30120130406025

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME

AND TECHNOLOGY (IJMET)

ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 4, Issue 6, November - December (2013), pp. 241-248
© IAEME: www.iaeme.com/ijmet.asp
Journal Impact Factor (2013): 5.7731 (Calculated by GISI)
www.jifactor.com

IJMET
©IAEME

APPLICATION OF TRANSIENT THERMAL ANALYSIS FOR THREE
FEEDER DESIGN OPTIMIZATION FOR SAND CASTING
Haider Hussain1,

Dr. A.I. Khandwawala2

1

2

(Research Scholar, Bhagwant University Ajmer (Rj.), India)
(Ex. Professor, Mechanical Engineering Department, SGSITS, Indore, India)

ABSTRACT
In the present scenario most focus is on defect free casting. In achieving this task computer
simulation is playing a key role. In sand casting, solidification related defects can be find out by
computer simulation on FEM based software very closely. One of the major solidification related
defect is shrinkage porosity. This defect may occur at the last freezing point of casting in its thickest
section. Feeders are required to remove shrinkage porosity from casting. Feeders are not the required
part of casting so it has to be removed after casting process. These removed feeders have been put in
furnace for reuse of metal again and it increases production cost. Feeders designs are required to be
optimized. In this work with the help of computer simulation on Ansys, hot spots have been
identified and three feeders have been designed and optimization procedure has been developed for
three feeders successfully. Three feeder optimization result from Ansys have been compared with
traditional modulus approach. Ansys optimizer is producing better results for this three feeder
casting.
Keywords: Feeder Design Optimization, FEM, Modulus Approach, Sand Casting, Shrinkage
Porosity.
I.

INTRODUCTION

Sand casting is the most widely used process for both ferrous and non – ferrous metals, and
accounts for approximately 90% of all castings produced [1]. In sand casting, sand mixed with
binders and water is compacted around wood or metal pattern halves to produce a mould. The
mould is removed from the pattern, assembled with cores and metal is poured in to the resultant
cavities. After cooling, moulds are broken to remove the casting. After casting is removed from the
sand moulds, sand mould is destroyed [2].

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In sand casting, molten liquid metal is poured into a cavity which takes the negative shape of
the object and the mould is made from sands. Heat removal is by heat transfer in sand mould, the
governing equations for heat transfer are [3]
డ்
డ௧

=ߙ

డమ ்

(1)

డమ ௫

Tሺ‫0 ,ݔ‬ሻ ൌ ܶ଴

(2)

Tሺ0, ‫ݐ‬ሻ ൌ ܶெ (Temperature at metal end)

(3)

Tሺ∞, ‫ݐ‬ሻ ൌ ܶ଴

(4)

Finite Element Method (FEM) is a powerful computational tool that is used to numerically
solve many engineering problems. Most of the Research on the area of casting processes modeling
uses FEM as a solver to the casting Process model. The numerical simulation of solidification
process using either Finite Difference or Finite Element Methods (FDM/FEM) involves the
following steps: [1]
1. Formulating an accurate mathematical model of the solidification process.
2. Specifying accurate values for thermal properties of material involved.
3. Performing the analysis to obtain the temperature history of casting and mould points.
4. Post – processing the results to visualize the solidification pattern and identify defects.
Feeders are designed to compensate the solidification shrinkage of a casting, and make it free
of shrinkage porosity. Feeder design parameters include the number, location, shape and dimensions
of feeder. Feed path and feeding distance influence the location and number of feeders. The volume
of the feeders must be minimized to increase the yield. The criterion is given by for getting feeder
yield ‫ܥ‬ிଷ:
‫ܥ‬ிଷ=ܰ௖ ‫ݒ‬௖ /൫ܰ௖ ‫ݒ‬௖ ൅ ∑௜ ‫ݒ‬௙௜ ൯

(5)

