INTRODUCTION
Composite materials are ideal for structural applications where high strength
to weight and stiffnesstoweight ratios are required by Hocheng
et al. (1997). Ferreira et al. (2001)
showed that turning experiments were observed with the performance of different
tool materials like ceramics, cemented carbide, Cubic Boron Nitride (CBN) and
diamond. Experimental results showed that only diamond tools are suitable for
use in finishing turning. In rough turning, the carbide tools can be used in
some retractions parameters. Machining characteristics of composites vary from
metals due to the following reasons: (1) FRP is machinable in a limited range
of temperature, (2) the low thermal conductivity causes heat build up in the
cutting zone during machining operation, since, there is only little dissipation
by the materials; (3) the difference in the coefficient of linear expansion
between the matrix and the fiber gives rise to residual stresses and makes it
difficult to attain high dimensional accuracy and (4) the change in physical
properties by the absorption of fluids has to be considered while deciding to
use a coolant by Malhotra (1990).
Cutting temperature is an important parameter in the analysis metal cutting
process. Singamneni (2005) demonstrated the mixed finite
and boundary element method (FEM) finally enables the estimation of the cutting
temperatures which is a simple, efficient method, and at the same time it is
quite easy to be implemented. Chang (2006a) showed a
model to accurately predict the cutting force for turning of carbon fiber reinforced
plastics composites using chamfered main cutting carbide tools. The objective
of this paper is to set up an oblique cutting CFRP model to study threedimensional
cutting temperature for a sharp worn tool with a chamfered main cutting edge.
THEORETICAL ANALYSIS
Composite materials are mainly molded parts, which require machining, especially
face turning, to obtain the desired dimensional tolerances. Bhatnagar
et al. (1995) showed that in machining of Fiber Reinforced Plastic
(FRP) composite laminates; it can be assumed that the shear plane in the matrix
depends only on the fiber orientation and not on the tool geometry. The available
reports on cutting temperature and associated influences are mostly related
to applications involving chamfered main cutting edge carbide tools.
Shamoto and Altintas (1999) demonstrated that the mechanics
of oblique cutting are defined by five expressions. Three of the expressions
are obtained from the geometry of oblique cutting and the remaining two are
derived by applying either maximum shear stress or minimum energy principle.
Since temperature is of fundamental importance in CFRP cutting operations, many
attempts have been made to predict it. Chang (2008)
presented a model to predict the cutting temperatures in turning of glassfiberreinforced
plastics with chamfered main cutting edge sharp worn tools, that can accurately
predict the cutting temperatures and the cutting forces.
Table 1: 
Tool geometry specifications (chamfered main cutting edge) 

For the case of chamfered main cutting edge, temperatures and forces depend
on nose radius R, worn depths d_{B}, cutting depth d, feed rate f, cutting
speed V, first side rake angle α_{S1}, second side rake angle α_{S2}
and parallel back rake angle α_{b} as shown in Table
1. The process for deriving the shear plane areas is divided into segments
with tool wear and without wear.
• 
Shear area in the cutting process with chamfered cutting edge
sharp tools without wear (Chang, 2006b) 
• 
Shear area in the cutting process with chamfered cutting edge
sharp tools considering wear 
Takeyama and Murata (1963) showed that the mechanism
of tool wear in turning can be classified into two basic types: (1) mechanical
abrasion is directly proportional to the cutting distance and independent of
the temperature and (2) physicochemical wear is considered to be a rate process
closely associated with the temperature. For simplification, the wear effect
of the tool edge is considered in the following such that the depth of tool
wear t_{W} in the direction of cutting depths and geometrical wear angle
φ_{A} on the tool face must be measured on line. Figure
2 and 3 reveal that the geometrical specification of tool
wear on the tool face (triangle CNM) can be derived from the values of t_{W}
and φ_{A} when already measured (Fig. 1, 2):

Fig. 1(ab): 
(a) Basic and (b) detailed model of the chamfered main edge
tool when wear (f>R, R ≠ 0) 

