Finite Elements in Analysis and Design41 (2005) 1160–1174

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Design and analysis of gasket sealing of cylinder head underengine operation conditions

Chang-Chun Leea, Kuo-Ning Chianga,∗, Wen-King Chenb, Rong-Shieh Chenb

aDepartment of Power Mechanical Engineering, National Tsing Hua University, Hsin Chu, Taiwan 300, ROCbDepartment of Research and Development, China Engine Corporation, TaoYuan, Taiwan 337, ROC

Received 20 January 2004; accepted 16 December 2004Available online 7 April 2005

Abstract

To avoid the escaping gas from the engine affecting the overall performance of the engine during operation, boththe proper pre-stressing force of the bolts as well as the gasket design are critical factors in enhancing the efficiencyof the sealing of the gasket. In this investigation, both the distribution of the contact pressure on the gasket, and thestresses of the cylinder head at different loading conditions, such as cold assembly, hot assembly, cold start, and hotfiring, are explored by numerical calculation based on the finite element method (FEM). The results reveal that theefficiency of the sealing of the head gasket depends on the pre-stressing force of the hold-down bolts, without takinginto consideration any thermal stresses resulting from the temperature distribution in the cylinder head. However,the location of maximum contact pressure on the gasket is transformed when the thermal loading is taken intoaccount. In addition, this research also conducts the parametric analyses for the pre-stressing force of the bolts andcompares the differences between cold assembly and cold start conditions.� 2005 Elsevier B.V. All rights reserved.

Keywords:Cylinder head; Gasket; Pre-stressing of bolts; Contact pressure

1. Introduction

Both the design and the development of the automobile engine are complicated processes.To acquire thebest performance of an engine in any operating condition in harsh natural environments, many analyticaltools and experimental methods are used to find the optimum parameters for engine design. However,

∗ Corresponding author. Tel.: +886 3 574 2925; fax: +886 3 574 5377.E-mail addresses:knchiang@pme.nthu.edu.tw(K.-N. Chiang),wkchen@china-engine.com.tw(W.-K. Chen).

0168-874X/$ - see front matter� 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.finel.2004.12.007

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numerous measured results point out that the gas escaping from the engine not only affects the outputefficiency of the horsepower substantially, but also pollutes the environment. Therefore, the guaranteethat the assembly between the cylinder head, bolts, and gasket is reliable and effective, through properanalytical procedures and tests becomes extremely important. Furthermore, the reduction of time andcosts are considered in the development process of a novel engine. The above-mentioned reasons arecritically deciding factors whether the goals of a novel engine being developed are achieved or not. Forsolving these foregoing issues, the thermal and structural analyses must be adopted in the engine designto save the time of actual modifications. In addition, in order to allow for the thermal stresses, which needto be blended into the structural analysis of the engine, the heat transfer analysis must take place priorto the structural analysis in order to calculate the results under loading conditions, such as hot firing, hotassembly, etc.

Due to the interface between the cylinder head and the gasket, as well as the interface between thecylinder head and the bolts, contact behavior takes place. The FEM used to deal with the contact problemof surfaces with a complicated geometry of the contact surface is more effective than the boundaryelement method. Wilson and Preson[1] provided the solution of a finite element analysis with differentdisplacements. Furthermore, Chan and Tuba[2] and Ohte[3] further developed the method of Wilsonand Preson, and used this modified method to solve some contact problems. However, the temperatureinside the engine structure is produced through various operating processes and loading conditions.Consequently, the mechanical problems of thermal contact need to be considered for the gasket sealingprocess. The behavior of thermal contact was studied by many researchers in the past. Medhusudana andFletcher briefly introduced the forming mechanism and the relative equations of thermal contact. Boththe objective and research direction associated with thermal contact were mentioned in this work[4].Mijar and Arora[5] reviewed these physical problems in the context of the mechanics of contact. Anexplanation of the phenomenon of contact and friction under static steady conditions were emphasizedin his literature. Belytschko and Neal[6] developed the numerical method with the pin ball algorithm toquickly search the domain of contact. To avoid consuming too much time by continuously tracking theelement to determine whether the contact calculation is incorporated or not under these situations withboth the large displacement and the analytical element that was destroyed, the pin ball algorithm can beused to simplify the search procedures for contact and estimating the penetration.

