INTRODUCTION
In marble industry, the sawing disc is the most important cutting tool
working in high speeds. It is manufactured in varied diameters to cut
marble blocks in different sizes. When the performance of the disc is
examined, in addition to the body of the disc, the mechanical properties
and sizes of the composite diamond segments at the teeth have also important
factors (Luo, 1997; Karagöz and Zeren, 2001; Ucun, 2004).
The disc is subjected to varied forces during the sawing process and
it gets damage under these loads. When depth of cut is increased, the
loads effecting on the disc are also increased (Wang and Clausen, 2002).
If the magnitudes of the loads are known, the stress analysis of the marble
disc is possible. The friction, depth of cut, revolution speed of the
disc, feeding rate and structure of the disc take big roles to determine
the loads. In addition, the mechanical properties of the marble also affect
the loads.
Xu et al. (2002) studied the evaluation of the loads acting on
the diamond grits during circular sawing of two kinds of granites with
a diamond segmented saw blade. Normal and tangential forces were measured
using a dynamometer. The forces and heat in the disc were increased with
increasing circular velocity. Konstanty (2002) presented a theoretical
model of natural stone sawing by diamond saws. The chip removal process
has been quantified with assisting of the toolmaker and the stonemason
in optimising the diamond saw composition and sawing process parameters.
Sung (1999) developed a new design of diamond segments used in marble
industry for drilling, cutting and polishing processes.
Exadaktylos and Kaklis (2001) focused on the Brazilian test configuration
of anisotropic rocks. An analytical solution for the anisotropic circular
disc compressed diametrically was presented. Circular sawblade was modified
to add features of electrolyticin process dressing (ELID) by Chen et
al. (2000). In their study, the tangential force, the depth of cut,
the voltage and current of ELID during cutting were determined. As a result,
ELID increased cutting efficiency of the saw blade.
The objective of this study is to investigate the stress analysis of
the marble cutting disc, which is significantly important in local marble
industry, under varied effective factors. In many cases, the failures
of the sawing discs are encountered as cracking and, consequently, occur
as fracturing at the tooth root region. Another possible failure is debonding
and fracture of bonded segment (Fig. 1). Both of these
two failures require the analysis of stresses at the disc. Higher stress
concentration regions are the possible crack initiation locations and
the stress analysis gives the possibility ofdetermining these regions
to take the necessary preventions. Equivalent stresses (Von Misses) are
analyzed in the marble cutting disc using finite element method in this
study. Maximum stress concentration regions of the disc are determined
and examined for safety. The normal and tangential loads are applied to
the tooth faces in the analysis. Those load levels depending on chosen
depth of cut, (i.e., 17.5, 40, 70 and 108 mm) are taken from two different
experimental studies (Xu et al. 2002; Ersoy and Atici, 2004). In
addition, the stress distribution which is formed under shock loads on
the disc is investigated. Four different cutting speeds (1000, 1500, 2000
and 2500 rpm) are taken for the disc in the analyses.

Fig. 1: 
Failures encountered in marble sawing discs 
MATERIALS AND METHODS
Numerical Model and Loading Conditions: The model for the marble
cutting disc is constructed using AutoCAD software program as shown in
Fig. 2. It is modeled in two parts; the body and the
diamond segments. Geometrical dimensions of the disc are given in Table
1.
The marble cutting disc is forced under different loads whose magnitudes
depend on cutting speed, feed rate, depth of cut, etc. It is also important
to know these loads for investigation of the fatigue damage which occurs
in the disc. Figure 3a shows kinematic behavior of the disc. In addition,
the normal and tangential forces acting on the tooth faces are shown in
Fig. 3b. Maximum forces occur at the first contact point
of the tooth and it decreases linearly to backward and upward of the tooth.
In finite element analysis, different normal and tangential forces are
used depending on varied depth of cut. These forces are taken from two
different previous experimental studies (Xu et al., 2002; Ersoy
and Atici, 2004), Table 2. If both forces are compared
to each other, the normal force is much bigger than the tangential force
for every depth of cut. For example, F_{N} = 320 N for 40 mm depth
of cut. On the other hand, F_{T} = 2.7 N only for the same depth
of cut.
Mechanical properties of the disc: Mechanical properties of the
body and diamond segments of the disc are given in Table
3. The body is mostly made of high speed steel and composite diamond
segments are produced using powder metallurgy techniques. Those segments
have diamond particles for better sawing process.
Finite Element Model: The ANSYS 5.4, a commercial finite element
software, is used in the analysis. The model as explained above is defined
as two parts; the body and the segments. Meshes are constructed using
8 nodded isoparametric finite elements. Shell elements are used for the
analysis with 14004 elements and 43146 nodes. The problem is assumed as
two dimensional. In addition, smaller elements are used in the tooth root
regions to get much more accurate result.

