M. FOLTA, A. DELI]: QUALITY OF PRECIPITATION ANNEALING OF HEAT-RESISTANT CAST STEEL ...
83–88
QUALITY OF PRECIPITATION ANNEALING OF
HEAT-RESISTANT CAST STEEL USING A TAGUCHI ANALYSIS
OCENA KVALITETE IZLO^EVALNEGA @ARJENJA TERMI^NO
OBSTOJNE JEKLENE LITINE Z UPORABO TAGUCHIJEVE
ANALIZE
Martin Folta
1
, Alen Deli}
2
1
[KODA AUTO University, Department of Production, Logistics and Quality Management, Na Karmeli 1457,
Mladá Boleslav, Czech Republic
2
TTU energetik d.o.o. Tuzla, 18. Hrvatske brigade br. 25, Tuzla, Bosnia and Herzegovina
Prejem rokopisa – received: 2020-05-08; sprejem za objavo – accepted for publication: 2020-10-26
doi:10.17222/mit.2020.074
In this study, the effects of temperature and time on the hardness of heat-resistant cast steel HK30 Nb obtained with centrifugal
casting were analysed using the Taguchi method. On the basis of the analysis of the obtained results, we reached reliable conclu-
sions on the improvement of the exploitation properties. The tests showed that precipitation annealing of a HK30 Nb casting can
improve the exploitation properties at high temperatures. The defined temperature and holding time comply with the results of
the mathematical analysis of the achieved properties, and the presumed research theory from this study can hence be confirmed.
The studies showed that the mechanical properties improved during the precipitation-annealing process. During this process,
significant transformations of the carbide phase occur in the microstructure, thereby changing its morphology, distribution, size
and composition, which was confirmed by testing the microstructure with a scanning electron microscope.
Keywords: Taguchi analysis, designed experiment, heat-resistant cast steel, precipitation annealing, microstructure, product
quality
V pri~ujo~i {tudiji avtorja s pomo~jo Taguchijeve metode analizirata vpliv temperature in ~asa izlo~evalnega `arjenja na trdoto
termi~no obstojne jeklene litine HK30 Nb izdelane s centrifugalnim litjem. Na osnovi dobljenih rezultatov analize sta pri{la do
zanesljivih zaklju~kov, ki omogo~ajo izbolj{anje uporabnih lastnosti izbrane litine. Preizkusi so pokazali, da izlo~evalno
`arjenje HK30 Nb litine lahko izbolj{a uporabne lastnosti litine pri povi{anih temperaturah. Definirane temperature in ~asi
zadr`evanja se ujemajo z rezultati dose`enih lastnosti na osnovi matemati~ne analize. Na osnovi predpostavljene raziskovalne
teorije v tej {tudiji sta avtorja potrdila prakti~no dose`ene lastnosti. [tudija je pokazala, da se mehanske lastnosti izbrane litine
izbolj{ajo s postopkom izlo~evalnega `arjenja. Med postopkom precipitacijskega `arjenja je pri{lo v mikrostrukturi do
pomembne pretvorbe karbidne faze, to je spremembe njene morfologije, velikostne porazdelitve in sestave, kar je bilo
ugotovljeno z metalografskimi preiskavami na vrsti~nem elektronskem mikroskopu.
Klju~ne besede: Taguchijeva analiza, oblikovanje eksperimenta, termi~no obstojna jeklena litina, izlo~evalno `arjenje,
mikrostruktura, kakovost izdelka
1 INTRODUCTION
1.1 Application of the designed experiment in research
The Taguchi method (TM) of experimental design,
based on the application of Taguchi’s experimental de-
signs, is a well-known, unique and powerful technique
developed to improve the quality of products and pro-
cesses. It represents a simple and efficient method of ex-
perimental design. The application of the method is not
limited to specific problems, and it is mainly used for ex-
perimental analyses and for the optimisation of products
and processes. Generally speaking, the TM application
procedure consists of several steps. The classic experi-
mental design is sometimes too complex and it takes a
long time. When the number of factors increases, it is
necessary to carry out numerous experimental tests. On
the other hand, the TM is based on the application of
special, partial factorial designs obtained from orthogo-
nal designs, which cover the entire experimental space of
interest with a minimum number of experiments in com-
parison with the classic experimental design, and partic-
ularly in comparison with full factorial designs. A lower
number of experiments implies a reduction in the time
and expenses. If a full factorial design has several factors
and variance levels for each factor, the total number of
experiments (N) can be obtained using the following
Equation (1):
N = L
k
(1)
where L is the number of variance levels and k is the
number of factors. For example, for the experiment with
4 factors and 3 levels, the application of the full factorial
design requires 34 = 81 experiments. On the other hand,
using Taguchi’s experimental design, with the standard 4
orthogonal sequence L9 (3), the number of required ex-
periments is reduced to only 9
1–2
.
