8/14/2019 euc98_04

1/11

Presented at European Adams users conference November 18 th 19 th 1998 Paris

NON-LINEAR MODAL ROLLING TYRE MODEL FOR DYNAMICSIMULATION WITH ADAMS

F. Mancosu, D. Da Re Pirelli Pneumatici Spa - D. Minen MDI Italy

1 The problem: road noise simulation

The prediction and the optimization (reduction)of the vehicle vibrations (low and highfrequencies 0-400 Hz) are an important goal inthe car optimization.The vibration sources in a running vehicle aredifferent: an important effort is coming from theinteraction between the road/tyre/vehicleensemble. The simulation of this interaction (in arunning car over a road profile) can help theunderstanding of the phenomena and can giveopportunity of sensitivity analysis andoptimizations without any physical constructions.The full system to be implemented in the

road/tyre/vehicle ensemble has to be validated(in time domain) taking into account signal in thefrequencies range of 0-400 Hz. This is the typicalrange of the road-noise phenomena.The simulation has to consider the realcharacteristics of the single components (road,tyre, and vehicle).

2 - The actors: road, tyres, and vehicleIt is important to define the actors (road, tyres,and vehicle) in a way that reproduces the realbehaviour of the components.In particular:

a) The road has to be represented physicallywith the right profile in 3D: see fig 1;

b) The tyre has to be defined considering:b1) the real modal characteristics up to 400

Hz (dumping included)b2) how the tyre reads the road profile in

vertical , longitudinal (brush model).c) The vehicle has to be represented taking in

account all the components influencing theforces generation.

Fig. 1: example of 3D road profile obtained byexperimental laser profile-meter

3 - Modeling the actorsThe actors have to be modeled considering that

the final road/tyre/vehicle ensemble has to beused in a common code for the simulations. It issimple to manage some pre-processor for thesub-model, but the common code has to be ableto include easily the modeling of the singledifferent components. The more usefully codefor the simulation is a multi-body code(ADAMS).In the past, practical design and analysis of multi-body, large displacement/small strain mechanicalsystems has been difficult due to the limitationsimposed by commercial analysis software. Nosingle software package was capable of " doing it

all ", and the resulting approximations and tediumof translating data among various packagesserved as a barrier to those seeking to performthe incorporation of flexible body informationinto ADAMS, or generation of more accuratecomponent dynamic loads for FEM codes.Such conditions led to the use of necessary,though not always adequate, approximations bypracticing engineers: the use of Guyan reductionfollowed by a forced mass lumping to modelflexible components in ADAMS, and the"guesstimation" of critical dynamic loadingconditions in FEM code. The recent introduction

of ADAMS/Flex has overcome many of theproblems associated with analysis of flexiblemultibody dynamics by employing flexibleelements whose component modes-based data isprovided by finite element codes.A procedure to realize the interface from FEMcode, as HKS/ABAQUS, to ADAMS is nowavailable. It provides an output file (.fil) forquantities such as physical mass, modal mass andstiffness, component modes, etc., for componentswhich had first been built as superelementmodels. An external translator utility (fil2mnf,first prototype release) completes the process,

reading the .fil file, modifying it (it realizes theorthogonalization procedure), and subsequentlywriting the data into a form which could be readas input to ADAMS (Modal Neutral File format).More, the obtained .mnf file could be completelymanaged by the new MNF toolkit (especially forInvariant calculation and Graphic reduction),obtaining a size-reduced .mnf file which containsall flexible data for flexible multibody analysis.

8/14/2019 euc98_04

2/11

2

Interfacing a Finite Element program with aLarge Displacement Multibody Dynamicsprogram achieves two very desirable goals:

ADAMS mechanical system model fidelitymay be dramatically enhanced when

component flexibility is accounted for

Realistic loads for a FEM analyses may beobtained in a natural way by incorporating aFEM model of a component in an ADAMSmechanical system model and simulating in-service events.

