[雙語(yǔ)翻譯]--外文翻譯---賽車輪胎設(shè)計(jì)中輪胎反包對(duì)輪胎耐久性和操作性影響（英文）

1、Optimization of reinforcement turn-up effect on tyre durability and operating characteristics for racing tyre designX. Yang, O.A. Olatunbosun ?Mechanical Engineering School, University of Birmingham, Edgbaston, Birmingha

2、m B15 2TT, United Kingdoma r t i c l e i n f oArticle history:Available online 28 June 2011Keywords:A. Elastomers and rubberE. Mechanical propertiesF. Elastic behavioura b s t r a c tThe damage occurring around the tyre

3、bead region has been pointed out as one of the causes of criticalfailure during the service life of a tyre. This study investigates the influence of the carcass (body) ply turn-up and bead reinforcement turn-up around th

4、e bead region on tyre durability and operating character-istics using finite element analysis (FEA). A slick motorsport tyre with two carcass plies was modelledin ABAQUS based on the material properties obtained from tes

5、ts and the profile provided by the tyremanufacturer. Various factors including the material property, the cross-section area, the spacing andangles of the reinforcement cords and the height of reinforcement turn-up, were

6、 characterized by numer-ical experiments using the design of experiment (DOE) method. The effects of these parameters on tyredurability and operating characteristics, in terms of mean response analysis of carcass stress,

7、 verticalstiffness, lateral stiffness, cornering stiffness and the strain energy density (SED) of elements in the crit-ical region, were determined from the finite element tyre model. Similarly, optimum reinforcement tur

8、n-up heights were obtained and provided predictive information for tyre design purpose. Furthermore itwas observed, from both experiment and prediction, that the vertical stiffness was rather high for therequirement of t

9、he Formula Student (FS) racing car. In order to reduce the tyre vertical stiffness andimprove the tyre durability, an improved tyre based on the original design but with single carcass plywas proposed. The FEA results on

10、 tyre durability and operating characteristics from both the originaland improved design tyres were compared. The FEA predictions indicated that the improved designmodel was capable of providing the required tyre charact

11、eristics as well as improved tyre durability. Itis therefore proposed that the predictive technology using FEA can be utilized to optimize the tyre rein-forcement turn-up effect in future tyre design.? 2011 Elsevier Ltd.

12、 All rights reserved.1. IntroductionAs the only contact component between vehicle and road, the pneumatic tyre has a challenging role because of its effect on vehi- cle riding comfort, maneuverability, fuel efficiency, e

13、tc. The spring rate of the tyre is usually one of the important operating character- istics considered by most FS racing teams in their choice of tyre. As pointed out by Clarke from FS Germany [1], FS tyres from differen

14、t tyre makers often have different sidewall stiffness and therefore natural spring rate. It is obvious that the sidewall stiffness gives a significant contribution to the tyre operating characteristics. The sidewall vert

15、ical deformation contributes mostly to the tyre vertical stiffness, which affects the riding comfort of the vehicle. Likewise, the sidewall lateral stiffness influences the steering behaviour of the vehicle substantially

16、 as mentioned by Wallentowitz and Gies [2]. The pneumatic tyre is a composite structure constructed from different components including various rubber components andreinforcement [3]. It is observed that reinforcement in

17、 the sidewall area, i.e. carcass ply, determines the sidewall mechanical character- istics. Moreover, all carcass ply ends are wrapped in tension around the tyre bead and the bead reinforcement is located to position the

18、 bead and protect it. Therefore the height of the carcass ply turn-up and bead reinforcement turn-up are believed to influence the verti- cal stiffness and lateral stiffness of tyre sidewalls and hence the cor- nering be

19、haviour of the tyre. Likewise, the spacing, cross-section area, angle and linear elastic modulus of these reinforcement cords also influence the vertical stiffness and lateral stiffness of the tyre sidewall and the corne

20、ring behaviour of the tyre. On the other hand, from the point of view of tyre fatigue and failure, the tyre region hosting the ends of carcass ply turn-up and bead reinforcement turn-up near the bead is one of the two cr

21、itical regions prone to breakage and delamination which may cause high loss of strength of reinforcement under load [3]. Damage to the bead region can cause the tyre to rotate unevenly and even fatigue [4]. The other vul

22、nerable region is the shoulder region around the belt edge. At present, FEA is widely accepted in the tyre industry as the pre- ferred tool for optimizing new tyre designs. Generally, the geometry of tyre cross-section a

23、nd the construction of tyre reinforcement are0261-3069/$ - see front matter ? 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.matdes.2011.06.014? Corresponding author.E-mail addresses: xxy761@bham.ac.uk (X. Yang), o

