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Simulation of tyre–pavement interaction for predicting contact stresses at static and various rolling conditions

Simulation of tyre–pavement interaction for predicting contact stresses at static and various rolling conditions
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  This article was downloaded by: [University of Illinois at Urbana-Champaign]On: 02 August 2013, At: 00:09Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK International Journal of Pavement Engineering Publication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/gpav20 Simulation of tyre–pavement interaction for predictingcontact stresses at static and various rolling conditions Hao Wang a , Imad L. Al-Qadi a & Ilinca Stanciulescu ba Department of Civil and Environmental Engineering, University of Illinois atUrbana–Champaign, Urbana, IL, USA b Department of Civil and Environmental Engineering, Rice University, Houston, TX, USAPublished online: 11 Apr 2011. To cite this article: Hao Wang , Imad L. Al-Qadi & Ilinca Stanciulescu (2012) Simulation of tyre–pavement interaction forpredicting contact stresses at static and various rolling conditions, International Journal of Pavement Engineering, 13:4,310-321, DOI:10.1080/10298436.2011.565767 To link to this article: http://dx.doi.org/10.1080/10298436.2011.565767 PLEASE SCROLL DOWN FOR ARTICLETaylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independentlyverified with primary sources of information.Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content.This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found athttp://www.tandfonline.com/page/terms-and-conditions  Simulation of tyre–pavement interaction for predicting contact stressesat static and various rolling conditions Hao Wang a * † , Imad L. Al-Qadi a and Ilinca Stanciulescu b a  Department of Civil and Environmental Engineering, University of Illinois at Urbana–Champaign, Urbana, IL, USA; b  Department of Civil and Environmental Engineering, Rice University, Houston, TX, USA (  Received 3 November 2010; final version received 19 February 2011 ) This paper describes the development of a 3D tyre–pavement interaction model to predict the tyre–pavement contact stressdistributions for future use in the mechanistic analysis of pavement responses. The ribbed radial-ply tyre was modelled as acomposite structure (rubber and reinforcement), and the tyre material parameters were calibrated through load-deflectioncurves. The steady-state tyre rolling process was simulated using an arbitrary Lagrangian Eulerian formulation. The modelresults are consistent with previous measurements and validate the existence of non-uniform vertical contact stresses andlocalised tangential contact stresses. The analysis results show that the non-uniformity of vertical contact stresses decreasesas the load increases, but increases as the inflation pressure increases. However, vehicle manoeuvring behavioursignificantly affects the tyre–pavement contact stress distributions. For example, tyre braking/acceleration inducessignificant longitudinalcontact stresses, while tyre corneringcauses the peakcontact stresses shifting towards oneside of thecontact patch. The model results provide valuable insights into understanding the realistic tyre–pavement interaction foranalysing pavement responses at critical loading conditions. Keywords: tyre–pavement interaction; contact stress; static; free rolling; braking; cornering Introduction Tyres serve many important purposes for a travellingvehicle including cushioning the vehicle against roadroughness, controlling stability, generating manoeuvringforces and providing safety, among others. Tyre type andconfiguration also affect pavement performance becausethe tyre imprint area transmits contact stresses to thepavement surface. Many studies have shown that theassumptions of contact stress distributions between tyresand pavement have significant effects on the prediction of pavement responses and performance (De Beer et al. 2002;Elseifi et al. 2005; Al-Qadi and Yoo 2007; Al-Qadi et al. 2008; Wang and Al-Qadi 2010). Previous researches have already proved that verticalcontact stresses under a loaded tyre are non-uniform, andtangential contact stresses are developed at the tyre–pavement interface (Tielking and Abraham 1994; De Beer et al. 1997). However, the exact distributions of thesecontact stresses are complex and depend on many factors,such as tyre type (bias-ply orradial-ply,dual tyres or singlewide-base tyre), tyre structure (geometry, tread pattern,rubber and reinforcement), pavement surface condition(texture and roughness), loading condition (wheel load andinflation pressure) and tyre rolling condition (free rolling,acceleration, braking and cornering). Tyre–pavement contact stresses can be measuredusing various experimental devices, including pressurecells, tri-axial pressure transducer, piezoelectric sensors,pressure-sensitive films and ultrasonic waves (Tielkingand Abraham 1994; De Beer et al. 1997; Douglas et al. 2000; Pau et al. 