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Vol.10,December2012826

Design of a Composite Drive Shaft and its Coupling for AutomotiveApplication

M.R. Khoshravan, A. Paykani*

Department of Mechanical Engineering, Parand Branch, Islamic Azad UniversityParand, Iran*[email protected]

ABSTRACT

This paper presents a design method and a vibration analysis of a carbon/epoxy composite drive shaft. The designof the composite drive shaft is divided into two main sections: First, the design of the composite shaft and second, thedesign of its coupling. Some parameters such as critical speed, static torque, fiber orientation and adhesive jointswere studied. Tsai-Hill failure criterion was implemented to control the rupture resistance of the composite shaft andthen its critical speed analysis and modal analysis were carried out using ANSYS. The behavior of materials isconsidered nonlinear isotropic for adhesive, linear isotropic for metal and orthotropic for composite shaft. The resultsshowed significant points about the appropriate design of composite drive shafts. The substitution of composite drive

shaft has resulted in considerable weight reduction about 72% compared to conventional steel shaft. Furthermore,results revealed that the orientation of fibers had great influence on the dynamic characteristics of the compositeshaft.

Keywords: Composite drive shaft; carbon/epoxy; design; modal analysis, natural frequency.

1. Introduction

Nowadays, composite materials are used in largevolume in various engineering structures includingspacecrafts, airplanes, automobiles, boats, sports'equipments, bridges and buildings. The widespreaduse of composite materials in industry is due to the

excellent characteristics such as, specific strengthand specific hardness or strength-weight ratio andhardness-weight ratio. The application of compositematerials started first at the aerospace industry in1970s, but nowadays after only three decades, it hasbeen developed in most industries. Meanwhile, theautomotive industry, considered as a pioneer inevery country, has been benefited fromtheproperties and characteristics of these advancedmaterials. Along with progress in technology,metallic automotive parts have been replaced bycomposite ones. Power transmission drive shafts areused in many applications, including cooling towers,

pumping sets, aerospace, structures, andautomobiles. Drive shafts are usually made of solidor hollow tube of steel or aluminum [1]. Forautomotive applications, the first composite driveshaft was developed by the Spicer U-Joint division ofDana Corporation for Ford econoline van models in

1985 [2].When the length of a steel drive shaft goesbeyond 1500 mm, it is manufactured in two pieces toincrease the fundamental natural frequency, which isinversely proportional to the square of the length andproportional to the square root of the specific

modulus. The nature of composites, with their higherspecific elastic modulus, which in carbon/epoxyexceeds four times that of aluminum, enables thereplacement of the two-piece metal shaft with asingle-component composite shaft which resonatesat a higher rotational speed, and ultimately maintainsa higher margin of safety. A composite drive shaftoffers excellent vibration damping, cabin comfort,reduction of wear on drivetrain components andincreases tire traction. In addition, the use of singletorque tubes reduces assembly time, inventory cost,maintenance, and part complexity [3]. Figure 1shows a photographic view of two-piece steel and a

one-piece composite drive shaft.Graphite/carbon/fiberglass/aluminum drive shafttube was developed as a direct response to industrydemand for greater performance and efficiency inlight trucks, vans and high performance automobiles.Since carbon fiber epoxy composite materials have


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DesignofaCompositeDriveShaftanditsCouplingforAutomotiveApplication,M.R.Khoshravan/826834

JournalofAppliedResearchandTechnology 82

more than four times specific stiffness of steel oraluminum materials, it is possible to manufacturecomposite drive shaft s in one-piece. The compositedrive shaft has many benefits such as reducedweight and less noise and vibration [4].

(a)

(b)

Figure 1. Photographic view of: a) two-piece steel;

b) one-piece composite drive shaft [5].

Numerous studies have been carried out to find outthe optimal design and analysis of composite driveshafts with different materials and fibers orientation.Pollard [5] studied different applications of compositedrive shafts for automotive industry. He comparedthe advantages and disadvantages of them atvarious conditions. Rastogi [6] implemented a FEAapproach to design and analyze a composite driveshaft with its couplings in different conditions.Rangaswamy et al. [7] optimized and analyzed aone-piece composite drive shaft using genetic

algorithm and ANSYS. They found that the use ofcomposite materials lead to the significant reductionin weight compared to steel drive shaft. They alsoreported that the fiber orientation of a compositeshaft strongly affects the buckling torque. Kumar [8]performed an optimum design and analyzed acomposite drive shaft for automobile applicationusing a genetic algorithm approach. He optimized

