CHAPTER 3 HARDNESS AND CASE DEPTH ANALYSIS THROUGH
OPTIMIZATlON TECHNIQUES
3.1 Introduction
Changing demands of dynamic market place have improved and increased the
commitment to quality consciousness. All over the world, companies are developing
quality management systems like IS0 9001-2000 and investing in total quality. One of
the critical requirements for the IS0 9001-2000 is adequate control over process
parameters. An auditing report of the IS0 indicates that the majority of the heat treatment
processes in industries present improper application of process variables and inadequate
control over the process parameters. Adequate control of process variables is possible if
the level at which each of the parameters has to be maintained. Optimization is one of
the approaches that help in finding out the right level or value of the parameters that have
to be maintained for obtaining quality output. Determination of optimum parameters lies
in the proper selection and introduction of suitable design of experiment at the earliest
stage of the process and product development cycles so as to result in the quality and
productivity improvement with cost effectiveness.
Investigations indicate that in surface hardening processes Heat treatment
temperature, rate of heating and cooling, heat treatment period, Quenching media and
temperature, Post heat treatment and pre-heat treatment processes are the major
influential parameters, which affect the quality of the part surface hardened. This
chapter deals with the optimization studies conducted to evaluate the effect of various
process variables in Gas Carburizing and Induction Hardening on the attainable Hardness
and Case depth.
In this study, Taguchi's Design of Experiment concept has been used for the
optimization of the process variables of Gas Carburizing process and Factorial design of
Experiment for the optimization of process variables of Induction Hardening process.
As explained in chapter 2, Taguchi's L27 orthogonal array and 3 Factorial array
have been adopted to conduct experiments in Gas Carburizing and Induction Hardening
processes respectively.
Optimum heat treatment conditions have been arrived by employing higher
hardness cum case depth are better as the strategies. The secondary objectives of
identif>ring the major influential variables on Hardness and Case depth have also been
achieved.
3.2 Gas Carburizing Process variables optimization using Taguchi's Method
In this study, Taguchi's L27 orthogonal array of Design of Experiment is used
for the optimization of process variables of Gas carburizing process to improve the
surface hardness and case depth of a Case hardened component. All these experiments
were camed out by Repetition Method. Two different optimization analyses (Response
Graph Analysis and Signal to noise Ratio analysis) have been done on the materials
selected for the study. The materials used were EN 29 and EN 34. Experiments have
been conducted on the machined component pinion of steering wheel assembly.
The normal procedure followed in converting the raw material into a finished
product is shown in Figure 3.1.
Raw Material selection
I 1 Raw Material +
Machining of pinion
1 Machining of pinion - I stage Gas carburiiing process
i Quenching
4 Tempering
Machining of pinion - I1 stage
Gas carburized component
Straightening f i - Finished component (Pinion)
Figure 3.1 Sequence of operations in Gas carburising process
3.3 Hardness of pinion
Hardness of a material is generally defined as resistance to permanent indentation
under static or dynamic loads. Engineering materials are subjected to various
applications where the load conditions and functional requirements may vary widely.
In automobiles, power steering is an important assembly in which Rack and
pinion are the major components subjected to twisting load. In order to improve the wear
resistance characteristics and have high reliability, the components (Rack and Pinion) are
subjected to case hardening.
The major problem in case hardening is inconsistency in hardness and case depth
obtained. The magnitude of hardness depends on the process variables of any surface
hardening process. Hence, in the present research, process variable optimization study
has been carried for obtaining higher surface hardness on the pinion material (Figure 3.2)
used in the power steering assembly of the automobile.
Before Carburizing After Carburizing
Figure 3.2 Pinion used in the power steering assembly of the automobile
3.3.1 Hardness optimization - Response graph method
Response graph method gives the output of interest to be optimized i.e., minimize,
maximize, targeted, etc. The output can be more that one and also it can be quantitative
or qualitative. The conditions underwhich gas carburizing experiments have conducted
are given in Table 3.1. The test results are reported in Table 3.2 and 3.3.
Table 3.1 Gas Carburizing-operating conditions
The experiments have been conducted based on L27 orthogonal array system proposed in
Taguchi's mixed level series DOE with interactions as given below:
S.No.
1
2
3
4
5
i) Furnace Temperature Vs Quenching time (AxB)
ii) Furnace Temperature Vs Tempering Temperature (AxC)
Factors
Furnace temperature
Quenching Time
Tempering Temperature
Tempering Time
Preheating
Notation
A
B
C
D I
Level 3
940°C
120 minutes
250°C
120 minutes
No preheating
Level 1
870°C
60 minutes
150°C
80 minutes
No preheating
Level 2
910°C
90 minutes
200°C
100 minutes
1 50°C
Table 3.2 Orthogonal array for Gas carburizing with Test results and S/N ratio
Material: EN 29 (Surface Hardness optimization)
Table 3.3 Orthogonal array for Gas carburizing with Test results and S/N ratio
Material: EN 34 (Surface Bardness optimization)
From the experimental result, the average effects of process variables under
consideration on the obtainable surface hardness have been calculated and the same are
presented in Table 3.4.