24、.a.olatunbosun@bham.ac.uk(O.A. Olatunbosun).Materials and Design 35 (2012) 798–809Contents lists available at ScienceDirectMaterials and Designjournal homepage: www.elsevier.com/locate/matdesThese strain energy functions

25、 are represented either in terms of the strain invariants which are functions of the stretch ratios or di- rectly in terms of the stretch ratios. The three strain invariants can be expressed as Eq. (1).I1 ¼ k2 1 

26、54; k2 2 þ k2 3I2 ¼ k2 1k2 2 þ k2 2k2 3 þ k2 3k2 1I3 ¼ k2 1k2 2k2 3ð1ÞFor incompressible material, I3 = 1. The stretch ratio (or stretch) k is defined as the ratio of the deformed gauge

27、 length L divided by theinitial gauge length L0. For only uni-axial tension test, Neo Hookean and Yeoh material constitutive models are suggested and supported by ABAQUS [13]. However, the Neo-Hookean model shows a limit

28、ation that the determination of coefficients from one deformation mode (uni-axial tension) has limited value in predicting behaviour in other deforma- tion modes, as described by Ghosh et al. [14]. Thus, the Yeoh strain

29、energy function (Eq. (2)) which includes only the first principal strain invariant I1 was suggested by Ghosh for modelling hyperelas- tic material properties using uni-axial tension test data.W ¼ C10ðI1 ? 3

30、2; þ C20ðI1 ? 3Þ2 þ C30ðI1 ? 3Þ3 ð2Þwhere W is the Yeoh strain energy function and Ci0 (i = 1, 2, 3) are theconstants to be determined. The stress–strain relation of uni-axial tens

31、ion is given in equation:rðk ? 1=k2Þ ¼ 2C10 þ 4C20ðI1 ? 3Þ þ 6C30ðI1 ? 3Þ2 ð3Þwhere r is the normal stress. The principal stretches are k1 = k and k2 = k3. Therefore

32、,I1 ¼ k2 1 þ k2 2 þ k2 3 ¼ k2 þ 2k ð4ÞThe Yeoh strain energy function in a hyperelastic material modelhas the advantage of covering a much wider range of deformation than other models a

33、nd can also predict the stress–strain behaviourin different deformation modes from data gained in one simple deformation mode like uni-axial tension. Furthermore, it can pre-dict the shear modulus variation with increasi

34、ng deformation. The limitation of Yeoh model is that it cannot interpret the biaxial testproperly since the second principal strain invariant I2 has significantinfluence on the strain energy function. For a biaxial defor

35、mation, the strain energy function is determined by the first and secondstrain invariants. Thus, the proper hyperelastic material model including the second strain invariant is needed to ensure modelvalidity. However, th

36、e biaxial test is more complex than the simple uni-axial test. As a compromise between the material model accu-racy and computational cost, the Yeoh model was used for model-ling the hyperelastic property of rubber herei

37、n. ABAQUS provides an evaluation function to determine the material model constants. Different strain energy functions were used for the evaluation process, and the evaluation procedure for tread rubber is shown in Fig.

38、3. The viscoelastic material property of rubber usually induces dis- sipative losses due to the internal damping effects. In this study, this effect was modelled by the viscoelastic properties in the time domain based on

39、 the stress relaxation test, which is effective and easy to conduct. The objective of this test is to observe the stress response over time when a step change of constant strain is applied to the spec- imen sample instan

40、taneously. The samples were stretched to dif- ferent strain levels and kept for 960 s as shown in Fig. 4. Stress values at different time intervals were recorded. Because the afore- mentioned test was for uni-axial stres

41、s relaxation, the relaxation modulus would be converted into shear stress relaxation in order to satisfy the requirement of evaluation process in ABAQUS [15]. The implementation of the evaluation process for a viscoelast

42、ic model is shown in Fig. 5. It needs to be implemented in conjunc- tion with hyperelastic or linearly elastic material data to obtain the parameters of a Prony series expansion of the dimensionless relaxation modulus. F

43、or details of the above material property test and the evaluated material model constants refer to Yang et al. [15]. Therefore, the hyperelastic material property of rubber was modelled using the Yeoh model in ABAQUS, wh

44、ilst the viscoelastic material property of rubber was also taken into account. In addi- tion, the material property of the reinforcement was considered to be linearly elastic.2.2. Tyre finite element detailsAn axisymmetr

45、ic finite element tyre model was built using ABAQUS based on the tyre structure CAD profile provided by the tyre manufacturer. The rubber components were meshed usingFig. 2. Axisymmetric finite element tyre model.Fig. 3.