Besides the aspect of contact problem, the behaviors of heat conduction between the body of the engineand the other components are also extensively investigated by FEM. Chyuan proposed a finite elementmodel of a cylinder structure with a twin-cam 16-valve. They also used an effective calculating methodby using the software of MSC/NASTRAN to predict the thermal and stress/strain analytical results atvarious loading conditions and operating environments[7]. Liu et al. [8] made use of the componentscomputer program (HCC) to analyze the transition of heat transfer for an engine. Their results revealedthat compared to the FEM, the distribution of temperature in the walls of the combustion chamber couldbe predicted accurately by the HCC method. The approach that was applied to the actual problems of heattransfer, such as with the Isuzu engine and the Caterpillar engine showed correct results in comparisonwith the experiments.

The pre-stressing force of bolts maintains the efficiency of the gasket sealing between the cylinderhead and the cylinder block. Therefore, the applied approach of the pre-stressing force is significantfor the calculation of the numerical simulation. Montgomery provided six different kinds of approachesto describe the pre-stressing force of the bolts. The style of solid bolt could be able to perform theapproximate condition was one of these approaches[9]. However, another critical factor that affects

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the sealing efficiency is the behavior of the gasket material. The gasket is made up of multilayers ofadiabatic material. Roub analyzed the response to the non-linear phenomenon of the gasket by means of asimplified model, with one degree of freedom in the direction of the thickness of the gasket. By using theanalytical element of the ANSYS� software (Solid 185) combined with the curve of the pressure versusthe displacement obtained from the experiment, the demand of the model for memory can be reducedby a substantial amount[10]. In addition, the problem is identical to the research of Roub. Shoji useda methodology with axial symmetry to solve the non-linear behavior of a gasket in the direction of itsthickness. The main idea of this literature was to introduce the pre-tension element into the simulation ofthe bolted assembly with the other components. Compared with the traditional method, the pre-tensionelement has many advantages over the method of controlling the raising and lowering of the temperature[11]. However, owing to the complicated engine structure and the lack of experimental data on engineperformance, especially of the cylinder head, there is little literature available that fully discusses thestructural analysis of the cylinder head. In this research, the commercial FEM software, ANSYS�, isintroduced into the numerical simulation of the structural analysis. This research is based on contacttheory and thermal stress analysis in order to investigate the efficiency of gasket sealing and stress/strainbehavior of a 2.0 L cylinder head under various loading conditions. Furthermore, the parametric analysesof the pre-stressing force of bolts between cold assembly and cold start conditions are also discussed inthis work. The results of this research could be regarded as a design reference for the automobile engine.

2. Fundamental theory

2.1. The contact theory

The main focus of this research is to explore the efficiency of gasket sealing. In accordance withthe distribution of contact pressure on the gasket, the location of the minimum contact pressure can bedetermined. The possibility of gas escaping is extremely high in the region of the weakest contact pressure.Generally speaking, penalty methods like the Lagrange multiplier methods and augmented Lagrangianmethod are widely used in the mechanical contact finite element simulation. However, the penalty methodssuffer from ill-conditioning that worsens as the penalty values are increased. The Lagrange multipliermethod introduces extra unknowns, and the resulting equation system is not necessarily positive-definite.The augmented Lagrangian method combines the penalty methods and the Lagrange multiplier methods,and inherits the advantages of both methods. The variational weak form of the augmented Lagrangianmethod on the contact region(�c) could be expressed as[12,13]:

�� =∫

�c

�(��N + �

2�2N

)d�, (1)

where� is the Lagrange multiplier,� is the penalty values and�N is the interpenetration rate of two contactbodies. Through the variational calculation, Eq. (1) could be transformed to its relative strong form as

Ma + f int − f ext + GT� + PCd = 0, (2)

