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Hindawi Publishing CorporationTe Scientic World JournalVolume , Article ID ,pageshttp://dx.doi.org/.//

Research ArticleExplicit Nonlinear Finite Element Geometric Analysis ofParabolic Leaf Springs under Various Loads

Y. S. Kong,1,2 M. Z. Omar,1,3 L. B. Chua,2 and S. Abdullah1,3

Department of Mechanical & Materials Engineering, Faculty of Engineering & Built Environment,Universiti Kebangsaan Malaysia (UKM), Bangi, Selangor, Malaysia

APM Engineering & Research Sdn Bhd, Level , Bangunan B, Peremba Square, Saujana Resort, Seksyen U, Shah Alam,Selangor, Malaysia

Center for Automotive Research, Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia (UKM), Bangi, Selangor, Malaysia

Correspondence should be addressed to M. Z. Omar; [email protected]

Received July ; Accepted September

Academic Editors: J. Escolano, S. J. Rothberg, and B. F. Yousi

Copyright Y. S. Kong et al. Tis is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Tis study describes the effects o bounce, brake, and roll behavior o a bus toward its lea spring suspension systems. Parabolic leasprings are designed based on vertical deection and stress; however, loads are practically derived rom various modes especiallyunder harsh road drives or emergency braking. Parabolic lea springs must sustain these loads without ailing to ensure bus andpassengersaety. In this study, the explicit nonlinear dynamic nite element (FE) method is implementedbecause o thecomplexityo experimental testing A serieso load cases; namely, vertical push, wind-up, and suspension roll areintroduced or the simulations.Te vertical stiffness o the parabolic lea springs is related to the vehicle load-carrying capability, whereas the wind-up stiffnessis associated with vehicle braking. Te roll stiffness o the parabolic lea springs is correlated with the vehicle roll stability. oobtain a better bus perormance, two new parabolic lea spring designs are proposed and simulated. Te stress level during theloadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolicspring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus saety and stability ispromoted, as well as the load carrying capability.

1. Introduction

Lea springs are widelyused in theautomotive industry as pri-

mary components in suspension systems or heavy vehiclesbecause they possess advantages such as a simple structure,excellent guiding effects, convenience in maintenance, lowcost, and prone to axle location. Lea spring designs aremainly based on simplied equations as well as trial-and-error methods. Simplied equation models are limited tothree-link mechanism assumptions and linear beam theory.According to beamdeection theory, the deection o a beamis based on the dimensional, cross-sectional prole o thecurrent beam. Te thickness o the cross-sectional proleo a parabolic lea spring contributes to the stiffness in the

vertical direction. Te higher vertical stiffness o the leaspring provides vehicles additional load-carrying capabilities.

Lea springs could be categorized into two types: multileaand parabolic lea. From a geometric perspective, a paraboliclea spring has a constant width but decreasing thickness

rom the center o its line o encasement in a parabolicprole, whereas a multilea spring maintains a constantthickness along its length []. Parabolic springs are predictedto perorm more efficiently compared with traditional multi-lea springs because the ormer is lightweight and has lessriction between steel leaves.

Lea springs absorb and store energy and then releaseit. Te characteristics o a spring suspension are chieyinuenced by the spring vertical stiffness and the staticdeection o the spring. Te ride requency and the load-carrying capabilities o the lea spring vehicle are affected bythe vertical stiffness o the installed lea springs. Te verticalstiffness o a lea spring is dened as the change in load per

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Te Scientic World Journal

unit deection in the vertical direction. Most lea springsare designed to operate with respect to the vertical loadingo the vehicle. However, lea springs are practically loadednot only by vertical orces but also by horizontal orces andtorques in the longitudinal directions. Te center o a springis elastically constrained against wind-up or rotation torque

along a longitudinal vertical plane because o its wind-upstiffness. Lea spring wind-upusually occurswhile the vehiclebrakes and accelerates. When a car suddenly starts or stops,ront-down or rear-down postures impose a rotational torqueon the spring, reerred to as a wind-up torque []. In addition,lea springs also sustain torsional load where the momentgenerated rom the vertical lateral plane when the vehiclerolls.