the design parameters with the objective ofminimizing the weight of the composite drive shaft.Chowdhuri et al. [9] replaced a two-piece compositedrive shaft by a one-piece steel shaft. Theyproposed two different designs consisting of

graphite/epoxy and aluminum with graphite/epoxy.Abu Talib et al. [3] implemented a finite elementanalysis to design composite drive shaftsincorporating carbon and glass fibers within anepoxy matrix. A configuration of one layer of carbonepoxy and three layers of glassepoxy was used.Their results showed that the buckling strength is themain concern over shear strength in the drive shaftdesign. Badie et al. [10] conducted a finite elementanalysis to study effects of design variables on thedrive shaft critical mechanical characteristics andfatigue resistance. They found out that stackingsequence has an obvious effect on the fatigue

resistance of the drive shaft.

An efficient design of composite drive shaft couldbe achieved by selecting the proper variables,which can be identified for safe structure againstfailure and to meet the performance requirements.Since the length and outer radius of drive shaftsare limited due to spacing, the design variablesinclude the inside radius, layers thickness, numberof layers, fiber orientation angle and layersstacking sequence. In the optimal design of thedrive shaft these variables are constrained by thelateral natural frequency, torsional vibration,

torsional strength and torsional buckling. In thepresent work an effort has been made to design aHM-Carbon/Epoxy composite drive shaft. A one-piece composite drive shaft for rear wheel driveautomotive application was designed andanalyzed using ANSYS software.

2. Design of a composite drive shaft

First, the fibers are selected to provide the beststiffness and strength beside cost consideration. Itis misunderstood that carbon fiber shafts are toostiff. Indeed, what we meant by too stiff, it isregarding the torsional stiffness rather than the

flexural stiffness. It is a best choice to use carbonfibers in all layers. Since the fiber orientation angle,that offers the maximum bending stiffness whichleads to the maximum bending natural frequency,is to place the fibers longitudinally at zero anglefrom the shaft axis. On the other hand, the angle of45 orientation realizes the maximum shear


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strength and a 90 angle is the best for bucklingstrength [10]. The main goal design is to achievethe minimum weight while adjusting the variablesto meet a sufficient margin of safety, which istranslated in a critical speed (natural frequency)

higher than the operating speed (above 9200 rpm),a critical torque higher than the ultimatetransmitted torque and a nominal stress (themaximum at fiber direction) less than the allowablestress after applying any of the failure criteria likethe maximum stress criteria (for example Tsai-Hillcriteria). Due to the physical geometry (largerradius) of the drive shafts used in the mentionedapplications including automotive applications, theshear strength, which specifies the load carryingcapacity,it is of minor design importance since thefailure mode is dominated by buckling thereforethe main design factors are the bending natural

frequency and the torsional buckling strength,which are functions of the longitudinal and hoopbending stiffness, respectively [10].

The material properties of the drive shaft wereanalyzed with classical lamination theory (CLT). Thevariable of the laminate thickness has a big effecton the buckling strength and slight effect on bendingnatural frequency. From the properties of thecomposite materials, at given fiber angles, thereduced stiffness matrix can be constructed. Theexpressions of the reduced stiffness coefficients Qijin terms of engineering constants are as follows [3]:

121

221

12662112

21212

2112

222

2112

111

,1

1,

1

E

E

GQE

Q

EQ

EQ

(1)

where E is the modulus of elasticity, G is themodulus of rigidity and is the Poissons ratio.

The second step is to construct the extensionalstiffness matrix [A]. This matrix is the summation of

the products of the transformed reduced stiffnessmatrix ][Q of each layer and the thickness of this

layer as [3]:

)(][][ 11

kkkN

k

zzQA (2)

The A matrix is in (Pa. m) and the thickness ofeach ply is calculated in reference to theircoordinate location in the laminate. The A matrix is

used to calculate xE and hE , which are the

average module in the axial and hoop directions,respectively from [3]:

][1

][1

11

212

22

22

212

11

A

AA

tE

A

AA

tE

h

x

(3)

The HM-Carbon/Epoxy composite drive shaft wasdesigned with the objective of minimizing theshaft weight which is subjected to the constraintssuch as torque transmission, torsional buckling

strength capabilities and natural bending

frequency.

2.1 Buckling torque

Since the drive shaft is long, thin and hollow, thereis a possibility for it to buckle. The expression ofthe critical buckling torque for thin-walledorthotropic tube is given as [3],

2/34/132 ])[272.0)(2(

r

tEEtrT hxcr (4)

Where r, is the mean radius and t is the totalthickness. It is obvious that the stiffness modulus

at hoop direction ( hE ) plays a big role in

increasing the buckling resistance. The factor ofsafety is the ratio of the buckling torque to theultimate torque.