2008). However, these measurementmethods are expensive and time consuming. In addition,the accuracy of the measurement depends on the interfacefriction between the tyre and measurement sensors, thesize and resolution of measurement sensors, the spaceinterval of measurement sensors in the contact area, theloaded surface characteristics, the rolling speed and theapplied driving force. During experiments, it is generallydifficult to consider all the tyre loading and operatingvariables because of the extensive large testing matrix andthe measurement difficulties associated with a rolling tyre. Therefore, development of a theoretical approach tosimulate tyre–pavement interaction would provide sig-nificant benefits. The simulation would show thecomparative interface stress distributions under varioustyre loading and rolling conditions. These analyses wouldprovide valuable insights into the load distributionmechanisms at the tyre–pavement interface, especiallyfrom a pavement design/analysis point of view. Theresearch presented in this paper describes the development ISSN 1029-8436 print/ISSN 1477-268X online q 2012 Taylor & Francishttp://dx.doi.org/10.1080/10298436.2011.565767http://www.tandfonline.com *Corresponding author. Email: hwang.cee@rutgers.edu†Present address: Rutgers, The State University of New Jersey, 623 Bowser Road, Piscataway, NJ 08854, USA.  International Journal of Pavement Engineering Vol. 13, No. 4, August 2012, 310–321    D  o  w  n   l  o  a   d  e   d   b  y   [   U  n   i  v  e  r  s   i   t  y  o   f   I   l   l   i  n  o   i  s  a   t   U  r   b  a  n  a  -   C   h  a  m  p  a   i  g  n   ]  a   t   0   0  :   0   9   0   2   A  u  g  u  s   t   2   0   1   3  of the aforementioned type of model and details theinsights this theoretical approach can provide into tyre–pavement interaction. Background on tyre models The two main types of tyres are bias-ply and radial-plytyres. The radial-ply tyre has become more popularbecause it causes less rolling resistance and heatgeneration compared to the bias-ply tyre. The typicalstructure of a radial-ply tyre is shown in Figure 1. Theradial-ply tyre has one or more layers of radial plies in therubber carcass with a crown angle of 90 8 . The crown angleis defined as the angle between the ply and thecircumferential line of the tyre. In addition, several layersof belts are laid under the tread rubber at a low crownangle. The radial ply and belt layers enhance the rigidity of the tyre and stabilise it in the radial and lateral directions.The tread layer of the tyre is usually patterned withlongitudinal or transverse grooves and serves as a wear-resistance layer that provides sufficient frictional contactwith the pavement and minimises hydroplaning throughgood drainage of water in wet conditions (Wong 1993).The tyre industry developed many simplified physicalmodels to predict tyre performance. These include theclassical spring-damper model, the tyre ring model and themembrane and shell model (Knothe et al. 2001). However,these models are usually unsuitable for quantitativeprediction of tyre–pavement contact stresses. Generalpurpose finite element (FE) software programs developedin the mid-1990s, such as ABAQUS, ANSYS, ADINA,provide more tools to simulate 3D tyre behaviour withrollingcontact.Asurveyofexistingliteraturerevealsmanypublished works on an FE modelling of a tyre by computersimulation. The complexity of tyre models varies,depending on the features built into the model, includingFE formulation (Lagrangian, Eulerian or arbitrary Lagran-gian Eulerian, ALE), material models (linear elastic,hyperelastic or viscoelastic), type of time domain(transient or steady state) and type of analysis (isothermal,non-isothermal or thermo-mechanical). Such tyre modelsallow one to analyse the energy loss (rolling resistance),tyre–terraininteraction,steady-stateortransientresponses,vibration and noise, and tyre failure and stability. From a pavement perspective, the contact stressesdeveloped at the tyre–pavement surface have been studiedbecause they determine the stresses caused in thepavement structure. Tielking and Roberts (1987) devel-oped an FE model of bias-ply tyre for analysing the effectof inflation pressure and load on tyre–pavement contactstresses. The pavement was modelled as a rigid flatsurface, and the tyre was modelled as an assembly of axisymmetric shell elements positioned along the carcassmid-ply surface. Zhang (2001) built a truck tyre modelusing ANSYS and analysed the inter-ply shear stressesbetween the belt and carcass layers as a function of normalloads and pressures. Shoop (2001) simulated the coupledtyre–terrain interaction and analysed the plastic defor-mation of soft soil/snow using an ALE adaptive meshformulation. He suggested that the assumption of a rigidtyre might be suitable for soft terrain analysis. Roque et al. (2000) used a simple strip model to simulate the crosssection of a tyre and concluded that the measurement of contact stresses using devices with rigid foundation wassuitable for the prediction of pavement responses. Meng(2002) modelled