Several studies have been conducted on lea springanalysis such as deection and stress analysis by using thenite element method (FEM) []. Te vertical stiffness andstress analysis conducted is based on the vertical loadingo the lea spring. Kong et al. perormed a simulation olea springs on the basis o vertical and longitudinal loading[]. Qin et al. published a research article on multi-leaspring and Hotchkiss suspension analysis []. Lea springunder varying load cases such as vertical push, wind-up,roll, and cornering analysis was demonstrated in the analysis.Te simulation results provided the vertical, wind-up, androll stiffness o the lea spring suspension system. Savaidiset al. evaluated the severe braking conditions o the axle[]. Te mechanical stress-strain behavior o the lea springswas calculated by FEM analysis. Another elastic lea springmodel was also developed or multi-body vehicle systems oa sport utility vehicle to simulate the axle wind-up undersevere braking []. A nonlinear FE ormulation based onthe oating rame o reerence approach was introducedwith a ull FE model o lea springs with contact andriction. When contact and riction are considered, nonlinearmodel analysis is considered instead o linear analysis. Fornonlinear model analysis, various models such as gun controlsystem were optimized through Pareto optimal solution []and electrohydrostatic actuator through signal compressionmethod []. Te nonlinear model is preerred to be solvedin dynamic scheme where static analysis could not encounterthe riction, material, and geometric nonlinearities.

Te most implemented algorithms in dynamic FE analy-sis (FEA) are the implicit and the explicit schemes. In implicitdynamic simulation, an extension o the Newmark methodknown as

-HH is used as a deault time integrator [].

Mousseau et al. implemented the implicit dynamic schemesto predict the handling perormance o a vehicle []. Tisapproach is time efficient and yields reasonable results. How-ever, the explicit dynamic method derived rom the Newmarkscheme was also widely adopted in dynamic analysis [,]. An explicit dynamic simulation or the stamping parto automotive components was perormed []. Te explicitmethod shows stability o convergence during simulation.Both the implicit and the explicit methods have their prosandcons. Te explicit technique entails a lower cost; however,given a slow case, the solutions are unstable. Given the samecondition, the implicit method provides moreaccurateresults[]. Te simulation o the crimping process, which uses

Solver

Postprocessing

PreprocessingGeometry, meshing,

material, properties, and

boundary conditions

Select appropriate

solving method

Result review

and graph plot

F : ypical FEA procedures by commercial sofware.

both the implicit and the explicit techniques, was conductedby Kugener []. Te simulation results indicated that theexplicit method is superior to the implicit method especiallywhen numerous contacts are considered. Other than thementioned two schemes, it is worth mentioning that the newdeveloped approach semi-implicit nite difference scheme is

implemented to analyze the second law o thermodynamicso uid [].

Te design o a parabolic lea spring in a bus presents achallenge to engineers given very complex and limited con-siderations. Road conditions and the driving behavior o thedrivers subject the lea springs to varying loading conditions,at times severely damaging the lea springs. Currently, leaspring designs ocus solely on the load-carrying capabilitiesor relative vertical stiffness. As mentioned in other previousstudies, the design o the lea spring with vertical stiffnessonly is insufficient when catastrophic ailures have the pos-sibility o occurrence. However, the experimental methods

veriying the stress under those varying loading modes are

too costly andcomplex to perorm. Tis paper aims to presentthe analysis o the stress level o the parabolic lea springsunder different loading conditions by computer-aided engi-neering. Te ailure modes o the lea springs normally occurunder harsh braking or suspension rolling while strikinga pothole. Te braking condition o the bus is associatedwith the lea spring wind-up, whereas pothole striking isrelated to the suspension roll. o promote bus saety undersuch conditions, newly designed parabolic lea springs areevaluated in simulations or their perormance. Te newlea spring designs are expected to provide enhanced rollresistance, improved load-carrying capability, and reducedoccurrence o potential ailure.

