橡胶材料的超弹性本构模型在轮胎分析中的应用
摘要
轮胎是汽车承载的主要部件,其结构主要是由橡胶材料构成的,橡胶材料超弹性本构模型的选择和材料常数的准确性对有限元分析的结果起到决定性的作用。
本文对多种超弹性本构模型进行对比并结合工程实际选择了Mooney-Rivlin模型、Neo-Hookean模型和Yeoh模型做重点研究。采用单向拉伸实验测得胎冠胶、胎侧胶、胎肩垫胶、钢丝夹胶、内衬层胶、上三角胶、下三角胶、子口护胶、钢丝包胶等九种轮胎纯橡胶部分的应力应变曲线并通过计算得到每种材料的5%定伸切线模量。根据拉伸实验数据和超弹性的基本理论获得三种超弹性本构模型的材料常数。
建立相应的输入的接口程序,将本文中的三种超弹性模型引入了TYSYS和ANSYS结构分析软件中,采用不同超弹性模型进行了轮胎的充气分析,研究了欠压、常压、超压等不同充气压力下轮胎充气外直径和断面宽度变化,分析了不同超弹性模型的计算结果并和实验结果作了对比。
借助ANSYS软件建立了三维刚性轮辋和刚性地面模型,研究了轮胎与轮辋接触状态下低于30mm下沉量时轮胎断面形状变化。针对橡胶材料采用Yeoh模型和定伸切线模量时下沉量与载荷关系的对比研究。研究了基于Yeoh模型的轮胎与轮辋和地面接触部位法向力和切向力的分布。分析了轮胎接触状态下胎冠胶剪应力与剪应变分布。
本文研究了轮胎分析中的橡胶超弹性本构模型,考查了材料模型对计算结果的影响,为提高轮胎结构分析的精度提供支持。研究了基于超弹性本构模型的轮胎力学性能,为轮胎结构的优化设计提供依据。
Tire is an important bearing part of automobile, which is mainly composed of rubber. The choice of the hyper-elastic constitutive models and the accuracy of the material constants play a decisive role for the finite element analysis.
In this paper, a variety of hyper-elastic models are compared. The Mooney-Rivlin, Neo-Hookean and Yeoh model are choosed according to actual condition. Stress-strain curves of tread rubber, sidewall rubber, shoulder rubber, wire’s filling rubber, inner liner rubber, upper apex rubber, lower apex rubber, toe and heel rubber and steel wire’s wrap rubber are obtained by peformed uniaxial tension test. And then the tangent modulus at definite elongation are gotten. The material constants of the three kinds of hyper-elastic models are obtained according to the uniaxial test data and the basic hyper-elastic theory.
A corresponding interface program is built with introduce the three kinds of hyper-elastic constitutive models to TYSYS and ANSYS by that. Inflation analysis of the tyre with diffent material models are performed by using ANSYS. The overall diameter and the section width are investigated under the underpressure, normalpressure and overpressure. The results are compared with the experiments.
The three-dimensional rigid rim and road model are bulit by using ANSYS. The shape changing of the section, the deformation of the position of the ryre-rim contact are investigated in the state of less than 30mm tyre center sinking under rim-tyre-road contact condition. The sinking-loading curves by using Yeoh model and the tangent modulus at definite elongation are compared. The distribution of normal stress and the tangential stress of rim-tyre-road contact position are studied. The shear stress and strain distribution of tread position are investigated.
Hyperelastic constitutive models in tyre analysis, and the influence of them to the calculation accuracy are studied in this paper, which provides support to the accuracy of tyre structure analysis. The mechanical properties of the tire based on hyperelastic constitutive models are studied, which is important to the optimization design of the radial tire.
