪信.有限元基础理论与ANSYS应用[M].北京:机械工业出版社, 2006.
[76] Zienkiewicz O, Taylor R著,曾攀等译.有限元方法(第5版)第1卷基本原理[M].北京:清华大学出版社, 2008.
[77]尚晓江,邱峰,赵海峰等. ANSYS结构有限元高级分析方法与范例应用[M].北京:中国水利水电出版社, 2006.
[78]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.
[79]林建忠,阮晓东,陈邦国等.流体力学[M].北京:清华大学出版社, 2005.
[80]付坚强,陈军,杨燕华.节流件阻力特性的CFD研究[J].热能动力工程. 2004, 19(5): 518-523.
[81]周光炯,严宗毅,许世雄等.流体力学(第二版)上册[M].北京:高等教育出版社, 2000.
[82]周光炯,严宗毅,许世雄等.流体力学(第二版)下册[M].北京:高等教育出版社, 2000.
[83] Launder B E, Spalding D B. Lectures in Mathematical Models of Turbulence[M]. London: Academic Press, 1972.
[84] Shih T H, Liou W W, Shabbir A, et al. A new k-εeddy-viscosity model for high reynolds number turbulent flows - model development and validation[J]. Computers Fluids. 1995, 24(3): 227-238.
[85] Yakhot V, Orszag S A. Renormalization group analysis of turbulence: I. basic theory[J]. Journal of Scientific Computing. 1986, 1(1): 1-51.
[86] Menter F R. Two-equation eddy-viscosity turbulence models for engineering applications[J]. AIAA Journal. 1994, 32(8): 1598-1605.
[87] Gibson M M, Launder B E. Ground effects on pressure fluctuations in the atmospheric boundary layer[J]. J. Fluid Mech. 1978, 86: 491-511.
[88] Launder B E, Reece G J, Rodi W. Progress in the development of a reynolds-stress turbulence closure[J]. J. Fluid Mech. 1975, 68(3): 537-566.
[89] Launder B E. Second-moment closure: present... and future?[J]. Inter. J. Heat Fluid Flow. 1989, 10(4): 282-300.
[90]江帆,黄鹏. Fluent高级应用与实例分析[M].北京:清华大学出版社, 2008.
[91] Zienkiewicz O, Taylor R著,符松,刘扬扬译.有限元方法(第5版)第3卷流体动力学[M].北京:清华大学出版社, 2008.
[92] ANSYS. ANSYS CFX-solver theory guide[R]. USA: ANSYS company, 2009.
[93] Richard Van Kasteel, Wang Cheng-guo, Qian Li-xin, et al. A new shock absorber model for use in vehicle dynamics studies[J]. Vehicle System Dynamics. 2005, 43(9): 613-631.
[94]容琼,吴静萍,姜曼松.圆管内流动的数值模拟[J].中国水运. 2006, 4(12): 109-110.
[95]徐芝纶.弹性力学(下)[M].北京:高等教育出版社, 2006.
[96]刘鸿文.板壳理论[M].杭州:浙江大学出版社, 1987.
[97]郑晓静.圆薄板大挠度理论及应用[M].吉林:吉林科学技术出版社, 1990.
[98] von Karman Th. Festigkeits problem in maschinenbau[J]. Enzyklopadie der Mathematischen Wissenschaften. 1910, 27(4): 348-351.
[99] Vincent J. The bending of a thin circular plate[J]. Phil. Mag. 1931, 12: 185-196.
[100] Wei-Zang Chien. Large deflection of a circular clamped plate under uniform pressure[J]. Acta Physica Sinica. 1947(2): 102-113.
[101] Nolte L J. Large deflections of clamped rectangular plates[R]. Hughes Aircraft Co Culver City Calif, 1957.
[102] Nash W A, Cooley I D. Large deflections of a clamped eiliptical plate subjected to uniform pressure[J]. Journal of Applied Mechanics. 1959, 26(2): 291-293.
[103] Chien Wei-zang, Pan Li-zhou, Liu Xiao-ming. Large deflection problem of a clamped elliptical plate subjected to uniform pressure[J]. Applied Mathematics and Mechanics. 1991, 13(10): 891-908.
[104]陈轶杰,顾亮,杨占华, et al.减振器节流阀片大挠曲变形研究[J].机械设计与制造. 2008(10): 90-92.