The sample calculation for Average effect of Process variables on surface
hardness is given below.
Variable: Furnace temperature, Variable level - Level 1, Material: EN 29 (Table 3.2)
Average effect = (77+77.5+78.5+79.5+80.5+77+79,5+78.5+77.5)9 = 78.39 HRA
Table 3.4 Average effect of process variables on surface hardness
Response graphs shown in Figure 3.3 (a) to 3.3 (e) are drawn using the values in
Table 3.4. 80
78 860 870 880 890 9M) 910 920 930 940 950
Furnace temperature in degree Celsius ( 4
Quenching time in minutes @)
Tempering Temperature in degree Celsius
Tempering time in minutes (dl
0 20 40 60 80 100 120 140 160 Preheating Temperature in degree Celsius
(el
Figure 3.3 (a) to (e) Process variables Vs Hardness
Influence of process variables on hardness
ANOVA analysis is carried out to determine the influence of main variables on
surface hardness and also to determine the percentage contributions of each variable.
Table 3.5 shows the results of percentage contribution of each variable.
Model Calculation for EN 29
Correction factor, C.F = [x yi] / Number of Experiments
= [77+77.5+....7.79]2 127 =168823.14
Total sum of squares, SST =x y i 2 - C.F =168866-168823.14 = 42.85
Sum of Squares of Variables,
Variable A, SSA = / 9 + x y 3 '/9]-C.F
Percentage contribution of each variable, A = (SSNSST)*lOO
= (7.47 142.85) *I00 = 17.43%
In the same way the percentage contribution of other variables are calculated.
Total contribution of variables, (A+B+C+D+E+AxB+AxC)
.'. Error =12.48%
Table 3.5 Percentage contribution of each variable on Surface hardness
Variables
Furnace temperature
Quenching Time
Tempering Temperature
Tempering Time
Preheating
Furnace Temperature and Quenching time
Furnace Temperature and Tempering Temperature
Error
Surface hardness EN 29 17.43%
18.21%
4.34%
7.94%
10.19%
25.43%
3.98%
12.48%
EN 34 17.79%
15.29%
6.34%
8.25%
12.36%
24.91%
5.28%
9.78%
Optimum set of variables for surface hardness are found by adopting the higher is
better strategy. The results are given in Table 3.6
Table 3.6 Optimum conditions for surface hardness
I Furnace temperature I 940°C 1 940°C I Variables
I I
Quenching Time 90 minutes 90 minutes 1
Surface hardness EN 29
I I
3.3.2 Prediction of mean response - Surface hardness
From Taguchis' methodology, equation (3.1) can be used to predict the surface
EN 34
Tempering Temperature
Tempering Time
Preheating
hardness obtainable.
/3 = T+ (HAopt -T) + (HBopt -T) + (HCopt - T) + (HDopt - T) + (HEopt - T) . . . (3.1)
Where,
,B -predicted mean response
2OO0C
120 minutes
150°C
T-mean of all observed hardness values;
HLPt, HBopt, HCopt HDo,tand HEopt - Hardness values obtained at optimum process
2OO0C
120 minutes
150°C
variable condition.
Model calculation for EN 29 material
T= {(77+77.5+78.5+79.5+80.5+77+79.5+78.5+77,5+79+80,5+80.5+80.5+79.5+78.5+78
+77+78.5+78+79.5+81+79,5+79.5+80.5+79))/27 (eom Table 3.2)
T = 79.0741
H&,t= 79.66667
HBopt= 79.944
HCopt= 79.3333 From Table 3.4
HDopt= 79.830
HEopt= 79.056
p (Surface hardness) = 79.0741+ (79.66667 -79.0741) + (79.944 -79.0741) +
= 8 1.5336 HRA
Similarly, for EN 34 the predicted mean response = 80.7802HRA
Optimum surface hardness value, for EN 29 is 81.5336HR4 and
for EN 34 is 80.7802HR.A
3.3.3 Hardness optimization - Signal to Noise Ratio Method
Signal noise (S/N) ratio analysis estimates the effect of noise factors on the
performance characteristics. It was developed as a proactive equivalent to the reactive
loss function. Signal factors (') are set by the designer to obtain the intended value of the 9 response variable. Noise factors (s') are not controlled or are very expensive or difficult
to control (Harisingh and Pradeep Kumar 2004, Davilkar, el al., 2003). The Gas
carbunzing conditions adopted in the experimentation are given in Table 3.1, and the test
results with S/N ratios are reported in Table 3.2 and Table 3.3.
