AP05_3.vp

Notation
q heat flux [W�m�2]
T0 bulk temperature [K]
T face temperature [K]
k contact heat-transfer coefficient [W�m�2K�1]
h heat-transfer coefficient [W�m�2K�1]

1 Introduction
The cylinder head is one of the most complicated parts of

an internal combustion engine. It needs to contain a combus-
tion chamber, intake and exhaust valve ports, valves with valve
seats and guides, a fuel injector and a complex of cooling pas-
sages. In the combustion chamber there are peaks of combus-
tion pressure and temperature of the order of 15 MPa and
2500 K. The heat fluxes and temperature nonuniformities
lead to thermal stress, which further escalates the mechanical
loading from combustion pressure. The maximum tempera-
ture of the head material is much lower, and the regions
around the combustion chamber need to be safely cooled to
prevent overheating. Placing the cooling passages very close
to the most exposed regions is not always possible because of
space demands, which results in limited cooling in these re-
gions. The parts of the engine head assembly are usually
made of different materials with varying thermal expansion.
These facts lead to many compromises in design, which can
be sources of failures in operation. Avoiding the risk of failure
in operation is one of the targets of engine designers. The de-
sign of the engine head must be tested under operational
conditions. This procedure is necessary, but expensive. FE
modeling of the cylinder head assembly operational condi-
tions is an appropriate complement to operational testing.

A detailed FE strength analysis can provide valuable infor-
mation about the temperature distribution and mechanical
stresses in the overall assembly of the cylinder head. This
information is especially useful in regions where experimen-
tal data is barely obtainable. Temperature and mechanical
stresses are analyzed using temperature field, combustion
pressure in the combustion chamber and other mechanical
loads, i.e. bolt pre-stress, moulded seats and valve guides, etc.
The resulting displacement/stress fields may be utilized for
the evaluating the operational conditions, i.e. the contact
pressure uniformity between the valves and valve seats as well
as strength and failure resistance of the assembly. Such infor-

mation contributes to a detailed understanding of the ther-
mal and mechanical processes in the cylinder-head assembly
under engine operation, which is a prerequisite for further
optimization of engine design.

In this study, we emphasize the problematic regions where
proper cooling is limited. The regions around the valve seats
experience thermal loading from in-cylinder burning gases
during the combustion period and also during the exhaust
phase – from burned gases flowing through the exhaust valve
and along the exhaust-port walls. Although the temperatures
of the exhaust gases are significantly lower than peak in-cylin-
der temperatures, the rapid movement of flowing gases and
the duration of the exhaust period exposes parts around the
exhaust valves to heat. The main portion of the heat accumu-
lated in the valve is conducted through the contact surface of
the valve seat. Deformations of these parts accompanied
by improper contact and the occurrence of leakage on the
conical valve contact face dramatically increase the thermal
loading of the valves and, may lead to their destruction. The
modeling of the operating condition of the combustion en-
gine needs to include a model of cooling with the possibility of
local boiling. The simplified model is used to increase the
heat transfer coefficient depending on the surface tempera-
ture in the cooling passages, which simulates local boiling.
This model is implemented in the heat transfer analysis.

2 Cylinder head assembly
In this study, the cylinder head of a large turbo-charged

direct-injection diesel engine is analyzed. The engine is used
in power generators. The basic parameters of the engine are:
bore 275 mm, stroke 330 mm, maximum brake mean effec-
tive pressure 1.96 MPa, nominal speed 750 rpm.

The cylinder head (Fig. 1, link 1) is made of cast iron. The
cylinder head assembly contains two intake valves (Fig. 1, link
6) and two exhaust valves (Fig. 1, link 7), which are made from
forged alloy steel. The valve guides (2, 3) and also the valve
seats (4, 5) are pressed into the head. The exhaust-valve seats
are cooled by cooling water flowing through the annular cavi-
ties around the seats. The fuel injector is situated in the center
of the cylinder, and it is held in place with pre-pressed bolt
connections. The bottom face of the cylinder head, which is
directly exposed to the in-cylinder gases, is cooled by special
bores, which represents a complication in the design of this
mechanically highly loaded region of the cylinder head. The

Czech Technical University in Prague Acta Polytechnica Vol. 45 No. 3/2005

Structural Stress Analysis of an Engine
Cylinder Head
R. Tichánek, M. Španiel, M. Diviš

This paper deals with a structural stress analysis of the cylinder head assembly of the C/28 series engine. A detailed FE model was created for
this purpose. The FE model consists of the main parts of the cylinder head assembly, and it includes a description of the thermal and
mechanical loads and the contact interaction between their parts. The model considers the temperature dependency of the heat transfer
coefficient on wall temperature in cooling passages. The paper presents a comparison of computed and measured temperature. The analysis
was carried out using the FE program ABAQUS.

Keywords: structural stress analysis, FEM, internal-combustion engine.

cylinder head assembly lies on the cylinder, and it is fixed with
six pre-pressed bolt connections.