[105]周长城,顾亮.减振器叠加节流阀片与节流阀开度研究[J].流体机械. 2006, 34(7): 19-23.
[106]周长城,顾亮.减振器多片叠加节流阀片特性分析与试验研究[J].拖拉机与农用运输车. 2006, 33(3): 40-43.
[107]周长城,顾亮.筒式减振器叠加节流阀片开度与特性试验[J].机械工程学报. 2007, 43(6): 210-215.
[108] ANSYS. Theory reference for ANSYS and workbench[R]. USA: ANSYS company, 2007.
[109]成大先.机械设计手册,第1卷[M].北京:化学工业出版社, 2004: 1-168.
[2] Lee K. Numerical modelling for the hydraulic performance prediction of automotive monotube dampers[J]. Vehicle System Dynamics. 1997, 28: 25-39.
[3]李世民,吕振华.汽车筒式液阻减振器技术的发展[J].汽车技术. 2001(8): 10-16.
[4]张德庆.汽车减振器的建模及仿真设计[D].镇江:江苏大学, 2003.
[5]袁长颂.液压减振器特性仿真及其参数化设计[D].安徽:安徽理工大学, 2005.
[6]俞德孚,马彪.悬架减振器外特性畸变及其对车辆运行的有害影响[J].兵工学报坦克装甲车与发动机分册. 1990(1): 32-39.
[7]俞德孚,刘晓璞,李晓雷.车辆悬架减振器外特性的高频畸变与高频设计[J].北京工业学院学报. 1988, 8(3(Ⅱ)): 82-89.
[8]高晓芳,苏德胜,邵敏.电流变液减振器技术的研究现状及发展方向[J].机械工程师. 2007(1): 21-23.
[9]姚喆赫,梅德庆.用于汽车悬架的磁流变减振器研究综述[J].机电工程. 2006, 23(1): 58-62.
[10] Duym S, Stiens R, Reybrouck K. Evaluation of shock absorber models[J]. Vehicle System Dynamics. 1997, 27: 109-127.
[11] Lang H H. A study of the characteristics of automotive hydraulic dampers at high stroking frequencies[D]. Michigan: The University of Michigan, 1977.
[12] Duym S W, Stiens R, Baron G V, et al. Physical modeling of the hysteretic behaviour of automotive shock absorbers[R]. SAE Paper, 970101.
[13] Yeh E C, Lu S H, Yang T W, et al. Dynamic analysis of a double-tube shock absorber for robust design[J]. JSME International Journal, Series C. 1997, 40: 335-345.
[14] Karadayi R, Masada G Y. Nonlinear Shock Absorber model[J]. ASME. 1989: 149-165.
[15] Besinger F H, Cebon D, Cole D J. Damper model for Heavy vehicle Ridedynamics[J]. Vehicle System Dynamics. 1995(24): 35-64.
[16] Worden K. Data processing and experiment design for the restoring force surface method, part I: Integration and differentiation of measured time data[J]. Mechanical Systems and Signal Processing. 1990, 4(4): 295-319.
[17] Audenino A, Belingardi G, Garibaldi L. An application of the restoring force mapping method for the diagnostic of vehicular shock absorbers dynamic simulation behaviour[C]. Italy: Dipartimento di Meccanica del Politecnico di Torino: 1990.
[18] Cafferty S, Worden K, Tomlinson G. Characterization of automotive shock absorbers using random excitation[J]. Proceedings of IMechE, Part D: Journal of Automobile Engineering. 1995, 209: 239-248.
[19] Schiehlen W, Hu B. Spectral simulation and shock absorber identification[J]. International Journal of Non-Linear Mechanics. 2003, 38: 161-171.
[20] Herr F, Mallin T, Lane J, et al. A shock absorber model using cfd analysis and Easy5[R]. SAE Paper, 1999011322.
[21] Tallec P L, Mouro J. Fluid structure interaction with large structural displacements[J]. Computer methods in applied mechanics and engineering. 2001, 190: 3039-3067.
[22]陈耀钧.轿车液阻减振器阻力特性模拟计算及分析[J].汽车技术. 1995(10): 7-13.
[23]黄志刚,郑慕侨,于立萍.阀片型减振器的外特性仿真[J].计算机仿真. 1996, 13(1): 36-44.
[24]李双义,毕凤荣,邹立明.双筒减振器阀片的大挠曲变形及特性分析[J].汽车技术. 1999(11): 22-25.
