Materials Sciences and Applications, 2010, 1, 152-157
doi:10.4236/msa.2010.13024 Published Online August 2010 (http://www.SciRP.org/journal/msa)
Analysis of Density of Sintered Iron Powder
Component Using the Response Surface Method
Prasanta Kumar Bardhan1, Suprs Patra2, Goutam Sutradhar3
1Department of Mechanical Engineering, JIS College of Engineering, Kalyani, India; 2Cwiss, IIT Kharagpur, West Bengal, India;
3Department of Mechanical Engineering, Jadavpur University, Kolkata, India.
Received March 18th, 2010; revised May 14th, 2010; accepted May 26th, 2010.
ABSTRACT
The continued growth of ferrous powder metallurgy in automobile and others engineering application is largely de-
pendent on the development of higher density materials and improved mechanical properties. Since density is a pre-
dominant factor in the performance of powder metallurgy components, it has been primarily considered for the present
investigation. An experimental investigation have been undertaken in order to understand the variation of density with
respect to the variation of process parameters viz., compaction load, sinter temperature and sintering time. The relation
among the various process parameters with density has been observed. A mathematical model has been developed us-
ing second order response surface model (RSM) with central composite design (CCD) considering the above mentioned
process parameters. The developed mathematical model would help in predicting the variation in density with the
change in the level of different parameters influencing the density variation. This model also can be useful for setting of
optimum value of the parameters for achieving the target density.
Keywords: Powder Metallurgy, Density, Sintering, Response Surface Model, Central Composite Design
1. Introduction
Growth of ferrous powder metallurgy (P/M) over the past
few decades has been outstanding as this technology is
providing itself as an alternate lower process cost to mac-
hining, casting, stamping, forging and other similar metal
working technologies [1,2]. Along with that it also prov-
ides some outstanding advantages such as high material
utilization, more refined microstructure that provides su-
perior material properties as well as greater microstruc-
ture homogeneity. Above all the net shape making proc-
ess by this P/M method is a result of material design that
provides consistent and minimal shrinkage after sintering
from the originally compacted parts [3]. The use of the
double press double sintering process is an accepted me-
thod for providing higher density parts. A low temperat-
ure presintering and a repress step are performed betw-
een the first compaction and final sintering steps [4-5]. In
P/M process a familiar method is double compaction and
double sintering method although this process is well ac-
cepted due to achievement of high density samples; how-
ever it suffers from high costing which sometimes is not
desirable. Another useful method in this regard is single
compaction warm compaction process in which powders
and tools are heated between 130◦ and 150◦ to achieve
high density product. This method also provides increa-
sed green strength and reduced ejection forces [5,6]. To
lower the production cost sometimes a relatively easier
method is employed for the preparation of the P/M
products known as single compaction method where the
desirable density can easily be achieved by controlling of
sintering temperature and time. As sintering is a predo-
minant factor for controlling the density of the P/M sam-
ples, variation of sintering time, temperature largely aff-
ects the density of the P/M components [7-11]. In some
cases a steam treatment or other secondary operations are
necessary to meet specific usage requirement. In another
version of the P/M process, powder are pressed to a pre-
form and hot forged immediately after sintering (Powder
Forge-P/F process). The powder forged parts are compa-
rable to conventional forged steel parts. P/M process pro-
duce 95-98% of full density compare to P/F process wh-
ich produces 100% density [3].
The effects of different types of powder on density, age
hardening on the pore closure and hardness of sintered
iron and iron copper alloy have also been studied. The ef-
fect of compaction pressure and powder particle size on
the pore structure and hardness of steam oxidized sint-
ered iron have also been investigated [9]. When an imp-

Analysis of Density of Sintered Iron Powder Component Using the Response Surface Method153
ermeable ferrous product is desirable, the sintered parts
of high density can be steam treated to close the surface
pores. It is also observed that the green density and sint-
ered density is a function of powder type and compaction
pressure [9].
Albeit, a large number of experimental investigations
have been carried out, only few of them substantiated
their observations with a theoretical model. However,
present day industrial application demands comprehen-
sive theoretical simulation before actual design. Consid-
ering these aspects we provided a theoretical model ba-
sed on our experimental results. Present study examines
the variation of density (R1) as a function of process par-
ameters (compactionload x1, sintering temperature x2,
and sintering time x3) of sintered iron P/M components.
The samples were produced by changing the process
parame- ters as per the design of experiment (DOE) and
the resp- onse surface methodology (RSM) has been used
to plan and analyze the density. The experimental plan
adopts the face-centered central composite design (CCD).