3 The FE model
The FE model includes all components mentioned above.

The real design of the cylinder head was slightly modified in
details to enable manageable meshing. The model of the cyl-
inder head block was created using PRO/ENGINEER 3D
product development software and was imported as a CAD
model, unlike the models of other components (valves, seats,
valve guides and fuel-injector), which were developed directly
in ABAQUS CAE. Some parts of the valves and fuel-injector
were considerably simplified or completely left out, as they

were considered to have a negligible influence on the results.
The mesh geometry of the basic parts is shown in. It consists
mainly of tetrahedron DC3D4 (158 586) and brick DC3D8
(41 844) elements. The bolts are modeled as beams B31.

4 Interactions and boundary
conditions
Although the thermal loadings of engine parts vary con-

siderably in time due to the cyclical nature of engine opera-
tion, the computations were performed assuming steady-state
heat fluxes evaluated on the basis of time-averaged values.
Taking into account the speed of the periodic changes and
the thermal inertia of the components of the cylinder head,

44 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/

Acta Polytechnica Vol. 45 No. 3/2005 Czech Technical University in Prague

Fig. 1: Cylinder head assembly

Fig. 2: Mesh geometry

the temperature variations are damped out within a small dis-
tance from the wall surface (~1mm), and this simplification is
therefore acceptable.

The thermal contact interactions between the individual
parts of the cylinder head assembly are described by heat flux
�qAB from the solid face A to B, which is related to the differ-
ence of their surface temperatures TA, TB according to

� ( )q k T TAB B A� � ,

where k is the contact heat-transfer coefficient. The values of
the coefficient used in the present analysis are summarized in
Table 1. They follow the values reported in [3]. The value of
k � 6000 Wm�2K�1 was used for all the metal contacts (Fig. 3,
Fig. 4; links 1–4, 6–11), except that of valves vs. their guides
(Fig. 3, Fig. 4; links 5, 7), where the value is k � 600 Wm�2K�1.
The boundary conditions of surfaces in contact with flowing
gases are described as a steady-flow convective heat-transfer

problem, where the heat flux q transferred from a solid
surface at temperature T to a fluid at bulk temperature T0 is
determined from the relation

� ( )q h T T� � 0 ,
where h denotes the heat-transfer coefficient. It depends
on the flow properties of the fluid and the geometry of the
surfaces.

The functional forms of these relationships are usually
developed with the aid of dimensional analysis. In the present
study, the values of gas-side heat-transfer coefficients and
bulk gas temperatures (i.e. for in-cylinder surfaces and intake
and exhaust port walls) were obtained from a detailed ther-
modynamic analysis of the engine operating cycle performed
using the 0-D thermodynamic model OBEH, (see [4]). The
analysis uses Eichelberg’s well-known empirical heat-transfer
coefficient correlation. The remaining boundary conditions
on the outside surfaces mostly exposed to the ambient air

Czech Technical University in Prague Acta Polytechnica Vol. 45 No. 3/2005

Fig. 3: Interactions and boundary conditions on the cylinder-head block

Fig. 4: Interactions and boundary conditions on other parts of the cylinder-head assembly

temperature are described using estimated values of the
heat-transfer coefficient; in special cases the heat-transfer is
neglected. More detailed information on the used values is
provided in Table 1in conjunction with Fig. 3 and Fig. 4.

The possibility of the cooling water exceeding the boiling
point was anticipated, (see [1]). The dependency of the heat-
-transfer coefficient on surface temperature is shown in Fig. 5.
This figure presents experimental data of the heat-transfer
coefficient increasing with the use of pure water boiling under
flow conditions, (see [2]).

The contact interactions between the head and the valve
guides/ports, the valves and the guides/ports, the head and
the gasket ring, the pre-stressed bolts and the valve springs
are included in the structural analysis of the head. Five basic
states were studied.

1) Assembly: The gasket ring is constrained in the cylinder
side. The head is bolted on the cylinder gasket ring with
six pre-stressed bolts fully constrained in the cylinder side.
The valve seats/guides are pressed into the head using
contact constraints. The valves interact with the guides by
special MPC constraints, and with the seats by contact
constraints. The pre-stressed valve springs are inserted
between the valve and the head. The fuel injector is con-
strained on the head bottom inner surface by contact and
pressed onto it by two pre-stressed bolts.

46 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/

Acta Polytechnica Vol. 45 No. 3/2005 Czech Technical University in Prague

Fig. 5: Dependency of the heat-transfer coefficient of the cooling passages on the surface overheat

Boundary
condition

description

Link Heat transfer
coefficient
[Wm�2K�1]

Bulk
temp.

