Engineering, 2010, 2, 635-640
doi:10.4236/eng.2010.28081 Published Online August 2010 (http://www.SciRP.org/journal/eng).
Statistical Modeling of Pin Gauge Dimensions of Root of
Gas Turbine Blade in Creep Feed Grinding Process
Ahmad Reza Fazeli
Manufacture and Production Engineer, Mapna Group (Mavadkaran Engineering Co.), Tehran, Iran
Received January 28, 2010; revised March 9, 2010; accepted March 13, 2010
Abstract
Creep feed grinding is a recently invented process of material handling. It combines high quality of the piece
surface, productivity, and the possibility of automatic control. The main objectives of this research is to study
the influences of major process parameters and their interactions of creep feed grinding process such as
wheel speed, workpiece speed, grinding depth, and dresser speed on the pin gauge dimensions of root of gas
turbine blade by design of experiments (DOE). Experimental results are analyzed by analysis of variance
(ANOVA) and empirical models of pin gauge dimensions of root are developed. The study found that higher
wheel speed along with slower workpiece speed, lower grinding depth and higher dresser speed, cause to
obtain best conditions for pin gauge dimensions of root.
Keywords: Creep Feed Grinding, Pin gauge dimension, Analysis of Variance, Regression,
Interactive Effect
1. Introduction
Grinding has traditionally been associated with small
rates of material removal and fine finishing operations.
Using an approach known as creep-feed grinding (Fig-
ure 1), a large-scale metal removal similar to milling can
be achieved. Using this approach, higher material re-
moval rates can be performed by selection of a higher
depth of cut and lower workpiece speed. The correct
selection of the cutting conditions and the wheel specifi-
cations can provide a greater material removal rate and a
finer surface quality. One of the most important applica-
tions of creep-feed grinding is the production of the aer-
ospace parts used in jet engines such as turbine vanes,
and blades where parts should have high strength to the
fatigue loads and creep strains. These parts are made
from nickel-based super-alloys such as Inconel, Udimet,
Rene, Waspaloy, and Hastelloy. They provide a higher
strength to weight ratio, and maintain high resistance to
corrosion, mechanical thermal fatigue, and mechanical
and thermal shocks [1].
Vafaeesefat modeled and predicted the grinding forces
of the creep feed grinding of supper-alloy materials using
neural network. This model was then used to select the
working conditions (such as depth of cut, the wheel
speed, and workpiece speeds) to prevent the surface
burning and to maximize the material removal rate. The
results showed that the combination of neural network
and an optimization system is capable of generating op-
timal process parameters [1].
Wange et al. [2] provided a thermal model that fo-
cused on the heat transfer to the fluid, workpiece and
grain for creep feed grinding. In their model, the conduc-
tion effect in the moving direction of the workpiece was
considered which was found to be very significant, espe-
cially for creep feed grinding. Moreover, the thermal
partition ratios to the workpiece, fluid and grain were
well defined and discussed. The results revealed that the
cooling effect of the fluid is more crucial especially at
larger grinding depth.
Hann [3], Malkin and Anderson [4], Malkin [5], Rowe
and Morgan [6] derived thermal partition and workpiece
Figure 1. Creep-feed grinding of gas turbine blade.