S/N ratio for maximizing the response factor as the objective (Maximizing the
surface hardness) is determined from the equation (3.2).
Where, yi - the experimental response values for the trials, and n - number of trials.
Optimum condition for surface hardness are found by adopting the higher the S/N
ratio is better as the strategy and results are given in the Table 3.6. The optimum
condition result obtained in S/N method matches with the optimum result obtained from
the response graph analysis.
Model Calculation for the Material EN 29
S / N ratio for maximizing the Case depth (10' Experiment run)
S/N = - 10 loglo { l / (7g2+ 7g2 )*2)
= 43.973 14
3.4 Case-depth in pinion
Depth of hardness penetration in any surface heat treated material is an important
factor in deciding the reliability and life of the part. Hence, it is necessary to measure the
case depth of the hardened layer in the given part. Case depth is defined as "the
peipendicular distance from the surface of the metallic material to the point at which the
change in hardness, chemical composition or microstructure of the case and core cannot
be distinguished" (Rajan, T.V., et al., 1998).
Process variable optimization to obtain the required case depth in the Pinion
material (Figure 3.4) subjected for Gas carburizing is done both by Response graph
analysis and by Signal to Noise ratio analysis. The trials are conducted as per Taguchi's
L27 orthogonal array approach.
Figure 3.4 Specimen of pinion material for case depth analysis
3.4.1 Case Depth optimization - Response graph method
The conditions underwhich the Gas carburizing experiments have been
conducted to anive at the optimum process variables are given in Table 3.1. The test
results are reported in Table 3.7 and 3.8.
Table 3.7 Orthogonal array of Gas Carburizing with Test results and S/N ratio
Material: EN 29 (Case -depth optimization)
Table 3.8 Orthogonal array of Gas Carburizing with Test results and SIN ratio
Material: EN 34 (Case-depth optimization)
The average effects of main factors on case depth are given in Table 3.9 for the
materials EN 29 and EN 34 respectively.
Table 3.9 Average effect of process variables on case depth
Preheating 0.7778 0.7556 0.85 0.8056
Response graphs are drawn using Table 3.9. Figure 3.5(a) to (e) (Response
graphs) shows the influence of process variables on the case depth for the Materials EN
29 and EN 34.
860 870 880 890 900 910 920 930 940 950
Furnace temperature in degree Celsius (a)
0 20 40 60 80 LOO 120 140
Quenching time in minutes @)
50 100 150 200 250 300
Tempering temperature in degree Celsius 0
20 40 60 80 100 120 140
Tempering time in minutes (a
0 20 40 €4 80 100 120 140 160 Preheating Temperature in degree Celsius
(e)
Figure 3.5 (a) to (e) Process variables Vs Casedepth
Influence of main variables on case depth
ANOVA analysis are carried out to determine the influence of main variables on
case depth and also to determine the percentage contributions of each variable. Table
3.10 shows the results of percentage contribution of each variable.
Model Calculation for EN 29
Correction factor, C.F = [' yi l2 1 Number of Experiments
= [0.7+0.95+. . . ... 0.812 127 =17.925
Total sum of squares, SST = yi - C.F
Sum of Squares of variables, Variable A, SSA = [&12 1 9 + ~ y 2 2 / 9 + ~ y 3 2 1 9 ] - C.F
= [6.166+5.522+6.25]-C.F
Percentage contribution of
Variable, A = (SSA/SST)*IOO = (0.013 10.29) *I00 = 4.48%
In the same way the percentage contribution of other variables are calculated.
Total contribution of variables= (A + B+ C+ D+E+AxB+AxC)
.'. Error =12.48%
Table 3.10 Percentage contribution of each variable on Case depth
Variables
Furnace temperature
Quenching Time
Tempering Temperature
Tempering Time
Preheating
Furnace Temperature and Quenching time
Furnace Temperature and Tempering temperature
Error
Case depth EN 29 4.48%
5.99%
9.13%
11.28%
16.28%
29.17%
8.18%
12.48%
EN 34 5.43 %
7.14%
11.41%
12.78%
15.49%
28.18%
9.16%
10.41%
Optimum conditions for Case depth are found by adopting the higher is better
strategy. The results are given in Table 3.6. It is significant to note that the optimum
conditions for hardness and case depth are the same.
