TSINGHUA SCIENCE AND TECHNOLOGY
ISSN 1007-0214 03/20 pp132-136
Volume 13, Number 2, April 2008
Thermal Stresses in a Cylinder Block Casting Due
to Coupled Thermal and Mechanical Effects*
XU Yan (徐 艳), KANG Jinwu (康进武)**,
HUANG Tianyou (黄天佑), HU Yongyi (胡永沂)
Key Laboratory for Advanced Materials Processing Technology of the Ministry of Education,
Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
Abstract: Thermal stress in castings results from nonuniform cooling. The thermal stress and the deformation can change the casting and mold contact conditions which then alter the heat transfer between the casting and the mold. The contact element method was used to study the interaction between a sand mold and
a casting. The contact status was then fed back to the heat transfer analysis between the sand mold and the
casting to re-evaluate the heat transfer coefficient based on the gap size or pressure between surfaces. The
thermal and mechanical phenomena are then coupled in two directions. The method was applied to analyze
stress in a stress frame specimen casting and a cylinder block. The results are more accurate than without
consideration of the contact effects on the heat transfer.
Key words: cylinder block; casting/mold (core) interaction; thermal stress; contact element method
Introduction
The solidification of castings is a complicated thermomechanical problem. There have been many numerical
simulations of the solidification process, but most consider only the one-way process that the nonuniform
cooling of the castings lead to thermal stress and deformation during solidification. However, the thermal
stress and the deformation can cause gaps or pressure
between the casting and the mold, which alter the heat
transfer at the mold/metal interface[1].
This paper describes an integrated simulation of the
coupled heat transfer, thermal stress, and deformation
during casting solidification.
Received: 2007-10-06; revised: 2007-10-26
﹡Supported by the National Key Basic Research and Development
(973) program of China (No. 2005CB724105)
﹡﹡To whom correspondence should be addressed.
E-mail: [email protected]
1
Coupling of Thermal and
Mechanical Effects
The flow diagram of the integrated finite difference
method/finite element model (FDM/FEM) thermal
stress analysis system for castings is shown in Fig. 1[2].
First, a 3-dimensional model of the casting and the
mold is created for the finite difference and finite element models. The implicit finite difference model was
solved to calculate the casting and mold temperature
distributions. Then, the temperature distributions were
translated to thermal loads in the finite element model
to calculate stress and deformation in the casting and
the mold with the commercial software ANSYS.
Finally, the contact information from the result calculated by ANSYS was translated into interfacial heattransfer coefficients for finite-difference analyses to
calculate the temperatures in the cast and the mold.
XU Yan (徐 艳) et al：Thermal Stresses in a Cylinder Block Casting Due to Coupled …
Fig. 1
1.1
133
Flow diagram of coupled thermo-mechanical simulation
Heat transfer coefficient at the casting/mold
interface
At the mold/metal interface, the casting and the mold
are in contact at discrete points, so there is an interfacial thermal resistance due to the cavities between the
surface, shown in Figs. 2 and 3. Because of difficulties
in predicting these interfacial thermal resistances, most
analyses assume constant value. However, the gap
formation changes in the contact pressure between the
casting and the mold will lead to variations of the
interfacial thermal resistance[3-8].
resistance Rinitial and the thermal resistance Rair due
to the air gap in series.
Rresis = Rinitial + Rair
Rair =
δ air
λair
(1)
(2)
where Rinitial is the interfacial thermal resistance when
there are no air gaps or any contact pressure between
the casting and the mold, which can be calculated using published correlations; λair is the thermal conductivity air; and δ air is the air gap size. When the casting and the mold are in close contact, the interfacial
thermal resistance is due to the Rinitial , and the thermal
resistance Rpress is due to pressure in parallel.
1
1
1
=
+
Rresis Rinitial Rpress
(3)
where
1
Rpress
Fig. 2 Thermal resistance at the interface between
the casting and the mold
= aP b
(4)
where P is the interfacial pressure between the casting
and the mold with a and b related to the softness of the
material and the interfacial surface roughness. δ air
and P are found from the stress calculation and are
initially set to zero.