Finite element analysis based software Ansys 12.0 has been used. Modal of casting is done in
Pro E wild fire and cylindrical feeders have been created in Ansys modeling. Element selection and
material property feeding is done latter. Convective load have been considered after proper meshing.
Proper boundary values of temperature have been provided and then transient thermal analyses have
been performed. DB log file has been assigned to Ansys optimizer and then design variable, state
variable and objective functions have been provided [5]. They are height of feeder, maximum
temperature difference of feeder and respective casting zone, inverse of feeder yield respectively
with suitable allowances and factor of safety. First order optimization has been performed through
Ansys 12.0.
In FEM, the field variables are the temperatures at all nodal points that vary with time
.Thermal properties like thermal conductivity, density, specific heat also vary with temperature and
hence the problem becomes non – linear transient in nature Galerkin’s weighted residual approach
has been reported[7]. The advantage of using FEM is the ability to handle complex boundaries, the
ease in implementing boundary condition. But this method requires much effort for formulation of
problem, data preparation and need long processing time [8].
In general, FEM is preferred as it allows a wider choice of element shapes and better
accuracy, while FDM based simulation programs are faster and easier to execute. Recent advances
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have been in the areas of automatic preprocessing (mesh generation), adaptive remeshing for better
accuracy in critical regions, heat transfer models for considering the effect of variable air gap and
mould coatings, convective and radiation heat transfer and improving the efficiency of
computation[9]. Feeder optimization has been performed using topology optimization [10], poison
equation approximation [11] and genetic algorithm [12].
P. Prabhakara Rao gives advantages of computer simulation based design enumerated. The
procedures thus described have been demonstrated with the above case study of application of Pro
CAST simulation at G.S alloy Foundry. It is demonstrated that the foundries can derive mileage by
resorting to FEM simulations of the casting process for process development and optimization. [13]
The application of casting simulation softwares in the foundries not only minimizes the
wastages of resources required for final castings, but also improves / enhances the quality and yield
of castings, which implies higher value addition and lower production cost. The experimental study
represents the effect of sizes of risers and necks on the solidification behavior of the aluminum alloy
castings. The simulated results are more or less similar with experimental results. [14]
The application of computer aided method, solid modeling, and casting simulation
technologies in foundries can able to minimize the bottlenecks and non value added time in casting
development, as it reduces the number of trial casting required on the shop floor. In addition, the
optimization of riser neck reduces or completely removes the occurrence of shrinkage defect in the
casting. The application of casting simulation software based on finite element method and vector
element method shows good results and matched with the experimental results.[15]
II.

DATA COLLECTION

Multi feeder optimization has been performed on a dumbbell casting of Aluminium-06. Three
feeders have been considered.
Volume = 1.178 M^3, Surface Area = 8.9e-2 M^2
Feeders can be optimized by modulus approach. The thickest section has highest value of
modulus [1]. The optimization can be performed on Ansys12. [5]
III.

FEEDER OPTIMIZATION

The use of negative of the gradient vector as a direction for minimization was first made by
Cauchy in 1847. In this method we start from initial trial point X1 and iteratively move towards the
optimum point.[4]
The method of steepest descent may appear to be the best unconstrained minimization
technique since each one-dimensional search starts in the best direction. Design optimization works
entirely with the ANSYS Parametric Design Language (APDL) and is contained within its own
module (/OPT). Design optimization is largely concerned with controlling user-defined, APDL
functions/parameters that are to be constrained or minimized using standard optimization methods
(e.g., function minimization, gradients, design of experiments).The independent variables in an
optimization analysis are the design variables. The vector of design variables is indicated by: [4]
ܺ ൌ ሾܺଵ ܺଶ ܺଷ … ܺ௡ ሿ

(6)

Design variables are subject to n constraints with upper and lower limits, that is,
ܺ௜ ൑ ܺ௜ ൑ ܺ௜ ሺ݅ ൌ 1,2,3, … , ݊ሻ
Where: n = number of design variables.

(7)

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The design variable constraints are often referred to as side constraints and define what is
commonly called feasible design space. Now, minimize
݂ ൌ ݂ሺܺሻ
Where:

(8)
f = objective function
ሺ݅ ൌ 1,2,3, … , ݉ଵ ሻ

Subject to ݃௜ ሺܺሻ ൑ ݃௜

(9)

݄௜ ൑ ݄௜ ሺܺሻ ሺ݅ ൌ 1,2,3, … , ݉ଶ ሻ

(10)

ܹ௜ ൑ ܹ௜ ሺܺሻ ൑ ܹ௜ ሺ݅ ൌ 1,2,3, … , ݉ଷ ሻ

(11)

g୧ ,h୧ ,W୧= state variables containing the design, with underbar and overbears representing lower and
upper bounds respectively. (input as min, max on OPVAR command) m_1+m_2+m_3= number of
state variables constraints with various upper and lower limit values. The state variables can also be
referred to as dependent variables in that they vary with the vector x of design variables. [4]
IV.