3.1 The Road3.1.1 Current implementationThe road is shown ad a meshed surface whichpenetrates into the Flexible tyre (see fig.2).A new extended 3D contact algorithm is

currently under development at MDI, and cantake care of flexible contacting bodies.Preliminary examples of application togetherwith a short description of the theoretical basis of the algorithm are shown hereby.The procedure for detecting a compenetrationcondition between a Flexible Body and a meshedtriangular surface and could be summarized intothe following steps:

1. An high speed searching algorithm findspotential road contact elements, described astriangular polygons;

2. A vector line along the Z-axis of a Markerbelonging to the Flexible Body is drawn;

3. The intersection Point where the Z-axis andthe Road Surface intersect is computed (j-point, see fig.1);

4. dz(i,j,i) and vz(i,j,i) are then computed asoutputs (j= computed road contact point);

5. A SFOSUB routine generates a force on i-Marker based on dz and vz.

The speed of the searching algorithm is almostindependent from the number of road elements.A search radius parameter can be supplied for

optimizing the search area.

i-markers on Flex Body

Road Profile

Flex Tire Profile

j-points on Flex Body

Fig. 2: detail of the deformation of the flexibletyre on a road profile

3.1.2 On going developmentTo avoid situations like those presented below, anew algorithm to detect compenetration betweenground irregularities and Flex Tyre needs to beintroduced. The Flex Tyre model is ideallydivided into several wedges: each wedge has a base constituted by i-

markers belonging to the deformable tyresurface, and therefore its volume issubjected to changes at each iteration step

at every iteration, the intersecting volumebetween the wedge and the 3D road profileis computed

by means of a look-up table derived fromFE, the resulting volume penetration load islumped to the nodes that constitute the baseof the wedge, proportionally to the distancefrom the center of gravity of the penetratingvolume

a proportional force is applied to each of thebase markers

3.2 Tyre generality3.2.1 Fea model: non-rolling tyreThe first step to describe the dynamic behaviorof the tyre is a finite element simulation. Thefinite element model describes any geometricaland physical characteristics of the tyre. Thedimensions and the complexity of the modeldont allow the simulation in the time domain.It is fundamental a good experimentalcharacterization of the static and dynamicproperties of the materials: all the data of themodel was obtained by experimental testsperformed both on rubber compound andreinforcing materials. The compound is staticallytested with tensile, compression and shearstresses to achieve a meaningful hyperelasticformulation of the strong non-linear behavior.

8/14/2019 euc98_04

3/11

3

The dynamic characterization was necessary todescribe the frequency-dependent properties, interms of elastic and hysteretic behavior. Thereinforcing materials, such as carcass and belts,have been also experimentally tested to achieveboth the positive part of the stress-strain curve

and the negative part, using a specialmethodology and device set up by Pirelli. Infigure 3 is shown an example of the dependenceof the elastic modulus from the frequency.

TREAD COMPOUND PROPERTIES

5.2

5.4

5.6

5.8

6

6.2

6.4

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

FREQUENCY[Hz]

[ M P a ]

ELASTIC MODULUS[ MPa]

Fig. 3: variations of the elastic modulus of atread compounds with the frequency.

The reinforcing material was implemented insidethe rubber element as additional stiffness asfunction of the properties of the cordsthemselves. The rubber compound propertieshave been implemented using a hyperelasticformulation (Mooney Rivlin).The finite element model is made up of 20thousands of brick elements (linear shapefunctions, 8 nodes each element) that givesomething like 80 thousands degrees of freedom.The model was generated in an axisymmetricway and it has been demonstrated that requires atleast 48 wedges to be able to properly evaluatethe eigenfrequency up to about 150 Hz. In thisspecific case an 80 wedges model was built toinvestigate higher frequencies, up to 400 Hz. Thehigher is the maximum frequency of interest thefiner should be the mesh of the model and thelonger is the computational time. In figure 4 isshown an example of mode shape at 131.4 Hz.To represent the real static working conditions of the tyre, it was carried out a preliminary set of analysis like the mounting on the rim, theinflation and the deflection with a specifiedvertical load. These analyses show strong non-linearity due to the contact kinematics and to thematerials. After these analysis some steady stateanalysis was performed in order to calculate themodal damping associated to each eigenvalue,

comparing the amplitude of the response at theeigenfrequencies with respect to the staticresponse.The steady state analysis is a linearized responseto harmonic excitation based on the physicaldegrees of freedom of the model. The response

can be achieved through the direct solution of theequations in matrix form, where the stiffness anddamping matrices are updated each frequencysince the definition of the isotropic linearviscoelasticity allows evaluating stiffness anddamping matrices as function of the frequency.While the response in this analysis is for linearvibrations, the prior static response is stronglynonlinear and the initial stress effects (stressstiffening) are included in the steady stateresponse.The finite element model can give any kind of data about any nodes of the model itself but it is

a huge model, unable to be used for time domaindynamic simulations. As a consequence a strongreduction of the physical degrees of freedom isneeded. Since the tyre acts as an interfacebetween the road and the hub it is advisable toretain just the degrees of freedom of the nodesinvolved in the foot print area and the degrees of freedom of the rim, which has to be linked to thehub.