Gv�0, (3)

wherev refers to the velocity field in both bodies; the Lagrangian multiplier is denoted by�, andGT� is thecontact force; the contact stiffness is denoted byPC, andPCd is the contact force (penalty force). Thefint,

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fext andMaare the internal, external and inertial forces, respectively. Eq. (2) is the governing equation ofthe contact finite element computation. Eq. (3) is the inequality constraints which describes the contactboundary of two contact bodies. The chief benefit of the augmented Lagrange method for the contactproblem is that it provides the robustness and stability for the penalty method, while at the same timebeing a simple procedure that does not involve additional equations for the discrete system. To accuratelysimulate the contact behavior between the cylinder head and the gasket under various conditions of engineoperation, the augmented Lagrangian method is adopted in the finite element analysis.

2.2. Thermal stresses

Due to the analyses of the operating conditions for the engine, both the hot assembly and the hot firingare included in this research. Hence, the heat transfer analysis concerning the cylinder head must becarried out prior to the structural analysis. According to the principle of conservation of energy, the heatcondition equation in the material can be expressed as

�2T

�x2 + �2T

�y2 + �2T

�z2 = 0, (4)

whereT is the temperature. The temperature distribution in the material can be obtained with appropriateboundary conditions. From the generalized Hooke’s law, the strain components of the element includingthe thermal strains are listed as follows:

�x = [�x − v(�y + �z)]/E + ��T ,�y = [�y − v(�z + �x)]/E + ��T ,�z = [�z − v(�x + �y)]/E + ��T ,�xy = xy/G,�yz = yz/G,�zx = zx/G, (5)

where� is the normal stress,� is the normal strain,E is the Young’s modulus of elasticity,v is thePoisson’s ratio,� is the coefficient of thermal expansion,�T is the incremental temperature,G is theshear modulus, is the shear stress, and� is the shear strain. After further calculation, the distribution ofthe contact pressure on the gasket and the strain/stress deformation of the entire structure can be obtained.

3. Finite element models and analysis procedure

3.1. Finite element models

To establish the analytical methodology of the cylinder head in respect to the structure, the line styleof a gasoline engine, having 4 cylinders and 4 strokes, is adopted in this research. The Pro/E modelprovided by China Engine Corporation for investigating the efficiency of gasket sealing is displayed inFig. 1. For the convenience of the observation of the distribution of contact pressure on the gasket, only1 cylinder head is considered in this study. It must be noted that the procedure as described above hasother advantages, including: (a) reduction of the complications of boundary conditions considered in the

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Fig. 1. Top view of 2.0 L cylinder head.

Fig. 2. The relative dimensions of the 2.0 L 2nd cylinder head (mm).

analytic processes, (b) economizing on the element counts of the finite element analysis. In other words,the computed time can be shortened substantially.

The relative dimensions of the cylinder head are illustrated inFig. 2and inFig. 4. It should be noted thatthe geometric structure of the cylinder head has an obvious difference between the part of the inlet valve

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Table 1Material properties of each component of the structural analyses

Young’s modulus (Gpa) Poisson’s ratio CTE (ppm/◦C ) k (W/m-◦C)

Exhaust valve (214N) 215 0.290 16.8 15.3Inlet valve (EN52) 90 0.290 13.0 23.4Cylinder head (Al alloy) 71 0.330 24.0 177.2Cylinder block (Al alloy) 71 0.330 24.0 177.2Liner (Cast iron) 107 0.295 11.7 0.0591Bolt (SCM 435) 205 0.29 11.2 N/AGasket Multielastic 0.29 32 1.968E-4

Fig. 3. The relation between pressure and compression in the gasket.

and the part of the exhaust valve. Moreover, the distances between the central line of the combustionchamber and the location of the bolts are not identical.Table 1lists the material properties of eachcomponent of the structural analyses in this research. The main body of the cylinder head and the blockare made of aluminum alloy (JIS H 5302, 1990). The material of the exhaust valve is steel (214N, 1960).The inlet valve is made of a new steel developed since 1960 (EN52, 1970). The pre-stressed bolts aremade of carbon–steel material (SCM 435). At the same time, the internal part of the gasket is in contactwith different components having dissimilar material characteristic (Fig. 3). In this research, both thestructures of the raised part multilayer, referred to as the stopper distribution at the inner ring, and thebody made up by the main body of the gasket are considered. The relative stress/strain curve can becalculated by means of the curve fitting method.Table 2displays the multilinear-elastic material propertyof the gasket used in the structural analysis.

