DESIGN OF EXPERIMENTS BASED FORCE MODELING OF THE FACE GRINDING PROCESS

DESIGN OF EXPERIMENTS BASED FORCE MODELING
OF THE FACE GRINDING PROCESS
Eric C. Johnson, Rui Li, and Albert J. Shih
Department of Mechanical Engineering
University of Michigan
Ann Arbor, Michigan
Hap Hanna
Powertrain Division
General Motors Corporation
Pontiac, Michigan
KEYWORDS
One such case is the combustion deck surface
of engine blocks and heads, as shown in Fig. 1.



Bimetallic Grinding, Grinding Force Model,
This deck surface seals against the head gasket
Electroplated CBN (ECBN), Response Surface
to prevent the hot, high pressure gas from
escaping the combustion chamber. The function
of this seal is related to the roughness, flatness,
ABSTRACT
and finish of the deck surface, and a high quality
finishing process is essential. The task of
A grinding force model is developed to predict
achieving this precision falls to either grinding or
the forces during the face grinding of cast iron
milling processes. Although more expensive,
and aluminum alloy 319. Design of experiments
grinding offers a better finish and is widely
methods are used to create a response surface
applied in such operation in automotive
of four process parameters: feed rate, inclination
powertrain manufacturing. This research studies
angle of the grinding wheel profile, offset angle
the force modeling in face grinding of the engine
between the grinding wheel and the workpiece,
combustion deck surfaces.
and the peripheral speed of the wheel. For each
material, three polynomial equations are
determined by regression analysis to represent
the forces in three directions. The model shows
better accuracy for cast iron than aluminum
alloy. The feed rate and inclination angle have
the most significant effect on the grinding forces.
The model is simple and can be implemented in
industry quickly after a few test runs. However, it
has limited accuracy, generally within 10-20%
on the prediction of grinding forces.
INTRODUCTION
FIGURE 1. FACE GRINDING PROCESS, USING AN
Grinding is an important surface finishing
ENGINE BLOCK DECK SURFACE AS AN
process and has broad industrial applications.
EXAMPLE.
Transactions of NAMRI/SME
241
Volume 36, 2008

---

The grinding process can be characterized by
experiments required to fit the model grows
combining physical properties of the workpiece
exponentially with the number of factors.
material, grinding wheel, and machine, with the
However, the number of experiments can often
controllable parameters of the process. The
be reduced by using design of experiments
distribution and shape of the grain cutting edges
(DOE) techniques. DOE is a systematic
strongly influence the force and surface finish
approach to experimental design in which
[Tonshoff et al. 1992]. The process parameters
multiple factors are varied simultaneously, while
and wheel and workpiece geometry control the
controlling for variance. Properly implemented,
material removal rate and chip thickness. The
DOE increases the efficiency of the information
friction force present at the cutting interface is
gathering. When DOE methods are combined
predominately determined by the material
with regression modeling, a polynomial
properties of the workpiece, as is the deflection
approximation of the response is obtained [Box
of the grinding wheel. As Brinksmeier et al.
1951]. This technique is called response surface
[2006] pointed out, the grinding process is the
methodology (RSM). Alauddin et al. [2007]
sum of the interactions among the wheel
recently combined RSM with dimensional
topology, process kinematics, and the workpiece
analysis to develop a grinding force model using
properties. Most analytical force models are
conventional abrasives. This study further
related to the topography of wheel, workpiece
expands the RSM method for modeling ECBN
properties, and chip thickness [Brinksmeier et al.
face grinding forces.
2006; Malkin 1989; Tonshoff et al. 1992]. In
addition to these physical/empirical models,
In this research, the forces arising in face
many newly developed modeling techniques like
grinding using an ECBN wheel are investigated.
artificial neural network have been utilized to
Cast iron and aluminum alloy 319 (AL319) are
model the grinding process [Brinksmeier et al.
studied. DOE methods were used to develop an
2006; Lee and Shin 2004]. Most of these models
empirical model to predict face grinding forces.
are derived from the basic grinding operations:
First and second order regression models were
horizontal surface grinding and cylindrical
derived to predict the normal, tangential, and
grinding, which are different from the
lateral specific grinding forces. The model is
configuration of vertical grinding the combustion
validated by comparing forces at intermediate
deck face.
grinding conditions.