Fig.4: Example of mode shape, which occurs at 131.4 Hz.

The reduction of the degrees of freedom can be

made, once known the stiffness matrix and all theapplied loads, through a rearrangement of the fullstiffness matrix. This procedure uses noapproximations. The nonlinear response, due tothe materials and the contact between tread androad surface, which occurs during the static pre-analysis, has been defined as pre-load prior to theelimination of the degrees of freedom. As aconsequence it has took into account the

8/14/2019 euc98_04

4/11

4

stiffening behaviour by pre-loading in ageometrically nonlinear analysis: stress stiffeningeffects has been included when the rearrangedstiffness matrix was created.While the reduced stiffness matrix uses noapproximations, the mass matrix needs more

degrees of freedom than just the ones, whichrefer to the nodes, involved into the contactpatch. Therefore some eigenmodes amplitudewas restrained as additional degrees of freedom:in this way the choosing of the retained degreesof freedom is no longer critical in order to get anaccurate mass matrix representation.

3.2.2 The brush model: rolling-tyre.Discretisation of the tread pattern

The road unevenness excites the tyre dynamics,and slipping phenomena in the contact patch canarise. For the simulation of these phenomena in

the foot print area, in lateral and tangentialdirections, a discrete brush model has beenimplemented. This model takes into account themain characteristics of the tread: slip stiffness,pitch sequences and size of the contact zone.

The discrete brush model is represented asindividual elastic elements linked to the tyre belt.Tangential and lateral slip velocities can resultfrom the tyre dynamics, and consequently thetread elements will have a shear deformation.The maximum deformation of the tread elementsis limited by the friction coefficient between the

tyre and the road.Nevertheless the values of longitudinal andlateral slip, due to the roughness of the road, arepretty small; therefore all brush elements in thecontact patch adhere to the road surface.

The elastic forces, which arise in the contactzone, depend on the slip stiffness, in tangentialand lateral directions, and the shear deformation.These forces are function of the contact patchsize, the tread pattern and the elastic modulus of the tread compound.In particular the size and shape of the contact

depend on the tyre structure; the stiffness of thetread elements is affected from the pitchsequences of the tread pattern. Finally, the slipstiffness of the tread elements also depends onthe tread compound.

According to the Lagrange method, we followthe tread elements from the entry to the exit of the contact. In fact, just the elements in contactwith the road will generate forces during rolling.

The tread elements will enter and leave thecontact patch with a law that depends on thepitch sequences.

In this case, the tread has been discretized withn elements and their deformation and position

in the contact patch is considered only at discretetime intervals. For example, in the tangentialdirection, at a time interval t , the position of thetread element increases by s, and thedeformation by u . Denoting with V r the rollingspeed, the following relationships subsist:

s = V r t

u = V sxt

where V sx is the slip velocity.For the generic tread element i in the contact

zone, the position and the deformation changeduring the rolling:

s i (t + t) = s i ( t) + s

u i (t + t) = u i ( t) + u

The deformation multiplied for the tread elementstiffness C cpi gives the local longitudinal force:the sum of these local forces over the contactpatch gives the total longitudinal force at a time t :

F C uc cpii

ni=

=

1

The tread elements stiffness C cpi has beendetermined by an internal Code (user subroutinewritten in Fortran and implemented in ADAMS),that is able to calculate those stiffness directlyanalyzing the tread pattern in the contact zone.The same procedure applies to the tangentialforce to evaluate the lateral force. In this case,the tread element deformation is due to the slipvelocity V sy in the lateral direction.

Therefore the simple modal model can simulatethe rolling conditions when linked to the discretecontact model. In fact, the modal modelreproduces only the eigenfrequencies andeigenmodes of the non-rolling tyre. All thedynamic effects affected from the forwardvelocity are neglected, such as, for example, theincrease of the first longitudinal mode relativedamping with the velocity of the of the tyre

8/14/2019 euc98_04

5/11

5

closed to 35 Hz. As well known, the relativedamping variation depends on the slipphenomena in the contact patch.For these reasons a discrete brush model (fig. 5)has been used as tyre-road interface of the modalmodel.