2. FE Explicit Model

Te standard simulation setup or any commercial FEA sof-ware is shown inFigure . As seen inFigure , the simulationcan be divided into three categories: preprocessing, solving,and postprocessing. First, computer-aided design models aregenerated or FE meshing. In this study, a manual hexahedraelement mesh is applied or the stressanalysis o the parabolicsprings. o obtain good simulation results, the quality othe mesh is optimized by the element quality index. Tematerials and properties o the lea springs and silencers havealso been assigned, and these details are shown in able .

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: Materials and properties o lea springs and si lencers.

Lea springs Silencers

Modulus o elasticity,, GPa Density, kg/m

Poisson ration . .

Boundary conditions to simulate the degree o reedom o thelea springs under varying loading conditions differ.

FE procedures need to be well developed to perorm acomplex FE nonlinear analysis. Selection o the appropriatesolving method is signicant. A conditionally stable explicitintegration scheme derived rom the Newmark scheme romthe RADIOSS solver has been introduced (RADIOSS is acopyright o Altair Hyperworks, Altair Engineering Inc.).In dynamic analysis, the equation o motion or discretestructural models is expressed as ollows:

+ + = , ()

where , , and represent the mass, viscous damping, andstiffness matrices., , and denote the displacement, veloc-ity, and acceleration vectors, respectively. is the externalorce vector. In the general Newmark method, the state vectoris computed as ollows:

+1= + + + 12 2 + 2 +1,

+1= + 1 + +1 ,()

where andare the specied coefficients that govern thestability, accuracy, and numerical dissipation o the integra-tion method []. A conditionally stable explicit integrationscheme can be derived rom the Newmark scheme given theollowing:

+1=+122 ++1 ,

+1= + +122 .

()

Te explicit central difference integration scheme canbe derived rom the relationships. Te central differencescheme is used when explicit analysis is selected. Te timestep must be smaller than the critical time step to ensurethe stability o the solution. Newmark nonlinear analysisefficiently captures energy decay and exhibits a satisactorylong-term perormance afer being tested [].

o reduce the dynamic effects, dynamic relaxation isused in the explicit scheme. A diagonal damping matrixproportional to the mass matrix is added to the dynamicequation

[]=2[] , ()

where is the relaxation value and is the period to bedamped. Tus, a viscous stress tensor is added to the stress

translation X

translation X, Z

Vertical load

RotationYRotationY,

RotationY,

(a)

Tire patchdistance

RotationY

translation XRotationY,

translation XRotationY,

(b)

F : Boundary conditions and loads applied: (a) vertical push,(b) wind-up.

tensor. In an explicit code, the application o the dashpot orcemodies the velocity equation without relaxation

+/2= /2+ ()to velocity equation with relaxation

+/2=(1 2)/2+(1 ) , ()where

= . ()

When this option is activated, the running time o thewhole simulation is increased. However, the damping periodor the system is controlled within acceptable limits.

3. Contacts and Load Cases

Tree different parabolic lea spring designs were analyzed inthis study. Each design was simulated with different loading

cases. Tereore, different simulation boundary conditionsetups or the vertical push, wind-up, and roll suitable to theload case were conducted accordingly. First, the boundaryconditions or the vertical push were perormed with reerotation around the-axis or the ront eye, whereas therear eye was constrained in the, translation and the, rotation. Te boundary conditions are complied with[]. Te center o the spring was allowed only in the-translation and therotation. Te vertical push boundarycondition setup is shown in Figure (a). For the wind-up loadcase setup, the applied boundary conditions or the eye weresimilar to the vertical push with ree rotation around theaxis or the ront eye, whereas the rear eye was constrained

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Tire patch

Parabolic leaf spring

Simpliedbeam axle

Shackle

Antiroll barShock eye leaf

F : Roll load case simulation model.

in the - translation and the - rotation. Afer maximumvertical loading is applied, a longitudinal orce was createdand applied at the center o the parabolic lea springs [].Te wind-up establishment o the parabolic lea springs isillustrated inFigure (b).