Research on vertical surface grinding is
limited. Lal and Srihari [1994] studied the
GRINDING KINEMATIC MODEL
mechanics of chip formation in face grinding. Lal
[1968] also investigated the effects that varying
The grinding forces can be represented in two
table speed, depth of cut, and workpiece
coordinate systems. One is a global coordinate
material had on face grinding force, but no
system defined relative to the machine. As
model was developed with these parameters.
shown in Fig. 2, the three force components in
However, experiments involving more modern,
the global coordinate system are: force normal
electroplated superabrasive wheels, are absent
to the ground surface FN; force against the feed
from the current annals of face grinding
direction, FL; and force normal to the feed
knowledge. ECBN grinding wheels do not
direction and ground surface, FT. The grinding
require periodic dressing and truing [Shi and
experiments measured forces relative to this
Malkin 2003], unlike a vitrified bond wheel. One
global coordinate system.
aim of the present research, which utilized an
electroplated cubic boron nitrite (ECBN) grinding



Another coordinate system is a local
wheel, is to fill this gap.
coordinate system, defined relative to the wheel
and workpiece contact surface. As shown in Fig.
The other aim of this paper is to develop an
2, forces Fn and Fl are normal and coincident to
effective face grinding force model. In the
the inclined contact surface, respectively, and lie
absence of established analytical models, a
in a plane at angle to the feed direction and
practical solution is to empirically correlate the
normal to the ground surface. Force Ft is tangent
response to the input variables with a polynomial
to the wheel rotation axis. Angle is the offset
approximation. This is known as response
angle between the wheel and workpiece. Angle
surface methodology [Cochran 1957]. For a
is the inclination angle of the wheel profile with
given polynomial degree, the number of
respect to the ground surface.
Transactions of NAMRI/SME
242
Volume 36, 2008

---

intervals tested was proportional to the model
order. Thus for a second order model, there are
three depths and three force intervals.
Four input parameters were selected: feed per
revolution f (mm/rev), angles and , and
peripheral cutting speed V (m/min). The
responses were the local specific normal and
tangential forces, kn and kt, respectively. The
local specific lateral force kl was negligible and
was not modeled. The local specific forces are
calculated from the local forces as:
k = F
F
n
k
[4]
n
t =
t
S
S
where S is the contact area between the tool
and workpiece, and kn, kt are the normal and
FIGURE 2. FN, FT, AND FL IN GLOBAL (MACHINE)
tangential grinding pressures, respectively. S
COORDINATE SYSTEM AND Fn, Ft, AND Fl IN
depends on the depth of cut and offset angle .
LOCAL (WHEEL/WORKPIECE) COORDINATE
SYSTEM.
The wheel was plunge ground into a workpiece,
and the resulting imprint measured on a
profilometer, to assist in the calculation of S. The
For analysis, the measured forces F
measured wheel profile and profile fit are shown
N, FT, and
F
in Fig. 4. The local specific forces that are
L are transformed to the local coordinate
system using the following equations:
predicted by the model can be converted to an
aggregate global force by the following
F = F cos? ? F sin? sin? + F sin? cos
procedure:
[1]
n
N
T
L
?
F = F cos? + F sin
[2]
t
T
L
?
1. Discretize contact surface into square
F = F sin? + F cos? sin? ? F cos? cos
[3]
grid elements. Each element is
l
N
T
L
?
associated with a particular ,
, and
The contact surface between the wheel and
material. An example is given in Fig. 5,
workpiece was discretized into several depth
which uses a Cartesian system of
intervals along the wheel axis, as shown in Fig.
uniformly sized square grid elements.
3. Each depth interval was associated with a
2. Calculate local specific forces kn and kt
certain inclination angle . Since the profile was
for each element using the prediction
divided into a finite number of discrete intervals,
models of Eqs. [6-9]. The material type of
was approximated as the gradient of the
each element will dictate which model to
straight line connecting the end points of each
use. kl may be assumed to be zero.
segment. It is dependent on the grinding depth.
The incremental force contribution of each
interval was determined by subtracting the force
600
measured at the shallower interval that
Valid region
500
preceded it, if any existed. The number of
Meas. Prof ile
m] 400
Prof ile Fit
µ
[
n 300
i
o
at 200
l
ev
E 100
0
55
60
65
70
75
Radial pos ition [m m ]
FIGURE 3. DEPTH OF CUT INTERVALS AND
FIGURE 4. PROFILE OF ELECTROPLATED CBN
ASSOCIATED INCREMENTAL CONTACT ANGLES.
GRINDING WHEEL IN THIS STUDY.
Transactions of NAMRI/SME
243
Volume 36, 2008