Vsx

Vx

Xe

Xi

u

a

Fig.5: discrete brush model

3.3 VehicleThe results presented in this paper are obtainedusing a fixed hub (cleat test) or a simple single-suspension (running on uneven road). Howeverwe can join the flexible body in each way to thechassis (through rigid joint or taking into accountof hub compliance) of a full vehicle model.

4. Component mode synthesisThe following chapters describe how the flexiblebody is taken into account in the ADAMSenvironment

4.1 The CMS approach (ComponentModes Synthesis)

A brief review of dynamic reduction techniquesin FEA code follows: this section will presentGuyan Reduction, Generalized DynamicReduction (GDR) and Component ModalSynthesis (CMS).Lets define the f -set, the degrees of freedomwhich are unconstrained (free) in dynamicanalysis. These are what remain of the g-set (allof the structural, or grid, degrees of freedom)after removal of the s-set (degrees of freedomeliminated by single point constraints) and the m-set (degrees of freedom eliminated by multipointconstraints). The f -set equations of dynamicequilibrium are

f f ff f ff f ff PuK u Bu M =++ &&& (1)

In dynamic analysis, we often have more finiteelement data than is necessary to obtain adequate

estimates of dynamic behavior. We may reduceour solution set by partitioning the f -set into the a(analysis)-set and the o-set (omitted degrees of freedom):

=

++

o

a

o

a

oooa

aoaa

o

a

oooa

aoaa

o

a

oooa

aoaa

P

P

u

u

K K

K K

u

u

B B

B B

u

u

M M

M M

&

&

&&

&&

(2)

Though equally valid for non-superelement(residual structure only) models, eq. (2) is mostfamiliar in the superelement context, with the a -set frequently referred to as the exterior, orboundary, degrees of freedom and the o-set, theinterior.

For static only, we have two sets of equations intwo unknown variable sets ( a and o), allowing aunique (uncoupled) solution for each. Solvingfor the lower partition of eq. (2) without massand damping leads to:

oooaoaooo PK uK K u11 += (3)

or,

ooaoao uuGu += (4)

Note that the solution for the ou interior degreesof freedom consists of two parts: the

aoa uG response to boundary displacements, and

the oou , or fixed-boundary solution to interiorloading. The static condensation results in eq.(4) suggest a framework for approximating thecoupled dynamic equations in (2).

A consistent way of presenting the variousapproximate dynamic reduction techniques isthrough the use of symmetric transformations.We can introduce the transformation:

{ } == oo

a

oooa

aa

o

a f u

u

I G

o I

u

uu (5)

which is just the static condensation in matrixform. Eq. (5) and its time derivatives can beused to transform eq. (2), which, ignoringdamping, is:

8/14/2019 euc98_04

6/11

6

=+

o

aoo

a

oo

aaoo

a

oooa

aoaa

P

P

u

u

K o

oK

u

u

M M

M M &&&&

(6)

The advantage of eq. (6) is that the dynamicreduction techniques in FEM code can all beconveniently explained in terms of their

corresponding oou approximations.

Guyan Reduction simply assumes:

aoao uGu &&&& = (7)

or, 0oou&& . The resultant upper partition of eq.(6) can thus be immediately solved for the a -setdegrees of freedom.Generalized Dynamic Reduction uses

approximate mode shapes to approximate the ooudegrees of freedom (Experimentally obtainedmode shapes could be used just as well.).Component Modes offer a further logicalextension by using the o-set eigenvectors to

approximate oou . We can simply write:

=q

a

oqoa

aa

o

a

u

u

G

o I

u

u

(8)

The q-set has been introduced to representgeneralized degrees of freedom in dynamicanalysis. The q-set is included as a partition of the a -set, and the t -set partition of the a -set isused to more clearly identify the "total" physicaldegrees of freedom on the boundary, hence:

[ ]{ }aq

t

oqot

tt

o

a uu

u

G

o I

u

u ==

(9)

where the prime in au has been introducedsimply to distinguish the previous physicalboundary degrees of freedom only set from the a -set. Each column of the first partition of represents the component's displacements dueto boundary motion and are frequently referred toas "constraint modes." The modes of the secondpartition are, upon proper transformation,referred to as the fixed boundary, or

"component" modes. 1 Use of the coordinatetransformation (9) yields a set of compact,stiffness-uncoupled, equations of a -set dynamicequilibrium. Since the basis vector set of (9) islinearly independent, one possible solutiontechnique is to first orthogonalize the set and

then solve the resulting uncoupled equations.