2.2 Lateral bending natural frequencyThe main point that attracts designers to usecomposite materials in the drive shafts is that theymake it possible to increase the length of the shaft.

The relationship between shaft's length and thecritical speed for both types of drive shafts areshown in figure 2. It is evident that for a specificapplication where the critical speed is about 8000rev/min, the longest possible steel shaft is 1250mm, while a composite one can have a length of1650 mm [5].


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Figure 2. The effect of shaft length on critical speed [5]

Critical speed of a shaft is obtained through thefollowing equation:

(5)

Where Ncris the critical speed and fis the bendingfrequency.Considering that the natural frequencyof a shaft according to the above equation isinversely proportional to the square of shaft'slength and is proportional to the square root ofYoung's modulus, the conventional steel driveshafts are made of two pieces to increase thenatural frequency of the shaft, which results inoverall increase in the weight of the shaft. So, inorder to increase the natural frequency, the length

of shaft should be reduced or /E ratio should

be increased. Despite the space limitations thatconfines outer shaft diameter , the only way toincrease the critical speed is to increase

/E ratio (specific modulus) [7].

One of the interesting properties of metals is thatalthough there is a clear difference in their density,their specific modulus is almost constant. By usingfiber-reinforced composites, fiber orientationarrangement turns possible in the drive shaft;

therefore, the bending modulus will be higher. Alsotheir relative density is low resulting in thedesirable specific modulus and an i increase in thecritical speed [4]. The natural frequency of thedrive shaft was obtained through Timoshenkotheory as the following equation [8]:

2 2

2

30

2nt s

p Erf K

L

(6)

wherentf

is the natural frequency, p is the first

natural frequency and ,E are properties of the

steel shaft.sK is given by the following equation [8]:

2 2 2

2 2

11 1

2

s

s

f Ep r

K L G

(7)

where G is the modulus of rigidity of steel shaft and

sf is equal to 2 for hollow cross sections. Then

critical speed is obtained in the following way [7]:

60cr nt N f (8)

2.3 Load carrying capacity

The composite drive shaft was designed to carrythe torque without failure. The torsional strength orthe torque at which the shaft fails, is directlyrelated to the laminate shear strength through

lms trT 22 (9)

where sT is the failure torque, l is the in-plane

shear strength of the laminate, mr is the mean

radius and t is the thickness [3].

2.4 Tsai-Hill failure criterion

By using Tsai-Hill failure criterion, it would bepossible to calculate the dimension for failure. Withthe thickness of 2.03 millimeters and the appliedloads, the 00 fibers will not be ruptured. With the

thickness of 2.2 millimeters and the applied loads,

the 090 fibers will not be ruptured. Because of

shafts torsion , the buckling is negligible [1].

(10)

2

2

22

EI

Ncr l A

EIf

mL

2 2 2

2

2

l t t l lt

lr tr lr ltr


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3. Modal analysis of composite drive shaftusing ANSYS

In this study, a finite element analysis wasconducted using ANSYS commercial software.

The 3-D model was developed and a typicalmeshing was generated by using Shell 99element. The drive shaft was fixed at both endsand it was subjected to torque in the middle. Thetorque transmission capability of the drive shaftwas taken as 3000 N.m, the length and the outerdiameter here were considered as 2 meters and120 millimeters, respectively [1]. The shaft rotatesat a constant speed about its longitudinal axis. Theshaft has a uniform, circular cross section. Theshaft was perfectly balanced, all damping andnonlinear effects were excluded. The stress-strainrelationship for composite material is linear andelastic; hence, Hooks law is applicable forcomposite materials. Since lamina is thin and noout-of-plane loads were applied, it wasconsidered as under the plane stress. Since thefiber volume of 60% is the standard fiber volumefraction for most industries, it was selected forcomposite drive shaft [11]. Table 1 shows themechanical properties of each layer of thelaminate. Among the various laminateconfigurations, [45] laminates possess the highestshear modulus and are the primary laminate typeused in purely torsional applications [6]. To meetthe minimum resonance frequency, the drive shaftmust have an adequate axial modulus and since

the axial modulus of a [45] laminate is rather low,0

0layer had to be added to the lay-up to improve

the resonance frequency [10]. Regarding thedesign correlations the appropriate fiberarrangement of the composite drive shaft was

obtained as ]45/0/90[ 0400 .

