Parabolic Leaf Spring Optimization

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11M-0069

PARABOLIC LEAF SPRING OPTIMIZATION AND FATIGUESTRENGTH EVALUATION ON THE BASE OF ROAD LOAD

DATA, ENDURANCE RIG TESTS AND NON LINEAR FINITEELEMENT ANALYSIS

Ahmet Kanbolat , Murathan Soner, Mustafa Karaağaç, Tolga Erdoğuş

OLGUNÇELİK

Copyright © 2011 SAE International

ABSTRACT

Parabolic leaf spring plays a vital role in the suspensionsystems, since it has an effect on ride comfort andvehicle dynamics. Primarily, leaf spring endurance mustbe ensured. Presently, there are two approaches todesign a leaf spring.

In traditional method, fatigue tests should be repeatedfor each case considering different material, geometryand suspension hard points. However, it takes a long

time and requires heavy budget to get the optimizedsolution.

In the recent method, numerical approach is used toobtain the fatigue life and the leaf geometry against theenvironmental condition on the base of materialproperties.

This paper presents a more precise method based onnon-linear finite element solutions by evaluating theeffects of the production parameters, the geometricaltolerances and the variations in the characteristics of thematerial. In other words, it is a hybrid method, between

the traditional and the recent ones, which correlates thereal life conditions and the results of computer aidedengineering. The leaf springs in different characteristicshave been produced and tested in the plant ofOlgunCelik plant.

The design methodology of this paper brings also apractical approach to the professionals in the industry. Itaims to create a design tool with 2D FEA which is wellcorrelated with 3D.The correlation of 3D and simple 2Dmethods with experiments are validated through adesign of experiment (DOE) study.

INTRODUCTION

Parabolic leaf springs are the components of thesuspension system. They perform isolation task intransferring vibration due to road conditions to body.There are various versions of the parabolic leaf springssuch as parabolic, multi-parabolic and z-leaf spring.Development of a leaf spring is a long process whichrequires lots of test to validate the design andmanufacturing variables.

We have used CAE to shorten this development cycle byimplying CAE as much as possible to reduce the tests. Asystematic procedure is obtained where CAE and testsare used together.

LEAF SPRING HYBRID DESIGN

METHODOLOGY

Every design method having CAE in the process mustbe based on validated virtual models. We have validatedour finite element analysis models by experimentalstudies. These studies were carried out by the controlled

manufacturing processes, measured manufacturingvariables and comparison of the test results and virtualmodel using real variables.

Primary output obtained from both test or finite elementanalysis of leaf springs are spring rate (force,displacement) and fatigue strength. In order tounderstand the parameters affecting fatigue strength ofthe leaf spring we have carried out a series ofexperiments in varying conditions. We have determined26 parameters affecting fatigue results (Table1)depending on our experience and leaf spring boundary


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diagram (Table 2). Some of the parametand other are minor.

Design process starts with conceptual pgeneral dimensions and shape of the leadetermined. Conceptual phase decision

experience and in-house software. Thenmodel with nominal parameters is createoptimized initially with nominal parameteto reach required force-displacement curspring rate and stress level which is onefactors defining the fatigue strength. Thefactors affecting fatigue are selected froin Table 1 depending on project type, kntolerances, supplier data etc. The effectvariables are studied in CAE by meansmodels. This step is known as Design of(DOE). As a result of this DOE study, nomodels but also decisions that are takengiven in Table 1 are optimized. Prototypafter having been produced.

Figure 1. Hybrid Design Proce

REFERENCE STUDY

In our reference study we have workedshown in Figure 2. It is a parabolic leaf slayers .The goal is to reach load-deflectigiven in Figure 6 with required fatigue lifconcept is created using in-house tools

Then a detailed finite element model is cnominal values.

rs are major

ase wheref spring areare based on

a finite elementd. Design isrs. The goal isve, henceof the importantn important

the list givenwn or unknownf thesef 3D and 2DExperimentonly the CADon parameterss are tested

ss

n leaf springpring with twon diagram. Initial designnd experience.

reated by using

Figure 2. Refer

The material used for leelastic modulus E=210Ganalysis.

The figure 3 representsfigure 4 represents 3Dused for fatigue analysis

Figure 3. S-

Finite element model ofproperties.

Table 3. Finite Eleme

Number of Element

Element Type

MPC TypeGlobal Element Siz

Number of Nodes

Friction Constant

ence Study Leaf Spring.

f spring is 51CrMov4 andPa, poison’s ratio 0.3 is used in

S_N curve of 51CrMov4 andodel hex. mesh which is to be

Curve of 51CrMov4

the leaf spring has the following

t Model Properties

s 80,216

Hexagonal 8

4 RBE25 mm

67.517

0.05


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Figure 4. 3D Model Hexagona

The front eye of the leaf spring was fixedtranslation and x and z rotation, allowingThe rear eye was constrained in y and zx and z rotation, allowing free x extensio

Axle load is applied in vertical direction.leaf spring components are defined propthe rubber pads.