---

TABLE 1. EXPERIMENTAL DESIGN.
Trial f
V
Trial f
V Trial f
V
1 -1 -1 -1 1
14 1 1 -1 1 27 0 -1 0 0
2 1 -1 -1 -1
15 -1
-1
1
1 28 0
1 0 0
3 -1 1 -1 1
16 -1
1 1 1 29 0 0 -1 0
4 1 1 -1 -1
17 -1 0 -1 1 30 0 0 1 0
5 -1 -1 1 -1
18 1 0
-1
-1 31 0 0 0 -1
6 1 -1 1 1
19 -1
0
1
-1 32 0
0 0 1
7 -1 1 1 -1
20 1 0 1 1 33 0 0 0 0
8 1 1 1 1
21 -1 0 -1 -1 34 -1 0 0 0
FIGURE 5. DISCRETIZATION OF CONTACT
9 -1 -1 -1 -1
22 1 0 1
-1 35 1 0 0 0
SURFACE INTO GRID ARRAY. EACH GRID
10 -1 1 -1 -1
23 1 0 -1 1 36 0 0 -1 0
ELEMENT IS ASSOCIATED WITH A PARTICULAR
, , AND MATERIAL.
11 1 -1 1 -1
24 -1 0 1 1 37 0 0 1 0
12 1 1 1 -1
25 -1 0 0 0 38 0 0 0 -1
13 1 -1 -1 1
26 1 0 0 0 39 0 0 0 1
3. Obtain local forces Fn and Ft for each
composite designs to name a few [Cochran
element by multiplying that element’s kn
1957].
and kt by its area S. For the example in
Fig. 5, S is the same for all elements.
This work used a central composite design to
4. Transform local forces into global
increase efficiency. A visual representation of
coordinate system using angles and
the design is shown in Fig. 6. In a central
of each element.
composite design, midpoints are added to a first
5. Sum elemental global forces to obtain the
order model to create a second order model. It
aggregate global force.
allows curvature of the main effects to be
studied. The modeling process is divided into
two steps:
EXPERIMENTAL METHODS
Screening Test. The screening test was an
Design of Experiments
exploratory 24 factorial experiment used to fit a
first order response surface. This forms the
A factorial experiment, in which the effects of
corner points of the cube in Fig. 6, and
multiple factors are tested simultaneously, can
corresponds to trials 1 to 16 in Table 1.
be used to develop a polynomial response
surface model. Given N levels of each factor,
Second Order Response Model. Midpoints
and k factors to be studied, a total of Nk unique
were added to the 24 factorial model to create a
combinations of experimental conditions are
second order response model. All factors were
possible. In a full factorial design all Nk
found to be significant in the screening test, thus
combinations are tested; this provides estimates
of each factor’s main effect, and also allows
interactions between factors to be examined in
full. Testing each factor at two levels will
produce a first order model. The second order
model that accounts for curvature can be
developed by testing factors at three levels. The
number of experiments required by a full
factorial design quickly becomes impractical to
handle as the model order and number of
factors increase. Fractional factorial designs,
which consist of a systematically selected
subset of the full factorial design, are effective
methods of reducing the number of tests [Finney
1945]. Many fractional factorial designs have
FIGURE 6. CENTRAL COMPOSITE DESIGN.
been enumerated: half-replicate, quarter-
ACTUAL COMPOSITE DESIGN INCLUDES
AND
replicate, central composite, and rotatable
IS FOUR DIMENSIONAL.
Transactions of NAMRI/SME
244
Volume 36, 2008