For the suspension roll study, loads are applied to pushthe suspension to a curb position. A moment is subsequently

applied to the suspension by increasing the vertical load onthe lef side and decreasing the load on the right side []. Telea spring is expected to hit the jounce stopper afer a mmdisplacement is imposed. In this case, the load is applied atthetire patch that represents thecontactso tire to theground.Te boundary condition o the parabolic lea spring can reelyrotate around the axis or the ront eye, whereas the rear eyeis attached to the shackle, and the shackle can rotate in the -axis only. Te ront module o conventional buses consideredin this study employed an antiroll bar to enhance the rollstiffness o the vehicle. Te antiroll bar can be idealized asa torsional stiffener connected between the sprung and theunsprung masses. When the roll bar undergoes a relative

rotation between the two masses, a restoring moment,,is generated, which is then related to its roll stiffness[].Te part o the antiroll bar that is connected to the vehiclesprung mass is xed in all degrees o reedom. Te total setupo the suspension roll model is shown inFigure .

Some parabolic lea springs are designed to endurevertical load, whereas others are also designed to sustainwind-up loads. Te vertical rate o the spring is calculatedbased on the beam deection theory. Te ormula or the

vertical rate or parabolic lea springs is indicated [] asollows:

=3

43

V, ()

where is the spring material elastic modulus, is thethickness at center o the spring,is the width at the centero the spring, is the length o cantilever, and

V is the

vertical rate actor. Besides that, lateral rate o the paraboliclea spring is also taken into design considerations. Te wind-up stiffness, is predicted through the vertical stiffness o thelea spring as shown in equation [] as ollows:

=24. ()In geometric nonlinear analysis, components will

undergo large deormations. Te nonlinearities always come

rom contact or materials. A general purpose contact isintroduced in Radioss which is FE commercial sofware. Teinterace stiffness, , is computed rom both the masters, ,and slaves segment,. Te interace stiffness relationshipbetween the master and slave is dened in equation

= + . ()

Friction ormulation is also being introduced in thiscontact interace. Te most well-known riction law is theCoulomb riction law. Tis ormulation provides accurateresults with just one input parameter which is Coulombriction coefficient,[].

4. Result and Discussions

Tree parabolic lea spring designs were prepared and sim-ulated or validation purpose. One o the ront paraboliclea springs was obtained rom the original bus modelas benchmark or the analysis. Te original parabolic leaspring was named as Baseline in the simulation case. Teprole design o Baseline is shown inFigure (a). Te newparabolic lea spring designs are named as Iteration andIteration , respectively where the designs are shown inFigures(b) and(c), respectively. o obtain a proper springcharacteristic o the Baseline model parabolic lea spring, anexperimental testing has been conducted. Te experimentalsetup is shown in Figure []. A verticalloadis appliedromthe centre o the lea spring while the displacement at thecentre is measured. Te ront and rear eye o the parabolicspring are allowed to rotate in in lateral axis and translate inlongitudinal axis. Te gradient o the orce versus deectioncurve is the vertical stiffness o the spring. Te simulationresult o Baseline model is compared to the experimentalresult or correlation purpose as shown inFigure (a). FromFigure (a), the vertical stiffness o the tested experimentalparabolic lea spring is N/mm while the simulation modelis N/mm. It can be concluded that the simulation modeland experimental test have a % good correlation. Aferthat, vertical stiffness o Iterations and parabolic leasprings is also plotted and compared to baseline model asshown inFigure (b). As seen inFigure (b), parabolic leaspring o Iteration has vertical stiffness o N/mm whilethe parabolic lea spring o Iteration is N/mm. Te

vertical stiffness o the lea springs plays important role

in determining the vehicle load-carrying capability. As thevertical stiffness o the lea spring is higher, the load capacityo the vehicle will also be greater. In order to examine the loadcapabilities and stability o designed parabolic lea springstoward original design, the parabolic lea springs in Iterations and should have different vertical stiffnesses. Te paraboliclea spring in Iteration has lower vertical stiffness whichmeans lower load-carrying capability while the Iteration has the greater vertical stiffness compared to the originalparabolic lea spring design (Baseline).