Fig. 2: 
Geometrical model for marble cutting disc 

Fig. 3: 
(a) Kinematical behaviors of marble cutting disc, (b)
normal and tangential forces effecting on a tooth 
Table 1: 
Geometrical properties of the disc 

Table 2: 
Normal and tangential forces in different depth of cut 

Table 3: 
Mechanical properties of segments and the disc 


Fig. 4: 
¼ of the marble sawing disc model and its boundary
conditions 
Boundary conditions are constructed around the hole circumference in
x, y, z directions to solve the problem and the region of the flange diameter
is held in z direction only. Figure 4 shows one fourth
of the finite element model of the marble cutting disc and boundary conditions
although whole disc model is used in the analysis.
RESULTS AND DISCUSSION
The effects of the loads in the marble sawing disc are analyzed as Von
Misses equivalent stresses. For four different depths of cut (i.e., 17.5,
40, 70 and 108 mm) the cutting forces (F_{C}) taken from Table
2 are applied to the disc as given in Fig. 2. The
critical stress which is on the tooth root regions is investigated in
the analysis. The highest stress occurs at the first contact between teeth
and marble block during the cutting process. Then, the stress variation
on the disc is obtained on a line from center to the tooth root as given
in Fig. 5.

Fig. 5: 
The Lines on which the stress variations plotted depending
on the depth of cut 

Fig. 6: 
Distribution of equivalent stress for 2500 rpm and 108
mm depth of cut. 
The cutting speeds of 1000, 1500, 2000 and 2500 rpm are used in the analysis
of the isotropic circular saw for every depth of cut and the equivalent
stress is investigated. Figure 6 shows the stress distribution
for 2500 rpm and 108 mm depth of cut. The distribution of the stress is
maximum around the hole circumference and it decreases towards outer diameter.
On the other hand, when the tooth root region is examined, it can be concluded
that this region has also high stress level in the disc, Fig.
6. It is most critical region on the disc because the stress intensity
factor is high in this region due to radius in the tooth root.

Fig. 7: 
Equivalent stress distribution in the marble sawing
disc for different cutting speeds (depth of cut 17.5, 40, 70 and 108 mm) 

Fig. 8: 
Equivalent stress distribution in marble sawing disc
under shock forces for different cutting speeds (depth of cut 17.5, 40, 70 and 108 mm) 
The stress level increases with increasing depth of cut and cutting speed
(Fig. 7). R is the radius of the disc while r is variable
from inner to outer diameter of the disc. If this ratio is around 0.1,
the stress level is maximum. Then, it decreases with increasing the ratio
up to 0.8. It is, however, increases again up to 0.9 which coincides with
the tooth root region in Fig. 5. The curves are similar
for all cutting speeds and depths of cut but the stress levels are different.
They mostly depend on the cutting speed as shown in Fig.
7. In addition, the variation of the stress distributions around the
hub reduces especially with increasing cutting speed in different depths
of cut. On the other hand, the variation of the stress distribution increases
with increasing cutting speed in the tooth root region.

Fig. 9: 
Comparison of the different cutting speed 
There are three major effects in the distribution of the stress level.
They are depth of cut, cutting speed of the disc and shock loading condition.
The depth of cut and cutting speed with constant hardness of the marble
is investigated so far. The forces used in the analyses are the mean value
of the measurements and the standard deviation of these measurements are
very large (BüyüksağşIş, 1998). Nevertheless,
not only these parameters but the type and microstructure of the marble
are also important in sawing process. Furthermore, the experience, knowledge
and skill of the operator who controls the cutting process also affect
the productivity of the disc. Marble blocks have variable hardness in
nature. Therefore, the disc is subjected to very high loadings called
shock loading during the sawing processes. On the other hand, the first
contact between the disc and the marble is also important to avoid from
shock loading. As a result, the regular loads are multiplied by 5 to examine
the effect of shock loading and the stress analyses are repeated.
The stress distribution curves differently occur than the curves under normal
cutting loads in the disc as a result of the applied shock forces (Fig.
8). When cutting speed is low, say 1000 rpm, the stress level varies especially
at the critical regions around the hole circumference and tooth roots with the
effect of the depth of cut, Fig. 8. It is also seen that the
stress level increases with increasing cutting speed but the range of it decreases
at the critical regions (Fig. 8). In addition, the highest
stress occurs at the tooth root location and clearly increases with increasing
cutting speed (Fig. 9).
CONCLUSION
The stress behaviors of the sawing disc used in marble industry are investigated
numerically in this study. Depending on the depth of cut and cutting speed,
the forces presented experimentally are applied to the disc to determine
the stress distribution under normal and shock loading conditions. As
a result of applied normal loads, maximum stresses occur around the hub
and the tooth root regions which can be defined as critical zones in the
disc during the sawing process. Therefore, the damage usually occurs in
tooth root region due to high stress intensity factor. In addition, the
increase in the depth of cut does not affect the other parts of the disc
and the stress level stays constant under the normal forces. Nevertheless,
a significant increase in the stress level occurs under the shock loads
in the other parts of the disc. Finally, the stress level increases with
increasing cutting speed.