[25]李希文.液压减震器动态特性的计算机仿真[J].航空学报. 1999(2): 75-79.
[26]黄恒,程广伟,邓楚南.车用减振器的外特性建模与仿真[J].汽车技术. 2005(11): 4-7.
[27]李幼德,李静,宋大凤等.汽车减振器弹簧阀片变形模型的研究[J].汽车工程. 2003, 25(3): 287-290.
[28]任卫群,赵峰,张杰.汽车减振器阻尼特性的仿真分析[J].系统仿真学报. 2006, 18(增刊2): 957-960.
[29]周长城.汽车减振器阀系解析计算与特性综合仿真[D].北京:北京理工大学,2006.
[30] ZHOU Changcheng, ZHENG Zhiyun, GU Liang, et al. Study on the availability opening size of throttle and affection to the velocity characteristic of shock absorber[J]. Beijing Institute of Technology. 2007, 16(1): 23-27.
[31]周长城,赵力航,顾亮.减振器叠加节流阀片的研究[J].北京理工大学学报. 2006, 26(8): 681-684.
[32]陈轶杰.油气弹簧阻尼阀参数解析计算与系统设计研究[D].北京:北京理工大学, 2008.
[33]陈轶杰,顾亮.油气弹簧环形节流阀片大挠曲变形分析与试验[J].吉林大学学报(工学版). 2009, 39(2): 388-392.
[34]陈勇,何辉.夏利轿车液力减振器簧片的变形分析[J].汽车技术. 2000(8): 10-16.
[35]贺李平,顾亮,辛国国等.减振器环形阀片大挠曲变形的高精度解析式[J].北京理工大学学报. 2009, 29(6): 510-514.
[36]江浩斌,杨如泉,陈龙等.麦弗逊式前悬架液力减振器阻尼特性仿真与试验[J].汽车工程. 2007, 29(11): 970-974.
[37]袁长颂.有限元法在减振器建模中的应用[J].客车技术与研究. 2007(2): 20-21.
[38]檀润华,陈鹰,赵凡等.汽车减震器新型数学模型的研究[J].汽车工程. 1998, 20(2): 113-117.
[39]吕振华,高源,王望予等.汽车转向系减振器原理及其阻尼特性的试验分析[J].汽车技术. 1997(7): 26-30.
[40]冯雪梅,刘佐民.减振器内部油压行为分布特征有限元分析[J].武汉理工大学学报. 2002, 24(5): 121-124.
[41]冯雪梅,刘佐民,魏东.减振器双节流孔闭式油路稳态行为特征有限元分析[J].机械设计与研究. 2003, 19(1): 66-69.
[42]单春贤.摩托车减震器阻尼特性热力学模型的建立与流场模拟分析[D].江苏大学, 2007.
[43]吕振华,伍卓安,李世民.减振器节流阀非线性特性的有限元模拟分析[J].机械强度. 2003, 25(6): 614-620.
[44]李世民.筒式液阻减振器液-固耦合动力学特性仿真技术研究[D].北京:清华大学, 2004.
[45]李世民,吕振华.汽车减振器液-固耦合动力学特性的分步间接耦合模拟分析[J].汽车技术. 2005(2): 12-16.
[46]吕振华,姜利泉.基于液-固耦合有限元分析方法的气-液型减振器补偿阀性能研究[J].工程力学. 2006, 23(11): 163-169.
[47]吕振华,李世民.筒式液阻减振器动态特性模拟分析技术的发展[J].清华大学学报. 2002, 42(11): 1532-1536.
[48] Johansen, Stein T. Multi-phase flow modeling applied to metallurgical processes.[J]. Modeling, Identification and Control. 2002, 23: 77-92.
[49] Lion A, Loose S. A thermomechanically coupled model for automotive shock absorbers: theory, experiments and vehicle simulations on test tracks[J]. Vehicle System Dynamics. 2002, 37: 241-261.
[50]余卓平,王欲峰,宁国宝等.汽车液压减振器热-机耦合动力学影响因素分析[J].机械设计. 2007, 24(11): 29-32.
[51]张立军,余卓平.汽车悬架液压减振器热机耦合动力学模型[J].同济大学学报(自然科学版). 2008, 36(12): 1691-1696.