When a car suddenly starts or stops, ront-down or rear-down posture occurs, imposing a rotational torque or wind-up torque on the lea spring []. Lea springs experience

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Springcentre

Y X

Z

Centre

Centre

Centre

18.9

18.1

17.3

16.5

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14.7

13.8

12.7

12.0

20.5

19.7

18.8

17.9

17.0

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13.8

12.7

19.9

19.1

18.3

17.4

16.5

15.6

14.5

13.4

12.0

120 50505050 100 170 100 206

120 50505050 100 170 100 206

120 50505050 100 170 100 206

120

170

220

270

320

420

590

(a)

(b)

(c)

690

896

120

170

220

270

320

420

590

690

896

120

170

220

270

320

420

590

690

896

F : aper prole o (a) Baseline, (b) Iteration , and (c) Iteration .

F : Experimental vertical stiffness test or lea springs.

longitudinal loading, in addition to vertical stiffness, espe-

cially when the vehicle brakes or accelerates. Meanwhile,wind-up analysis is perormed in two stages. In the rst stage,the spring is pushed to a vertical curb position; in the secondstage, a longitudinal load is applied on the lea spring center.Te situation is considerably more difficult in case o braking.Te acting brake orce yields an S- shaped deormation othe lea spring. Tis S deormation changes the kinematicso the ront axle system, resulting in unwelcome swerving othe vehicle []. Such deormation is particularly undesirablebecause the moment o the inertia o the axle around the axis can lead to periodic deormations, where the axleaccepts a torque higher than the riction limit or a short timeand then slips when the inertial orce disappears. Vibration

and loss o braking efficiency or traction then occur [].Tereore, the deormation o the S shape during braking isundesirable. o predict the wind-up stiffness o the paraboliclea spring, af load is applied to the tire patch to obtainthe wind-up moment versus the angle curve, as shown inFigure . InFigure , the wind-up stiffness o the paraboliclea spring in the Baseline is . kNm/degree, whereas thatin Iteration is . kNm/degree. Te wind-up stiffness othe parabolic lea spring in Iteration is . kNm/degree,indicating that Iteration has a higher wind-up stiffnesscompared with Iteration and the Baseline. Tis resultsuggests that S deormation is reduced under the samebraking condition.

For the suspension roll study, a . g gravitational orceis applied to the lef side, and the load on the right sideis decreased to . g o the gravitational orce. In this case,

the same antiroll bar, axle, and linkages are implemented toensure consistency in the simulation. o determine suspen-sion roll stiffness, the roll angle o the suspension is measured,as shown inFigure . Te roll angleis measured based onthe rotation o the solid axle in the-axis connecting the lefand the right parabolic lea springs. Te roll moment versusthe roll angle curve or Baseline, Iteration , and Iteration is plotted inFigure . Te curve depicts an almost linearrelation. Te roll stiffness indicated by the gradient o theroll moment versus the roll angle curve and generated by theparabolic lea spring in the Baseline is . kNm/degree. Teroll stiffness in Iteration is . kNm/degree, whereas thatin Iteration is . kNm/degree. On the basis o the roll

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Experimental

Baseline

45000

40000

35000

30000

25000

20000

15000

10000

5000

00 20 40 60 80 100 120 140

Displacement (mm)

Vertica

lload(

N)

(a)

Baseline Iteration 2

Iteration 1

50000

45000

40000

35000

30000

25000

20000

15000

10000

5000

00 20 40 60 80 100 120 140

Displacement (mm)

Vertica

lload(

N)

(b)

F : Graph o vertical stiffness comparison: (a) Baseline and experimental, (b) Baseline, Iteration , and Iteration .

12

10

8

6

4

2

00 1 2 3 4 5 6


Iteration 1

Wind-up angle (deg)

Wind-upmoment(kN

m/deg

)

F : Comparison o wind-up moment versus wind-up angle curve.

Antiroll bar

AxleLeaf springs

524797GlobalAngle = 8.696

524809

Z

YX

F : Roll angle measurement o suspension system.