Fig. 2: 
Specifications of tool face with wear 
Coefficients a_{1}, b_{1}, … h_{2} a re shown
in Appendix A; b_{3}, c_{3}, a_{4},
b_{4}, c_{4}, … r_{5} are shown in Appendix
B. The contact length of the tool edge can be considered as two types, as
shown in Fig. 2, 3. Since, the distinction
between types of contact length causes different cutting conditions, the shear
plane areas with tool wear differs accordingly:
as shown in Fig. 2

Fig. 3: 
Contact length L_{f} and L_{P} 
From the above diagram, the contact length is:
Therefore, the projected contact length (l_{p}) on the projection line (i.e., on the plane of the work piece) is also derived:
Energy method to predict cutting force: Wang et
al. (1995) illustrated that the normal and shear forces along the fiber
direction were calculated by assuming that the measured resultant force is equivalent
to that present in the workpiece at the tool point. Transformation equations
used to obtain the normal (N_{s}) and shear forces (F_{s}) along
the fiber direction in terms of the principal (F_{c}) and thrust components
(F_{t}) are shown in Eq. 21 and 22
(Wang et al., 1995):
where θ denotes the angle between the fiber orientation and the trim plane.
Bhatnagar et al. (1995) showed that while the
classical Merchant (1944) is applicable to homogeneous
methods and their alloys, he applies this model in the machining of FRP in the
θ cutting direction as a first approximation.

Fig. 4: 
Condition of tool tip wears with chamfered main cutting edge
tool 
He assumes the shear plane angle as the fiber angle where failure occurs. By
substituting θ for Ψ in Merchant’s model, a basic relationship
for the two components of the cutting force with the geometry of the cutting
can be obtained:
τ_{S} = τ_{compsite} = τ_{fiber} V_{f}
by Rosen and Dow (1987) (V_{f} is fiber contains):
where, f_{t} is the friction force in orthogonal cutting for unit width of cut and where, t_{1 }is the undeformed chip thickness (Fig. 1b):
where, α_{e} is the effective rake angle; α_{S2}
is the second normal side rake angle; α_{b} is the parallel back
rake angle; φ_{e} is the effective shear angle equals to fiber
orientation angle, θ (Hocheng et al., 1997);
η_{c} is the chip flow angle which was determined that minimized
the total cutting energy U; β is the mean friction angle by Merchant
(1944); and τ_{S} is the shear stress by Rosen
and Dow (1987). The cutting power is a function of at least α_{b},
α_{S1}, α_{S2}, d, W_{e}, C_{S}, C_{e},
f, V,θ_{ref}, θ, β, τ_{S} and η_{c}.
The value of η_{c }for the total minimum power U_{min }
to be used in Eq. 27 was obtained by calculating U for a
range of values η_{c} according to the computer flow chart (Fig.
5). Therefore, (F_{H})_{Umin } was determined by solving
Eq. 28 in conjunction with the energy method by Reklaitis
et al. (1984):
where, the frictional force is determined by:
where, N_{t} the normal force on the tip’s surface with minimum energy where the frictional force is determined by:
Calculation of flank wear: The tool tip wear is shown in Fig. 4. For simplification, the wear effects of front edge and main edge are omitted. The only effect to be controlled is the setting condition perpendicular to the vertical line. Thus, the flank wear V_{B} is a function of t_{W}, θ_{e} and α_{e}. The approximate flank wear is shown as follows:
Solid modeling of carbide tip: The chamfered main cutting edge tool has a more complex geometry. To develop a 3D finite element model for thermal analysis, a solid model of the tip can be established in three steps. First, the Tip CrossSection Profile (TCSP) perpendicular to the main cutting edge was measured using a microscope, then CAD software, SolidWorks^{TM}, was used to generate the tip body by sweeping the TCSP along the main cutting edge with the specified pitch. Finally the tip’s main cutting edge was simulated to remove unwanted material and create a solid model of turning tip geometry, as shown in Fig. 6.
Finite element model: The finite element analysis software Abaqus^{TM} is used in this study. The finite element mesh of the carbide tip is shown in Fig. 6 which was modeled by 58,000, fournode hexahedral elements. As shown in the top view of Fig. 6, 8*6 nodes are located on the projected contact length between the tool and the workpiece, 3*6 nodes are located on the chamfered width of the main cutting edge and 1*6 nodes are placed on flank wear. These should provide a reasonable solution in the analysis of tip temperature distribution in turning. The initial condition of finite element analysis has a uniform temperature of 25°C in the tip. Because the tip does not rotate in the experiment, free convection boundary condition is used when applied for the surface of tip contact with the workpiece.
Modified carbide tip temperature model: Magnitude of the tip’s
load is shown in the following Eq. 32 and 33:
where, A' is the area of friction force action, U_{f} is the friction
energy, W_{e} is the tip’s chamfered width, d is the cutting depth,
V_{b } is the flank wear of the tip and for simplification, the value
of V_{b} is set to be 0.1 mm.