本文对多种超弹性本构模型进行对比并结合工程实际选择了Mooney-Rivlin模型、Neo-Hookean模型和Yeoh模型做重点研究。采用单向拉伸实验测得胎冠胶、胎侧胶、胎肩垫胶、钢丝夹胶、内衬层胶、上三角胶、下三角胶、子口护胶、钢丝包胶等九种轮胎纯橡胶部分的应力应变曲线并通过计算得到每种材料的5%定伸切线模量。根据拉伸实验数据和超弹性的基本理论获得三种超弹性本构模型的材料常数。
建立相应的输入的接口程序,将本文中的三种超弹性模型引入了TYSYS和ANSYS结构分析软件中,采用不同超弹性模型进行了轮胎的充气分析,研究了欠压、常压、超压等不同充气压力下轮胎充气外直径和断面宽度变化,分析了不同超弹性模型的计算结果并和实验结果作了对比。
借助ANSYS软件建立了三维刚性轮辋和刚性地面模型,研究了轮胎与轮辋接触状态下低于30mm下沉量时轮胎断面形状变化。针对橡胶材料采用Yeoh模型和定伸切线模量时下沉量与载荷关系的对比研究。研究了基于Yeoh模型的轮胎与轮辋和地面接触部位法向力和切向力的分布。分析了轮胎接触状态下胎冠胶剪应力与剪应变分布。
本文研究了轮胎分析中的橡胶超弹性本构模型,考查了材料模型对计算结果的影响,为提高轮胎结构分析的精度提供支持。研究了基于超弹性本构模型的轮胎力学性能,为轮胎结构的优化设计提供依据。
Tire is an important bearing part of automobile, which is mainly composed of rubber. The choice of the hyper-elastic constitutive models and the accuracy of the material constants play a decisive role for the finite element analysis.
In this paper, a variety of hyper-elastic models are compared. The Mooney-Rivlin, Neo-Hookean and Yeoh model are choosed according to actual condition. Stress-strain curves of tread rubber, sidewall rubber, shoulder rubber, wire’s filling rubber, inner liner rubber, upper apex rubber, lower apex rubber, toe and heel rubber and steel wire’s wrap rubber are obtained by peformed uniaxial tension test. And then the tangent modulus at definite elongation are gotten. The material constants of the three kinds of hyper-elastic models are obtained according to the uniaxial test data and the basic hyper-elastic theory.
A corresponding interface program is built with introduce the three kinds of hyper-elastic constitutive models to TYSYS and ANSYS by that. Inflation analysis of the tyre with diffent material models are performed by using ANSYS. The overall diameter and the section width are investigated under the underpressure, normalpressure and overpressure. The results are compared with the experiments.
The three-dimensional rigid rim and road model are bulit by using ANSYS. The shape changing of the section, the deformation of the position of the ryre-rim contact are investigated in the state of less than 30mm tyre center sinking under rim-tyre-road contact condition. The sinking-loading curves by using Yeoh model and the tangent modulus at definite elongation are compared. The distribution of normal stress and the tangential stress of rim-tyre-road contact position are studied. The shear stress and strain distribution of tread position are investigated.
Hyperelastic constitutive models in tyre analysis, and the influence of them to the calculation accuracy are studied in this paper, which provides support to the accuracy of tyre structure analysis. The mechanical properties of the tire based on hyperelastic constitutive models are studied, which is important to the optimization design of the radial tire.
引文
1 Fazilay Laraba-Abbes ,et al. A new‘tailor2made’methodology for the mecha-nical behavior analysis of rubber-like materials :Ⅱ. Application to the hyperelastic behaviour characterization of a carbon2black filled natural rubber vulcanizate . Polymer , 2003 , 44 (3) : 821~840.
2 Edvige Pucci , et al. A note on the gent model for rubber-likematerials . Rubber Chemistry and Technology , 2002 , 5(5) : 839~851.
3刘勇,杨卫民.轮胎材料与结构的研究进展.轮胎工业. 2002, 22(3):131~135.
4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.
5黄筑平.连续介质力学基础[M].北京:高等教育出版社, 2003.
6朱艳峰,刘锋,黄小清,李丽娟.橡胶材料的本构模型.橡胶工业. 2006, 53(2): 119~125.
7 Arruda E M ,Boyce M C. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. Journal of the Mechanics and Physics of Solids ,1993 , 41 (2) :389~412.