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30

35

40

25

20

15

10

5

00 1 2 3 4 5 6 7 8 9


Iteration 1

Roll angle (deg)

Ro

llmoment(kNm

)

F : Graph o roll moment versus roll angle.

stiffness, the parabolic lea spring in Iteration contributesmost to the roll stiffness o the suspension system, ollowedby Iteration and then the Baseline. Te suspension rollstiffness is closely associated with the vehicle body roll. Underthe inuence o the lateral inertia orce, the vehicle bodyproduces a roll angle about the roll axis, approximatelydetermined by

=roll , ()

whereis the vehicle sprung mass,rollis the height o thecentero gravity o the vehicle bodyabovethe roll axis, andis the total roll stiffness o suspension and tires []. Accord-ing to (), the vehicle body roll is inversely proportional tothe suspension roll stiffness, with the suspension roll stiffnessdened as ollows:

= + + , ()where the

is the ront suspension roll stiffness,

is

the device roll stiffness such as antiroll bar, and is therear suspension roll stiffness. Te suspension ront, rear rollstiffness, and the contribution o the antiroll bar constitutethe amount o the vehicle body roll; thus, an increase inany o them reduces the vehicle body roll. Te vehicle bodyroll reduces the stabilizing moment because o insufficientroll stiffness, leading to vehicle instability. Tereore, theparabolic lea springs in Iteration exhibit the highestsuspension roll stiffness compared with those in Iteration and the Baseline, thereby providing the vehicle the highestroll stability.

External loads applied to a component, particularlysprings that undergo repeated cyclic loading, produce stress.

In real-lie settings, stresses would not be uniaxial, biaxial,and/or even multiaxial or most cases. Alternatively, anequivalent stress can be calculated rom multiaxial stresses.Te von Mises stress is a widely known equivalent stress,which is implemented or stress analysis o the lea spring inthis study. Te stress levels o machine components are ofen

monitored and controlled within the limit o the materialthat can sustain stress to prevent component ailure. Te vonMises stress contours o the Baseline, Iteration , andIteration o parabolic lea springs under vertical and wind-up loadcases are illustrated in Figure . o improve the visualizationo stress analysis, a comparison o von Mises stress across thelength o the lea spring or vertical push is plotted and showninFigure . Te von Mises stress o parabolic lea springsunder wind-up loading is plotted in Figure . Te stress levelo each lea in the Baseline, Iteration , and Iteration canbe clearly visualized and compared. As shown in Figures and , the overall von Mises stress level o the paraboliclea springs ranges rom MPa to MPa at the region mm to mm away rom the center o the spring. Tehighest von Mises stress level o the rst lea until the ourthlea o the parabolic lea spring in Iteration ranges rom MPa to MPa. Te stress level o the Baseline rangedrom MPa to MPa in the high-stress region. Iteration exhibits the lowest von Mises stress rom about MPato MPa, under the same load, ollowed by the Baseline;however, the highest stress is shown by Iteration . For wind-up analysis, the von Mises stress or the Baseline rangedrom MPa to MPa or all leaves o the paraboliclea spring. Te stress is evenly distributed during the wind-up load case or Baseline. Under the same load, the vonMises stress or Iteration is also distributed rom MPato MPa. Te stress level or Iteration ranged rom MPa to MPa. Te variation in stresslevelis typicallysmall when the Baseline is compared with Iteration . In thewind-up cases, the parabolic lea spring o Iteration has anarrower stress range and amplitude compared with thoseo the Baseline and Iteration . Te entire stress distributioncan be affected by the design taper prole o the cantilevero the parabolic spring itsel. However, the entire simulationmodel or Baseline, Iteration , and Iteration remains withinacceptable limits with an even stress distribution. Iteration contributes the highest value o wind-up stiffness.