Load is gradually increased from 0 to mwhich describes the fully loaded vehicleDesign load Fv is less then maximum lodescribes normal loaded vehicle conditio

Figure 5. Leaf Spring Chassis

Figure 6. Theoretical Leaf SpriDeflection Diagram.

The shape of the parabolic leaf spring chduring the load application. This requiresdisplacement analysis option for finite so

l Mesh

in x, y and zfree y rotation.translation and

and y rotation.

aterials of theerly including

ximum loadondition.d andn in Figure 6.

Assembly

ng Load-

anges a lotlarge

lver. Moreover,

after certain deformationhence require contact orequirements, nonlinearnecessary.

Von- Misses stress of

under the maximum lomain leaf spring is givefigure 9.As it can be wquite homogenous aloindication of optimized lof the leaf spring is desiuniformly along the leng

Displacement of the leafdirectly related to springdistribution is given in Fidisplacement along the lconditions. It is confirmedimensions and physicagoals.

Figure 7. Leaf 1 Von -Under Maximum Load.

Figure 8. Leaf 1 StresL

, two layers touch to each othertions. As a result of thisfinite element solution is

main leaf is shown in Figure 7

d. Stress distribution along then in Figure 8 and helper leaf inll seen that stress level is keptg the leaf spring. This is an

eaf spring design. The thicknessgned so that stress is distributedh.

spring is very important as it israte. The displacementgure 10. Figure 11 showslength at different loadd that design with nominall parameters are satisfying the

isses Stress Distribution

s Distribution Along The Mainaf Spring


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Figure 9. Helper Leaf (Leaf 2 ) StressAlong The Leaf Spring

Figure 10. Displacement Distribut Maximum Load.

Figure 11. Vertical Displacement AloUnder Different Load Condi

Vertical Rig Fatigue Tests

Prototypes are produced with controlledparameters that can simulate the real mvariability. The fatigue test of leaf springblock cycle loading of 100,000 cycles. Alprototypes passed the required fatigue tcontinued until failures are occurred.

istribution

ions Under

g The Lengthtions

variation innufacturingare made by

l of thest. Tests are

Vertical rig test machinemeasurements are mad

Figure 12. Vertical Tes

Worst life is found to be

higher than required life.results of the numerical

Table 4. Rig Test Cycl

In addition to this studydisplacement amount aperformed by main layehave been measured bymain layer of parabolic lresults revealed that %1stress distribution of parwhich finite elements an

Table 5. Strain Gauge

ROAD LOAD D

In order to validate theroad load data are takeleaf spring. Strain glocations and verticalVehicle is used in fullyStress levels of 1243Mp

on which test and strain gaugeis shown in Figure 12

t Machine

125,000cycles which is %25

This result is very close tostudies as shown Table 4.

in the rig test processd stress levels that have beenin F design and F max loadsbinding strain gauges on theaf spring and the physicaldeflection appeared among the

abolic leaf spring main layers foralyze has been made (Table 5).

easurement Result

TA

design finally on real life usage,from an instrumented prototype

ges are bonded on severalisplacement is also measured.loaded condition on bad roads.a and maximum displacement of


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194 mm are measured. Experimentallyand displacement values are in verywith finite element studies.

Figure 13. Instrumented Leaf SpringLoad Data Collection.

Design of Experiment (DOFinite Element Models

After having nominally optimized designfactors affecting fatigue life are optimizeand the limits of some of the important fTable 1 are defined.

DOE gives the effect of variation in paralevel hence fatigue life. We can see if thstill satisfy fatigue life requirements evencombination of variation of parameters. Iratio of which parameters affect the fatig

In the examination of production, materitolerances (Table 1) three-dimensional cspring which is analyzed in nominal valuagain in maximum and minimum geomet

In the same boundary conditions f inite elstudy in different parameter tolerance vaon.

By a predictive approach, 2D finite elemsome parameters is used in order to readespite some parameters need an analyof detailed 3D model. ( Figure 14 and Fi

Figure 14 2D Hex Mes

acquired stressood correlation

Used In Road

) Study on

solution, other. The variationctors given in

eters on stressleaf spring willin case of worstalso gives thee life most.

l and designad data of leafs is modeled

ry tolerances.

ements analyzeriations is kept

nt model inh results fastere study by way

gure 15 ).

Figure 15. 2

For the highest stress dispring for which finite elmax & min geometrical tparameter variations pr

changing tolerance valuparameters.

At the end of physical ttolerance deflection of 4affect the fatigue valuethe total of other param%15 (Figure 16).

As a result, unnecessarchanges are eliminated.