Taguchi wanted to find an effective manner of their
statistical presentation, and he defined three situations:
Materiali in tehnologije / Materials and technology 55 (2021) 1, 83–88 83
UDK 620.1:539.4.016:539.4.016:621.785:669.018.2 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 55(1)83(2021)
*Corresponding author's e-mail:
martin.folta@savs.cz (Martin Folta)

• smaller is better – when the target value of the re-
sponse is around zero (e.g., emission of harmful
gases, energy consumption),
• larger is better – when the goal is to reach the maxi-
mum target value of the response (e.g., product yield,
conversion of reactants into products),
• nominal is best – when the goal is to reach the mean
target value of the response (e.g., particle size, prod-
uct properties).
The main idea behind the Taguchi methodology is to
apply the experimental-design technique with a view to
defining the levels of controllable factors, which make
the process robust and with the presence of uncontrolla-
ble factors (noises). Such noises have a significant effect
on the response of the process, i.e., on the product qual-
ity, and either it is not possible to control them or it is
economically too demanding to maintain them at a cer-
tain constant value. The noises are the main reason for
the occurrence of variation in the system. Using the
Taguchi method, the product quality is defined as the de-
viation of a certain response from the desired value. Ex-
periments are carried out in such a manner as to establish
the variability range occurring as a result of variance for
controllable factors and uncontrollable factors (noises).
Taguchi recommends using the orthogonal array of the
experimental design, the full experimental design, one
for each of the two groups of factors (controllable vari-
ables and noises). Unlike the traditional Fisher approach,
which implies that the error is distributed randomly
within the design, the Taguchi design enables an analysis
of the effect of the error (noises) on the response.
2,12–14
The levels of the process parameters form the inner
array, while the full noise design makes the outer array.
The outer array consists of four rows, n = 22 (2-level,
2-factor full design), while the inner array has eight col-
umns, m = 23 (2-level, 3-factor full design). Such a de-
sign, as developed by Taguchi, is depicted as a classic
design of controllable factors, which makes the inner ar-
ray, with the addition of the outer noise array in each
corner of the inner array.
In such a manner, there are 22 × 23 = 32 defined ex-
perimental conditions, and the response of the process is
observed for each set of conditions (yij), while the sig-
nal-to-noise ratio (S/N) is calculated for each point of the
inner array. In such a case, the combination of controlla-
ble factors corresponding to the highest S/N value repre-
sents the worst production conditions within the bound-
aries of the tested effects of noises.
In the experiment theory, which covers experimental
planning with the creation and analysis of experimental
designs, for operational implementation of the designed
plan arrays and mathematical processing of experimental
results, two basic statistical methodologies are used –
dispersion and regression analysis.
3–6,8,12–15
Correlation-analysis methods enable statistical evalu-
ations of the quantitative measures of the regression de-
pendence of variables. The simple correlation coefficient
is taken as the quantitative measure of linear depend-
ence, while the quantitative measure of linear depend-
ence of one dependent variable on several independent
variables is known as the multiple-correlation coeffi-
cient. When introducing a new variable or omitting one
of the previously mentioned independent variables in a
multiple-regression model, the multiple-correlation coef-
ficient can be lower, higher, or it can remain unchanged.
Based on that, we estimate the effect of the introduced or
omitted independent variable on the total variability of
the dependent variable. Therefore, by removing the lin-
ear dependence caused by the effect of the other inde-
pendent variables in the linear regression model, we can
obtain the quantitative measure of dependence known as
the partial correlation coefficient.
4,7
1.2 Precipitation annealing
The obstacles to the movement of dislocations are
spatial or three-dimensional, such as the separated
phases of carbides, nitrides or intermetallic seams. These
phases occur when the melting boundaries of foreign at-
oms (atoms of alloyants) in the crystal grid of the basic
metal are exceeded.