Fig. 6: 
Solid model of the chamfered edge tool 
L_{f} is the contact length between the cutting edge and the workpiece
Eq. 19 L_{p} is the projected contact length between
the tool and the workpiece, as referred to in Fig. 7 and can
be determined by Eq. 20 and the following condition:
where, ρ is the density, c is the thermal conductivity and k is the heat capacity.
The boundary condition on the square surface at the cutting edge, opposite from the turning tip, also assumed to be maintained in turning, is assigned to be 25°C. The heat generation in turning is applied as a line load on the main cutting edge. The contact between tool and chip is wide in stainless steel machining according to Eq. 19 to 20. Compared to the 0.36 mm feed per revolution, the characteristic length of the elements at tip and cutting edges is much larger, around 3.29 mm. This allows the use of line heat flux at the cutting edge in finite element analysis. The heat generation assuming the cutting edge is perfectly sharp, the friction force, and the chip velocity are multiplied to calculate the line heat generation rate, q_{f}, on cutting edge q_{f} = F_{f}V_{c}.
Assuming K is the heat partition factor to determine the ratio of heat transferred
to the tool, the heat generation rate q_{tool} on each cutting edge
is given by Li and Shih (2005):
In this study, K is assumed to be a constant for all cutting edges. The inverse heat transfer method is used to find the value of K under certain turning speeds.
Inverse heat transfer solution and validation: The flowchart for inverse
heat transfer solution of K was obtained by the Abaqus^{TM } solver
and is summarized in Fig. 5.

Fig. 7: 
Experimental setup 

Fig. 8: 
Cutting temperatures versus cutting time for different values
α_{S1} and α_{S2} with unchamfered and chamfered
sharp tool at d = 3.0 mm, f = 0.33 mm rev^{1}, V = 252 m min^{1}
and C_{s} = 30° (CFRP) 
By assuming a value for K, the spatial and temporal temperature distribution
of the tip can be found. The inverse heat transfer method is applied to solve
K by minimizing an energy function on the tip surface determined by Eq.
3536 and finite element modeled temperature at specific
infrared locations, as shown in Fig. 7 on the tip face. Using
an estimated value of K, the heat generation rate is calculated and applied
to nodes on the tip’s main and end cutting edges. The discrepancy between
the experimentally measured temperature by infrared pyrometer, j by time t_{i},
T^{ti}_{j} and finite element estimated temperature at the
same infrared location and time, T^{ti}_{j} determines the
value of the objective function by Li and Shih (2005):
where, n_{i} is the number of time instants during turning and n_{j} is the number of thermocouples selected to estimate the objective function.
After finding the value of K, the finite element model can be used to calculate temperature at locations of thermocouples not used for inverse heat transfer analysis. The tool tip’s temperature predicted from finite element model is compared with experimental measurements to validate the accuracy of proposed method.
EXPERIMENTAL PROCEDURES
Experimental set up is shown in Fig. 7. Workpiece is observed in Fig. 7. to be held in the chuck of a lathe and the cutters that were mounted with a dynamometer were employed for measuring the three axes compound of forces (F_{H}, F_{V} and F_{T}).