A. R. FAZELI 636
temperature in dry grinding that failed to take into ac-
count the cooling effect of the fluid.
Lavine et al. [7] presented a conical grain model, with
grain slope set to one. Lavine and Jen [8] derived a sep-
arate thermal model among the fluid, wheel and work-
piece to predict the occurrence of boiling.
Wange et al. [9] depicted that the grinding energy
when the fluid begins to cause boiling is defined as the
critical grinding energy for the workpiece burning. The
results showed that the workpiece burning can be pre-
dicted or evaluated to avoid the working conditions of
burning occurrence.
Shafto et al. [10] proposed that workpiece burning
could be explained by the phenomenon of fluid film
boiling.
Ohishi and Furukawa [11] derived the relationship
between the grinding heat flux and grinding zone tem-
perature at burning using the fraction of the grinding
energy entering into the workpiece at 10%.
Wange et al. [12] modeled the grinding force of the
creep feed grinding using the improved back propagation
neural (BPN) network in view of avoiding the workpiece
burning. The results showed that the grinding energy can
be accurately predicted by the application of the grinding
force model and that a larger size of wheel is available to
have a better working efficiency.
Pin gauge dimension is one of the important geomet-
rical dimensions in root of gas turbine blade that plays an
important role in correct assembly of blade on disk of
turbine. If this important dimension is not properly con-
trolled and goes out of its tolerance range (within 0.062),
the blade will not fit on the disk of turbine.
Figure 2 shows the gas turbine blade. Figure 3 illus-
trates the pin gauge dimension that is one of the impor-
tant geometrical dimensions in root of gas turbine blade.
In this research, the influences of major process pa-
rameters and their interactions of creep feed grinding
process such as wheel speed, workpiece speed, grinding
depth and dresser speed on the root geometrical dimen-
sions of gas turbine blade is studied using design of ex-
periments (DOE).
It is desirable to know the effects of the major pa-
rameters and interactive influences among the process
Figure 2. Pin gauge dimension.
Figure 3. Gas turbine blade.
parameters on root geometrical dimensions and relation-
ship between root geometrical dimensions and process
parameters to obtain the best conditions of parameters
for optimum production.
For modeling and determining the influences of main
parameters and interaction effects among parameters of
the process on root geometrical dimensions, design of
experiments method (DOE) has been employed. DOE is
a statistical method which is used to find the significance
of interactive effects among variables and relations
among process parameters using variance analysis. Fi-
nally, using this model and the suitable pin gauge dimen-
sion, input parameters has been achieved for optimum
production.
2. Description of Material
We have chosen Inconel 738 LC supper-alloy as the ex-
perimental sample. This supper-alloy provides higher
strength to weight ratio, and maintains high resistance to
corrosion, mechanical thermal fatigue, and mechanical
and thermal shocks. The chemical composition of this
supper-alloy is presented in Table 1.
3. Experimental Modeling
3.1. The Output Parameters
Output parameter, pin gauge dimension measured in
terms of mm with inside micrometer 0-25, 0.01 mm pre-
cision.
3.2. The Input Parameters
Input parameters were selected from the various para-
meters of creep feed grinding process such as the proper-
ties of the work piece material, tools, dresser rotational
speed, rigidity of machine tools and type of coolant. The
selected parameters are:

