摘要
21世纪以来我国汽车工业飞速发展,汽车的安全舒适性能已经是消费者关注的重要性能。为了达到隔振减振的效果,汽车结构中采用许多橡胶柔性连接,主要应用在发动机悬置系统、驱动系统、车身系统等;操纵稳定性影响汽车的安全性,为了提高车辆的操纵稳定性,汽车前后悬架、操纵机构中也采用很多橡胶柔性连接。汽车研发技术不断的提高要求汽车子系统也要向高性能方向发展,汽车用橡胶结构件自身设计过程中的计算机仿真分析越来越受到重视,而在工程实际中橡胶超弹性材料参数的缺少给仿真分析带来不便。
描述橡胶材料力学性能的本构模型有多种形式,橡胶超弹性材料参数获得的传统方法来自橡胶材料基础试验,需要制备专门的试件,由于某些原因无法得到标准试件;试验标准不完善、国内试验条件的不足和试验设备的缺乏导致这些标准试验很难完成。在这种情况下,本文应用仿真分析、优化算法结合的反求方法的思路,提出了橡胶超弹性材料参数的反求方法。
在反求过程中引入响应面优化的方法,对响应面建立过程中两种拟合方法进行了比较分析,证明了移动最小二乘拟合的响应面精度很高,能够用于反求优化。用已知参数的橡胶结构件对本文方法进行了验证,反求出的参数与传统方法得到的参数很接近,验证了本文方法的有效性和可行性。本文进一步研究了不同本构模型参数的反求都获得了比较理想的结果。
对国内某车型结构中的缓冲橡胶块进行了反求,涉及了橡胶结构件试验的基本方法,求得的参数与试验结果吻合很好,可以用于该结构件的仿真分析。对于汽车结构中或其他工程中的橡胶件,可以结合实际工况和仿真分析选取比较合适的本构模型,模拟橡胶件实际工况做相应的试验,采用本文方法获得材料参数。
通过以上的研究可知,在无法得到标准试件,缺少试验条件的情况下,本文反求方法简单、实用、准确度足够,可以研究几乎所有的超弹性本构模型,也可以应用于橡胶的大变形情况以满足更多的工程实际需要,工程中意义重大,为处理橡胶超弹性材料参数问题提供了新的研究方法和途径。
With the rapid development of our country automobile industry, the automobile performances of the traffic safety and riding comfort become more important concerned by customers. In order to reduce and isolate the automobile vibration, rubber flexibility connections are widely used in engine system, drive system, body system and so on. The controllability and stability directly impact on the automobile safety, so rubber flexibility connections are also used in front and rear suspension systems as well as the control mechanism. With the automobile research techniques improving, the automobile subsystems are also required to develop into the high-performance direction. The computer simulation analysis becomes more and more important in the rubber structure design. However, the lack of hyperelastic material parameters brings lots of difficulties in the actual engineering conditions.
There’re many forms of constitutive models when describing rubber materials mechanics performances. The traditional method to get hyperelastic material parameters is based on rubber material foundation experiment, which needs special test samples. Actually, the experiment can be hardly completed because of those problems such as the hardly obtained special test samples, the imperfect test standards, as well as the lack of both test conditions and instruments. Based on those unsolved problems, this article proposes a inverse method to get the hyperelastic material parameters according to the idea of the inverse method of the combination with simulation analysis and optimization algorithm.
During the inverse, this article introduces the surface optimization method, compares and analyzes two kinds of fitting methods in establishing response surface. It proved that the response surface has high precision fitted by the moving least square and can be applied to the reverse optimization.
In this article, the inverse method is verified via the given parameters of the rubber structural element, and the result shows that the parameters coming from reverse method are very close to the ones coming from the tradition methods. Though the verification, it proves the validity and feasibility of the reverse method referred in this article. Besides, this article also researches the parameter inverse of different constitutive models and also gets the ideal results.
Carry on the inverse of the automobile rubber cushion blocks involved with the essential method for the rubber structural element experiment. The parameters solved are very close to the test results, and they can be applied to simulation analysis. As a result, in the automobile structure or other projects, we can select the appropriate constitutive models for the rubber structural element, combined with simulation analysis and actual working conditions, also carry on the corresponding test for the rubber element in the working condition simulations, and then obtain the material parameters used the inverse methods referred in the article.
According to the research above, on the conditions of unavailable standard samples as well as the lack of the test equipment, the inverse method referred in this article is simple, practical and high-accuracy compared with the traditional methods, and nearly can be applied to all the hyperelastic constitutive models also the large deformation of the rubber and to meet the actual needs in engineering problems. It’s rather significant in engineering and provides new research methods and approaches to dealing with the rubber hyperelastic material parameters.