3.4.2 Prediction of mean response - Case depth
P = T+ (C&pt -TI + (CBopt -TI + (CCopt - T) -i- (CDopt * T) + (CEOp,- T) ...( 3.3)
Where,
,B -predicted mean response
T-mean of all observed case depth values;
CAopt, CBopt, CCopt, CD ,,,, and CE - Case depth values obtained at optimum
process variable conditions
Model calculation for EN29 material
T= {(0.70+0.95+0.75+0.85+0.90+0.90+0.85+0.75+0.80+0.95+0.95+0.80+0.70+0.6~
0.80+0.75+0.70+0.80+0.85+0.75+0.65+0.70+1.00+0.85+0.95+0.95+0.80))/27
(from Table 3.7) T = 0.81481
CLPt= 0.8333
CBOpt= 0.83889 I from Table 3.10
CCopt= 0.8667
CD 0.8333
CE opt= 0.85
p (Case depth) = 0.81481+ (0.8333-0.81481) + (0.83889 -0.81481) +
(0.8667 - 0.81481) + (0.8333- 0.81481) + (0.85 - 0.81481)
= 0.879605 mm
Similarly for EN 34 the predicted mean response = 0.96265 mm
Optimum Case depth value, for EN 29 = 0.96265 mm and for EN 34 = 0.8945 mm
3.4.3 Case depth optimization - Signal to Noise Ratio Method
Gas carburizing conditions adopted in the experimentation are given in Table 3.1,
and the test results with S / N ratio are given in Table 3.7 and Table 3.8. Optimum
condition for Case depth are found by adopting the higher the S / N ratio is better as the
strategy and results are given in the Table 3.6. The optimum condition result obtained in
S / N method matches with the optimum result obtained from the response graph analysis.
Model Calculation for the Material E.i 29
S/N ratio for maximizing the Case depth (13 '~ Experiment run)
SIN = - 10 loglo { I / (0.7'+ 0 .7~)*2)
= 2.92256
3.5 Induction hardening process variables optimization using Factorial Method
In this study 3 Factorial Design Matrix is used to optimize the process variables
for obtaining improved surface integrity of surface hardened components. The
experiments are conducted to study the influence of process variables on Surface
hardness and Case depth as per Classical DOE. A11 these trials have been carried out by
Randomization method. ANOVA analysis with F-Test has been camed out to determine
the influence of each factor and their interactions. Regression analysis is done to develop
a modeling equation to predict the hardness. AISI 4340 and AISI 1055 are the materials
used in this Induction hardening process experiment. The normal procedure followed in
converting the raw material into a finished product is shown in Figure 3.6.
Raw material selection
f
Machining of Rack Raw nlaterial
I Induction hardening process
I Machined component
t Tempering
Straightening A u Induction hardened component
Figure 3.6 Sequence of operation in Induction Hardening
3.5.1 Hardness optimization on Rack
Induction surface hardened low alloyed medium carbon steels are widely used for
critical automotive and machine applications such as rack and pinion, propulsion shaft,
crankshaft and steering knuckles, which require high surface hardness with low
distortion. Rack is a critical component used in the power steering of automobiles.
Normally, the rack is surface hardened by Induction hardening to withstand the wear
loads. Literatures show that in the case of induction hardening process, the power
potential, scan speed (Heating Time), quench flow rate and frequency are the major
influential variables, which controls the surface hardness, hardness penetration depth
(HPD) and level of distortion. The present study demonstrates the optimization of
critical process variables involved in the Induction hardening of a Rack material used in
the power steering of the automobile.
In order to study the influence of process variables on the hardness in the AISI
4340 and AISI 1055 Rack materials, Induction hardening experiments are conducted.
Table 3.1 1 shows the details about the operating conditions. Table 3.12 and Table 3.13
shows the Experimental results in the 33 Design Matrix for the materials AISI 4340 and
AISI 1055 respectively. Table 3.14 and Table 3.15 shows the ANOVA with F-Test of
the materials AISI 4340 and AISI 1055 respectively.
Table 3.11 Induction hardening operating conditions
The experiments have been conducted based on 33 full factorial DOE.