---

TABLE 2. WORKPIECE DIMENSIONS
Material Thickness
Length
Cast iron
6 mm
60 mm
AL 319
12 mm
60 mm
a midpoint was added for each of the four
factors. The entire second order experimental
design includes the first order trials from the
screening test, plus trials 17 to 39 in Table 1.
Experimental Setup
The grinding experiments were conducted on
a Fadal CNC vertical machining center. A 150
mm diameter, 60-grit electroplated CBN grinding
FIGURE 7. WORKPIECE ORIENTATIONS.
wheel was used. A Kistler 9273A piezoelectric
(A) CAST IRON AND (B) BIMETALLIC
dynamometer was used to measure three force
components during grinding. A 5% concentration
Cast Iron. A cleanup pass and spark out were
of water based cutting fluid, Hocut TR2000-C,
performed prior to each test. For each test
was used. Although CBN wheels generally
condition, five passes were made, to approach
perform best with oil-based coolants, industry is
the steady state depth of cut described by
moving towards water-based coolants for
Malkin [1989]. The physical parameter ranges
environmental considerations [Carius 1989].
are given in Table 3.
Dimensions of the workpieces used are given in
Table 2.
AL319. Grinding aluminum is complicated by
the fact that the aluminum alloy tends to build up
The wheel’s rotational velocity was converted
on the wheel, due to its high ductility. The
to linear cutting speed, V, in the model. The
buildup was managed in the experiments by
inclination angle was calculated based on
grinding cast iron alongside the aluminum alloy,
incremental depth of cut as illustrated in Fig. 3.
to scrape the aluminum build-up from wheel
The model was based on rather than directly
surface. The cast iron workpiece was positioned
on depth of cut. The angles and were
at the high and low offset angles listed in Table
normalized by taking their sine for use in the
2,
= 0° and = 45°. The aluminum plates
model.
were placed directly adjacent to the cast iron
plates, at = ?6.8° and = 36.1°, as illustrated
in Fig. 7B. The aluminum force was calculated
by subtracting the cast iron force from the
TABLE 3. LEVELS OF CODED FACTORS
measured bimetallic force, using values found in
cast iron response surface experiments. The
Model
Coding
Factor Units Factor?
1 0 -1
rest of the experimental procedure was identical
to that of the cast iron experiments, with the
f
(mm/rev)
Y
0.125 0.0875 0.050
parameter values listed in Table 3. The AL319
(rpm)
N
12000 8000 4000
V
experiments consisted of the first order
(m/min)
Y
5742 3828 1914
conditions, trials 1 to 16 in Table 1.
*
*
*
0.707 0.382 0.000
sin
-
Y
**
**
0.589
N/A
-0.118
a†
( m)
N
150 65 20
RESULTS
††
††
††
0.035 N/A 0.005
sin †
-
Y
‡
‡
‡
The ratio of the normal and tangential cutting
0.078 0.017 0.005
*
**
pressures, kt/kn, is considered to be a
Cast iron. AL319.
†
representation of the frictional behavior, f, that
is dependent upon depth of cut, a. Both parameters are
given, however sin is used in the model.
††
‡
First order model. Second order model.
Transactions of NAMRI/SME
245
Volume 36, 2008

---

300
300
Cast iron, k = 0.254k
V = 3828 m/min
t
n
250
? = 0°
AL319,
]
k = 0.443k
250
a
t
n
P
[k
200
)
,

200
n
]
? = 0.1
a
i
r
o
P
t
150
s
[k
a
150
? = 0.08

c
k t
(
k t
? = 0.06
100
100
t
ed
c
? = 0.04
? = 0.02
50
r
edi
P
50
? = 0
0
0
0
200
400
600
800
0.02
0.04
0.06
0.08
0.1
0.12
0.14
k [kPa]
n
f [mm/rev]
FIGURE 8. RATIO OF NORMAL AND TANGENTIAL
FIGURE 10. TANGENTIAL PRESSURE RESPONSE
FORCES FOR CAST IRON AND AL319.
LINES, CAST IRON MATERIAL
is material dependent. They can be related by:
for cast iron material. Because the second
order model did not include all full factorial
k
µ k
[5]
terms, the effects of all factors and interactions
t
= f n
could not be independently discerned using