Furthermore, the software based on the FEM, ANSYS�, is adopted to analyze the 2.0 L cylinder head.Before the simulation continues, several assumptions are made with regard to modeling the structure ofthe cylinder head, and they are: (1) The 4 cylinder heads possess a structural symmetry in their entirety,hence the 2nd cylinder head removed from the complete model in order to reduce the calculated time andto set a more simple boundary. (2) For the pre-stressing of the bolts, the construction of a partial block isneeded to look into the efficiency of the gasket sealing. (3) According to the actual dimensions, the full

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Table 2Material properties of the gasket

Stopper Body

Stress (MPa) Strain Stress (MPa) Strain

10 0.019 25 0.2550 0.038 400 0.30

250 0.057400 0.076

Fig. 4. The relative dimensions of the 2.0 L 2nd block and the bolts (mm).

thickness of the gasket is 0.4 mm except for the raised portion of the stopper at the location of the innerring (0.12 mm raised,Fig. 4). In addition, owing to the assumption of the symmetry of the 2nd cylinderhead, only half of the 2nd cylinder head with other interrelated components, such as one inlet valve andone exhaust valve, are consequently introduced into the structural analysis. BothFigs. 5and6 show thefinite element model of half of the 2nd cylinder head after being adequately modified. The element typeused in the analysis is a solid element (Solid 45), and its degrees of freedom are three displacements thatare orthogonal with each other. Moreover, the area-to-area contact pair (contact 174, target 170) has madeuse of simulating the contact condition at the interface between the cylinder head and the gasket. When itcomes to the pre-stressing of the bolts, the Pre-tension element (PRETS 179) with one degree of freedom(the direction of applied force) is adopted to simulate the tightening level in the assembly process of theengine. However, the locations of the bolts are just at the symmetrical axis of adjacent cylinder heads, so

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Fig. 5. The modeling process of relative components for the 2nd cylinder head of the 2.0 L engine.

Fig. 6. The FEM model for the structural analysis. (a) Other components. (b) Half of the 2nd cylinder head. (c) The full FEMmodel of the 2nd cylinder head.

the pre-stressing of the bolts will have an influence on the adjacent cylinder heads. For this reason, halfof the pre-stressing of the bolts is considered to be part of the 2nd cylinder head. The total amount of theelements and nodes in the FEM model are 32,430 and 17,880, respectively.

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Fig. 7. The temperature distribution of the main body of the cylinder head at 6,500 rpm.

3.2. Analysis procedure

For the investigation of gasket sealing, the major loading conditions in the process of engine operationsuch as cold assembly, hot assembly, cold start, and hot firing, will be considered. However, the effectof temperature distribution on the main body of the cylinder head should be brought into the boundaryconditions of heat transfer for simulating the operating situations of both the hot assembly and the hotfiring. Therefore, the heat transfer analysis must be performed prior to the structural analysis because ofthe demand for observation of the thermal stresses that are generated. The two procedures for the analyseswill be discussed in the following paragraphs.

3.2.1. Thermal analysisSeveral assumptions concerning both the FEM model and the boundary conditions in the thermal

analysis are as follows: (1) Owing to the fact that the coefficient of thermal conductivity of the gasketbetween the cylinder head and the block is extremely small, the gasket material is adopted as beingadiabatic. Because of this assumption, the structure of the engine above the gasket is modeled to becalculated by finite element analysis. (2) The components such as the bolt, valve guide, valve seat,and so on, contribute little to the heat transfer of the temperature distribution of the whole cylinderhead. Therefore, besides the inlet valve and the exhaust valve, other components are neglected in thethermal analysis. Other relative setting data such as heat transfer coefficients (HTC) are obtained fromactual experiments and previous literature[14]. The maximum temperature occurs at the highest operatingspeed. Hence, the maximum horsepower output at 6,500 rpm is considered in this research. The analyticalresult is indicated inFig. 7. The maximum temperature appears at the area around the spark plug, and thenext one occurs at the location between two adjacent combustion chambers. The nodal temperature andother related data, after numerical simulation can be further used as input data in the following structuralanalysis.