A second order response surface model (RSM) has been
used to develop a predicting equation of density based on
the data collected by a statistical design of experiments
[12-14]. The analysis of variation (ANOVA) shows that
the observed data fits well into the assumed second order
RSM model. It is worth mentioning that this model is one
of the most widely used methods to solve the optimiza-
tion problem in manufacturing technology [10]. In the
experiment, porosity of the samples, compacted and sin-
tered under different conditions were investigated by the
optical microscope [7]. It is found that porosity of the
samples decreases with the increase of compaction load,
sintering temperature and sintering time.
2. Experimental Procedures
The iron powder used in the present study was supplied
by Kawasaki Steel Corporation Chiba Works, chiba, Ja-
pan. The said company has clarified chemical analysis
and particle size distribution of the above powder mate-
rial. The data has shown in Tables 1 and 2.
The iron powder was compacted in a closed cylindri-
cal die using 120 Ton hydraulic press (Lawrence & Ma-
yo) for green stage product. During compaction, the die
was lubricated with Zn-stearate. The sintering process
was carried out in a vacuum furnace of capacity (1450˚C)
Table 1. Chemical Analysis of iron powder (weight%)
C Si Mn P S O Fe
0.0010.02 0 .17 0.013 0.010 0.129Balance
Table 2. Powder Properties. Apparent Density (gm/cc): 2.94;
Flow (s/50gm): 24.7. Sieve Distribution
Sieve Number Size Cumulative wt%
+100#
+150#
+200#
+250#
+325#
–325#
> 150 um
> 106 um
> 75 um
> 63 um
> 45 um
< 45 um
8.5
20.1
22.9
9.5
16.8
22.2
using argon as an inert gas.
One of the major objectives of present investigations is
to shade light on the density of the compacted sintered sa-
mples. In this context 60 different P/M components (dia-
25 mm) were produced according to design of experi-
ment (DOE). Related density (R1) of these samples were
measured by hydrostatic weighing method against the va-
riation of controllable process variables like compaction
load (x1), sintering time (x3) and sintering temperature
(x2). The results obtained through the experiments are
given in Tables 3 and 4 and the available data have been
analyzed by response surface method using Minitab sof-
tware (version 14).
From the results of ANOVA a mathematical model
has been proposed for the evaluation of density, RCCD
(Density) of the powder metallurgy components. The
proposed model is expressed as
RCCD (Density) = – 0.820967 + 0.218738 x1
+ 0.008407x2 – 0.571286 x3
+ 0.007148x1
2 – 0.000002x2 2
+ 0.064705x3
2 – 0.000333x1x2
– 0.020574x1x3 + 0.000767x2x3
3. Results and Discussion
In the present study iron powders, sintered at various tem-
perature and time are investigated. The samples are co-
mpacted under different load range (14.6 ton-29.49 ton)
according to the design of experiment (DOE).
Table 3. Symbols, levels and values of process parameters
Symbols Levels
Process parameters
(Independent variables) Actual Coded Actual Coded
Compaction load (Ton) z1 x1 17.66 20.075 26.4 9 –1 0 +1
Sintering temperature (℃ ) z2 x2 975 1050 1125 –1 0 +1
Sintering time ( hrs) z3 x3 1 1.5 2 –1 0 +1

Analysis of Density of Sintered Iron Powder Component Using the Response Surface Method
154
Table 4. Observed Density—values for different settings of process parameters based on 23 full factorial design
Coded Value of Parameters Actual Value of Parameters Response variables R1
Sl.