The effect of these phases is reflected in their distri-
bution and type (coherent, semi-coherent, incoherent),
size and distance. When coming across precipitates, dis-
locations can cut them off or pass by them, which again
requires a certain amount of energy in the case of an ex-
ternal load, causing an increase in the yield stress  Re
4
which is calculated as per Equation (2):
ΔRe ln
4
22
=
⋅
⋅
Gb
L
L
b π
(2)
where:
G – the shear modulus;
b – the Burgers vector;
L – the distance between particles.
For precipitation hardening, it is preferable to have as
many as possible of equally scattered small hard parti-
cles (precipitates) whose dislocations will have to pass
rather than 'cut' them.
9–11
The basic mechanisms taking place in the micro-
structure in a precipitation-annealing process are:
• Transformation of coarse primary carbides M7C3,
separated in the form of a grid over the dendritic
austenitic boundaries of the grains,
• Separation of fine secondary carbides M23C6 and
transformation of coarse primary carbides MC.
10
2 EXPERIMENTAL PART
The experimental part of this research is presented by
the application of the designed experiment. The precipi-
tation annealing was carried out on cut-off segments of
castings, at three selected temperatures (750, 850 and
950) °C, with holding times at each temperature of (60,
120 and 180) min, and subsequent quick cooling
M. FOLTA, A. DELI]: QUALITY OF PRECIPITATION ANNEALING OF HEAT-RESISTANT CAST STEEL ...
84 Materiali in tehnologije / Materials and technology 55 (2021) 1, 83–88

(quenching) in water. The studies included the annealing
temperatures and times, at which the processes taking
place in the microstructure resulted in a change in the
structure and properties. The temperature of 750 °C was
the operating temperature during the use of this material,
while the other two temperatures were selected in order
to establish if there was any possibility of increasing the
operating temperature of the motor, an important objec-
tive of the conducted studies.
In this study, the Taguchi method was used to deter-
mine the effect of the heat-treatment parameters on the
mechanical properties, i.e., on the hardness. The most
suitable sequence was L
9
(3
2
) (the standard orthogonal se-
quence), which requires 9 experimental tests in the ex-
perimental design for three levels of testing, where the
two factors, the temperature and time, were taken into
consideration. Eventually, the values of the two parame-
ters, temperature and time, were selected and the experi-
mental conditions are given in Table 1.
Table 1: Parameters and levels of precipitation annealing
Process factor Unit Level 1 Level 2 Level 3
Temperature °C 750 850 950
Time Minute 60 120 180
The relevant categories of the S/N (signal to noise)
ratio were selected depending on the nature of the re-
sponse. For a more detailed test of the importance of the
effect of the main factors and their interactions on the re-
sponse, it is possible to use the analysis of variance
(ANOVA). However, instead of the ANOVA analysis,
Taguchi recommended the analysis of the mean values
and the S/N ratio using 2-D graphics of the response.
We examined the importance of controllable factors
using the S/N ratio approach. It is usually required to
have a low value of hardness after precipitation anneal-
ing. For that reason, "smaller is better" for the S/N ratio
was used for the above-mentioned parameters. Irrespec-
tive of the category of performance characteristics, a
high value of the S/N ratio corresponds to better perfor-
mances. Therefore, the best level of process parameters
is the level with the highest S/N ratio.
With a view to determining the effect of the values of
the precipitation-annealing factors on the target function,
an analysis of the S/N value was carried out using the
analysis of the mean values of the hardness results.
Within the analysis, we created the main effects plots,
which show the values of the target function at each fac-
tor level. The main effect of a factor can be defined as
the average change of the target function when the factor
changes from a lower to a higher level. The slope of the
line on the plot shows that an increase in the value of a
factor results in an increase in the value of the target
function. The size of the slope determines the strength of
the effect of the factor on the value of the target function.
The analysis of the effect of each control factor on
the hardness was derived from Table 2.
Table 2: Control factors and mean hardness results
Temperature – °C Time – min Hardness – HB
750 60 214.00
750 120 208.33
750 180 207.00
850 60 206.00
850 120 201.17
850 180 203.00
950 60 200.50
950 120 199.00
950 180 195.33
The S/N ratio for the hardness is shown in Table 3.
The S/N ratio is shown for each level of control factors,
as well as its change when the settings of each control
factor are changed from one level to another.
Table 3: Results of the S/N ratio ("smaller is better") for the hardness
Level Temperature Time
1 –46.43 –46.31
2 –46.17 –46.14
3 –45.94 –46.09
Difference min.-max. 0.49 0.21
Ranking 1 2
The effect of each control factor on the hardness can
be presented more clearly with a relevant plot, see Fig-
ure 1.