[52]张立军,余卓平,阳鹏.汽车液压减振器热-机耦合特性试验研究[J].汽车技术. 2005(4): 28-31.
[53] Bathe K J, Zhang H, Wang M H. Finite Element Analysis of incompressible and compressible fluid flows with free surfaces and structural interactions[J]. Computers and Structures. 1995, 56: 193-213.
[54] Belytschko T, Flanagan D P, Kennedy J M. Finite element methods with user-controlled meshes for Fluid-Structure Interaction[J]. Computer Methods in Applied Mechanics and Engineering. 1981, 33: 669-688.
[55] Hughes T J R, Liu W K, Zimmermann T K. Lagrangian-Eulerian finite element formulation for incompression viscous flows[J]. Computer Methods in Applied Mechanics and Engineering. 1981, 293: 329-349.
[56] Tezduyar T E. Stabilized finite element formulations for incompressible flow computations[J]. Advances in Applied Mechanics. 1991, 28: 1-44.
[57] Wang X. Analytical and computational approaches for some fluid-structure interaction analyses[J]. Computers and Structures. 1999, 72: 423-433.
[58]郭术义,陈举华.流固耦合应用研究进展[J].济南大学学报. 2004, 18(2): 123-126.
[59] Mitra S, Sinhamahapatra K P. 2D simulation of fluid-structure interaction using finite element method[J]. Finite Elements in Analysis and Design. 2008, 45: 52-59.
[60]钱若军,董石麟,袁行飞.流固耦合理论研究进展[J].空间结构. 2008, 14(1): 3-15.
[61]张潇,王延荣,张小伟等.基于多层动网格技术的流固耦合方法研究[J].船舶工程. 2009, 31(1): 64-67.
[62] Bathe K J, Zhang H, Ji S. Finite element analysis of fluid flows fully coupled with structural interactions[J]. Computers and Structures. 1999, 72: 1-16.
[63] Bathe K J, Zhang H, Zhang X. Some advances in the analysis of fluid flows[J]. Computers and Structures. 1997, 64: 909-930.
[64] Zhang H, Zhang X, Ji S, et al. Recent development of fluid-structure interaction capabilities in the ADINA system[J]. Computers and Structures. 2003, 81: 1071-1085.
[65]骆清国,刘红彬,龚正波, et al.柴油机气缸盖流固耦合传热分析研究[J].兵工学报. 2008, 29(7): 769-773.
[66]汪玉,周璞,刘东岳等.考虑流固耦合作用的舰船抗冲击仿真计算[J].振动与冲击. 2005, 24(1): 73-79.
[67]邬海军,郭鹏程,廖伟丽, et al. ANSYS在水轮机部件流固耦合振动分析中的应用[J].水电能源科学. 2004, 22(4): 64-66.
[68]黄俊,周正东,戴耀东等.腹主动脉瘤的流固耦合分析方法研究[J].现代生物医学进展. 2009, 9(2): 334-336.
[69]弓三伟,邹正平,杨振亚等.汽轮机末级叶片流固耦合数值模拟[J].热能动力工程. 2009, 24(1): 31-38.
[70]陆忠东,吴光强,殷学仙等.液力变矩器流固耦合研究[J].汽车技术. 2009(2): 37-42.
[71] Saeed Moaveni著,王崧,董春敏,金云平等译.有限元分析-ANSYS理论与应用(第二版)[M].北京:电子工业出版社, 2005.
[72] Clough R W. The finite element method in plane stress analysis[J]. Proceedings ofAmerican Society of Civil Engineers. 1960, 23: 345-378.
[73]王勖成.有限单元法[M].北京:清华大学出版社, 2003.
[74]薛守义.有限单元法[M].北京:中国建材工业出版社, 2005.
[75]张洪信.有限元基础理论与ANSYS应用[M].北京:机械工业出版社, 2006.
[76] Zienkiewicz O, Taylor R著,曾攀等译.有限元方法(第5版)第1卷基本原理[M].北京:清华大学出版社, 2008.
[77]尚晓江,邱峰,赵海峰等. ANSYS结构有限元高级分析方法与范例应用[M].北京:中国水利水电出版社, 2006.
[78]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.
[79]林建忠,阮晓东,陈邦国等.流体力学[M].北京:清华大学出版社, 2005.
[80]付坚强,陈军,杨燕华.节流件阻力特性的CFD研究[J].热能动力工程. 2004, 19(5): 518-523.