Table 3.12 33 Design Matrix for Induction hardening with Test results
Material: AISI 4340 (Surface hardness)
Table 3.13 33 Design Matrix for Induction hardening with Test results
Material: AISI 1055 (Surface hardness)
Influence of main variables on Surface hardness of Rack material
Model Calculation (AISI 4340)
Total sum of the run
Number of Treatments
Number of Levels
= (83+8 1+82+. . ..63+66+63) = 5958
= 3 (3 Factors)
= 3
Number of replicates (r) = 3
Total of the observations under all factor levels = N = abcr = 3x3x3x3=8 1
Correction factor, (C) = (5958)2/8 1
=438244
Sum of Squares of Treatment, (SST) = (832+8 1 ~ + 8 2 ~ + . . . 632+662+632)
= (440832) -C
=2588
Sum of Squares of Treatment with replicates, (SST,)
Sum of Squares of Replicate, (SSR)
Sum of Squares of Error, (SSE)
= 1/3(246~+ 249'+.. .192~) = 1 /3(1322244)-C
=2504
= 1/27(1980~+1989~+1989~)-c
= 2
= SST-SST, - SSR
= 2588-2504-2
=82
Sum of Squares of Main effect (P, S and Q)
Sum of Square of Power Potential, SSP = [1/27(2154~+1974~+1830~)]-~ = 1952
Sum of Square of Scan Speed, SSS = [1/27(2034~+1956~+1 96g2)]-c = 130.66
Sum of Square of Quench flow rate, SSQ = [1/27(2007~+1992~+1959~)]-~= 44.66
Two-way interactions of Sum of Squares (PS, SQ and PQ)
Sum of Square of Power Potential and Scan Speed = [1/9(72g2+ ...5942)] -C=177.34
Sum of Square of Scan Speed and Quench flow rate = [119(6902+ ....6452)]-~=46.68
Sum of Square of Power Potential and Quench
flow rate = [1/9(723~+.. .5942)]-~= 33.34
Three way interactions of Sum of Square (PSQ)
Sum of Square of Power Potential, Scan speed and Quench flow rate =SST, - {SSP-SSS-SSQ-SSPS-
SSSQ-SSPQ)
Table 3.14 ANOVA with F-Test
Material: AISI 4340 (Surface hardness)
Variable
Replicates
P
S
Sum of
Squares
2
1952
130.66
TOTAL
Degrees of
Freedom
2
2
2
8 0
Mean
Square
1
976
65.33
F
0.6345
619.289
4 1.453
Significant
Ranking
1
2
Regression analysis is done using MATLAB and the Regression equations (Equation to
predict the hardness of the material AISI 4340) are found and given below.
AISI 4340 Coeff =
The coeficients for the formation of hardness equation are, 111.5611
-4.1474 -2.3059 -0.2889
Equation to predict the hardness of the material AISI 4340
Table 3.15 ANOVA with F-Test
Material: AISI 1055 (Surface hardness)
Similarly, for the material AISI 1055, equation to predict the hardness is given by
0 2 4 6 8 10 Power Potentid In kW/sq.Inch
(a)
0.5 I 1.5 2 2.5
Scan speed in m/minutes @)
/ -C AlSl 4340- AlSl 1054
0 5 10 15 20 25 Quench Flow rate in Litres /minutes
0
Figure 3.7 (a) to (c) Process variables Vs Surface hardness
3.5.2 Case depth optimization in Rack
After Induction hardening a steel component is usually hardness/ Case depth
tested. And the value obtained is a good indication of the effectiveness of the treatment.
The case depth can be measured either by Visual examination or by Hardness
measurement. The case depth1Hardness test is carried out by pressing a ball or point with
a predetermined force into the surface of the specimen. The hardness figure is function
of the size of the indentation for the Brine11 (HB) and Vickers (HV), tests and of the
depth of the penetration for Rockwell (HRC) test. The above three methods are the most
commonly used tests and each has its special range of application and between them they
cover almost the whole for the hardnesslcase depth field that is of interest of the steel
producer and user.
The present study explains the optimization of critical process variables involved
in the Induction hardening of a Rack material (Figure 3.8) used in the power steering of
the automobile to get higher case depth.
Figure 3.8 Cut section of an Induction hardened Rack component
In order to study the influence of process variables on the Case depth of the Rack
material below the teeth and back of the bar for the AISI 4340 and AISI 1055 Rack
materials Induction hardening experiments are conducted.
Table 3.11 shows the details about the operating conditions.
Table 3.16 and Table 3.17 shows the Experimental results in the 33 Design Matrix for the
materials AISI 4340 and AISI 1055 respectively.
Table 3.18 and Table 3.19 shows the ANOVA with F-Test of the material AISI 4340 for
case depth Below the teeth and Back of the bar respectively.
Table 3.20 and Table 3.21 shows the ANOVA with F-Test of the material AISI 1055 for
case depth Below the teeth and Back of the bar respectively.
