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FOUNDRY JANUARY/FEBRUARY, 2013
Application of Concept of ‘Modulus’ in Non-Ferrous FoundriesG. M. Rajendra PrasadA/14, K. H. B. Colony
Puttenahalli, Bengaluru - 560 064
Email : [email protected]
1. Modulus = Volume / Surface Area
Volume indirectly indicates the ‘amount of heat’ present
in the molten metal, and Surface Area refers to the ‘area
through which that heat can be removed’ for solidificaion
to take place.
On page 149 of the book “Directional Solidification of
Steel Castings” by Wlodawer, you find the following
equation for solidification time of a steel casting poured
in a green sand mould :
Solidification Time = 2.1 (Modulus)2
where, solidification time is in ‘minutes’, and casting
modulus is in ‘centimeters’.
In case of 100 mm dia x 100 mm height casting (Fig. 1),poured in a sand mould, total cooling surface area can
be divided into 3 groups :
(i) Surface Area in contact with sand mould at the
bottom (heat loss by conduction),
(ii) Surface Area in contact with sand mould on the side
(heat loss by conduction + heat loss by
convection),
(iii) Surface Area in contact with atmosphere at the top
(heat loss by radiation).
For molten steel, with no cover on top, one gets
solidification time of 5.0 minutes (Fig. 1).
If one calculates geometrically, he would get
solidification time of 5.8 minutes. This difference
(between 5.0 and 5.8 minutes in solidification time) is
because of radiation heat loss at 1640 ºC (pouring
temperature of steel). The top surface is no longer
merely the geometrical area, but something more than
that. This is called Apparent Surface Area (ASA). This
ASA can be increased (by chilling in the casting), or
decreased (by insulating the feeders).
This alters the modulus, and it is called Modulus
Extention Factor (MEF).
To produce a sound casting we need to know:
(i) % of shrinkage to be fed by the Feeder,
(ii) % of contraction required for Pattern making,
(iii) Size of Feeder, and
(iv) Number of Feeders required.
2. Shrinkages
ΔV L-L
= Loss of ‘super heat’ in molten metal for
solidification to begin.
ΔV L-S
= Loss of ‘latent heat’ during solidification.
ΔV S-S
= Contraction in ‘solid state’ from solidification
point to room temperature.
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100 mm dia x
100 mm H
100 mm dia x
100 mm H
100 mm dia x
100 mm H
100 mm dia x
100 mm H
↓ ↓ ↓ Sand Mould
Top InsulationInsulation
Sleeve
Insulation
Sleeve
Steel 5.0 minutes 13.4 minutes 7.5 minutes 43.0 minutes
Copper 8.2 minutes 14.0 minutes 15.1 minutes 45.0 minutes
Aluminium 12.3 minutes 14.3 minutes 31.1 minutes 45.6 minutes
(a) (b) (c) (d)
Top Insulation
Molten Metal
under solidification
Molten Metal
under solidification
Molten Metal
under solidification
Molten Metal
under solidification
↓ ↓
Fig. 1 : Solidification Time for Various Metals (under different insulation conditions)
Metal Solidification Time (in minutes)
spaceforAuthor’sphoto
FOUNDRY JANUARY/FEBRUARY, 2013
Metal ΔΔΔΔΔV L-L + ΔΔΔΔΔV L-S ΔΔΔΔΔV S-S
Steel 6 % 8%
Copper 6.7% 5.7%
Aluminium 8.3% 8%
ΔΔΔΔΔV S-S is 8% in Steel on volumetric basis. On linear scale,
it becomes 2%. This indicates the ‘contraction
allowance’ to be provided while making the Pattern.
3. Feeding Distance (or Feeding Range)
Feeding Distance is directly proportional to the density
of the alloy and its specific heat, and inversly proportional
to the thermal conductivity of the solidifying alloy.
(Alloy Density x Specific Heat)
Alloy Thermal Conductivity
where, ‘X’ depends on the metal/alloy of the casting.
As ‘X’ increases, feeding distance increases (but the
actual data for different metals is not available). To
evaluate its value in case of copper / aluminium, one
has to pour a plate in copper or in aluminium, to ascertain
the value of ‘X’, and to examine shrinkage-free length
by radiographic testing (Fig. 2).
• In case of plate shape Steel Casting (width : thickness
in the ratio of 5:1), Feeding Distance is 4.5 T
• For Stainless Steel Feeding Distance is almost 12 T
where, ‘T’ indicates the thickness of the plate shape.
Total Feeding Distance is the sum of End Effect +Feeder Effect. In plain carbon steel casting, total feeding
distance of 4.5 T consists of 2.5 T (end effect) + 2.0 T
(feeder effect).
Feeding Distance for Different Alloys (plate shape)
Cast Alloy Feeding Distance
Steel (plate shape) 4.5 T
Aluminium (plate shape) 11 T
Copper (plate shape) 8 T
Bar shape : In case of a Bar shape (1:1), Feeding
Distance is lower, i.e. shorter (see Wlodawer).
4. Calculation of Feeder Modulus
In case of Steel casting :
Mfeeder = 1.2 Mcasting
This helps to calculate the feeder size.
Similar equation for Copper and Aluminium will haveto be established.
Now you know the following to get a sound casting :
(i) Size of Feeder(s)
(ii) Number of Feeder(s)
(iii) Contraction Allowance on Pattern
As regards to MEF, one can get it from figures.
Wlodawer’s “Directional Solidification of SteelCastings” has a wealth of information for SteelCastings. *
But no such book is available for copper or aluminiumalloys. It will have to be established for these alloys, so
that sound copper/aluminium castings can also be made
without trials. (As of now, it is not possible, as no data isavailable.)
For S. G. Iron foundrymen, the books on ‘Gating &
Feeding’ can be obtained from <www.sorelmetal.com>.
(This is because gating & feeding of steel castings is
different from that of S. G. Iron.)
Reference1. Wlodawer – “Directional Solidification of Steel
Castings”.
2. Beeley, Foundry Technology
3. Feeding Range, Cast Metals Research Journal
(AFS), June 1975, Volume 11, No. 2
* This book is out of print now. Interested readers may pleasecontact G. M. Rajendra Prasad (the author) by email<[email protected]> or by Mobile : 094805 04635.
Feeding Distance = X
↓
Feeder
End Effect Feeder Effect
↓
↓
→
Centerline Shrinkage
↓Feeder
↓Plate Casting
----------- -----------↓
Feeder
End Effect Feeder Effect
↓
↓
↓Feeder
↓Plate Casting
Fig. 2 : Unsound Casting (left), and Sound Casting (right)
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