The friction coefficients for cast iron and
ANOVA. Rather, terms were manually selected
AL319 are the slope of two lines plotted in Fig.
based on previously developed analytical
8, 0.25 and 0.44, respectively. Lal [1968] found
models, minimization of the PRESS statistic
[Allen 1971], and visual inspection of the
f = 0.27 for cast iron, which is close to the value
found in this study. The ratio of k
prediction surfaces vs. experimental data.
t for cast iron
(kt,CI) to AL319 (kt,Al) was found to follow a linear
relationship, plotted in Fig. 9.
For cast iron, the following models were found
to characterize the normal and tangential
grinding pressures (units are in kPa):
Response Model
kn = 71+
2
8691f + 23453f sin?
[6]
The dominant factors were f and , which are
+
2
40048 sin ? ? 3476sin? sin?
related to the equivalent chip thickness. Fig. 10
kt = 20 +
2
1988f + 13300f sin? ? 0.0351fV
shows the response of kt to f at varying levels of
[7]
+
2
7133 sin ? ? 876 sin? sin?
The normal and tangential grinding pressure
60
models for AL319 were (units are in kPa):
ratio k
/ k
= 0.511
50
t,Al
t,CI
]
k
f
V
n =
48 + 236 ?1916 sin? ? 0.0041
a
40
P
+ 16117f sin? ? 358f sin?
[8]
[
k
30
+ 0.2727V sin?
319
L
k
f
t =
32.3 + 26.3 + 21.7 sin? ? 4.9 sin?
,
A
20
[9]
k t
+ 21.4f sin? ? 5.6f sin? + 4.4V sin?
10
0
0
20
40
60
80
100
Model Validation
k , cast iron [kPa]
t
A set of experiments was performed using
FIGURE 9. RATIO BETWEEN TANGENTIAL
parameter combinations that were not included
PRESSURES OF CAST IRON AND AL319.
Transactions of NAMRI/SME
246
Volume 36, 2008

---

TABLE 4. CAST IRON VALIDATION TESTS.
TABLE 5. AL319 VALIDATION TESTS.
Test Width
f
A
V
Test Width
f
a
V
(mm)
(mm/rev)
( m) (deg) (m/min)
(mm)
(mm/rev)
( m) (deg) (m/min)
V1 6 0.05 85 0 1914
V6 12 0.05 85 -6.8 1914
V2 6 0.075 75 15 4785
V7 12 0.075 75 8.1 4785
V3 6 0.1 100
30 2781
V8 12 0.1 100
22.5
2781
V4 18 0.06 20 0 2393
V5 18 0.08 65 0 4307
Three validation experiments, V6, V7, and V8
in Table 5, were performed for AL319. Cast iron
in the 39 tests defined in Table 1. The
was ground simultaneously. The cast iron
predictions of the cast iron and AL319 models
workpiece was positioned at the same offset
were validated by comparison with these tests.
angles listed in Table 4, so that the data from
The parameter values used in the validation
those tests could be subtracted from the
experiments were interpolative, that is, they fell
measured aggregate bimetallic force. The
within the high and low parameter boundaries
AL319 workpieces were placed adjacent to the
defined in Table 3. The measured global forces
cast iron. The validation test parameters for
were used for comparison; the predicted global
AL319 are given in Table 5 and the results are
forces were derived from the predicted local
plotted in Fig. 12.
grinding pressures using the procedure
illustrated in Fig. 5.
Discussions
Five validation experiments, V1 to V5 in Table
4, were performed for cast iron. Results of
For cast iron, the experimental vs. predicted FT
predicted and measured F
in Fig. 11B shows the accuracy is within 13.1%
N and FT are plotted in
Fig. 11.
± 5.1%. For FN in Fig. 11A the accuracy falls to
(A)
20
(A)
10
Measured
Measured
8
Predicted
15
Predicted
]
]
6
[N
[N

10

N
N
F
F
4
5
2
0
0
V1
V2
V3
V4
V5
V1
V2
V3
Validation test (cast iron)
Validation test (AL319)
(B)
(B)
3
4
Measured
Measured
Predicted
Predicted
3
2
]
]
[N
[N


T
2
T
F
F
1
1
0
0
V1
V2
V3
V4
V5
V1
V2
V3
Validation test (cast iron)
Validation test (AL319)

FIGURE 11. PREDICTED AND MEASURED (A)

FIGURE 12. PREDICTED AND MEASURED (A)
FN, AND (B) FT, FOR CAST IRON VALIDATION.
FN, AND (B) FT, FOR AL319 VALIDATION.
Transactions of NAMRI/SME
247
Volume 36, 2008