Figure 1 shows the level, which needs to be selected
for the precipitation-annealing parameters (the level with
the highest point on the plot), and the relative effect that
each parameter has on the S/N ratio (the slope of the
line). As presented with the plots showing the effect of
the S/N ratio, the slope of the line between different lev-
els can clearly show the power of the effect of each con-
trol factor. It is particularly clear that the temperature has
a strong effect on the hardness. The time has a weaker
effect, which is shown by the small slope of the line.
M. FOLTA, A. DELI]: QUALITY OF PRECIPITATION ANNEALING OF HEAT-RESISTANT CAST STEEL ...
Materiali in tehnologije / Materials and technology 55 (2021) 1, 83–88 85
Figure 1: Effects of the main factors on the S/N ratio for the hardness

Table 4 presents the results of the ANOVA for the
hardness. In this case, the precipitation-annealing tem-
perature is also a more significant factor than the time
for the hardness. The best precipitation-annealing param-
eters for the hardness are 950 °C and 180 min.
Table 4: Hardness-variance analysis
Factor
Degree of
freedom
Sum of
square
Mean
square
(MS)
F ratio P value
Tempera-
ture
2 0.36026 0.36026 36.92 0.003
Time 2 0.07639 0.07639 7.83 0.041
Error 4 0.01952 0.01952
Total 8 0.45617
A comparison between the Taguchi prediction and
the actual (experimental) results was made.
The best hardness results were obtained for the tem-
perature of 950 °C and the time of 180 minutes. There
was little difference between the Taguchi prediction and
the actual S/N ratio results, and there was little variation
in the hardness values (195.33 and 196.24), resulting in a
difference of 0.91 HB.
Exponential model:
The array design that meets the stated requirements
for the two-factor design case is presented in Table 5.
The coded parameter values are +1 for the maximum
value and -1 for the minimum value of the physical pa-
rameter. When there is an intermediate level, the coded
value is zero. In this case, the coding is done using the
following equations:
Factor coding:
X
xx
xx
xx
x
i
ii
ii
ii
i
=
−
−
=
−
00
2
max min
Δ
(3)
x
xx
i
ii
0
2
=
−
max min
(4)
X
i
– the coded parameter value (independent variable),
i – the number of independent variables (I = 1,2,3,...),
 i
– the physical-parameter value at the upper or lower
levels,
  i
– the physical-parameter value at the design centre
and

i
– the interval for variance – the difference between
the physical-parameter values from the centre to the
maximum and minimum values, respectively.
In the factorial design for the two factors of variation,
five experimental points were obtained, with the fifth ex-
perimental point representing the experiment at the de-
sign centre.
Substitute for T: x
i
=lnT, x
0i
+ x
i
=lnT
max
, x
0i
– x
i
=lnT
min
,2 x
i
=lnT
max
–lnT
min
We get:
X
TT
TT
1
12 =+
−
−
ln ln
ln ln
max
max min
(5)
Substitute for t:
x
i
=lnt, x
0i
+ x
i
=lnt
max
, x
0i
– x
i
=lnt
min
,2 x
i
=ln
t
max
–lnt
min
We get:
X
tt
tt
2
12 =+
−
−
ln ln
ln ln
max
max min
(6)
XT
1
8475 57104 =− .l n. (7)
Xt
2
1821 84513 =− .l n ( ). (8)
YbbXbXbXX =+ + +
011221 212
(9)
YXX
XX
=+++
+
531567 00308 001485
0001783
12
12
...
.
(10)
M. FOLTA, A. DELI]: QUALITY OF PRECIPITATION ANNEALING OF HEAT-RESISTANT CAST STEEL ...
86 Materiali in tehnologije / Materials and technology 55 (2021) 1, 83–88
Table 5: Orthogonal array design
Exp. point No.
Array of coded values Linear model Exponential model
X
0 X
1 X
2 X
12
HB HB
1 1 –1 –1 1 214 5.365976
2 1 –1 1 –1 207 5.332719
3 1 1 –1 –1 200.5 5.300814
41111 195.33 5.27469
51000 201.17 5.30415
Figure 2: Effects of the interaction of the temperature and time on the
hardness (HB)

After decoding, we get:
[] ln( ) . . . ln( ) . TT =− − 531567 0308 8475 57104 (11)
Model:
HB T t
Tt
(,)
.
..