4.2 FEA data conversion to Adamsinterface4.2.1 Integration of component flexibility inADAMSA high level goal when implementing flexiblebodies in ADAMS was that a flexible body couldbe integrated into a mechanism in a way similarto a rigid body and interact with the mechanismthrough ADAMS joints and forces.Early in the development cycle, the need for

Component Mode Synthesis became evident.Attempts to model the effect of attachments tothe flexible body using only componenteigenvectors required an extremely large numberof eigenvectors to be considered. While theADAMS implementation of modal flexibility isgeneral enough to accept any kind of modeshape, the FEM code interface has been set up toexport the computationally-determinedcomponent modes.Though c-set degrees of freedom are provided incomponent modes synthesis, theyve typicallynot been used when generating modes for input

to ADAMS/Flex. (Though their use holdspromise.) Since the resulting simplificationyields the familiar Craig-Bampton modes, thissection will refer to them as such. There havebeen certain challenges however:

1.) Embedded in the Craig-Bampton modes are 6rigid body modes. Since ADAMS provides itsown large displacement rigid body motion, thesemodes need to be removed from modal basis.

2.) The constraint modes partition are staticcorrection modes and provide no information

about the resonant frequencies of the degrees of freedom that they provide. An ADAMS userneeds to have information about the frequencycontent contributed by a flexible body mode sothat response in these frequencies may be 1 Free-free modes are allowed in component modes via c-setdegrees of freedom. The transformation:

=c

oaoqoq

oG

eliminates redundant singularities .

8/14/2019 euc98_04

7/11

7

controlled to ensure numerical integrationrobustness.

3.) Craig-Bampton constraint modes can not besafely disabled without imposing an unacceptableconstraint effect between the boundary degrees-

of-freedom.

Orthogonalizing the Craig-Bampton basis of modes eliminated all of these problems. Allmodes get an associated frequency and the rigidbody modes show up as zero frequency modesand can be easily disabled. A user can choose toenable or disable modes for the dynamicsimulation on a mode-by-mode basis.Lets start to describe of how inertia, stiffness,damping and mode shapes of the flexible bodyare handled in ADAMS.Inertia:

The mass matrix of a flexible body in ADAMS isnot constant. As the flexible body is deformed,the center of mass shifts, and the inertia tensorchanges. These effects are accounted for inADAMS by formulating the mass matrix in termsof inertia invariants which are computed in a pre-processor. The large translational DOFs, thelarge rotational DOFs and the modal DOFs arecoupled through this mass matrix. This is themechanism by which spinning gives rise todeformation, etc.

Stiffness:

The generalized stiffness from the finite elementanalysis is diagonalized and used directly byADAMS.

Damping:ADAMS uses modal damping specifiedseparately by the user as a fraction of criticaldamping. Damping can be specified on a mode-by-mode basis. Users are encouraged to usedamping to control modal response. In otherwords, it is recommended that rather thandisabling a mode, because it is assumed to lieoutside the frequency range of interest, that the

mode should instead be critically damped. Thiswill eliminate the dynamic response of this modewhile allowing ADAMS access to it to satisfyboundary conditions.

Mode shapes:After using the mode shapes to compute theinertia invariants, the modes do not contribute intheir entirety to the ADAMS simulations. Only asubset of each mode shape is passed to the

ADAMS solver, the subset that corresponds tothose nodes where connections have been madeor where forces are being applied. This allowsthe solver to satisfy boundary conditions atconnections and to project the applied load onthe mode shapes.

4.2.2 Used FEA-ADAMS InterfaceThe used interface is based on specific ABAQUSinstructions and an external translator utilityfunction. After ABAQUS run, the providedoutput (.fil) contained generated superelementdata for the flexible component,; it has been useda good beta version of Abaqus translator ( ByHKS) that converts this output into a formsuitable for ADAMS.Output quantities for each superelement include: Node data Element connectivity

Constraint data Physical mass Modal mass and stiffness Component modesThe above allows a complete characterization of the mass and stiffness properties of a part interms of its modal components (and, of course,physical mass), as well as graphical display of the part itself (via grid and element data) withinADAMS.