No. x1 x
2 x 3 Compaction load. (Ton)Sintering. Temp. (℃)Sintering. Time (Hrs.) Density (g/cm3)
1 –1 –1 –1 17.66 975 1 6.07
2 1 –1 –1 26.49 975 1 7.78
3 –1 1 –1 17.66 1125 1 6.00
4 1 1 –1 26.49 1125 1 6.87
5 –1 –1 1 17.66 975 2 6.07
6 1 –1 1 26.49 975 2 7.78
7 –1 1 1 17.66 1125 2 6.00
8 1 1 1 26.49 1125 2 6.74
9 –1.6818 0 0 14.65 1050 1.5 5.94
10 1.6818 0 0 29.50 1050 1.5 7.84
11 0 –1.6818 0 22.08 923.87 1.5 6.46
12 0 1.6818 0 22.08 1176.13 1.5 6.39
13 0 0 –1.6818 22.08 1050 0.659 6.38
14 0 0 1.6818 22.08 1050 2.341 6.53
15 0 0 0 22.08 1050 1.5 6.38
16 0 0 0 22.08 1050 1.5 6.50
17 0 0 0 22.08 1050 1.5 6.50
18 0 0 0 22.08 1050 1.5 6.60
19 0 0 0 22.08 1050 1.5 6.50
20 0 0 0 22.08 1050 1.5 6.50
21 –1 –1 –1 17.66 975 1 6.07
22 1 –1 –1 26.49 975 1 7.93
23 –1 1 –1 17.66 1125 1 6.00
24 1 1 –1 26.49 1125 1 7.75
25 –1 –1 1 17.66 975 2 6.15
26 1 –1 1 26.49 975 2 7.79
27 –1 1 1 17.66 1125 2 6.00
28 1 1 1 26.49 1125 2 7.74
29 –1.6818 0 0 14.65 1050 1.5 5.89
30 1.6818 0 0 29.50 1050 1.5 8.04
31 0 –1.6818 0 22.08 923.87 1.5 6.38
32 0 1.6818 0 22.08 1176.13 1.5 6.39
33 0 0 –1.6818 22.08 1050 0.659 6.38
34 0 0 1.6818 22.08 1050 2.341 6.53
35 0 0 0 22.08 1050 1.5 6.38
36 0 0 0 22.08 1050 1.5 6.50
37 0 0 0 22.08 1050 1.5 6.50
38 0 0 0 22.08 1050 1.5 6.50
39 0 0 0 22.08 1050 1.5 6.50
40 0 0 0 22.08 1050 1.5 6.50
41 –1 –1 –1 17.66 975 1 6.07
42 1 –1 –1 26.49 975 1 8.02
43 –1 1 –1 17.66 1125 1 6.00
44 1 1 –1 26.49 1125 1 7.79
45 –1 –1 1 17.66 975 2 6.15
46 1 –1 1 26.49 975 2 7.79.
47 –1 1 1 17.66 1125 2 6.00
48 1 1 1 26.49 1125 2 7.77
49 –1.6818 0 0 14.65 1050 1.5 6.06
50 1.6818 0 0 29.500 1050 1.5 7.79
51 0 –1.6818 0 22.08 923.87 1.5 6.38

Analysis of Density of Sintered Iron Powder Component Using the Response Surface Method
155
Table 1 continued
52 0 1.6818 0 22.08 1176.13 1.5 6.39
53 0 0 –1.6818 22.08 1050 0.659 6.38
54 0 0 1.6818 22.08 1050 2.341 6.53
55 0 0 0 22.08 1050 1.5 6.38
56 0 0 0 22.08 1050 1.5 6.50
57 0 0 0 22.08 1050 1.5 6.50
58 0 0 0 22.08 1050 1.5 6.50
59 0 0 0 22.08 1050 1.5 6.50
60 0 0 0 22.08 1050 1.5 6.50
Figure 1 shows the microstructures of P/M samples
sintered at fixed temperature (1050˚C) and for fixed sin-
tering time (1.5 hrs.) under different compaction load.
The white portion of the figure indicates iron grains and
the black portions indicate porous area of the specimen.
From the figure it is quite evident that with gradual incr-
ease of compaction load the porosity of the samples gr-
adually decreases. Similar behavior is also observed with
the variation of sintering time and sinter temperature, the
porosity changes (not shown in figure). Decrease in poro-
sity would increase the density. That phenomenon actua-
lly reflected in the Figure 2.
In Figure 3, Compaction load has been altered betw-
een 14.65 Ton to 29.50 Ton and sintering time has been
changed between 0.6 to 2.3 hrs at invariant sintering te-
mperature of 1050˚C. The response variable under consi-
deration shows a completely diverse nature when it is pl-
otted against sintering temperature and sintering time at a
fixed compaction load of 22.08 Ton (Figure 4). In this
case, the range of variation of the parameters is similar to
that of previous two cases. It is worth mentioning, in all
the cases the hold values are mean value of the range of
variation corresponding to each variable. Average values
are preferred because of the inherent nature of the RSM
model. Variation of density against sintering temperature and
compaction load is presented in Figure 2. The figure
exhibits an increasing tendency in density due to change
in sintering temperature from 975˚C to 1176˚C and com-
paction load from 14.65 Ton to 29.50 Ton at a fixed sint-
ering time of 1.5 hrs. Identical nature of variation is not-
ed in simultaneous increase of compaction load and sint-
ering time. This observation is illustrated in Figure 3.
