stress distribution in interference fitted assemblies … · 2015. 4. 9. · 129 int. j. mech. eng....

129

Int. J. Mech. Eng. & Rob. Res. 2014 Chetankumar K Jotawar et al., 2014

STRESS DISTRIBUTION IN INTERFERENCEFITTED ASSEMBLIES WITH DIFFERENT

MATERIAL

Chetankumar K Jotawar1*, Chethan B R2 and Pawan C H1

*Corresponding Author: Chetankumar K Jotawar,, [email protected]

Interference fitted assemblies find wide engineering applications such as bearing bushes, linersin cylinder blocks and cup sealing in Governor covers. The strength of any such assembliesdepends on various geometric features, amount of interference and other physical conditions ofthe mating surfaces. This paper presents the details of analysis carried out to study the effect ofdifferent Tension rod cup material on aluminum governor cover and geometric parameters onstress distribution at the mating surface of interference fitted assemblies. This work covers,analysis based on Lame’s approach and finite element method—to evaluate the principal stressesand Von Mises stresses on the performance of interference fitted assemblies. For the FiniteElement Analysis (FEA), an appropriate finite element model was developed to analyses thepattern of contact stresses in interference fitted assemblies effect and under varying geometricparameters such as contact length, mating diameter and amount of interference. A comparativestudy of both the methods has been carried out.

Keywords: Stress distribution, Interference assemblies, Lame’s approach, Finite elementmethod

LITERATURE REVIEWThe reliable functioning of an interference fitdepends on the correct size relationshipbetween the mating parts of the assembly. Thatis, mating surfaces of the parts must fittogether to fulfill the purpose for which it hasbeen designed. By varying the sizes of twomating parts, innumerable types of fits can be

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1 Department of Mechanical Engineering, East Point College of Engineering & Technology, Bangalore, India.2 Manufacturing Engineering, Bosch Ltd., Adugodi Bangalore, India.

obtained. Depending upon the actual limits ofthe hole and shaft the fits are classified intoclearance fits, transition fits and interferencefits. Interference fitted assemblies provideintimate contact between mating parts,intended to be held permanently as a solidcomponent. The absence of clamping makesthem compact and aesthetic in appearance.

Research Paper

130


They have an excellent load bearing abilityunder static as well as dynamic loadingconditions. These assemblies find wideengineering applications such as bearingbushes, pump impeller on shaft, small endbush in connecting rod, a crank pin in a castiron web, liners in cylinder block, valve seats,gears, locomotive wheel on axle, stator of afan, fitting rotors of turbines and compressorson shafts and mechanical drives andassembling of bearing races (Johnson Harold,1981; and Firsov, 1982). Hence, it isworthwhile to study the strength of theinterference fitted joints. The stress distributionat the interface of interference fittedassemblies depends on various parameterssuch as amount of interference, physicaldimensions, material properties, diameter andcontact length, geometrical inaccuracies andsurface roughness of mating members.Several investigations have been carried outto study the effect of material properties,surface finish of mating surfaces and amountof interference on load bearing ability ofinterference fits. Also, different methods weresuggested to improve the load bearing abilityof the interference fits such as glow dischargetreatment of sleeves, surface hardening ofpins, ageing of assemblies, surface hardeningof bores, oxidation of shafts, vibrostrengthening and heat treatment of matingsurfaces (Andreev, 1978; Dobrovenskii Yu andManokhin, 1978; Papshev, 1980; andRamamoorthy and Radhakrishnan, 1992).

In this work, an attempt has been made tostudy the effect of Tension rod cup made ofdifferent materials on aluminium Governorcover, influence critical geometric featuressuch as length of contact, mating diameter and

amount of interference on stress distributionat the interface of Tension rod cup andGovernor cover hole of the interference fittedassembly. This analysis is done for selectionof material for tension rod cup for betterinterference with aluminium Governor cover.As soon in Figure 1.

Figure 1: Governor Cover and TensionRod Cup

GEOMETRIC MODELINGThe size of pin and the bush are selected insuch a way as to cover the actual dimensionalranges in many practical applications anddetails are given in Figure 2. For the analysis,different combinations of pin of aluminium,brass and steel are considered. Tension rodcup is assembled into Governor cover hole.

X cover Hole and Cup dimension

Hole ID Ø8H8(+0.022)

Seal Cup OD Ø8.2h11(–0.09)

Minimum interference – 0.088

Maximum interference – 0.2

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Selection of materials in the present studyis based on: (i) mechanical properties suchas high resistance to wear and corrosion andstrength, (ii) commonly used bearing/bushingmaterial, (iii) stress withstanding capacity(steel, brass and aluminium can be used ashigh, medium and low withstanding stressapplications respectively), (iv) weight of thematerial. Based on the requirement like light,medium and heavy the appropriate materialis chosen, and (v) cost and availability of thematerial. Further, the selection of materialcombination is decided based on the strengthof materials. Hence, aluminium, brass andsteel are considered based on their relativelylow, medium and high strength in terms ofhardness and modulus of elasticity.Accordingly, when the assembly involves onlysteel parts (pin and bush) it gives high strengthcombination. On the other hand when theassembly involves only aluminium parts (pin

and bush) a low strength combination isobtained. In order to get a medium strength,hybrid assembly using two different metals isadopted.

METHODOLOGYAnalysis based on Lame’s criterionThe stress distribution at the joint surface ofan interference fitted assembly can beassessed on the basis of Lame’s equation.The contact stress at the interface of joint isgiven by

bbp

p

bcbc

EEb

22

22111

2 ...(1)

where, 1 is Lame’s stress in Nmm-2, is theabsolute interference, b is the mating radius(d/2), c is the outside radius (D/2) of bush, p,b, Ep and Eb are the Poisson’s ratio andmodulus of elasticity of pin and bushrespectively. The contact stress at the interfaceof joints for a pair of pin and bush made ofsame material is given by

2

1 14 c

bb

E ...(2)

and r = –1, where r is the radial stress atthe mating surface (Rothbart Harold, 1964).