ADAMS uses a special flexible body descriptionfile called the Modal Neutral File (MNF) to

communicate with a variety of Finite ElementPrograms. It has been used a beta version of atranslator (by HKS). The translator extracts nodelocations, element connectivity, nodal massinformation mode shapes and the correspondinggeneralized mass and stiffness from the .fil fileand deposits this information in the MNF. Inaddition to formatting the MNF the routineprovides the orthogonalization of the componentmodesMoreover it has been used a MDI toolkit: a set of library functions suitable for reading, modifyingand writing the MNF platform: the User can

modify the original .mnf file performing meshsimplification and computing the inertiainvariants.

4.3 Next improvementsThe FLEX_BODY in ADAMS has deformationsthat are described via a superposition of modeshapes. In the current implementation, the modes

8/14/2019 euc98_04

8/11

8

that make up the modal basis of theFLEX_BODY are assumed tohave been obtained by linearizing the flexiblebody about an unstressed configuration, as iscustomary in linear finite element analysis.This implementation is obviously a limitation for

users of nonlinear finite element analysis codeslike ABAQUS. An ABAQUS user is likely towish to linearize the nonlinear finite elementmodel about an operating point which is differentfrom the undeformed position. In this particularcase, as the tyre comes into contact with theground, it reaches a state of nonlineardeformations which ABAQUS can use as anoperating point for the linearization.The source of this limitation is that alinearization about a stressed state contains anassociated modal preload which currently theMNF format does not accomodate and

ADAMS/Solver does not account for.The following ingredients are missing to allowADAMS and ABAQUS to correctlycommunicate and process flexible componentsrepresented by modes obtained in a stressedstate:

1. ABAQUS must export node locations to theMNF that correspond to the deformedlocations of the nodes, not the inputconfiguration;

2. The MNF format must be enhanced so that itcan account for generalized forces

associated with the deformed configurationand ABAQUS must compute these forcesand store them in the MNF;

3. The ADAMS/Solver must be enhanced toaccount for this preload.

Note that any future removal of this limitationwill probably keep a requirement that thelinearization is performed at an operating pointthat corresponds to a static equilibrium.To overcome this limitation, the currentsimulation in FE is done accordingly to what isdescribed in section. This means the Tyre model

goes through the following sequence of calculation steps:1. inflation at the nominal pressure;2. squeezing against a rigid surface which

represents the road;3. static concentrated loads on contacting

nodes based on resulatnt forces coming from2

At this point the Mode extraction is requested.The model is ouput in the undeformed

configuration shape, with a linearized stiffnesscorresponding to the one at the end of step 3.

5 Adams implementation of the sub-models5.1 Flexible BodyIn order to implement into ADAMS the PirelliFlexible Tyre model, it has been developed afirst release of a customized ADAMS/Viewinterface, including macro and command files.From the mnf file (after fil2mnf routine),ADAMS reads all modal data to build up aFlexible body, but it doesnt read the Ids of theinterface nodes. Providing an external file whichcontains the hardpoints (nodes) list of theFlexible Body, the implemented macroautomatically creates markers on nodes (hub andfoot-print area) and all the objects for Road-Tyreinterface: dummy parts, joints, motions, impactforces, state variables, design variables,measures, etc.A modified Flexible Body dialogs box (see fig.6) permits the User to select the Node list for theFlexible Tyre and to decide where to attach theTyre (ground, chassis, etc.)In order to get kinematics information fromADAMS analysis and to correctly define thebrush model of the tyre an equivalent rigid tyre(having equal mass and inertia information,location and orientation) has been created. It is

joined to the chassis through a Revolute jointplus a Motion or an Applied Torque, independence of type of the performed analysis(deflection, cleat tests, running on uneven road,etc.).The resulting model after the execution of themacro is represented in figure 7: it is possible tosee the rigid part coaxial with the flexible body,the markers in the footprint, the forces andmotions applied on the markers.

8/14/2019 euc98_04

9/11

9

Fig.6: customized dialogs box for the automaticcreation of the Flexible Tyre Model

Fig.7: flexible tyre model after the execution of the macro

The impact forces applied on each hard point of the footprint area drive the deflection; the user

can decide the deflection time and the deflectionamplitude.

5.2 Brush modelTo better manage the brush-model behavior,earlier described, we have written an user Adams

variable subroutine which receives as inputs thecurrent angular speed of the tyre, the rollingradius and the speed of the hub and returns theglobal longitudinal slip force. This one iscorrectly splitted on the nodes of the footprint,moreover the resultant torque (force time rollingradius) is applied on the hub of the equivalentrigid tyre part. In this way it is possible tocalculate the rigid contribution of the tyre to thevariations of the slip. It is useful to simulateacceleration/deceleration maneuvers of thevehicle.