A. R. FAZELI 637
Table 1. The chemical compositions of Inconel 738 LC sup-
per-alloy.
Min Max Min Max
Element
Percentage
Element
Percentage
C 0.09 0.13 Nb 0.6 1.1
Cr 15.7 16.3 Ta 1.5 2
Co 8 9 W 2.4 2.8
Al 3.2 3.7 Fe - 0.3
Ti 3.2 3.7 Si - 0.05
(AI + Ti) 6.5 7.2 Mn - 0.05
B 0.007 0.009 S - 0.003
Zr 0.03 0.06
Mo 1.5 2
Ni Bal.
- The wheel speed.
- The workpiece speed.
- The grinding depth.
- The dresser speed.
3.3. The Experiment Conditions
Grinding wheel type was Strato/Tyrolit (F13A70FF1)
and coolant type was Cutzol zt 130 (oil Canada).
3.4. The Experimental Design
It is difficult and expensive to perform all experiments.
The DOE method can be employed as an efficient tech-
nique to accomplish the suitable and necessary experi-
ments with high accuracy. To investigate multiple inter-
actions between parameters [13] in this study, a frac-
tional-factorial design was employed with two levels for
each parameter (+,-), quadrant fraction with resolution
(IV).
Since we have several steps of grinding to accomplish
the grinding of root, steps of grinding are divided to three
sections (P1, P2, and P3) and in each section, we use a
constant grinding depth.
Table 2 shows the input parameters of the process.
The procedure includes 16 experiments. Since the con-
sidered levels for each of the input parameters are two
levels, the number of experiments is conducted to deter-
mine whether three levels is necessary for each parame-
ter or not, which is called the center points. If these
points were recognized as the effective points by the
analysis of variance, then the experiments should be per-
Table 2. The parameter levels.
High
Level
Low
Level
Parameters
25 17
Wheel speed ( m/s ) V
180 100
workpiece speed (mm/min ) f
0.15 0.05
dresser speed (µm/rev ) E
0.9 0.6
Grinding depth (mm) P1
0.6 0.3
grinding depth (mm) P2
0.08 0.04
grinding depth (mm) P3
formed in three levels. Table 3 indicates the center
points. Figure 4 shows the flow chart of the analysis.
This subject has to attend that we use absolute value of
difference between the measured dimensions and nomi-
nal dimension of pin gauge in statistical analysis. There-
fore using design of experiments and ANOVA analysis,
according to the input parameters, this absolute value is
minimized.
4. Analysis of the Experimental Results
The analysis of variance (ANOVA) is a statistical me-
thod to investigate the importance and effect of the pa-
rameters. After statistical calculations and implementa-
Figure 4. Flow chart of the analysis.

A. R. FAZELI 638
Table 3. The applied center points in this study.
E (µm/rev) F (mm/min) V (m/s) P3 (mm) P2 (mm) P1 (mm) Run
21 0.1 140 0.06 0.45 0.75
1
21 0.1 140 0.06 0.45 0.75
2
21 0.1 140 0.06 0.45 0.75
3
tion of the F-test on the experimental data by ANOVA,
probability values of each parameter are extracted from
the table of variance analysis. The risk level is consid-
ered as 0.05 for the ANOVA.
Once the experimental results are obtained, the coeffi-
cients and analysis of variance (ANOVA) are calculated
with MINI TAB software to determine the significance
of the parameters, and P-Values are used to determine
which parameter is most significant. The F-ratio test is
conducted to check the adequacy for the proposed model.
Through experiments, pin gauge dimensions are col-
lected and then fed into a DOE/STAT program to con-
struct statistical regression equations in order to achieve
the initializing of input parameters for optimum produc-
tion.
After the initial variance analysis and elimination of
the unimportant parameters (with low effect coefficient)
and use of projection (due to lack of repeat), and with
regards to the calculated values of F and P for each one
of the effective parameters which is extracted from the
table of variance analysis, it can be concluded that the
center points have no effect (P = 0.175). Therefore, the
two levels design is appropriate and we do not need to
consider the effective parameters in three or more levels.
The risk level of less than 0.05 for parameters in Ta-
ble 4 shows that the related parameter is significant. The
R squared and the adjusted R squared are shown in bot-
tom of the Table 4. Also, the lack of fitness is insignifi-
cant which shows the adequacy of the developed model.
Figure 5 indicates the residuals analysis graph of the
regression model. As it is observed, the residuals have a
normal distribution.
Figure 6 shows the graphs of each input parameter
effect on the pin gauge dimension. Figure 7 indicates
interactions effects of the parameters on the pin gauge
dimension.
Figure 7 shows that for the pin gauge dimension there
are significant interactive influences among grinding
depth (first section) and workpiece speed.
According to the graphs of mean parameter effect and
the graphs of the parametric interactions effect, higher
wheel speed, dresser speed, grinding depth (first section)
and lower grinding depth (second and third section) and
slower workpiece speed, lead to smaller absolute value
of pin gauge dimension.
Finally, a hierarchical model was developed for pin
gauge dimension by multiple linear regression technique.
The insignificant terms were removed from the model
Figure 5. Residuals analysis graph of the regression model.
Figure 6. The graphs of mean parameter effect on the pin
gauge dimension.
Figure 7. The graphs of the parametric interactions effect
on the pin gauge dimension.