Table 3.16 33 Design Matrix for Induction hardening with Test results
Material: AISI 4340 (Case depth)
Table 3.17 33 Design Matrix for Induction hardening with Test resuits
Material: AISI 1055 (Case depth)
Influence of main variables on case depth of rack material (below the teeth and back
of the bar for AISI 4340)
Model Calculation (Case depth - below the teeth)
Total sum of the run = (2.4+2.6+2.5+ .... 1.6+1.4+1.5) = 142
Number of Treatments = 3 (3 Factors)
Number of Levels = 3
Number of replicates (r) = 3
Total of the observations under all factor levels Correction factor, (C)
= N = abcr = 3x3x3x3=81 = (1 4212/8 1
=248.93
Sum of Squares of Treatment, (SST) = (2.42+2.62+2.52+ ...1.62+1.42+1.52)
= (261.56)-C
Sum of Squares of Treatment with replicates, (SST,)
Sum of Squares of Replicate, (SSR)
Sum of Squares of Error, (SSE) = SST-SST, - SSR
Sum of Squares of Main effect (P, S and Q)
Sum of Square of Power Potential, SSP = [1127(57.6~+46.2~+38.2~)]-~ = 7.05
Sum of Square of Scan Speed, SSS = [1/27(49.32+46.82+45.92)]-~ = 0.23
Sum of Square of Quench flow rate, SSQ = [1/27(48.g2+48. 1 ~ + 4 5 ~ ) ] - ~ =0.32
Two way interactions of Sum of Squares (PS, SQ and PQ)
Sum of Square of Power Potential and Scan Speed = [1/9(20.12+ ... 12.g2)] -C =0.52
Sum of Square of Scan Speed and Quench flow rate = [1/9(17. 12+. . . . 13.8~11-c =0.9 1
Sum of Square of Power Potential and Quench flow rate = [119(212+. . . 12.3~)]-c = 0.45
Three way interactions of Sum of Square (PSQ)
Sum of Square of Power Potential, Scan speed and
Quench flow rate =SST, - {SSP-SSS-SSQ-SSPS-
SSSQ-SSPQ)
= 12.20-7.05-0.238-0.32-0.52-0.91
0.45
=2.7 12
Table 3.18 ANOVA with F-Test
Material: AISI 4340 (Case depth below the teeth)
TOTAL - 80
Model Calculation ( Case depth- back of the bar)
Total sum of the run = (4.3+4.3+4.3+ .... 1.0+1.1+1.2) = 191.8
Number of Treatments = 3 (3 Factors)
Number of Levels = 3
Number of replicates (r) = 3
Total of the observations
under all factor levels = N = abcr = 3x3x3x3=8 1
Correction factor, (C) = (191.8)2/81
=454.16
Sum of Squares of Treatment, (SST) = (4.32+4.32+4.32+ .. .1 .02+1 ,12+1 .22)
= (535.93)-C
=81.8
Sum of Squares of Treatment
with replicates, (SST,) = 1/3(12.9'+12.3~+. . .3.32)
=1/3(1604.44)-C
=80.65
Sum of Squares of Replicate, (SSR) = 1127(63~+63.5'+65.3~)-~
= 0.111
Sum of Squares of Error, (SSE) = SST-SST,- SSR
= 81.8-80.65-0.1 11
=1.039
Sum of Squares of Main effect (P, S and Q)
Sum of Square of Power Potential, SSP = [1/27(84.62+71.12+36.12)]-~ = 46.417
Sum of Square of Scan Speed, SSS = [1/27(72. 12+55.82+63.9')]-~ = 4.923
Sum of Square of Quench flow rate, SSQ = [1127(67.9~+64.5~+59.4)]-c =1.359
Two way interactions of Sum of Squares (PS, SQ and PQ)
Sum of Square of Power Potential and Scan Speed = [1/9(35.12+. . .10.8~)] -C =14.19
Sum of Square of Scan Speed and Quench flow rate = [1/9(27.4~+ .... 18.g2)]-c = 4.65 Sum of Square of Power Potential and Quench flow rate = [119(28.2~+. .. 10.5')]-c = 0.508
Three way interactions of Sum of Square (PSQ)
Sum of Square of Power Potential, Scan speed
and Quench flow rate +ST, - {SSP-SSS-SSQ-SSPS-
SSSQ-SSPQ}
= 80.65-46.417-4.923-1.359-14.19-
4.65-0.508
=8.603
Table 3.19 ANOVA with F-Test
Material: AISI 4340 (Case depth back of the bar)
Regression analysis is done using MATLAB and the Regression equations
(Equation to predict the Case depth - (Below the teeth and Back of the bar) of the
material AISI 4340) are found and given below.
AISI 4340 Coeff =
The coefficients for the formation of case depth (below the teeth and back of the bar) equation are,
4.3660 8.0291 -0.2265 -0.6135 -0.2127 -0.2797 -0.0367 -0.0500
Equations to predict the Case depth (below the teeth and back of the bar) of the material AISI 4340 are given under.