[K]

Insulated surfaces
(negligible

heat-transfer rate)

20 0
(adiabatic)

–

Free surfaces
(contact with
ambient air)

29 5 320

Cooling passages 30 (see Fig. 4.) 350

In-cylinder surfaces 21 450 1120

Intake-port
surfaces

22 800 330

Exhaust-port
surfaces

23 800 700

Table 1: Description of the boundary condition

Measured
point

Temperature [K]

Measured Computed

1 425 551.8

2 509 533.1

3 442 424.1

4 0 430

5 412 422

6 448 432

7 415 425

8 468 478

9 394 427

10 430 490.6

11 400 432.6

12 361 437.9

13 414 523.8

Table 2: Comparison between the computed with measured
temperatures

2) Average pressure load: The assembly is loaded by aver-
age in-cylinder pressure p � 1.96 MPa on the head bottom
outer surface and valve bottoms.

3) Maximum pressure load: The head bottom outer surface
and valve bottoms are loaded by maximum in-cylinder
pressure p � 12 MPa.

4) Maximum pressure and temperature load: The assem-
bly is loaded by maximum pressure and the temperature
field from the previous steady state heat transfer analysis.

5) Average pressure and temperature load: The assembly is
loaded by the average pressure and temperature field
from the previous steady state heat transfer analysis.

5 Results
The experimentally determined temperatures provided

by the engine manufacturer were compared with the com-
puted results. The thermocouples were placed in special
bores. All the bores were situated at a distance of 18 mm from
the bottom margin of the cylinder head, Fig. 6. Despite a lack
of further detailed information on the conditions of the
experiment (errors caused by the measuring equipment, in-
fluence of the location and fixation of the thermocouples in
the bores, etc.), the authors found the data provided to be a
usable and useful resource for verification of the presented
model. A comparison of the computed and measured tem-
peratures is presented in Table 2.

Czech Technical University in Prague Acta Polytechnica Vol. 45 No. 3/2005

Fig. 7: Contact pressure on the intake valve seat

Fig. 6: Distribution of measured points P1–P13 over the head

As an example of the structural analysis, the contact pres-
sure distribution between the intake valve and the seat is
shown in . The idealized contact surface is conical. Two edge
circles of this surface establish the inner and outer path that
the contact pressure is mapped in. The position of both the
inner and outer circles is measured as an angle coordinate
in the cylindrical system associated to the axis of the valve.
The curves document a strong dependency of the valve/seat
contact in relation to temperature loading. In a cold state, the
inner edge transfers more loads, whereas in the hot state the
outer edge is simply overloaded.

6 Conclusion
The experimental data provided by the engine manufac-

turer was compared with the computed results. The thermo-
couples were placed in special bores at a distance of 18 mm
from the bottom margin of the cylinder head. The heat trans-
fer analysis acknowledged the importance of including the
assumption of local boiling in the analysis. The structural
analysis results have not been fully evaluated yet. The influ-
ence of valve seat deformation due to assembly, pressure and
thermal loading on the contact pressure distribution between
the valves and seats is significant.

7 Acknowledgments
This research was conducted in the Josef Božek Research

Center of Engine and Automotive Engineering, supported
by the Ministry of Education of the Czech Republic, project
No. LN00B073.

References
[1] Španiel, M., Macek, J., Diviš, M., Tichánek, R.: “Diesel

Engine Head Steady State Analysis, MECCA – Journal of
Middle European Construction and Design of Cars, Vol. 2
(2003), No. 3, p. 34–41, ISSN 1214-0821.

[2] McAssey, E. V., Kandlikar, S. G.: Convective Heat Transfer
of Binary Mixtures under Flow Boiling Conditions. Villanova
University, Villanova, PA USA.

[3] Horák, F., Macek, J.: “Use of Predicted Fields in Main
Parts of Supercharged Diesel Engine.” Proceedings of
XIX. Conference of International Centre of Mass and
Heat Transfer. New York: Pergamon Press, 1987.

[4] Macek, J., Vávra, J., Tichánek, R., Diviš, M.: Výpočet oběhu
motoru 6c28 a stanovení okrajových podmínek pro pevnostní
a deformační výpočet dna hlavy válce. ČVUT v Praze, Fa-
kulta strojní, VCJB, 2001 (in Czech).

[5] Macek, J., Vítek, O., Vávra, J.: Kogenerační jednotka s ply-
novým motorem o výkonu větším než 3 MW – II. ČVUT
v Praze, Fakulta strojní, 2000 (in Czech).

Ing. Radek Tichánek
phone: +420 2 2435 2507
tichanek@fsid.cvut.cz

Department of Automotive and Aerospace Engineering

Ing. Miroslav Španiel, CSc.
phone: +420 2 2435 2561
spaniel@lin.fsid.cvut.cz

Department of Mechanics

Ing. Marcel Diviš
phone: +420 2 2435 1827
divis@student.fsid.cvut.cz

Department of Automotive and Aerospace Engineering

Josef Božek Research Center
Czech Technical University in Prague
Technická 4
166 07 Praha 6, Czech Republic

Acta Polytechnica Vol. 45 No. 3/2005 Czech Technical University in Prague

Fig. 8: Contact pressure distribution on the intake valve seat