A. R. FAZELI 639
Table 4: The variance analysis (ANOVA) for the pin gauge
dimension of root of blade
Parameters Coefficient P-Value
Constant
P1
P2
P3
f
E
V
P1xP2
P1xP3
P1xf
P1xE
P1xV
-0.3
0.683
-0.067
1
-0.001
0.74
0.012
-0.222
-1.166
0.001
-1.366
-0.028
0.001
0.174
0. 758
0.460
0.04
0.017
0.012
0.19
0.322
0.032
0.04
0.01
R-Sq = %97.89 R-Sq(adj) = %89.43
and the final models were developed with significant
terms which were determined by ANOVA Equation (1)
for pin gauge dimension.
10.30.683(P1)0.067(P2)P30.001(f )
0.74(E)0.012(V)0.222(P1P2)1.166(P1 P3)
0.001(P1f )1.366(P1E) - 0.028(P1V)
R  

 
(1)
20.330.738(P1)0.56(P2)0.075P30.0002(f )
0.21(E)0.014(V)1.105(P1 P2)0.031(P1V)
0.019(P2 V)
R 


(2)
30.130.453(P1)0.033(P2)0.0005(f )
0.255(E)0.006(V)0.683(P1E)0.272(P1P2)
0.0008(P1f )0.11(P2V) -0.018(P1V)
R 

 
(3)
5. Discussion
Figure 8 summarizes the wheel speed on the pin gauge
dimension at grinding depth (first section). The results
show that an increase of wheel speed combined with the
increase of grinding depth (first section), produces small
absolute value of pin gauge dimension.
Figure 9 shows the effect of workpiece speed on the
pin gauge dimension at grinding depth (first section).
The results show that a decrease of workpiece speed
combined with the increase of grinding depth (first sec-
tion) produces small absolute value of pin gauge dimen-
sion.
Figure 10 summarizes the dresser speed on the pin
gauge dimension at grinding depth (first section). The
results show that an increase of dresser speed combined
with the increase of grinding depth (first section), pro-
duces small absolute value of difference between the
measured dimensions and nominal dimension of pin
gauge dimension.
Reasonably, with higher wheel speed, grinding depth
(first section) and slower workpiece speed, machining
forces apply equally on the other side of root. Therefore
Figure 8. Effect of the wheel speed on the pin gauge dimen-
sion at grinding depth (first section).
Figure 9. Effects of the workpiece speed on the pin gauge
dimension at grinding depth (first section).
Figure 10. Effects of the dresser speed on the pin gauge
dimension at grinding depth (first section).
Grinding depth (mm)

A. R. FAZELI 640
absolute value of pin gauge dimension decreases.
6. Conclusions
In this study, the creep feed grinding process has been
optimized by selection of significant input parameters
including the wheel speed, dresser speed, grinding depth
and slower workpiece speed. Finally, by means of
ANOVA, the main effects of the input parameters and
their interactions on the pin gauge dimension were de-
termined. Based on the statistical analysis of the experi-
mental data the following conclusions can be obtained.
1) According to the variance analysis and the effect of
interactions between the input parameters, it can be con-
cluded that with higher wheel speed, dresser speed,
grinding depth (first section) and lower grinding depth
(second and third section) and slower workpiece speed,
the pin gauge dimension decreases and as a result the pin
gauge dimension reaches a suitable level.
2) In the creep feed grinding process center points
have insignificant effects on the pin gauge dimension. It
means that the process can be modeled with two levels
for each input parameters.
3) Finally, with the large number of effective parame-
ters in the creep feed grinding process, consideration of
the creep feed grinding process through the design of
experiments is shown to be the efficient method for
achieving the acceptable results.
7. References
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