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STATIC AND DYNAMIC FEA ANALYSIS OF A COMPOSITE LEAF SPRINGBy Himanshu Arun Raut

Thesis Advisor: Dr. Andrey Beyle

Thesis Defense CommitteeDr. Wen Chan, Dr. Kent Lawrence

Department of Mechanical and Aerospace Engineering

ContentsIntroductionMotivation and objectiveMaterial propertiesGeometryAnalytical calculationsBoundary Conditions & SimulationResults ConclusionFuture workAcknowledgementReferences

Leaf springs function by absorbing the normal forces and vibration impacts due to road irregularities by means of the leaf deflection and stored in the form of strain energy for a short period of time and then dissipated. Steel leaf springs along with other alloys such as 55Si2Mn90 and similar type of cold rolled steels have been used. Composites have been a suitable replacement for such materials sue to several reasons.Firstly, Composites have a better elastic strain energy storage capacityComposites also have a high strength to weight ratioIn addition to this composite leaf springs prevent sagging as in the case of steel leaf springs which tend to make the ride more bumpy. Introduction

Fig.1&2. Nomenclature of a leaf spring.General arrangement of leaf spring over axle

The objective of this study is to analyze the composite leaf spring structure that is being manufactured by the industry for Chevrolet Corvette Grand model. The leaf spring is made up of reinforced fiberglass epoxy.The composite leaf spring was designed to withstand forces incurred by weight of the car(1500 Kgs=3300lbs. approx.) along with other external loads up to a certain limit. It was suggested that the same leaf spring may be used to support commercial light tractor trailer. It was observed that the leaf sprig was unable to perform optimally as it did for the automobile for the same load operating conditions.Delamination and micro-cracks started to appear on the central region where the leaf spring is clamped to the axel. Motivation and Objective

Motivation and Objective(contd..)We aim to show the cause of failure for the composite leaf spring by the use of finite element simulations and by means of analytical calculations. Alternative designs and compatible material changes have been suggested in the later part of the sections.

Fig3.Reinforced fiberglass epoxy composite leaf spring

Fig4.Closeup of midsection

Material PropertiesCompositeMaterialE1 (GPa)E2 (GPa)1223G12 (GPa)G23 (GPa)

Glass/Epoxy61.40113.4540.2590.4365.3624.685Kevlar/Epoxy108.2763.8140.340.2462.1191.531Carbon/Epoxy210.97.7440.30.33.6082.978

MaterialE1 (GPA)E2 (GPA)1223G12 (GPA)G23 (GPA)

Glass Fiber85.585.50.230.233535Kevlar Fiber151.174.10.350.152.91.782Carbon Fiber300140.30.1586.087Epoxy Matrix330.30.31.111.154

Table1. Anisotropic material properties calculated from fiber and matrix (calculated for 70% fiber)

Table2. Fiber and matrix material properties

Anisotropic material properties for composite are calculated by the following methodObtain the compliance matrix for the fiber and matrix C1 and C2Calculate for the two elements of compliances bij for the plane strain state for fiber and matrix. Calculate bulk moduli K23 for the fiber and matrixCalculate the effective elastic properties of the Unidirectional compositeSubstitute values of the effective elastic properties for the composite material in the compliance matrixCalculate the inverse of this compliance matrix

Geometry

Fig.5 drawings for front views of leaf spring assembly

Fig.6 drawings for front and top views of clamp and bushing

Analytical calculationsCalculations are performed under the following assumptionsThe leaf spring is a part of a circular ring and possesses symmetryThe leaf spring is made up of linier anisotropic material and the pole is located at the center of the two circlesThe angle between the applied force and the transversal axis is 0Bending of the linearly anisotropic curved beam occurs due to the application of end force which is applied at the center of the cross section

Note: All calculations are performed on PTC Mathcad Prime 3.1. Please refer reference [8]

Analytical calculations for radial ,normal and shear stresses [1]

Fig.6 reference [1]

Reference [2]