8 Gent A N. A new constitutive relation for rubber. Rubber Chemistry and Technology , 1996 , 69 (1) :59~61.
9 Mooney M J. A theory of large elastic deformation . Journal of Applied Physics , 1940 ,11 (6) :582~592.
10 Tschoegl N W. Constitutive equations for elastomers. Journal of Polymer Science, 1971 (12) :1 959~1 970.
11 Ogden R W. Non-Linear Elastic Deformations. Chichester ,U K: Ellis Horwood , 1984.
12 Yeoh O H. Some forms of the strain energy for rubber . Rubber Chemistry andTechnology ,1993 ,66 (5) :754~771.
13 Valanis K C ,Landel R F. The st rain energy function of a hyperelastic material in terms of t he extension ratios . Journal of Applied Physics ,1967 ,38 (12) :2 997.
13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.
14陈良森,扶名福,兰志文.不可压各向同性超弹性物质的响应函数.南昌大学学报. 2002, 24(4): 7~11.
15范成业,庄茁,黄克智.超弹性材料过盈配合的解析解和数值解.工程力学. 2003, 20(4): 15~18.
17邹雨,庄茁,黄克智.超弹性材料过盈配合的轴对称平面应力解答.工程力学. 2004, 21(6): 72~83.
18于建华,魏泳涛.不可压缩超弹性材料的有限元应力分析.西南交通大学学报. 1998, 33(1): 41~45.
19黄友剑,王明星,张友南.有限元分析中超弹材料模型采用的弹性体试验.特种橡胶制品. 2001, 22(5): 52~55.
20王登祥.轮胎胶料有限元分析的实验基础及计算.轮胎工业. 2000, 18(12): 721~730.
21张治国,郑明军,谢基龙.弹性车轮瞬态动力响应的有限元仿真方法研究.北方交通大学学报. 2003, 27(1): 25~27.
22薛小香,姚振汉,李鹏,李强.子午线轮胎的轴对称非线性有限元分析.橡胶工业. 2003, 50(5): 292~297.
23 J. D. Walter. Cord-Rubber Tire Composites: Theory and Applications. Rubber Chemistry and Technology. 1978,51:525-576
24 J. D. Walter, H. P. Patel. Approximate Expressions for the Elastic Constants of Cord-Rubber Laminates. Rubber Chemistry and Technology. 1979,52:171-183
25 R.Y. Kim, A. S. Crasto. Failure of Carbon Fiber-Reinforced Epoxy Composites under Combined Loading. Proceedings of the Ninth International Conference on Composite Materials (ICCM IX), vol. V, Composites Behavior, A.Miravete, ed., University of Zaragoza, Cambridge, England: Woodhead Publishing Limited, 1993:15-22.
26 S. R. Swanson. Biaxial Failure Criteria for Toughened Resin Carbon/Epoxy Laminates. Proceedings of the American Society for Composites Seventh Technical Conference, Lancaster, PA: Technomic Publishing Co., Inc., 1992:1075-1083
27 R.Y. Kim, A. S. Crasto. An Improved Test Specimen to Determine Composite Compression Strength. Proceedings of the Ninth International Conference on Composite Materials (ICCM IX), vol. V, Composites Properties and Applications, A.Miravete, ed., University of Zaragoza, Cambridge, England: Woodhead Publishing Limited, 1993.p.621-630
28俞淇,周锋,丁剑平,充气轮胎性能与结构,华南理工大学出版社,1998年,
29任旭春,姚振汉,一种新的橡胶-帘线复合材料的模型及其参数识别方案,工程力学, 2006,23(12):180~187.