Figure 2.Surface Plot of density (R1) Vs. compaction load
(x1) and sintering temperature (x2) for a fixed value of sin-
tering time (x3)
(a) (b)
(c) (d)
Figure 1. Microstructure of the iron P/M specimen at dif-
ferent load (Original Photographs at 700×). (a) Compaction
load 29.50 Ton, Sintering temperature 1050˚C Sintering
time 1.5 hrs; (b) Compaction load 26.49 Ton, Sintering
temperature 1050˚C, Sintering time 1.5 hrs; (c) Compaction
load 22.08 Ton, Sintering temperature 1050˚C, Sintering
time 1.5 hrs; (d)compaction load 17.66 Ton, Sintering tem-
perature 1050˚C, Sintering time 1.5 hrs
Figure 3. Surface Plot of density (R1) Vs. compaction load
x1 and sintering time (x3) for a fixed value of sintering tem-
perature(x2)

Analysis of Density of Sintered Iron Powder Component Using the Response Surface Method
156
Figure 2 and Figure 3 demonstrate an interesting fea-
ture. A closure look at the figures exhibit that at high
enough compaction load role of temperature variation is
not very prominent. However, role of temperature varia-
tion is quite evident in Figure 4 where the densification
parameter is negative which clearly confirms compact
swelling of the material. Table 5 presents the ANOVA
(Analysis of variances) for the second order response
surface equations, which quite clearly shows that second
order response surface model fit well into the observed
data. Observed density data and the predicted density
data are depicted in Figure 5.
The figure shows that the experimental data resembles
well with the predicted data. A comparative graph has
been made between the predicting values of density with
the observed values of densities. It is observed that the
predicted values are mostly matching with the observed
values with 10-15% error, which is accepted for any pre-
dicting analysis. It may be concluded that our predicting
values is quite in sequence with the actual values. This is
also evident from the findings that co-efficient of deter
mination (R-Square) value is 89.8 %. Hence, it may be
concluded that the prediction made by this developed
model corroborates well with the experimental observa-
tions.
4. Conclusions
In the present study, a detail microstructure analysis has
been made which confirms that the density of the P/M
product considerably increases with the increase in comp
action load, sintering temperature and sintering time. The
results obtained have been analyzed through the response
surface model. A second order response surface method
(RSM) has been used to develop a predicting equation of
density based on the data collected by a statistical design
of experiments known as central composite design (C-
CD). The analysis of variance (ANOVA) shows that the
observed data fits well into the assumed second order
RSM model. Pertinent microstructural analysis is also
present.
Figure 4. Surface Plot of density (R1) Vs. sintering tem-
perature (x2) and sintering time (x3) for a fixed value of
compaction load (x1)
5.56.06.57.07.58.0
5.5
6.0
6.5
7.0
7.5
8.0
RSM model
R-Square=89.8%
Predicted values of density (g/cm3)
Observed value of density (g/cm3)
RSM model
R-Square = 89.8%
Figure 5. Plot between observed density data and predicted
density for RSM model
Table 5. Analysis of Variance for R1 (Density)
Source DF Seq. SS Adj. SS Adj. MS F P
Regression 9 17.86968 17.86968 1.98552 39.85 0.000
Linear 3 16.6457 0.09896 0.03299 0.66 0.579
Square 3 0.8621 0.86206 0.28735 5.77 0.002
Interaction 3 0.3619 0.36195 0.12065 2.42 0.077
Residual Error 50 2.4911 2.49111 0.04982
Lack-of-Fit 5 0.5991 0.59906 0.11981 2.85 0.026
Pure Error 45 1.8920 1.89205 0.04205
Total 59 20.3608
DF: Degrees of freedom, SS: Sum of Square, MS: Mean Square of variation, F: F-test, P: Value of probability
R-Sq = 89.8%

Analysis of Density of Sintered Iron Powder Component Using the Response Surface Method157
7. Acknowledgements
Authors are very much grateful to All India Council For
Technical Education, New Delhi [F. No. 8021 /RID/
NPROJ/R&D-174/2002-03/ (Revalidated 2003-2004) for
funding this Project. Authors also like to acknowledge
their sincere thanks to M/S Kawasaki Steel Corporation
Chiba Works, Chiba, Japan for sending 4 Kg iron Pow-
der along with the certificate of chemical analysis free of
cost for this study. Authors also acknowledge the facili-
ties received from the Metal Forming Laboratory, Me-
chanical Engineering Department. Jadavpur University,
Kolkata, India.
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Nomenclature
x1 coded value of Compaction load
x2 coded value of Sintering temperature
x3 coded value of Sintering time
R1 density of sintered iron component
Rccd Predicting equation of density of sintered
iron component
z1 actual value of
Compaction load