=
1339397
0 26103 0 027027
(12)
In order to analyse the effect of the interaction of the
factors of precipitation annealing on the hardness, a 3-D
surface diagram was created by varying two factors si-
multaneously, as shown in Figure 2.
The value of the multiple-regression coefficient
ranges from 0 R = 1. The closer the value of the multi-
ple-regression coefficient to 1, the greater is the interde-
pendence between the independent and dependent vari-
ables. The coefficient of determination R
2
(R square) de-
termines the quality and reliability of the mathematical
model. For the analysed process, the coefficient of deter-
mination R
2
= 0.965, which means that 96.5 % of the
variability is attributed to the effect of independent vari-
able x on the hardness.
3 RESULTS AND DISCUSSION
The microstructure in the precipitation-annealed state
was examined with a QUANTA Scanning Electron Mi-
croscope FEI SIRION 400NC, equipped with an EDS
(energy-dispersive X-ray spectroscopy) system by
INCA, Oxford Instruments, at the University Centre for
Electron Microscopy, Institute for Materials Technology,
University of Maribor.
The microstructure examined on SEM images at a
5000× magnification is shown in Figure 3. The marked
micro-zone in the microstructure was examined using a
quantitative EDS analysis.
Having examined the carbide phase with the scanning
electron microscope (SEM), it was observed that in the
microstructure of the sample precipitation-annealed at
850 °C for 180 minutes, large amounts of Nb and C on a
single carbide were confirmed with the quantitative EDS
analysis; hence, it can be claimed that it is NbC carbide
(Figure 4, spectrum 1/b), Table 6).
M. FOLTA, A. DELI]: QUALITY OF PRECIPITATION ANNEALING OF HEAT-RESISTANT CAST STEEL ...
Materiali in tehnologije / Materials and technology 55 (2021) 1, 83–88 87
Figure 4: Details of the microstructure from Figure 3, with the locations of the quantitative EDS analysis marked: a) Cr23C6 and b) NbC
Table 6: Quantitative EDS analysis of the microstructure at the locations marked in Figure 4
Spectrum/
Figure
Amounts of elements (%)
Phase
C O Si Cr Ni Fe Nb
1 / a) 7.48 26.19 1.34 32.07 6.75 23.67 Cr23C6
1 / b) 19.16 80.84 NbC
Figure 3: Microstructure of the representative sample T6 (850 °C/
180 min) after precipitation annealing at a higher magnification of
5000×

5 CONCLUSIONS
This research was focused on the quality of the pre-
cipitation annealing of heat-resistant cast steel by carry-
ing out a designed experiment. We used the Taguchi
method to determine the effect of heat-treatment parame-
ters on the mechanical properties. We examined the im-
portance of controllable factors using the S/N ratio ap-
proach. An analysis of the S/N value was carried out
using the mean values of the hardness. The results can be
summarized as follows:
The research confirmed that the microstructure plays
the key role in the achievement of certain properties, as
well as the fact that it is susceptible to change during ex-
ploitation or under the influence of external factors, pri-
marily the temperature; hence, the examination of the
microstructure is of utmost importance. It is particularly
important to study the carbide phase, which, with an
austenitic basis, completes the microstructure. This study
sheds light on its influence and, in some segments, it is
in full agreement with the studies conducted on these
phenomena and cited in the reference list.
In the process of precipitation annealing, significant
transformations of the carbide phase take place in the
microstructure, changing its morphology, distribution,
size and composition. The breaking of the primarily sep-
arated, coarse carbide film along the boundaries of
austenitic grains, redistribution in the array and special
separation of fine dispersed carbides in the array, which
are the carriers of all major properties, are the effects
achieved in the microstructure during precipitating an-
nealing,
The application of the designed experiment in our re-
search confirmed that the Taguchi method is a conven-
tional tool that differs from traditional applications. Es-
pecially in our case, it showed that the mechanical
properties improved during the precipitation-annealing
process.
Acknowledgment
This paper was created based on the knowledge and
practical experience of both authors in the area of the
above-presented topic without any specific grant from
funding agencies in the public, commercial or non-profit
sectors. No benefits in any form have been received, or
will be received, from any commercial party related di-
rectly or indirectly to the subject of this paper.
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M. FOLTA, A. DELI]: QUALITY OF PRECIPITATION ANNEALING OF HEAT-RESISTANT CAST STEEL ...
88 Materiali in tehnologije / Materials and technology 55 (2021) 1, 83–88