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Fig. 8. The gas pressure of the 2.0 L engine at different cycle durations at specific operation speeds.

3.2.2. Structural analysisAccording to the applied loadings originating from different categories of mechanics, this linear-elastic

analytical procedure could further be divided into three load steps by means of the superposition principlefor simulating various operating processes of the engine. The final results of the structural analysis arecomposed of the outputs of these three load steps.

a.Assembly loadingsThe major percentage of the loading applied to the engine is the assembly loading. This mainly refers

to the pre-stressing of the bolts, and it plays an important role in preventing gas from escaping from theinternal part of the engine. In other words, in addition to the design of the gasket itself, the efficiency ofthe sealing of the gasket depends mainly upon the correctness of the pre-stressing of the bolts. In order toavoid an insufficient sealing of the gasket, the bolts are pre-stressed in the range of 28–32 kN. In the caseof the assembly loadings, the structure of the whole cylinder is approximately half symmetrical, hencethe structural symmetric planes should have symmetric displacement boundary conditions. In addition,the displacements of the nodes at the bottom of the block are fixed to avoid the rigid body motion.

b.Thermal loadingsIn the case of thermal loadings, the nodal temperatures resulting from the prescribed thermal analysis

are assigned to all corresponding nodes of the FEM model of the 2nd cylinder head in order to calculate thethermal stress/strain of the cylinder head structure. The boundary condition associated with displacementis the same as the case of the assembly loadings.

c.Gas pressureThe gas pressure created as a result of the firing of the spark plug is imposed on the surface of the

combustion chamber. However, the magnitude of the gas pressure varies with different durations ofthe cycle (Fig. 8). For the steady state analysis, the average gas pressure is introduced into the loadingconditions for the numerical simulation of cold starts and hot firing. In this research, the maximum average

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gas pressure, 6.7 MPa, produced at a higher speed during the operating process of the engine is expectedto substantially reduce the efficiency of the gasket sealing.

4. Results and discussions

In this research, the location of the weakest contact pressure on the gasket is used to investigate theefficiency of the gasket sealing. The analytical results under different operating processes of the enginewill be discussed in detail.

Fig. 9. The distribution of the contact pressure on the gasket with raised portion (Pre-stressing of bolt: 48 kN).

Fig. 10. The weakest contact pressure on the gasket at different magnitudes of the pre-stressing force (cold assembly).

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Fig. 11. The distribution of theY -axial stress for both the main body of the cylinder head and the gasket. (cold assembly) (a)Isotropic view. (b) Isotropic view (meshed). (c) Isotropic view. (d) Isotropic view (meshed).

4.1. Cold assembly

The gasket sealing of the automobile in a motionless state is considered to be purely without any otherexternal loading. Therefore, the maximum source of loading in this case is the pre-stressing of the bolts.In addition, the magnitude of pre-stressing the bolts with regards to dissimilar styles of engine structureand stroke volume is not identical. For this reason, the parametric analysis for the pre-stressing of boltsis implemented. The results reveal that the weakest contact pressure on the gasket appears at the raisedlocation of the inner ring between two adjacent combustion chambers (Fig. 9). This situation resultsfrom the fact that the distance between the bolts and the foregoing location on the gasket is the greatest.Moreover, the maximum contact pressure on the surface of the gasket at the inlet part is slightly differentfrom the exhaust part by virtue of the structural asymmetry.