引文
[1]户原春彦[日].防振橡胶及其应用.北京:中国铁道工业出版社,1982
[2]白龙浩.发动机悬置动力仿真及特性分析:[大连理工大学硕士学位论文].大连:大连理工大学,2004,1-2
[3]张晨彬.发动机橡胶悬置的研究与优化:[东南大学硕士学位论文].南京:东南大学,2006,1-3
[4]戴永谦.发动机悬置软垫断裂模拟:[大连理工大学博士学位论文].大连:大连理工大学,2006,8-16
[5]吴琳琪.车用膜式空气弹簧垂向弹性特性有限元分析及优化:[江苏大学硕士学位论文].镇江:江苏大学,2007,1-10
[6]王进文,田玉坤,王象民.国内外汽车用橡胶制品技术进展.橡胶科技市场,2007,(14):1-5
[7] Jaehwan Choi .Development of Modeling and Analysis Technique for the Rub -ber Bushings in Automobile.1998 ABAQUS Users’Conference
[8] Smith G W, Thornhill J W. Analysis of Elastomeric Spring-Eye Bushing Using ABAQUS.1998 ABAQUS Users’Conference
[9] Lee Nak Kyu,Lee Myung Sik,Kim Heon Young, Kim JoongJae .Design of Engine Mount Using Finite Element Method and Optimization Technique .SAE 980379
[10]王利荣,吕振华.橡胶隔振器有限元建模技术及静态弹性特性分析.汽车工程,2002,24(6):480-485
[11]上官文斌,吕振华.汽车动力总成橡胶隔振器弹性特性的有限元分析.内燃机工程,2003,24(6):50-55
[12]赵振东,雷雨成,袁学明.悬架橡胶衬套变形响应的非线性有限元分析.上海汽车,2005,(9):23-25
[13]晏红文,田红旗,黄友剑等.有限元法在机车车辆橡胶元件设计中的应用.机车电传动,2007,(6):29-33
[14]唐建华,胡培龙.某越野军车悬置元件设计与试验验证.汽车科技,2010,(4):19-23
[15]黄友剑,潘世文,郭红锋.网格重划在汽车用橡胶制品设计中的应用.橡胶科技市场,2008(4):22-24
[16]张振秀.橡胶制品有限元分析的研究应用:[青岛科技大学硕士学位论文].青岛:青岛科技大学,2005,8-16
[17]何志刚,董大鹏,王国林等.轮胎超弹性本构材料参数确定的影响因素分析.机械工程学报,2008,44(12):296-302
[18]李晓芳,杨晓翔.橡胶材料的超弹性本构模型.弹性体,2005,15(1):50-58
[19]刘龙权.三元乙丙橡胶密封件冲切加工性能研究与应用:[上海交通大学博士学位论文].上海:上海交通大学,2005,5-12
[20]高宽.薄板成型过程中的摩擦系数反求技术研究:[湖南大学硕士学位论文].长沙:湖南大学,2006,6-15
[21]李晓专.基于micr+GA和有限元的薄板材料参数的反求:[湖南大学硕士学位论文].长沙:湖南大学,2005,3-8
[22] Backus G.E.and Gilbert J.F.,Uniqueness in the inversion of inaccurate gross earth data, Phil.Trans.Roy.Soc.London,1970,(266):123-192
[23]李守巨.基于计算智能的岩土力学模型参数反演方法及其工程应用:[大连理工大学博士学位论文].大连:大连理工大学,2004,25-29
[24] ZABARA S N,MORELLA S V, SCHNU R D. A spatially solution of inverse elasticity problem using boundary element method commun. Appl Number methods, 1989, (5): 547- 553
[25] MANI A TTY A, ZABARA S N, STEL SON K. Finite element analysis of some inverse elasticity problems. J Eng Mech ASCE, 1989, (115): 1302- 1316
[26] Mahnken R,Stein E. A unified approach for parameter identification of inelastic material models in the frame of the finite element method. Computational Method sin Application Mechanical Engineering,1996,136 (3-4):225-258
[27] Mahnken R. A comprehensive study of a multiplicative elastoplasticity model coupled to damage including parameter identification .Computers and Structu -res, 2000,74(2):179-200
[28]刘迪辉,钟志华.Barlat 1991模型的材料参数反求.机械工程学报,2006,42(4):47-51
[29]韩利芬.基于神经网络的薄板冲压成形中的反演问题研究:[湖南大学博士学位论文].长沙:湖南大学,2006,3-6
[30]周磊.基于噪音分布的驾驶室几何参数反求技术:[湖南大学硕士学位论文].长沙:湖南大学,2006,3-7
[31]高晖,李光耀等.基于遗传算法的转向盘性能参数识别.汽车工程,2008,30(5):434-436
[32]谭飞.瞬态响应的一种功能梯度梁的材料参数反求方法:[湖南大学硕士学位论文].长沙:湖南大学,2008,5-7