---

7.9% ± 16.1%. One explanation may be that FN
Allen, D.M. (1971). “Mean Square Error of
is affected by vertical deflection of the grinding
Prediction as a Criterion for Selecting Variables.”
wheel. This can be caused by deflection of the
Technometrics, Vol. 13(3), pp. 469-475.
workpiece, machine, and grinding wheel. The
deflection will directly relate to the depth of cut a.
Box, G.E.P. and K.B. Wilson (1951). “On the
In the model presented in this paper, the
Experimental Attainment of Optimum
inclination angle was used, rather than a itself.
Conditions.” Journal of the Royal Statistical
Thus, a possible improvement may be to
Society Series B, Vol 13(1), pp. 1-45.
integrate a directly into the model.
Brinksmeier E., J.C. Aurich, E. Govekar, C.
For AL319, Fig. 11B shows a reasonable
Heinzel, H.W. Hoffmeister, F. Klocke, J. Peters,
prediction of FT, with an error of 17.9% ± 5.8%.
R. Rentsch, D.J. Stephenson, E. Uhlmann, K.
The FN predictions in Fig. 11A are only within
Weinert, and M. Wittmann (2006). “Advances in
26.1% ± 5.2% of the measured values. In
Modeling and Simulation of Grinding
additional to the possibility of deflection
Processes.” Annals of the CIRP, Vol. 55(2), pp.
discussed above, the AL319 forces are more
667-696.
susceptible to experimental uncertainty because
they are obtained by subtracting the cast iron
Carius, A.C. (1989). “Effect of Grinding Fluid
forces from the bimetallic data. The uncertainty
Type and Delivery on CBN Wheel Performance.”
of both measurements is compounded. By using
presented at Society of Manufacturing
a cast iron workpiece that is longer than the
Engineers, Modern Grinding Technology, Novi,
aluminum workpiece, the aluminum results can
Michigan.
be improved by directly measuring the cast iron
force during each aluminum experiment.
Cochran, W.G. and G.M. Cox (1957).
Experimental Designs. Wiley, New York.
CONCLUSIONS
Finney, D.J. (1945). “The Fractional Replication
of Factorial Arrangements.” Ann. Eugen. Vol 12,
This study predicted the specific forces in the
pp. 291-301.
ECBN face grinding of cast iron and AL319. On
the basis of DOE, a second order polynomial
Lal, G.K. (1968). “Forces in Vertical Surface
response surface model was built for cast iron,
Grinding.” International Journal of Machine Tool
and a first order model was constructed for
Design Research, Vol. 8, pp. 33-43.
AL319. Among four grinding parameters studied,
the feed rate and inclination angle had the most
Lee, C.W. and Y.C. Shin (2004). “Modeling of
significant effect on the grinding forces. The
Complex Mfg. Processes by Hierarchical Fuzzy
model demonstrated more accurate grinding
Basis Function Networks with Application to
force prediction for cast iron than AL319. The
Grinding Processes.” J. Dyn. Sys., Meas.,
local specific forces may be integrated over an
Control, Vol. 126, pp. 880-890.
arbitrary workpiece geometry to calculate the
aggregate global grinding force. These simple
Malkin, S. (1989). Grinding Technology: Theory
models are very suitable for industrial
and Application of Machining with Abrasives.
applications, however accuracy is limited to 10-
Wiley, New York.
20%. For a given grinding wheel and workpiece
material, DOE methods can be used to quickly
Shi, Z., and Malkin, S., 2003, “An Investigation
characterize and predict grinding performance.
of Grinding With Electroplated CBN Wheels,”
Annals of the CIRP, 52(1), pp. 267–270.
REFERENCES
Srihari G. and G.K. Lal (1994). “Mechanics of
Vertical Surface Grinding.” Journal of Materials
Alauddin, M., L. Zhang, and M.S.J. Hashmi
Processing Technology, Vol. 44, pp. 14-28.
(2007). “Grinding Force Modelling: Combining
Dimensional Analysis with Response Surface
Tonshoff H.K., J. Peters, I. Inasaki, and T. Paul
Methodology.” Int. J. Manufacturing Technology
(1992). “Modeling and Simulation of Grinding
and Management, Vol. 12, pp. 299–310.
Processes.” Annals of the CIRP, Vol. 41(2), pp.
677-688.
Transactions of NAMRI/SME
248
Volume 36, 2008

---