5.3 Cleat test simulationsThe cleat tests simulations are carried out as inthe Pirelli comfort approach. The basic curvesare read from external files as splines and theyprovide to excite the flexible tyre.

6 Models Validations6.1 GeneralityIt has been modeled a 195/65 R15 tyre size.The below paragraphs show the different modelsvalidations: at first the proposed tyre model staticand modal validations, theThe following paragraphs show the validation of the model running over: a) single obstacle, b)single obstacle, c) real road.

6.2 Static and modal validationsIn the figure 8 there is the comparison betweenthe static deflection curves obtained by Abaqusand ADAMS.In figure 9 and 10 there the eigenfrequenciescalculated in Abaqus and ADAMS with differentboundary conditions. In both the simulations thehub of the flexible body is constrained, then inthe case of the figure 9 the nodes of the footprintare free, in the case of the figure 10 the nodes areconstrained.

8/14/2019 euc98_04

10/11

10

Deflection curves

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 2 4 6 8 10 12 14 16 18 20

mm

ABAQUS

ADAMS

Fig 8: comparison between static deflectioncurves obtained by Abaqus and ADAMS

Comparison between the Eigenfrequency calculated by ABAQUS and ADAMS

0

20

40

60

80

100

120

140

160

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

NModo

ABAQUSADAMS

Fig 9: comparison between eigenfrequenciesobtained by Abaqus and ADAMS.Footprint nodes free .

0

20

40

60

80

100

120

140

160

180

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Number of modes

ABAQUSADAMS

Fig 10: comparison between eigenfrequenciesobtained by Abaqus and ADAMS.Footprint nodes constrained .

It is possible to see the good correlation betweenthe two approaches (Adams, Abaqus).

6.3 Single obstacleThe obstacle is a single triangular obstacle high15 mm and long 20 mm.The simulation has followed the basic curve approach.Figures 11 and 12 show the experimental data,

i.e. the basic curves: vertical and longitudinalforce variations in fig. 5.5, and Rolling radiusvariation in fig. 5.6. Those data refer to a verticalload of 450 kg.

-500

-400

-300

-200

-100

0

100

200

300

400

500

0 0.05 0.1 0.15 0.2 0.25 0.3

position [m]

f o r c e v a r i a t

i o n s

[ N ]

vertical forcelongitudinal force

Fig.11: vertical and longitudinal forces at 425Kg (basic curves measured at 3 km/h)

-25

-20

-15

-10

-5

0

5

10

15

20

0 0.05 0.1 0.15 0.2 0.25 0.3

position [m]

r o l l i n g r a

d i u s v a r i a t

i o n s

[ m m

]

Fig.12: rolling radius variations at 425 Kg(basic curves measured at 3 km/h)

Figures 13 and 14 report the Adams simulationand experimental results, regarding the cleat testat fixed hub and at 30 km/h.

8/14/2019 euc98_04

11/11

11

-1500

-1000

-500

0

500

1000

1500

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

time [sec.]

v e r t

i c a l

f o r c e

[ N ]

calculatedexperimental

Fig.13: experimental and calculated vertical force at 30 km/h

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

time [sec.]

l o n g i

t u d i n a l

f o r c e

[ N ]

calculatedexperimental

Fig.14: experimental and calculated longitudinal forces at 30 km/h

The experimental and the simulated results arecomparable.

6.4 Running on uneven roadThe simulation has been performed linking theflexible tyre to a simple mono-suspension with alumped mass of 400 kg. In this case theexperimental data are not available. In figure 15is shown an example of the results of thesimulation: there is the radial acceleration at thehub.

Fig.15: rim acceleration in Z direction in road noise simulations.

7 ConclusionsAn automatic procedure to create a modal modeltyre is presented. The linking of this model witha multibody vehicle model is very simpleThe MNF format must be enhanced so that it canaccount for generalized forces associated with

the deformed configuration and ABAQUS mustcompute these forces and store them in the MNF.

A new extended 3D contact algorithm iscurrently under development at MDI; it detectsthe compenetration between ground irregularitiesand the Flexible Tire.The model has to be fully validated for the roadnoise simulations; at the moment no experimentaldata are available in order to do a comparison.