Figure 3 illustrates the domain of a finite elementmesh. Once the finite element mesh and the layerswere created, the orientation of materials wasdefined for the shell element and the layermaterials for each of these elements have beenallocated. The other steps included placing the

boundary conditions and selecting appropriatesolvers. The drive shaft rotated at maximumspeed so the design should include a criticalfrequency. If the drive shaft rotates at its naturalfrequency, it can be severely vibrated or evencollapsed. The modal analysis was performed tofind the natural frequencies in lateral directions.

The mode shapes for all material combinationswere obtained to their corresponding criticalspeeds.A number of fundamental modes, all ofthem critical frequencies, were obtained. Thedynamic analysis shows that the first natural

frequency is 169.64 Hz, and according to it thecritical speed is equal to 10178 rpm, which is muchmore than the critical rotational speed of 4000 rpm.

According to the equations obtained in theprevious section, natural frequency of a specificcomposite drive shaft is 4570.2 rpm.This value isvery different from the initial one because someassumptions have been used for obtaining naturalfrequency in Timoshenko theory [8].

Property HM carbon/epoxy

)(11 GpaE 190

)(22 GpaE 7.7)(12 GpaG 4.2

12 0.3

)(11 Mpact 870

)(22 Mpact 540

)(12 Mpa 30

)/( 3mkg 1600

fV 0.6

Table 1. Mechanical properties for each

Lamina of the laminate.

Figure 3. The mesh configuration of composite shaft.

Figure 4 depicts the deformation rate change forcomposite drive shaft at the first natural frequency.Figures 5 and 6 show the displacement rate of


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composite drive shaft in different directions at firstmode. The natural frequencies of composite driveshaft are given in Table 2.

Figure 4. The deformation formof composite shaft at first mode.

Figure 5. The displacement rate of compositeshaft in x-direction at first mode.

Frequency number Frequency (Hz)

1 169.64

2 182.67

3 226.734 255.98

5 278.44

Table 2. Natural frequenciesof composite drive shaft.

Figure 6. The total displacement contourof composite shaft at first mode.

3.1 Effect of fiber angle

The fibers orientation angle has a big effect on thenatural frequency of the drive shaft. As we can sein figure 7, the fibers must be oriented at zerodegree to increase the natural frequency byincreasing the modulus of elasticity in thelongitudinal direction of the shaft. The drive shaftloses 38% of its natural frequency when thecarbon fibers oriented in the hoop direction at 90instead of 0. The cost factor plays a role inselecting only one layer of carbon/epoxy. Thestacking sequence has no effect on the naturalfrequency since there is no load applied whendefining the natural frequency.

Figure 7. The effect of changing the carbon fiberorientation angle in a drive shaft of stacking

]45/0/90[0

4

00 on the natural frequency.


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3.2 Design of adhesive joints in composite driveshafts

The joints used for connecting composite materialscan be metallic or non-metallic. Steel fasteners,

due to the possibility of galvanic corrosion withcarbon-epoxy materials, are mainly made oftitanium or stainless steel. Other alloys such asaluminum or steel can be used provided that nocontact with the surface willoccurre . Joints weredivided into metal screws and rivets.Non-metallicconnectors were created from reinforced thermoset or thermoplastic resins. By using thisconnection, structural weight reduces andcorrosion problems disappear [12]. In this part, thethickness of the adhesive and the length of theadhesive bond were computed.

Then, a finite element analysis of this type of bondwas performed using ANSYS software. The"Araldite" adhesive was used in this study. Thefollowing correlations were used to calculate therequired parameters [1]:

max

2

tanh

2

m

c

c

a

a

G la

Gee

(11)

Where l is the length of adhesive bond. Forobtaining reasonable results the only possible wayis to increase the value of e. so the thickness ofthe adhesive and the length of the adhesive bondwere obtained 12 millimeters and 4.5 centimeters,respectively. The details of the bond were given intable 3.

For analysis, a FE model was applied using the 3 -D linear solid elements. A suitable mesh for finiteelement modeling of adhesive layer was needed.The shear distribution stress of the adhesive wasdemonstrated in figure 8. The application of theappropriate adhesive, resulted in a decreased In

the maximum shear stress in the adhesive at theedges of the connection; however, if the stressesremain the same in the middle connection, thestart of failure will depend on the relative shearstrength values within the adhesive [6].

Property Value

E 2.5 Gpa

G 1 Gpa

ce 0.25

l 45 mm

Layers orientation

Table 3. Mechanical properties of the adhesive [12].