30 T. Belytschko等,连续体和结构的非线性有限元,庄茁等译,清华大学出版社,2002年
31陆明万,罗学富,弹性理论基础,第二版,清华大学出版社,2001年
32 L. O. Faria, J. T. Oden and Yavari. Tire Modeling by Finite Element. Tire Science and Technology. 1992,20(1):33~56
33 S. K. Clark. A Note on Heat Generation due to Surface Rubbing. Tire Science and Technology. 1975,3(3):89~195
34 A. R.Willia.轮胎的评价.轮胎工业.2003,3(20):135~139
35 A. Ridha and M. Theves.刘大众译.轮胎力学进展.轮胎工业.1995,12(15):737~742
36 Ergin Tonuk, Y. Samim Unlusoy. Prediction of Automobile Tire Cornering Force Characteristics by Finite Element Modeling and Analysis. Computer and Structures. 2001,13(79):1219~1232
37 D. H.Guan, L. H.Yam, M. P, Mignolet. Experimental Modal Analysis of Tire. Experimental Techniques. 2000,24(6):39~45
38 R.W. Scavuzzo, Richards. Tire Vibration Modes and Effects on Vehicle Ride Quality, Tire Science and Technology. 1993,21(1):23~39
39 E. Kung.,李静平.子午线轮胎的径向振动.轮胎工业. 1994, 8:37~43
40 D. C. Prevosek , C. W. Bering and Y. D. Kwon. Application of Fracture Mechanics in Tire Endurance Analysis. Kautschuk Gummi Kunststoffe. 1985,38:363~375
41 J.DeEskinazi, K.Ishihara, H.Voil, and T.C.Warholic, Towards Preedicting Relative Belt Edge Endurance with Finite Element Method. Tire Science and Technology. 1990,18(4):216~236
42闫相桥.轮胎有限元分析技术及其在轮胎结构优选中的应用.固体力学学报. 2001, 22(2): 150~163
43闫相桥,王友善等.子午线轮胎带束层中应力有限元分析.轮胎工业. 2000, 20(8): 463~467
44王友善,刘培华等.有限元分析在轮胎结构设计中的应用.橡胶工业.2005,52(10): 613~617
45王友善,尹海山.载重子午线轮胎带束层端部翘曲分析.轮胎工业. 2006,26(12): 741~745
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59 L.O. Faria, J.M. Bass, J.T. Oden, E.B. Becker, A Three-dimensional rolling contact model for a reinforced rubber tire, Tire Sci. Technol. 17 (3) (1989) 217–233.
60 L.O. Faria et al., Tire modeling by finite elements, Tire Sci. Technol. 20 (1) (1992) 33–56.
61 A.M.Burke, O.A. Olatunbosun, Static tyre-road interaction modelling,Meccanica 32 (1997) 473–479.
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2 Edvige Pucci , et al. A note on the gent model for rubber-likematerials . Rubber Chemistry and Technology , 2002 , 5(5) : 839~851.
3刘勇,杨卫民.轮胎材料与结构的研究进展.轮胎工业. 2002, 22(3):131~135.
4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.
5黄筑平.连续介质力学基础[M].北京:高等教育出版社, 2003.
6朱艳峰,刘锋,黄小清,李丽娟.橡胶材料的本构模型.橡胶工业. 2006, 53(2): 119~125.
7 Arruda E M ,Boyce M C. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. Journal of the Mechanics and Physics of Solids ,1993 , 41 (2) :389~412.
8 Gent A N. A new constitutive relation for rubber. Rubber Chemistry and Technology , 1996 , 69 (1) :59~61.
9 Mooney M J. A theory of large elastic deformation . Journal of Applied Physics , 1940 ,11 (6) :582~592.
10 Tschoegl N W. Constitutive equations for elastomers. Journal of Polymer Science, 1971 (12) :1 959~1 970.
11 Ogden R W. Non-Linear Elastic Deformations. Chichester ,U K: Ellis Horwood , 1984.
12 Yeoh O H. Some forms of the strain energy for rubber . Rubber Chemistry andTechnology ,1993 ,66 (5) :754~771.
13 Valanis K C ,Landel R F. The st rain energy function of a hyperelastic material in terms of t he extension ratios . Journal of Applied Physics ,1967 ,38 (12) :2 997.
13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.
14陈良森,扶名福,兰志文.不可压各向同性超弹性物质的响应函数.南昌大学学报. 2002, 24(4): 7~11.
15范成业,庄茁,黄克智.超弹性材料过盈配合的解析解和数值解.工程力学. 2003, 20(4): 15~18.
17邹雨,庄茁,黄克智.超弹性材料过盈配合的轴对称平面应力解答.工程力学. 2004, 21(6): 72~83.
18于建华,魏泳涛.不可压缩超弹性材料的有限元应力分析.西南交通大学学报. 1998, 33(1): 41~45.
19黄友剑,王明星,张友南.有限元分析中超弹材料模型采用的弹性体试验.特种橡胶制品. 2001, 22(5): 52~55.