OPTIMIZATION OF DUMBBELL CASTING WITH MODULUS APPROACH AND
ANSYS

For removing shrinkage porosity defect, three feeders are designed here by modulus approach
and Ansys 10.0 design optimizer for dumbbell casting. Dumbbell has been considered in four
sections A, B, C, D. First modulus approach has been used and then Ansys Optimizer applied.
Modulus ApproachTable 1 Dumbbell casting data (Section wise)
S Volume M ଷ Surface Area Modulus=V/A
A 1.6 × 10ିଷ
B 1.176×10ିହ
C 1.25× 10ିସ
D 1.765×10-5
10ି଺
E
3.9×10-6
10ିସ
F 1.56×10-5
G
3.9×10-6

M ିଶ
6× 10ଶ
6.13 × 10ିଷ
1.5 × 10ିଶ
6.126 × 10ିଷ
1.099×10-3
3.75×10-5
1.0995×10-3

Calculation for first feederDiameter of feeder = D୤ଵ , Height of Feeder = Hf1
Hf = 1.5 D୤ଵ, Volume of feeder = V୤ଵ
Vf = 0.375 π Dଷ
୤ଵ
Area of feeder A୤= 1.75 π Dଶ
୤ଵ

244

0.0267
ଵ
2.87 M 10ିଷ
×
6.67× 10ିଷ
2.88 × 10ିଷ
3.547×10-3
0.416
3.55×10-3


Modulus of feeder Mf =

୚౜భ
୅౜భ

Also Modulus of feeder = 0.214 D୤ଵ
Modulus of feeder = 1.2 × modulus of region around Hot Spot.
0.214 D୤ଵ =
D୤ଵ =

1.2 × 0.0267 M

149.7 MM

Height of Feeder First = 223.5 MM
Modified area of last freezing region= Surface area of hot spot region-area of feeder bottom
= 6.02×10-2 - (π/4)×(0.1497)2
= 0.042399 M2
Modified modulus of last freezing point
= 1.6×10-3/0.042399
= 0.037736
0.214×D୤ଵ = 1.2×0.037736
D୤ଵ = 0.212 M
D୤ଵ = 212 MM
H୤ଵ = 317 MM
As above the height and diameter of feeder second and third has been find out and these values are as
followsD୤ଶ =

64.97 MM, H୤ଶ = 97.46 MM

D୤ଷ =

26.3

MM, H୤ଷ = 39.47 MM

Feeder Yield=
Total Volume of Casting/ Total Volume of Casting + Total Volume of Feeders
So feeder yield by Modulus method is = 13.36%
The process of analysis of this case with Design optimizer of Ansys 12.0 (An FEM Based
general purpose software) has been search out for three feeders. Here we have taken height of
feeders as a design variables, State variable S1 = FT1-CT1 (always positive), State variable S2 =
FT2-CT2 (always positive), State variable S3 = FT3-CT3 (always positive) with suitable allowances
and factor of safety so that hot spot must not remain in casted part. It should be in respective feeder.
FT= maximum feeder temperature for respective zone, CT= maximum casting temperature of
catchment. Following are the graphs as a result of optimization. Figure1 is showing the temperature
according to cooling. It can be seen that higher temperature are with feeders as compare to casing.
This assures that the shrinkage porosity will be in feeders only.
Fig. 1 is showing the temperature variation on the central plane of Casting and Feeders.

245


Figure 1: At centre plane of dumbbell shape casting with optimized feeders

Figure:2: Difference of maximum feeder temperature with corresponding maximum temperature of
casting zone

Figure 3: Inverse of feeder yield during entire optimization process
From figure 3, it is clear that the feeder yield is = 50.76 %
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V.

CONCLUSION

Feeder yield comes out from modulus method = 13.36 % and Feeder yield comes out from
feeder optimizer = 50.76 %. So net advantage gained by Ansys 12.0 design optimizer is = 36.90 %.
Optimization on Ansys works better for small castings. Importing IGES file, Modeling, Meshing, in
Ansys may produce problem for complicated shapes. After optimization of feeder design, the
suggested value can be check by animation on the center plane and temperature contour can be plot
at every time step. Three feeder design optimization can be perform on Ansys 12 which is low priced
general purpose FEM based software. Ansys optimizer can produce better feeder design as compare
to modulus approach for design of feeder but optimization process on Ansys requires more time and
skill to work as compare to modulus method of feeder optimization but it giving accurate result.
VI.

ACKNOWLEDGEMENTS
We are highly thankful for Bhagwant University and close friends & family members.

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