Radial Stresses (MPa)Radius766768770772774776778780782784786

Theta000000000000100.0540.0950.1240.1410.1460.1390.1210.0920.0510200.1070.190.2480.2810.2920.2790.2420.1840.1030300.1610.2840.3710.4220.4370.4180.3640.2760.1540400.2140.3790.4950.5620.5830.5570.4850.3670.2060500.2680.4730.6180.7030.7280.6960.6060.4590.2570600.3210.5680.7410.8430.8730.8430.7260.5510.3080700.3740.6620.8640.9831.0180.9730.8470.6420.3590800.4270.7560.9871.1221.1631.1110.9670.7330.410900.4810.851.1091.2611.3071.2481.0870.8240.46101000.5330.9431.2321.41.4511.3861.2060.9150.51201100.5861.0361.3531.5391.5941.5231.3261.0050.56201200.6391.1291.4751.6771.7371.6591.4441.0950.61301300.6911.2221.5951.8141.881.7951.5631.1850.66301400.7431.3141.7161.9512.0221.9311.6811.2740.71301500.7951.4061.8362.0872.1632.0661.7981.3630.76301600.8471.4971.9552.2232.3032.21.9151.4520.81201700.8981.5882.0742.3582.4432.3332.0311.540.86201800.9491.6792.1922.4922.5822.4662.1471.6270.911019011.7682.3092.6252.7212.5952.2621.7150.9602001.0511.8582.4262.7582.8582.732.3761.8011.00802101.1011.9472.5422.892.9952.862.491.8871.05602201.1512.0352.5753.0213.132.992.6031.9731.1040

Table3.Analytical results

16

Fig8. Radial stress for curved section plane Fig9. Radial stress for mid section plane

Fig10.

18

Analytical Radial stresses(MPa)ComputationalRadial Stresses(MPa)% error

000020.2920.52744.640.5830.6063.79560.8730.891.9181.1631.1740.93101.4511.450.07121.7371.730.4142.0222.1124.26162.3032.281.009182.5822.5371.744202.8582.9272.357223.132.9884.75

Computational and Analytical Results ComparisonTable4. Radial stress at r = 766mm Fig11.

Boundary conditions and simulations

rot z = freerot x, y=0x, y, z=0

rot z = freerot x, y=0x = freey, z=0

A remote mass of 375 Kg is attached at the center of the bottom face to promote forced vibrations.

Fig12. boundary conditions

Meshing has been done by using body sizing and by use of hex dominant method with element type as all quad. Mid side element nodes are selected to KEPT. This generates a mesh with brick elements particularly SOLID 186. SOLID186 is a higher order 3-D 20-node solid/brick element. The middle mesh was generated using sphere of influence[3]Fig13. Meshing for geometry Fig14. Meshing element reference [3]

Static Analysis ResultsFig15. Fig16.

Transient Analysis ResultsFig15. Vid1.

Fig16a,b,c,d

Vid1.

Varying thickness model results fiberglass epoxy

Fig17. (a) Model for thickness 22 mm (b) Model for thickness 18 mm

Varying thickness model results fiberglass epoxy

Fig18. (a) Model for thickness 22 mm (b) Model for thickness 24 mm

When the spring constant is low the effective force decreases thereby reducing the radial and shear stressesSince k is proportional to the thickness, the reduction of the spring constant will mean reducing the thickness of the leaf spring. This will result in increase in the tensile and compressive stresses on the top and bottom faces of the leaf springHere the objective is to compromise the thickness that moderates the level of delamination stresses with tensile and compressive stresses in a safe level

The reinforced fiberglass epoxy fails doe to delamination stress built up specifically in the mid sectionThe deflection due to dynamic loading induces tensile forces on the laminate layers. This results in tensile radial stress built up along with inter laminar shear stresses.The leaf spring model can be improved by changing the design as illustrated in the results section.The thickness of the leaf spring needs to be reduced in order to minimize the delamination stresses (r)max

Conclusion

Fig19. Delamination stresses (r)max as a function of b/a for =3.568Reference [2]

Experimental study can be performed for the same model to validate the result using 3 point and 4 point bend set upEye end design can be studied to reduce the chances of local delamination due to concentration of interlaminar shear stress.[@]

Hybrid composites can be used as study material for heavy axel loadings

Future Work

Reference [4]Fig20.

Acknowledgement

I would like to thank Dr. Andrey Beyle for his inspiring guidance, encouragement and for investing his valuable time in mentoring me.I would also like to thank the committee members who are present here for giving their valuable time and opinion.In the end I would like to thank my colleagues and friends who help me along the way

References

Lekhnitskii, S.G.; Tsai, S.W.; and Cherom, T.: Anisotropic plates. Gordon and Breach Science Publishers, New York, 1968ANSYS Documentation > Mechanical APDL > Element Reference > I. Element Library > SOLID 186William L. Ko, T.: Delamination Stresses in Semicircular Laminated Composite Bars Jan 1988 NASAShokrieh MM, Rezaei D. Analysis and Optimisation of composite leaf springs. Comp Struct 2003;60:317-25

Thank You!Questions?