ANALYSIS BASED ON FEMTo investigate the stresses produced at theinterface of a joint finite element analysis hasbeen used. The model considered for theanalysis is symmetric in respect of geometryand loading, a 2-D axisymmetric model wasanalyzed using ‘ansys’ finite element analysispackage. The geometric features of the pairsused in the analysis are shown in Figure 1.

Figure 2: Dimension of Pin and Bush

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Stress distribution at the contact surface is ofmain concern and the analysis was carried outon the assumption that the materials arehomogeneous and isotropic in nature.

The pin and bush were modeled using eightnoded quadrilateral solid elements and contactbetween the pin and bush was modeled usingcontact pair elements. The appropriatematerial properties such as modulus ofelasticity and Poisson’s ratio, wereincorporated in the analysis. To take thebenefit of the symmetry of the problem one halfof the model was considered. Figure 2 showsthe arrangement of a finite element model usedin the analysis of stress. Finite element gridsat the joint surface are supposed to be in anode to node contact state. With respect tosymmetry of loading, the displacement wasgiven to nodes of the elements in radialdirection in such a manner that they end upwith the required interference along the whole

length of the bush at the contact zone andappropriate boundary conditions were appliedagainst axial movement and contact stressdue to interference is obtained. The resultspresented in this paper refer to the conditionof static structural analysis. The variousparameters considered in the analysis arematerial, length of contact (l), mating diameter(d), outside diameter of bush (D) and amountof interference () on stress distribution at theinterface of pin and bush of the interferencefitted assembly.

RESULTS AND DISCUSSIONStress Distribution PatternFigure 4 shows the fringe pattern of firstprincipal stress (1) and Von-Mises stress (v)distribution in a brass pin-brass bush with0.008 and 0.2 interference. Similar stressdistributions were observed in cases of pairsmade of different materials also, with only themagnitudes of the stresses varying. The stresspattern shows that stresses are symmetricallydistributed along the contact length and

Figure 3: Arrangement of Finite ElementModel

Figure 4: Stress Distribution in Pinand Bush (a) First Principal,

and (b) Von-Mises

(a) Principal Stress

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maximum stress intensity is observed at boththe edges of the joint. The stresses gave riseto set of fringes which originate at points ofmaximum stress and vary with the magnitudeof the displacement. Fringes are bands ofconstant stress and each fringe represents arelative stress with respect to neighboringfringe. Stress gradient is maximum at theinterface of the joint and gradually decreasesalong the thickness of pin and bush.

COMPARISON OF RESULTSThe stresses produced from finite elementanalysis differ slightly from that obtainedthrough Lame’s approach. Stresses producedin case of finite element analysis are aboutmore than the value obtained through Lame’sapproach. Because, interference fit problemsare studied with Lame‘s approach, which isprimarily applied in the elastic range. However,there is a deviation from this and practically,the mating surface of pin contracts (plasticallydeformed) due to pressure exerted by the innersurface of the bush and inner surface of thebush expands (plastically deformed) as a resultof pressure generated by pin. This results in

Figure 4 (Cont.)

(b) Von-Mises Stress

Figure 5: Variation of Stresses (N/mm2)with Different Pin Materials (a) Lame’s

Approach, and (b) FEA

(a)

(b)

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strain hardening at the interface of both pin andbush. Hence, stresses obtained from FEA islarger than Lame‘s approach and the trend ofcontact stress variation satisfactorily agreeswith the Lame‘s approach. Figure 5 shows thevariation of contact stress with respect todifferent pin materials. The variationcorresponding to Lame’s equation and finiteelement analysis for the cases with differentpin materials at 0.088mm interference areclearly indicated. Figure 6 shows thecomparison of stress variation correspondingto Lame’s equation and finite element analysiswith different bush materials. The trend of thevariation of contact stresses agreessatisfactorily with the results obtained throughLame’s approach. It is seen that a pair withdifferent pin and bush materials produces astronger assembly than the one with a pairmade of same material having lower hardness.

It is observed that a pair (pin/bush) madeof different materials can withstand higherstresses because ductile materials becomestronger when they are deformed plasticallyby cold working. Cold working results in strain

hardening which in turn increases the hardnessand strength, and reduces ductility (VanvlackLawrence, 1989). Hence, the enhancedhardness and strength of the pin/bush result ingreater resistance to plastic deformation at thecontact surfaces of the interference fittedassemblies.

CONCLUSIONFrom the study following conclusions may bedrawn:

• Assemblies with steel pin-aluminium bushcan withstand higher stresses than the brasspin and aluminium pin.

• Assemblies with pin and bush made ofdifferent materials produce a strongerassembly than the one with a pair made ofsame material having lower hardness.Hence, wherever interference fit with higherstresses is required, it is desirable to carryout the assembly of pin and bush made ofdifferent materials.

• A change in contact length of the bush, doesnot affect the stress distribution at theinterface of the joint (i.e., stressconcentration is almost constant along thecontact length).

• The outer diameter of the bush hassignificant influence on stress distributionat the joint surface of bush. Because, stressconcentration decreases with increase inouter diameter of the bush.

• Stresses produced along the contact zonebased on FEA differ slightly and the trendof variation of contact stresses agreessatisfactorily with the results obtainedthrough Lame’s approach.

Figure 6: Comparison of Stress (N/mm2)Variation with Different Pin Materials

(a) Aluminium, (b) Brass, and (c) Steel

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stress distribution in interference fitted assemblies … · 2015. 4. 9. · 129 int. j. mech. eng....

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