a low-profile radial smooth tyre on rigidpavement surface using ABAQUS and analysed thevertical contact stress distributions under various tyreloading conditions. Ghoreishy et al. (2007) developed a3D FE model for a 155/65R13 steel-belted tyre and carriedout a series of parametric analyses. They found that thebelt angle was the most important constructional variablefor tyre behaviour, and the change of friction coefficienthad great influence on the pressure field and relative shearbetween tyre treads and road. Objective and scope Thispaperpresentsthedevelopmentofa3DFEmodelofanair-inflated ribbed tyre and the simulated interactionbetween this tyre and a non-deformable pavement surface.Initially, static vertical and transverse contact stresses at thetyre–pavement interface were analysed and compared withthe previously collected experimental measurements. Uponthe validation of the developed model, tyre–pavementcontact stresses at various rolling conditions (free rolling,braking/acceleration and cornering) were investigated.Thesepredictedcontactstressesprovidetherealisticloadinginput for the mechanistic analysis of pavement responses. Simulation of tyre–pavement interaction  Descriptions of tyre model  Theoretically, a tyre model should consider three maincharacteristics: (1) the composite structure and the Radial plyBeadsSteel beltsRibsSidewallGrooves Figure 1. Schematic illustration of a radial-ply tyre (fromMichelin Website dated on 27 July 2010).  International Journal of Pavement Engineering 311    D  o  w  n   l  o  a   d  e   d   b  y   [   U  n   i  v  e  r  s   i   t  y  o   f   I   l   l   i  n  o   i  s  a   t   U  r   b  a  n  a  -   C   h  a  m  p  a   i  g  n   ]  a   t   0   0  :   0   9   0   2   A  u  g  u  s   t   2   0   1   3  anisotropy due to the significant difference in stiffnessbetween rubber and reinforcement, (2) the relatively largedeformationduetoflexibilityoftyrecarcassduringcontactwith pavement surface and (3) the near-incompressibilityand the non linearity of rubber material (Wong 1993).The tyre models commonly used for tyre design purposesmust accurately predict the deformation of the whole tyreand the interaction of internal components as well. Thisstudy focuses on tyre deformation with respect to thecontact region and the resulted contact stress distributionsat the tyre–pavement interface. This focus allows for thedevelopment of relatively simple models to ensure highcomputational efficiency.The cross-sectional views of the modelled radial-plytyre having five longitudinal ribs are shown in Figure2(a),(b).Theouterradiusofthetyreis506mm,andthetyreheight is 220mm. The wall-to-wall tyre width is 275mmand the contact width, including ribs and grooves, isapproximately200mm.Thetyrethicknessinthetreadareais 18mm with 13-mm tread depth. The width of each rib isaround 30mm with 10-mm grooves between adjacent ribs.Thetyremodelcomprisesoneradialply,twosteelbeltsandarubbercarcass(sidewallandtread).Thetwosteelbeltsareoriented at þ 20 8 and 2 20 8 with respect to the hoop(circumferential) direction, while the radial ply isperpendicular to the circumferential direction of the tyre.Thetwosteelbeltsarelocatedapproximately15and17mmaway from the outer surface of the tread, respectively.The rim was modelled as a rigid body and in contact withthe bead at the end of sidewall. To optimise computationspeed and resolution, a finer mesh was chosen for aroundthe tread zone, and a coarse mesh was used in the sidewall.The FE tyre model was built in two steps. First, a 2Daxisymmetric tyre model was built with four-nodeaxisymmetric continuum elements for rubber. Thesebilinear elements allow for the consideration of twistingthe rubber-cord composite that generally takes place intyres during loading. The radial ply and layered steel beltswere modelled as surface membrane elements withembedded rebar layers. These reinforced surface mem-brane elements were embedded in ‘host’ continuumelements. Then, the 3D tyre model was generated byrevolving the 2D mesh around its symmetric axis usingsymmetric result transfer and symmetric model generationcapability in ABAQUS (2007).  Modelling tyre–pavement interaction The tyre–pavement interaction is essentially a rollingcontact problem. Several challenges exist when modellingthe tyre–pavement interaction via a two-solid contactmechanics approach, such as nonlinear material propertiesof pavement layers, transient contact conditions, large tyredeformation, intricate structure of the tyre and nonlinearfrictional interface (Laursen and Stanciulescu 2006). Dueto the complexity of the problem, it is difficult to solve thetyre–pavement contact problem via a two-solid contactmechanics approach. In this study, the pavement was TreadBelt(a)(b)(d)(c)SidewallRadial plyBead Figure 2. Simulation of tyre–pavement interaction: (a) cross section of tyre structure, (b) cross section of tyre mesh, (c) inflating tyrewith internal pressure, and (d) applying load on tyre and rolling.  