[33]谭江华,罗文波.橡胶材料分子链网络本构模型的研究进展.材料导报,2008,22(7):31-34
[34]徐立,吴桂忠.有限元分析中橡胶应变能函数的若干形式.橡胶工业,1999,(46):707-711
[35]郑明军.橡胶件的静、动态特性及有限元分析: [北方交通大学硕十学位论文].北京:北方交通大学, 2002,5-20
[36] Marckmann G.Verron E, A theory of network alteration for the Mullins effect. Journal of the mechanics and physics of solids,2002,(50):2011~2028
[37]赵振东,汽车悬架与橡胶衬套的设计机理及对于整车性能影响的研究:[同济大学博士学位论文].上海:同济大学, 2002,45-51
[38]魏泳涛,于建华.橡胶有限元分析之研究.四川联合大学学报,1997(5):78-84
[39] D.J.Chaylton,J. Yang.有限元分析所用橡胶弹性特性的表征方法(袁立译).橡胶译丛,1996(3):182~244
[40] Yeoh O H. Some forms of the strain energy for rubber. Rubber Chem. and Technol,1993 , 66 (5):754~771
[41]朱艳峰.橡胶类材料硬化的本构研究与非线性有限元分析:[广东工业大学硕士学位论文].广州:广东工业大学, 2005,6-15
[42] Charlton D J, Yang J. A review of methods to characterize rubber elastic behavior for use in finite element analysis. Rubber Chem. and Technol. , 1994 ,67 (3) : 481~503
[43] Alan.N.Gent. Engineering with Rubber-How to Design Rubber Components. Hauser publishers.2001
[44]杨晓翔.非线性橡胶材料的有限单元法.北京:石油工业出版社,1999
[45]黄剑龙.基于Mooney-Rivlin模型和Yeoh模型的超弹性橡胶材料有限元分析.橡胶工业,2008,(55):467~471
[46]黄庆专.橡胶Mooney-Rivlin模型及其系数最小二乘解法.热带农业科学,2009(5):20-23
[47]庄茁等译,ABAQUS/Standard有限元软件入门指南.北京:清华大学出版社,150-160
[48]郑明军,王文静等.橡胶Mooney-Rivlin模型力学性能常数的确定.橡胶工业2003(50):462-465
[49]左亮,肖绯雄.橡胶Mooney-Rivlin模型材料系数的一种确定方法.机械制造,2008,(7):38-40
[50]周宏慧,张亚新,黄友剑等.橡胶制品的组合静态性能分析及计算.机械工程师,2009, 6(7):64-66
[51]钟志华,李光耀.薄板冲压成型过程的计算机仿真与应用.北京:北京理工大学出版社, 1998
[52]曹银锋.板料冲压成型仿真过程中的材料参数反求技术研究:[湖南大学硕士学位论文].长沙:湖南大学,2002,4-10
[53]高晖,韩利芬,李光耀等.基于micro GA和有限元的薄板塑性材料参数识别.中国机械工程,2005,16(18):1678-1681.
[54]赵新铭,刘宁,张剑.岩土力学反分析的数值反演方法.水利水电科技进展,2003,23(2):55-58
[55]杨文采.非线性地球物理反演方法:回顾与展望.地球物理学进展,2002,17(2):255-261
[56]李守巨,刘迎曦,冯颖.基于混合遗传算法的动力系统阻尼参数识别方法.计算力学学报,2004,21(5):551-556
[57]傅慧萍,乔志德,张宇文.基于模拟退火算法的水下航行流体动力参数辨识.系统仿真学报,2001,13(4):434-435
[58] Fang K T,Wang Y. Number theoretic methods in statistics.New York,Chapman and Hall,1994,237-245
[59] Schnur D S, Zabaras M. An inverse method for determining elastic material properties and a material interface. International Journal of Numerical Method in Engineering, 1992,33:2039-2057
[60]高晖.汽车接触碰撞仿真中的关键技术研究: [湖南大学博士学位论文].长沙:湖南大学,2007,3-5
[61]张勇.基于近似模型的汽车轻量化优化设计方法: [湖南大学博士学位论文].长沙:湖南大学,2008,14-21
[62]任露泉.试验优化技术.北京:机械工业出版社,1987
[63]王海亮.基于耐撞性数值仿真的汽车车身结构优化设计研究:[上海交通大学博士学位论文].上海:上海交通大学,2002,41-63
[64]龙述尧,刘凯远,胡德安.移动最小二乘近似函数中的样条权函数的研究.湖南大学学报,2003,30(6):10-13
[65]孙光永,李光耀,钟志华,张勇.基于序列响应面法的汽车结构耐撞性多目标粒子群优化设计.机械工程学报,2009, 45(2):224-230
[66]张勇,李光耀,钟志华.基于移动最小二乘响应面方法的整车轻量化设计优化.机械工程学报,2008,44(11):192-196
[67]刘文卿.试验设计.北京:清华大学出版社,2005
[68]曹银锋,李光耀,钟志华.金属成型材料参数反求技术.计算力学学报,2004,21(3):291-296.
[69]危银涛,杨挺青,杜星文.橡胶类材料大变形本构关系及其有限元方法.固体力学学报,1999,20(4):281-289
[70]王梦蛟,王培国,薛广智译.[英]特雷劳尔L R G.橡胶弹性物理力学.北京:化学工业出版社,1982