Figure 16. ParameterSpring Fatigue

In addition to these parachanges on leaf springnew 10 new parametersgeometry, material and

Von Misses Results

stribution brought about in leafments analyze is performed inolerances and differenttotype samples are produced by

s of production and material

sting, it is determined thatparameters in parametersn leaf spring in the rate of %85,ters affect it in the rate of about

limits on tolerances & design

ffects On Parabolic Leaf

meters effects of designithin the rate tolerances for the(Table 1) by applying newroduction variables are


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determined by using design of experiment studymethods.

Data related to the alternative studies made by eachvariable of new 10 parameters will be presented in otherpaper.

CONCLUSIONS

This study is made as a reference in order to provide a

robust design against process, material and geometricvariables by using computer-aided engineeringtechnologies on the base of the factors effecting

parabolic leaf spring fatigue and other parameters.Correlation with computer-aided engineering has beenprovided in the light of data obtained from the physical

test results made at OlgunCelik Laboratory and roaddata.

It is aimed to reach capability of manufacturing the rightproduct that is more light by less cost ( prototype,material, energy and engineering) at one sitting instead

of ineffectual design and prototype costs that made bytrial-and error method .

At the end of study it is well understood that when

tolerances changes in regard with noise factors definedin the design of two-layered parabolic leaf spring is

examined effects of geometric tolerances providing ratevalue on the stress distributions brought about over leafspring is not much effective and that the changes

brought about in process of heat treatment, sandblastingand quenching, material affect much stress distributionover leaf spring under load, accordingly, leaf spring

fatigue.

REFERENCES

1. Dassault Systems, 1998, “CATIA V4 Manuals,” IBMCATIA Training Center.

2. MSC.PATRAN User’s Manual, 1994, MacNeal-

Schwendler Corporation, U.S.A.

3. MSC.NASTRAN User’s Manual, 1994, MacNeal-chwendler Corporation, U.S.A.

4. Fatigue Strength Evaluation for the LeafSpring of Commercial Vehicle Considering U BoltFixing Force. SAE Technical paper 2007-01-0853

5. Mechanics of Materials (2nd Edition) by Egor P.Popov (Hardcover - Apr 7, 1976)

6. Fundamentals Of Strength Of Materials by Dr.

Debabrata Nag, Dr. Abhijit Chanda 2010

7. Leaf Spring Design Requirements For RearSuspensions Nick Kazan William Smith-Scott Henry

8. SAE HD788, 1990, “Design and Application of LeafSpring”

CONTACT INFORMATION

Ahmet Kanbolat

OlgunCelikCumhuriyet Bulvarı Organize Sanayi Bölgesi 45030Manisa / YurkeyE-mail : [email protected]

ACKNOWLEDGMENTS

DEFINITIONS/ABBREVIATIONS

DOE Design of experiment

CAE Computer aided

en ineerin


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APPENDIX :

Table 1. Parameters affecting Fatigue life of Leaf Spring

No Parameter Process

1 Parabolic leaf spring section thickness effects on Fatigue Manufacturing

2 Parabolic leaf spring eye axis distance effects on Fatigue Design

3 Parabolic leaf spring shackle position and geometry effects on Fatigue Design

4 Parabolic leaf spring materials effects on Fatigue Material

5 Parabolic leaf spring eye diameter effects on Fatigue Design

6 Parabolic leaf spring free arc and free height effects on Fatigue Design

7 Parabolic leaf spring heat treatment effects on Fatigue Manufacturing

8 Parabolic leaf spring sand blasting parameters effects on Fatigue Manufacturing

9 Parabolic leaf spring quenching Parameters effects on Fatigue Manufacturing

10 Parabolic leaf spring rubber silencers geometry effects on Fatigue Design

11 Parabolic leaf spring clamping rivet holes effects on Fatigue Design

12 Parabolic leaf spring standard section form effects on Fatigue. Design

13 Parabolic leaf spring centre tightening bolt effects on Fatigue Material

14 Parabolic leaf spring clamping force effects on Fatigue Design

15 Silencer Types and different silencer model effects on Fatigue Design

16 Bushing type effects on Fatigue Design

17 Bush geometry effects on Fatigue Design

18 Parabolic leaf spring chassis assembly effects on Fatigue Design

19 Parabolic leaf spring sheet plate effects on Fatigue Material

20 Parabolic leaf spring centre flatness length effects on Fatigue Design

21 Parabolic leaf spring edge form effects on Fatigue Design

22 Parabolic leaf spring friction force between layers effects on Fatigue Material

23 Parabolic leaf spring side edge cut geometry effects on Fatigue Design

24 Parabolic leaf spring eye form effects on Fatigue Design

25 Parabolic leaf spring eye wrapping form effects on Fatigue Design

26 Parabolic leaf spring section width tolerances effects on Fatigue Design


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Table 2 Leaf Spring Boundary Diagram

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Parabolic Leaf Spring Optimization