1.2
Fig. 3
Casting and mold interface
Two interface thermal resistance formulas are used
here to analyze the overall thermal resistance. As the
casting and the mold separate, the interfacial thermal
resistance, Rresis , is the result of the initial thermal
Stress calculation
In previous models, the mold was not considered or
was treated as rigid in casting solidification simulations. However, the green-sand molds have some
strength that resists casting deformation. Therefore, the
contact element method in ANSYS was used to simulate the interaction between the casting and the mold
before shake-out. The contact results were then translated to the finite difference model to evaluate the
interfacial thermal resistance.
134
Tsinghua Science and Technology, April 2008, 13(2): 132-136
1.3 Translation of gap and pressure from FEM to
FDM
The stress distribution predicted by FEM is used to
predict the gap sizes and pressures used to calculate the
interfacial heat transfer coefficients. For the thermal
analysis, first, the center points of the external surfaces
of the finite difference model of casting (such as point
M in Fig. 4) are identified. Then, the FEM contact elements nearest this point are found, and projected onto
the target surface of the contact element (for example,
P is the projection of M). The gap size and the pressures of the four nodes on the target surface nearest
this point calculated in the stress calculations are then
used to calculate the contact state (gap and pressure) at
point P. Then, the contact state of the interface center
point, M, is approximated as being equivalent to that at
point P. Finally, the interfacial thermal resistance at
point M in the finite difference model is evaluated
using Eqs. (1)-(4).
Fig. 5 Temperature distributions in a frame specimen predicted using constant and variable thermal resistance (at 36 min)
Fig. 4 The match of the finite difference model and
the finite element model
1.4
Application to a stress-frame specimen
The temperature distributions at 36 min in a stress
frame as shown in Fig. 5, are predicted using constant
and variable thermal resistance. The two temperature
distributions differ with less cooling predicted by the
variable coefficient model. The difference between the
highest and lowest temperatures predicted by the variable interfacial thermal resistance model is higher than
predicted by the constant interface thermal resistance
model, as shown in Fig. 6. Higher temperature differences mean a more non-uniform temperature distribution, which usually leads to higher stress, so the
simulation based on the variable interfacial thermal
Fig. 6 Differences between highest and lowest
temperature
resistance model are more conservative.
The deformation of the middle of the frame predicted by the contact element method is shown in Fig.
7a. Figures 7b and 7c show the contact state at the interface between the frame and the mold. The distributions of air gap sizes and the contact pressure were
then used to calculate the heat transfer coefficients using Eqs. (2) and (4), as shown in Fig. 7d. As shown in
Fig. 7, increases of the contact pressure increase the
heat transfer coefficient, which increases the heat
XU Yan (徐 艳) et al：Thermal Stresses in a Cylinder Block Casting Due to Coupled …
135
Fig. 7 Effect of gap size and pressure distributions on the heat transfer coefficient at the casting/mold interface
(at 36 min)
transfer. The air gap has the opposite effect.
2
Engineering Application
The coupled thermo-mechanical analysis was also applied to analyze the solidification of a simplified cylinder block model. The cylinder block and the mold
were meshed with hexahedron FEM elements to improve the accuracy and efficiency of the stress simulation, as shown in Fig. 8. Contact elements are generated at the surfaces of the cylinder and the mold. The
cylinder material is gray cast-iron and the mold is resin
bonded sand.
The deformation of the cylinder and the mold in selected special sections (designated in Fig. 8b) before
shake-out is shown in Fig. 9. The heat transfer coefficients at the cylinder interface are shown in Fig. 10.
The cylinder block cools more slowly in the simulations based on the variable interfacial thermal resistance than with the constant interfacial thermal resistance, but the differences between the highest and the
lowest temperatures are less, which differs from the result of the frame casting.
The tension stress distribution in the cylinder block
is shown in Fig. 11. The stress is higher at the positions
where the cylinder block walls are thinner , which
agrees with the practical experience.
Fig. 8 Finite element models of the mold and the cylinder block
Tsinghua Science and Technology, April 2008, 13(2): 132-136
136
3
Conclusions
An integrated simulation system was developed to analyze combined thermo-mechanical effects during casting solidification. The resulting casting stress distributions predicted using variable interfacial thermal resistances that depend on the gap size and contact pressure
differ from predictions using constant coefficients. The
coupled thermo-mechanical analysis gives more accurate results that are more conservative. The integrated
system was then applied to numerical simulations of
the solidification process of cylinder block castings.
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