Table 3.20 ANOVA with F-Test - Material: AISI 1055 (Case depth below the teeth)
Variable
Table 3.21 ANOVA with F-Test - Material: AISI 1055 (Case depth back of the bar)
Sum of
Replicates
P
S
Similarly equation to predict the Case depth (below the teeth and back of the bar) of the
material AISI 1055
YBT= 3.4984-0.1 683P-0.2474s-0.0111Q ...( 3 . 8 )
I Squares
2
2
2
0.0274
3.340
0.770
PSQ
ERROR
TOTAL
8
52
80
0.860
0.5926
Significant Degrees of
0.0137
1.60
0.385
Ranking Freedom
0.1075
0.01 14
Square
Mean
1.201
140.350
33.772
F
J
1
2
9.423 7
+ AlSI 4340 Below the teem * AlSI 1055 Below the teeth
* AIS14340 Back ofttic bar - AlSI 1055 Back of th_e bar, --
Power potential in kW/sq.inch (a)
AS1 4340 Back of the tee& -C AlSI 1055 Back of tbe tc*llj - " AISI 4340 Back of the bar d+ AlSI 1055 Back of tbc bar - - - - .- - - -. -. -- .-
Scan speed in m/minutes @)
AlSl4340 Belaw tl!e teeth * AlSl 1055 Below the teeth
-A- .41514340 Back of the bar - AISI 1055 Back of the bar
5 10 1.5 20 25
Quench flow rate in Litres/minutes
Figure 3.9 (a) to (c) Process variables Vs Case depth
3.6 Results and Discussion
3.6.1 Optimization of carburizing process variables
The present research is concerned with the optimization of process variables
and identification of the root cause for the inconsistency in hardness and case depth and
distortion in Gas carburized materials, e.g., pinion. After holding extensive consultation
with the personnels of all the departments in the industry in which this research has been
carried out, it is concluded that preheating, carbon potential, holding position, furnace
temperature, carburising time, quenching medium, quenching temperature, quenching
time, tempering temperature and tempering time are the influential variables responsible
for the surface integrity of the components. Based on this a Cause and Effect Analysis is
made and Shewerts' diagram (Figure 3.10) is drawn.
TEMPERATURE
QUENCHING MEDIUM
WORN CUITER TEMPERATURE
3.10 Shewerts' diagram for Gas carburizing process
The optimization result (Table 3.6) and Response graphs (Figure 3.3(e), Figure
3.5(e)) indicates that preheating the material before subjecting to Gas carburizing process
improves the hardness and case depth. Even though, this process is employed to relieve
the internal stresses, no remarkable microstructural changes occur during this process.
Internal stresses are developed during machining and grinding. This pre-carburizing
process removes these stresses. It holds well with the remarks given by Shen-Chih Lee
and Wei -Youe Ho (1989) in their paper "The effects of surface hardening on Fracture
Toughness of Carburized steel". Further, it is observed that the extent to which the
stresses can be relieved depends on the temperature employed, holding time and
uniformity in cooling.
Table 3.5 and Table 3.10 shows that fiunace temperature is having a significant
effect on obtainable hardness and case depth. The reason for this may be given as below.
At higher hmace temperature, formation of water vapour is less. Water vapour is a
strongly decarburizing gas but whether this decarburizing tendency will actually reveal
itself in practice depends on a number of factors. The first is the concentration in which
the water vapour is present and the second is the nature of the carburizing gases in
particular gas mixture under consideration. There is perhaps, more contradictory
evidence on this subject of the effect of water vapour in gas carburizing and in the heat
treatment of steeis than any other single item and it is quite clear that a lot more work
remains to be carried out before an absolutely clear picture is obtained. It is possible that
in small amount, water vapour actually has a beneficial effect on carburizing, an effect
which seems to be catalytic in nature. However, the present study shows that higher
fimace temperature (940°C) gives high hardness and case depth.
In the present analysis, Optimum Gas Carburising Process conditions to obtain
higher surface hardness with more case depth are given in Table 3.22.
Table 3.22 Optimum Gas Carburising Process conditions
Analysis of variance is done for EN 29 and EN 34. The ANOVA results (Tables
3.5 and 3.10) and optimum conditions for hardness and Case depth (Table 3.6 - Response
graph and S/N ratio) indicate that the interaction between Furnace temperature and
quenching time is having 25 - 30% influence on the hardness and case depth. Further,
the present optimization analysis shows that Signal to noise ratio method has also given
the same optimal variable levelshest treatment combination levels with the Response
Graph analysis.
To check the optimum results obtained through Taguchis' DOE, confirmation
trials are canied out and the results are tabulated in Table 3.23. From the table it is clear
that the predicted conditions for higher hardness and case depth suits well with the
experimental results.