H. Wang et al. 312    D  o  w  n   l  o  a   d  e   d   b  y   [   U  n   i  v  e  r  s   i   t  y  o   f   I   l   l   i  n  o   i  s  a   t   U  r   b  a  n  a  -   C   h  a  m  p  a   i  g  n   ]  a   t   0   0  :   0   9   0   2   A  u  g  u  s   t   2   0   1   3  modelled as a non-deformableflat surface to achieve bettercomputation efficiency. This assumption is consideredreasonable because the tyre deformation is much greaterthan the pavement deflection when wheel load is appliedon the tyre and transmitted to the pavement surface.The tyre–pavement interaction was simulated in threeprogressive steps, as shown in Figure 2(c),(d). First, anaxisymmetric tyre model was loaded with uniforminflation pressure at its inner surface. Second, a 3D tyremodel was generated and simulated in contact withpavement under the applied vertical load. To consider thelarge tyre deformation, large displacement formulationand geometry nonlinearity in ABAQUS were used.Finally, the tyre was rolled on the rigid flat surface atvariousangularvelocitiesandtransportvelocities.Thetyrerolling process was modelled using the steady-statetransport analysis in ABAQUS. The steady-state transportanalysis utilises implicit dynamic analysis and considersthe tyre inertia and the frictional effects at the tyre–pavement interface (ABAQUS 2007).In the steady-state transport analysis, the ALEformulation was used rather than traditional Lagrange orEulerian formulations (Nackenhorst 2004). The ALE usesa moving reference frame, in which rigid body rotation isdescribedinanEulerianformulationandthedeformationisdescribed in a Lagrange formulation. This kinematicdescription converts the steady-state moving contactproblem into a pure spatially dependent simulation. Thus,the mesh needs to be refined only in the contact region.Hence, a mesh convergence analysis was performed with aseries of progressively finer FE meshes. The predictedcontact stress results were compared for each mesh untilchanges in numerical results were , 5% (Figure 3).The contact between the tyre and pavement surfaceconsists of two components: one that is normal to thesurfaces and the other that is tangential to the surfaces. Thetreatment of the normal contact condition is to enforceimpenetrability in the normal direction using the penaltymethod or Lagrange multipliers method. However, for thetangential interaction between two contacting surfaces, thetypical Coulomb friction law is used (Wriggers 2002).This model assumes that the resistance to movement isproportional to the normal stress at an interface. In thiscase, the interface may resist movement up to a certainlevel; then the two contacting surfaces at the interface startto slide relative to each another. If the relative motionoccurs, the frictional stress remains constant and the stressmagnitude is equal to the normal stress at the interfacemultiplied by the friction coefficient. Contact stress verification The study focuses on the contact patch shape and stressdistribution at the tyre–pavement interface rather than theinternal stresses in the tyre structure. Rubber is a near-incompressible and hyperelastic material with viscoelas-ticity. However, tyre manufacturers usually do not revealinformation on material properties and tyre structure.Hence, the rubber was simulated as linear elastic materialwith a Poisson’s ratio close to 0.5. Different parts of rubberelements (sidewall, shoulder, belt rubber and tread) weremodelled having variable elastic stiffness. The steelreinforcements (radial ply and belts) were modelled as alinear elastic material.Tyre load-deflection curves from experimentalmeasurements were used to calibrate the tyre modelparameters. The elastic properties of rubber and ply/beltreinforcement were adjusted to obtain deflection valuesclose to experimental measurements provided by tyremanufacturer. The initial elastic modulus of eachcomponent was based on tyre models in the literature(Zhang 2001; Ghoreishy et al. 2007). Sensitivity analysisshowed that tyre deflection is primarily affected by radialply, sidewall stiffness and the steel belt crown angles.Good agreements were achieved between the predictedand measured deflections under various loading and tyrepressure levels as shown in Figure 4. The final selectedelastic material properties of each tyre component arepresented in Table 1. To examine the accuracy of the developed model, thepredicted contact stresses at the tyre–pavement interface 5006007008009001000020406080Circular sectors in contact area    V  e  r   t   i  c  a   l  c  o  n   t  a  c   t  s   t  r  e  s  s   (   k   P  a   ) 050100150200020406080Circular sectors in contact area    L  o  n  g   i   t  u   d   i  n  a   l  c  o  n   t  a  c   t  s   t  r  e  s  s   (   k   P  a   ) (a)(b) Figure 3. Mesh convergences of (a) vertical and (b) longitudinal contact stresses.  International Journal of Pavement Engineering 313    D  o  w  n   l  o  a   d  e   d   b  y   [   U  n   i  v  e  r  s   i   t  y  o   f   I   l   l   i  n  o   i  s  a   t   U  r   b  a  n  a  -   C   h  a  m  p  a   i  g  n   ]  a   t   0   0  :   0   9   0   2   A  u  g  u  s   t   2   0   1   3
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