Figure shows the von Mises stress contours o theparabolic lea springs when the roll load case is applied.Te highest stress level is observed at the outer edge o the

parabolic lea spring during suspension under roll loading.Te stress levels o all parabolic lea spring variants are thenplotted into a graph inFigure , which reveals that the mainlea and lea o Iteration obtain the maximum rangeo the von Mises stress amplitude ranging rom MPato MPa. Te remaining leaves ranged rom MPato MPa. By comparing the von Mises stress o thesimulation, the level o stress o this roll loading approachesthe yield strength o the material, which is MPa [].Iteration is ound to possess a very low saety actor underthis condition. For the Baseline, the stress values o leaves and ranged rom MPa to MPa, whereas thoseo leaves and ranged rom MPa to MPa. Te

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Contour plotStress (vonMises)Analysis system

7.930E + 02

7.049E + 026.168E + 02

5.287E + 02

4.406E + 02

3.525E + 02

2.644E + 021.763E + 02

8.818E + 01

7.380E 02

Y XZ

(a)

Y XZ

Contour plot

No result

Stress (vonMises)Analysis system

7.987E + 02

7.100E + 02

6.212E + 02

5.325E + 02

4.437E + 02

3.550E + 02

2.662E + 021.775E + 02

8.875E + 01

0.000E + 00

(b)

Y XZ


7.027E + 02

6.246E + 02

5.465E + 02

4.685E + 02

3.904E + 02

3.123E + 02

2.342E + 021.562E + 02

7.808E + 01

0.000E + 00

(c)

Y XZ


1.206E + 03

1.072E + 03

9.379E + 02

8.039E + 02

6.700E + 02

5.360E + 02

4.020E + 022.680E + 02

1.340E + 02

3.285E 02

(d)

Y XZ


1.087E + 03

9.667E + 02

8.458E + 02

7.250E + 02

6.042E + 024.833E + 02

3.625E + 02

2.417E + 02

1.209E + 02

2.570E 02

(e)

Y XZ


9.836E + 02

8.743E + 02

7.650E + 02

6.557E + 02

5.465E + 024.372E + 02

3.279E + 02

2.186E + 02

1.094E + 02

8.877E 02

()

F : von Mises stress contour o parabolic lea springs: (a) Baseline model vertical push, (b) Iteration vertical push, (c) Iteration vertical push, (d) Baseline model wind-up, (e) Iteration wind-up, and ( ) Iteration wind-up.

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100

01000 800 600 400 200 0 200 400 600 800 1000

Distance across length (mm)

vonMisesstress

(MPa)

Iteration 1: leaf 1

Iteration 1: leaf 2

Iteration 1: leaf 3

Iteration 1: leaf 4

Baseline: leaf 1

Baseline: leaf 2

Baseline: leaf 3

Baseline: leaf 4

Iteration 2: leaf 1

Iteration 2: leaf 2

Iteration 2: leaf 3

Iteration 2: leaf 4

F : von Mises stress across length plot o vertical push.

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104011701300

910780650520

390260130

010 00 75 0 50 0 25 0 0 250 500 750 1000

Distance across length (mm)

vonM

isesstress

(MPa)

Iteration 1: leaf 1

Iteration 1: leaf 2

Iteration 1: leaf 3

Iteration 1: leaf 4

Baseline: leaf 1

Baseline: leaf 2

Baseline: leaf 3

Baseline: leaf 4

Iteration 2: leaf 1

Iteration 2: leaf 2

Iteration 2: leaf 3

Iteration 2: leaf 4

F : von Mises stress across length o wind-up loading.


Y XZ

1.354E + 031.204E + 03

1.053E + 03

9.029E + 02

7.524E + 02

6.019E + 02

4.514E + 02

3.010E + 02

1.505E + 020.000E + 02

(a)


Y XZ

1.420E + 031.262E + 03

1.104E + 03

9.466E + 02

7.888E + 02

6.311E + 02

4.733E + 02

3.155E + 02

1.578E + 020.000E + 00

(b)


Y XZ

1.274E + 03

1.133E + 03

9.910E + 02

8.495E + 027.079E + 02

5.663E + 024.247E + 02

2.832E + 02

1.416E + 02

0.000E + 00

(c)

F : von Mises stress contour o parabolic lea springs under roll load case: (a) Baseline model, (b) Iteration , and (c) Iteration .

stress ranges o the Baseline and Iteration are almost thesame. Te design o the Baseline model has a low saety actor.