20王登祥.轮胎胶料有限元分析的实验基础及计算.轮胎工业. 2000, 18(12): 721~730.
21张治国,郑明军,谢基龙.弹性车轮瞬态动力响应的有限元仿真方法研究.北方交通大学学报. 2003, 27(1): 25~27.
22薛小香,姚振汉,李鹏,李强.子午线轮胎的轴对称非线性有限元分析.橡胶工业. 2003, 50(5): 292~297.
23 J. D. Walter. Cord-Rubber Tire Composites: Theory and Applications. Rubber Chemistry and Technology. 1978,51:525-576
24 J. D. Walter, H. P. Patel. Approximate Expressions for the Elastic Constants of Cord-Rubber Laminates. Rubber Chemistry and Technology. 1979,52:171-183
25 R.Y. Kim, A. S. Crasto. Failure of Carbon Fiber-Reinforced Epoxy Composites under Combined Loading. Proceedings of the Ninth International Conference on Composite Materials (ICCM IX), vol. V, Composites Behavior, A.Miravete, ed., University of Zaragoza, Cambridge, England: Woodhead Publishing Limited, 1993:15-22.
26 S. R. Swanson. Biaxial Failure Criteria for Toughened Resin Carbon/Epoxy Laminates. Proceedings of the American Society for Composites Seventh Technical Conference, Lancaster, PA: Technomic Publishing Co., Inc., 1992:1075-1083
27 R.Y. Kim, A. S. Crasto. An Improved Test Specimen to Determine Composite Compression Strength. Proceedings of the Ninth International Conference on Composite Materials (ICCM IX), vol. V, Composites Properties and Applications, A.Miravete, ed., University of Zaragoza, Cambridge, England: Woodhead Publishing Limited, 1993.p.621-630
28俞淇,周锋,丁剑平,充气轮胎性能与结构,华南理工大学出版社,1998年,
29任旭春,姚振汉,一种新的橡胶-帘线复合材料的模型及其参数识别方案,工程力学, 2006,23(12):180~187.
30 T. Belytschko等,连续体和结构的非线性有限元,庄茁等译,清华大学出版社,2002年
31陆明万,罗学富,弹性理论基础,第二版,清华大学出版社,2001年
32 L. O. Faria, J. T. Oden and Yavari. Tire Modeling by Finite Element. Tire Science and Technology. 1992,20(1):33~56
33 S. K. Clark. A Note on Heat Generation due to Surface Rubbing. Tire Science and Technology. 1975,3(3):89~195
34 A. R.Willia.轮胎的评价.轮胎工业.2003,3(20):135~139
35 A. Ridha and M. Theves.刘大众译.轮胎力学进展.轮胎工业.1995,12(15):737~742
36 Ergin Tonuk, Y. Samim Unlusoy. Prediction of Automobile Tire Cornering Force Characteristics by Finite Element Modeling and Analysis. Computer and Structures. 2001,13(79):1219~1232
37 D. H.Guan, L. H.Yam, M. P, Mignolet. Experimental Modal Analysis of Tire. Experimental Techniques. 2000,24(6):39~45
38 R.W. Scavuzzo, Richards. Tire Vibration Modes and Effects on Vehicle Ride Quality, Tire Science and Technology. 1993,21(1):23~39
39 E. Kung.,李静平.子午线轮胎的径向振动.轮胎工业. 1994, 8:37~43
40 D. C. Prevosek , C. W. Bering and Y. D. Kwon. Application of Fracture Mechanics in Tire Endurance Analysis. Kautschuk Gummi Kunststoffe. 1985,38:363~375
41 J.DeEskinazi, K.Ishihara, H.Voil, and T.C.Warholic, Towards Preedicting Relative Belt Edge Endurance with Finite Element Method. Tire Science and Technology. 1990,18(4):216~236
42闫相桥.轮胎有限元分析技术及其在轮胎结构优选中的应用.固体力学学报. 2001, 22(2): 150~163
43闫相桥,王友善等.子午线轮胎带束层中应力有限元分析.轮胎工业. 2000, 20(8): 463~467
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