Values with unit
940°C
90 Minutes
2OO0C
120 Minutes
S.No.
01
02 -
03
04
Process Variables
Furnace Temperature
Quenching Time
Tempering Temperature
Tempering Time
Table 3.23 Experimental trials Vs Predicted values by Taguchis' DOE
EN 34 ( Nickel Molybdenum alloy steel) are characterized by higher tensile
strength and toughness values, improved fatigue strength, impact resistance and shear
strength. EN 29 (Chromium Molybdenum alloy steel) steels are generally case
carburized. Increasing Chromium content increases the wear resistance of case.
However, toughness in the core is somewhat reduced by increasing Chromium content.
The experimental values (EN 29: Maximum case depth -1 mm and Maximum hardness - 81.5 HRA, EN 34: Maximum case depth - 0.9625mm and Maximum Hardness - 80.5
HRA) on case depth and Hardness shows that Chromium Molybdenum steel is giving a
slightly higher hardness and case depth than the Nickel Molybdenum alloy steel.
Experimental values
It is because of presence of more amount of Molybdenum in EN 29. The addition
of Molybdenum improves hardenability, ductility, toughness, and elevated temperature
properties of the steel and also Molybdenum inhibits grain growth and makes the steel
less susceptible to temper brittleness.
EN 29
Predicted values by calculation
(optimum conditions Values)
Hardness
HRA
8 1
8 0
8 1
80
8 1
EN 34 EN 29
Case
depth
fIlIIl
0.90
0.90
1.00
1.00
0.90
EN 34
Hardness
HRA
79
80
79
80
80
Case
depth
mm
0.80
0.90
0.80
0.80
0.90
Hardness
HRA
81.5336
Case
depth
mm
0.96265
Hardness
80.7802
Case
depth
mm
0.89454
3.6.2 Optimization of Induction hardening process variables
Cause and Effect Analysis is made and Shewerts' diagram (Figure 3.1 1) is drawn
for the Induction hardening process. From this, the major contributing process variables
have been identified.
QUENCH FLOW RAT€
QUENCHING MEDIUM
TEMPERANRE
TEMPERANRE
Figure 3.11 Shewerts' diagram for Induction hardening process
Analysis of variance is done for AISI 4340, AISI 1055.The ANOVA results, and
F-Test results (Tables 3.14, 3.15, 3.18, 3.19, 3.20 and 3.21) shows that Power potential
has more influence on the hardness and case depth of the Induction hardened
components. This matches with the suggestion given by Mehmet Cengiz Kayacan and Oguz
Colak 2004. In order to obtain the significance and effect of each factor and their
interaction, the sum of the squares, Degrees of fieedom, Mean square and F are
calculated fxst. Based on these calculations the Ranking and significance of each
variable are done. F-Test ranking also shows that Power potential is the number one
variable having effect on surface hardness and case depth.
Figures 3.7 (a) to (c) and Figure 3.9 (a)to (
(Power potential 5.5 kw/inch2, Scan speed 1.72
003775
litres/min) the hardness and case depth is maximum for the materials AISI 4340 and
AISI 1055 with low distortion.
In the present experimental analysis, optimum induction hardening conditions to
obtain high hardness and with low distortion is given in Table 3.24.
Table 3.24 Optimum Induction hardening Process conditions
/ S.No. I Process Variables I Values with unit 1 I O1 I Power Potential I 5.5kW/ inchZ I
I I
02 1 Scan Speed / 1.72 &minutes
I O3 I Quench Flow rate / 15 Litreslminutes I
Regression analysis is done and the controlling equation to predict the Hardness
and Case depth of Induction hardened components at any parametric conditions has been
developed. To check the Regression equations confirmation trials are carried out and the
results are tabulated in Table 3.25. It shows that there is a good match between the
experimental results and predicted regression results.
I I
Table 3.25 Confirmation trials results Vs Predicted optimum results
04 Frequency 1 lOWz
a - Predicted values from Regression equation b - Confirmation trials values
Trials
01
02
03
04
Case depth back of the bar in mm
a
4.40
3.91
3.42
2.88
b
4.40
3.50
3.30
2.50
Experimental
conditions
Hardness in
HRA
4.5
5.0
5.5
6.0
87.0
83.7
80.4
76.8
b
85.0
82.0
79.0
76.0
Distortion in
mm
Case depth below the
teeth in mm
1.30
1.5
1.72
2.0
a
2.04
1.74
1.43
1.08
a
2.70
2.45
2.20
1.92
P S Q a
10.0
12.5
15.0
18.0
b
2.50
1.95
1.50
1.00
b
2.5
2.2
2.0
1.8