Finally, the stresscontour o leaves and o Iteration is alsoplotted, with the stress amplitude ranging rom MPa to MPa. Meanwhile, the stress levels o leaves and rangerom about MPa to MPa in the high-stress region.A MPa stress reduction is observed when Iteration andthe Baseline are compared. Te saety actor o the paraboliclea spring o Iteration is higher compared with those oIteration and the Baseline in this case. Te parabolic leaspring in Iteration has a lower probability o ailure underthis load case compared with those o Iteration and theBaseline.

In a vertical load case, Iteration exhibits higher verticalstiffness compared with both Iteration and the Baseline. In

addition, Iteration possesses a higher resistance to longi-tudinal loading compared with Iteration and the Baseline

during wind-up loading. Te roll stiffness o Iteration is alsoslightly greater than those o Iteration and the Baseline. Testress level o Iteration is lower than those o Iteration andthe Baseline even in the case o vertical and roll loads, as listedin able . Te parabolic lea spring in Iteration must be ableto successully sustain the load or a longer period. However,a low-stiffness spring is avorable or the ride dynamics oany ground vehicle, which is ofen a compromise with vehiclehandling. Te latter usually preers a high-stiffness spring.o identiy the most suitable parabolic lea spring design,many other actors should be considered, depending on theapplication and user perception o the vehicle. Nevertheless,theparaboliclea spring in Iteration with the highest vertical

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: Summary o vertical, wind-up, and roll stiffness and stress or Baseline, Iteration , and .

Vertical stiffness(N/mm)

Wind-up stiffness(kNm/degree)

Roll stiffness(kNm/degree)

Maximum verticalstress(MPa)

Maximumwind-up stress

(MPa)

Maximum rollstress(MPa)

Baseline . .

Iteration . .

Iteration . .

1000

1250

1500

750

500

250

010 00 75 0 500 25 0

0 250 500 750 1000Distance across length (mm)

vonMisesstress

(MPa)

Iteration 2: leaf 1

Iteration 2: leaf 2

Iteration 2: leaf 3

Iteration 2: leaf 4

Iteration 1: leaf 1

Iteration 1: leaf 2

Iteration 1: leaf 3

Iteration 1: leaf 4

Baseline: leaf 1

Baseline: leaf 2

Baseline: leaf 3

Baseline: leaf 4

F : von Mises stress across length plot o roll load case.

stiffness is shown to be the most suitable based on the loadcase simulation results.

5. ConclusionsAn explicit dynamic nonlinear geometric scheme wasadopted to simulate the vertical push, wind-up, and roll loadcases o the parabolic lea spring o a bus. An FE-basedprocedure dealing with the evaluation and assessment o theparabolic lea spring o the bus was presented. Modelingdetails or an accurate calculation o the spring are discussed.New parabolic lea spring designs are included in the analysisto obtain an improved bus load-carrying capability, brak-ing resistance, and roll resistance, which were determinedthrough the analysis o vertical stiffness, wind-up stiffness,and roll stiffness. In addition to the vertical, wind-up, androll stiffness provided by the parabolic lea springs, the stress

level o the spring component itsel is plotted and monitoredto ensure alling within the controlled limit. Hence, noailures are expected when the new parabolic lea springdesigns are implemented in the vehicle. In this analysis, thedesigned parabolic lea spring with higher vertical stiffnessleads to higher wind-up and roll stiffness. Te new paraboliclea spring design with the highest vertical stiffness shouldpossess higher load-carrying capability, braking instabilityresistance, and roll stability compared with the others. Testress level observed or the new lea spring designs underthese circumstances is lower compared with the originaldesign. Te chances o ailure are reduced, and vehicle saetyis enhanced under a braking or pothole strike condition.

Vehicle saety is increased because o the increase in suspen-sion reliability.

Acknowledgments

Tis work is nancially supported by Universiti KebangsaanMalaysia a.k.a Te National University o Malaysia underresearch Grant code Industri-- and APM Engineer-ing and Research Sdn Bhd.

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