The result for the pre-stressing of the bolts with parametric analysis is shown inFig. 10. All analyticalresults in this case indicate that the weakest contact pressure on the gasket occurs at the same position and

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Fig. 12. The weakest contact pressure on the gasket at different magnitudes of the pre-stressing force (cold starts).

passes the safety factor of the design criteria (greater than 1.1 times the gas pressure). The contact pressuredecays from 103.25 to 59.12 MPa as the pre-stressing force of the bolt decreases from 64 to 32 kN. Itshould be noted that the phenomenon of the efficiency of gasket sealing dependents mainly upon themagnitude of the pre-stressing force under cold assembly conditions. In addition, the distribution of theY -axial stresses of the main body of the cylinder head and the gasket are shown inFig. 11. The maximumstress appears in the adjacent region of the gas wall as a result of the irregular geometry in the structure(101.9 MPa). Moreover, the neighboring regions associated with the location of the bolts are subjectedto compressing stresses (407.7 MPa). However, because of the structural asymmetry, the distribution ofthese compressing stresses is slightly different between the inlet side and the exhaust side of the cylinderhead.

4.2. Cold starts

The operating condition of a cold start is simulated by means of the loading composed of both theassembly loading and the gas pressure. The distribution of the contact pressure on the protruding portionof the gasket, and the position of the least effective gasket sealing are the same as with the condition ofthe cold assembly. According to the results shown inFig. 12, the rising of the lowest contact pressurefrom 39.94 to 70.34 MPa depends on the increase of the pre-stressing force of the bolt. Compared to theresults of the cold assembly situation, the sealing capacity for the gasket diminishes substantially as aresult of the active direction of the gas pressure being opposite to the pre-stressing force of the bolt (Fig.13). The analytical results also conform to the safety factor in spite of the reduction in sealing capacity.

4.3. Hot assembly

The loadings made up by the pre-stressing force of the bolt and the thermal loading are used to simulatethe state of thermal balance reached by the burst of gas being fired repeatedly. It should be noted that the

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Fig. 13. The comparisons of the weakest contact pressure between the operating conditions of the cold assembly and cold starts.

Fig. 14. The distribution of the contact pressure on the gasket with raised portion (Pre-stressing of bolts: 32 kN).

thermal loading comes from the temperature distribution of the nodal result in the heat transfer analysis.The analytical result shows that the distribution of temperature in the internal structure of the cylinder headhas an influence on the distribution of the contact pressure on the gasket (Fig. 14). The original positionof the weakest contact pressure during cold assembly and cold starts becomes the maximum point as aresult of the effect of thermal stress. In other words, the proper thermal stress could be used to improve theefficiency of gasket sealing through our proposed novel design, with relatively few engine components.

4.4. Hot firing

In the hot assembly, the operating process of hot firing is to simulate the moment of the spark plugfiring. Therefore, in this case gas pressure is added into the applied loadings. The distribution of the

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contact pressure on the surface of the gasket is almost the same as the condition of the hot assemblyexcept for the fact that the contact pressure is reduced. However, the sealing capacity of the gasket fallswithin the safety factor of the design criteria.

5. Conclusions

In this research, the structural analyses of a cylinder head under various loading conditions are accom-plished by means of the numerical simulation of finite element analysis. The main results combined witheach analysis concerning the different operating processes of the engine can be separated into two parts asfollow. First, the capacity of gasket sealing mainly depends upon the pre-stressing of the bolts, which arethe source of the maximum external loading on the inner structure of the cylinder head. In addition, thelocation of the weakest contact pressure on the raised portion of the gasket can be transferred as a resultof the effect of thermal stress/strain. In this investigation the analytical results indicate that the thermalstresses provide a positive support for the efficiency of gasket sealing. However, because of the oppositedirection to the pre-stressing applied to the bolts, under the operating conditions with gas, the pressurewill increase the possibility of gas escaping. Therefore, an effective method was proposed to enhance thesealing capacity of the gasket by increasing the magnitude of the assembly force without exceeding thematerial strength of each component in the engine structure. At the same time, the structure of the gasketin the region of the worst sealing can be improved in the early stages of design. This is especially true forthe raised portion.

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