[81]周光炯,严宗毅,许世雄等.流体力学(第二版)上册[M].北京:高等教育出版社, 2000.
[82]周光炯,严宗毅,许世雄等.流体力学(第二版)下册[M].北京:高等教育出版社, 2000.
[83] Launder B E, Spalding D B. Lectures in Mathematical Models of Turbulence[M]. London: Academic Press, 1972.
[84] Shih T H, Liou W W, Shabbir A, et al. A new k-εeddy-viscosity model for high reynolds number turbulent flows - model development and validation[J]. Computers Fluids. 1995, 24(3): 227-238.
[85] Yakhot V, Orszag S A. Renormalization group analysis of turbulence: I. basic theory[J]. Journal of Scientific Computing. 1986, 1(1): 1-51.
[86] Menter F R. Two-equation eddy-viscosity turbulence models for engineering applications[J]. AIAA Journal. 1994, 32(8): 1598-1605.
[87] Gibson M M, Launder B E. Ground effects on pressure fluctuations in the atmospheric boundary layer[J]. J. Fluid Mech. 1978, 86: 491-511.
[88] Launder B E, Reece G J, Rodi W. Progress in the development of a reynolds-stress turbulence closure[J]. J. Fluid Mech. 1975, 68(3): 537-566.
[89] Launder B E. Second-moment closure: present... and future?[J]. Inter. J. Heat Fluid Flow. 1989, 10(4): 282-300.
[90]江帆,黄鹏. Fluent高级应用与实例分析[M].北京:清华大学出版社, 2008.
[91] Zienkiewicz O, Taylor R著,符松,刘扬扬译.有限元方法(第5版)第3卷流体动力学[M].北京:清华大学出版社, 2008.
[92] ANSYS. ANSYS CFX-solver theory guide[R]. USA: ANSYS company, 2009.
[93] Richard Van Kasteel, Wang Cheng-guo, Qian Li-xin, et al. A new shock absorber model for use in vehicle dynamics studies[J]. Vehicle System Dynamics. 2005, 43(9): 613-631.
[94]容琼,吴静萍,姜曼松.圆管内流动的数值模拟[J].中国水运. 2006, 4(12): 109-110.
[95]徐芝纶.弹性力学(下)[M].北京:高等教育出版社, 2006.
[96]刘鸿文.板壳理论[M].杭州:浙江大学出版社, 1987.
[97]郑晓静.圆薄板大挠度理论及应用[M].吉林:吉林科学技术出版社, 1990.
[98] von Karman Th. Festigkeits problem in maschinenbau[J]. Enzyklopadie der Mathematischen Wissenschaften. 1910, 27(4): 348-351.
[99] Vincent J. The bending of a thin circular plate[J]. Phil. Mag. 1931, 12: 185-196.
[100] Wei-Zang Chien. Large deflection of a circular clamped plate under uniform pressure[J]. Acta Physica Sinica. 1947(2): 102-113.
[101] Nolte L J. Large deflections of clamped rectangular plates[R]. Hughes Aircraft Co Culver City Calif, 1957.
[102] Nash W A, Cooley I D. Large deflections of a clamped eiliptical plate subjected to uniform pressure[J]. Journal of Applied Mechanics. 1959, 26(2): 291-293.
[103] Chien Wei-zang, Pan Li-zhou, Liu Xiao-ming. Large deflection problem of a clamped elliptical plate subjected to uniform pressure[J]. Applied Mathematics and Mechanics. 1991, 13(10): 891-908.
[104]陈轶杰,顾亮,杨占华, et al.减振器节流阀片大挠曲变形研究[J].机械设计与制造. 2008(10): 90-92.
[105]周长城,顾亮.减振器叠加节流阀片与节流阀开度研究[J].流体机械. 2006, 34(7): 19-23.
[106]周长城,顾亮.减振器多片叠加节流阀片特性分析与试验研究[J].拖拉机与农用运输车. 2006, 33(3): 40-43.
[107]周长城,顾亮.筒式减振器叠加节流阀片开度与特性试验[J].机械工程学报. 2007, 43(6): 210-215.
[108] ANSYS. Theory reference for ANSYS and workbench[R]. USA: ANSYS company, 2007.
[109]成大先.机械设计手册,第1卷[M].北京:化学工业出版社, 2004: 1-168.