Figure 8. Shear stress distribution in theadhesive bond connection.

4. The weight comparison betweencomposite and steel drive shafts

The entire vehicle drive shaft consists ofseveral rotating masses. About 17-22% of thepower generated by the engine was wasteddue to rotating mass of power train system.Power was lost because a lot of energy wasneeded to rotate/ move heavy parts. Thisenergy loss could be reduced by decreasingthe amount of rotating mass. In figure 9, a masscomparison between steel and composite driveshafts has been done. The substitution ofcomposite shaft has resulted in considerableweight reduction about 72% compared toconventional steel shaft. Due to an excessiveweight reduction the geometry would becomeslender which would lead to a large deflection.

6[ 45 / 0 / 45]

T


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Deflected rotating shaft would be prone tofatigue failure. Fatigue analysis of compositedrive shaft was comprehensively performed byBadie et al. [10]. It was found that, the stackingsequence has an effect on the fatigue

resistance. The best stacking is to locate thelayers of 45

0fiber orientation angles together

and far near the inner face of the torque tube.In addition, the cross-ply configuration must belocated exposed to the outside with theseniority of the 90

0layer at the outer face

location.

Figure 9. Mass comparison betweensteel and composite shaft (Kg).

5. Conclusions

In this paper a two-piece steel drive shaft was

considered to be replaced by a one-piececomposite drive shaft. Its design procedure wasstudied and along with finite element analysissome important parameter were obtained. Thecomposite drive shaft made of high moduluscarbon/epoxy multilayered composites has beendesigned. Modal analysis was conducted to obtainnatural frequencies of the composite shaft. Theeffect of changing the carbon fiber orientationangle on natural frequency was also studied. Thereplacement of composite materials has resulted inconsiderable amount of weight reduction about72% when compared to conventional steel shaft.

Also, the results showed that the orientation offibers has great influence on the dynamiccharacteristics of the composite shafts.

Nomenclature

][A Stiffness matrix

66A shear stiffness component

E modulus of elasticity

hE average modulus in the hoop direction

xE average modulus in the axial direction

G modulus of rigidityK torsional spring rateL length

[N] force matrixr radiusrm mean radiusT torquet thickness

Poissons ratio stress density

ec Adhesive thickness

References

[1] D. Gay, S. V. Hoa, S. W. Tsai. Composite materials:design and application, CRC press, 2004.

[2] P.K. Mallick, S. Newman. Composite materialstechnology. Hanser Publishers. pp. 206-10, 1990.

[3] A. R. Abu Talib, A. Ali, M. A. Badie and et al.Developing a hybrid, carbon/glass fiber-reinforced, epoxy

composite automotive drive shaft. Mater. & Des. Vol.31, 2010, pp. 514521.

[4] D.G. Lee, H.S. Kim, J.W. Kim, J.K. Kim. Design andmanufacture of an automotive hybrid

aluminum/composite drive shaft. Compos. Struct. Vol.63, 2004, pp. 8799.

[5] A. Pollard. Polymer matrix composite in drive lineapplications. GKN technology, Wolverhampton, 1999.

[6] N. Rastogi. Design of composite drive shafts for

automotive applications. Visteon Corporation, SAEtechnical paper series. 2004.2004-01-0485.

0

2

46

8

10

12

Weight

Composite

Steel


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[7] T. Rangaswamy, S. Vijayrangan. Optimal sizing andstacking sequence of composite drive shafts. Mater. sci.,Vol. 11, 2005,India.

[8] A.J. Kumar. Optimum design and analysis of acomposite drive shaft for an automobile. Master's degreethesis, Department of Mechanical Engineering, BelkingeInstitute of Technology, Sweden, 2007.

[9] M.A.K. Chowdhuri and R. A. Hossain. Design analysisof an automotive composite drive shaft. Int. J. Eng. andTech., Vol. 2, 2010, pp. 45-48.

[10] M.A. Badie, A. Mahdi, A. M. S. Hamouda. Aninvestigation into hybrid carbon/glass fiber reinforcedepoxy composite automotive drive shaft .Mater. & Des.,Vol.32, 2011, pp. 1485-1500.

[11] D.G. Lee, N.P. Suh. Axiomatic design and fabricationof composite structures: Applications in robots, machine

tools, and automobiles. Oxford University Press, 2006.

[12] S. Pappada, R. Rametto. Study of a composite tometal tubular joint. Department of Materials andStructures Engineering, Technologies and Process,CETMA, Italy, 2002.

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