Fig. 9: 
The cutting temperatures vs. C_{s} for different values
α_{S1} and α_{S2} with chamfered and unchamfered
sharp tool at d = 3.0 mm, f = 0.33 mm rev^{1}, V = 252 m min^{1},
respectively. 
Table 2: 
Properties of the work materials (roving continuous strand,
hardness, HS: 55~60) 

The work material used was 0°; unidirectional filament wound fiber of CFRP
with Vinylester resin composite materials in the form of bars having a diameter
of 40 and 500 mm length by Liu (2002). Table
2 shows some of the physical and mechanical properties of CFRP prior to
carrying out the cutting experiments. The cutting tools used in the experiments
are Sandvik H1P (K type) by Brookes (1992). Carbidetipped
tools with following angles are used: back rake angle = 0°; side rake angle
= 6°; end relief angle =7°; side relief angle = 9°; end cutting
edge angle = 70°; side cutting angle = 20, 30, 40° and nose radius =
0, 0.1 mm. Tool composition: WC 85.5%, TiC 7.5%, Ta (Nb)C 1% and Co 6% (30),
HV = 1850, density = 12.9 g cm^{1}, thermal conductivity = 60W/m°K
and heat capacity = 235 J/kg°K. Oblique turning tests were carried out
for each tool. The experimental tests are as follows: dry cutting; cutting velocity
equals to 252 m min^{1}; cutting depth equals to 3.0 mm; feedrate equals
to 0.33 mm rev^{1}. Block diagrams of performance are drawn as shown
in Fig. 5. The cutting force, cutting temperature was observed
and discussed.
RESULTS AND DISCUSSION
The cutting forces: Chang demonstrated in turning of CFRP with chamfered
main cutting edge sharp tools, the resultant cutting force, Fr, is about 15%
less than that for unchamfered main cutting edge sharp tools (Chang,
2006a). As well as in the case of turning CFRP with chamfered main cutting
sharp worn tools, it shows the theoretical cutting forces are good agreement
with the experimental values.
Temperature of surface of tip: Inverse heat transfer utilizes the temperature
measured by infrared on the surface of tip as the input to predict the heat
flux on the chamfered main cutting edge tools. This method determines the heat
partition factor using the optimization method. Knowing the temperature of cutting
tools (Fig. 6) and how this chamfered main cutting edge tools
decreases the temperature of the tool tip surface, as indicated in the following:
Based on Li and Shih (2005), according to Eq.
3435, the flowchart for inverse heat transfer solution
of K is described in Fig. 5. After finding the value of K,
the finite element model can be applied to calculate temperature at tips, the
results are shown in Fig. 810. Figure
8 and 9 show the cutting temperatures vs cutting time
for different values α_{S1} and α_{S2} with chamfered
and unchamfered sharp tool at C_{s} = 30°. Figure
9 shows temperature distribution with chamfered cutting edge inserts (a)
heat flux (b) near the tool nose at C_{s} = 30, α_{S1}
= 30° and α_{S2} = 30°, d = 3.0 mm, f = 0.33 mm rev^{1}
and V = 252 m min^{1} (CFRP).

Fig. 10: 
Temperature distribution with chamfered cutting edge inserts
(a) heat flux (b) near the tool nose at C_{S} = 30°, α_{S1}(α_{S2}),
= 10°(10°) d = 3.0 mm, f = 0.33 mm rev^{1} and V = 252
m min^{1} (CFRP) 
• 
From Fig. 8, it proved that the cutting
edge temperature of the chamfered main edge tool was lower than unchamfered
main cutting edge tool 
• 
According to Fig. 89,
the tip temperatures of chamfered main cutting edge tool were not high and
the inverse (calculated) data correlates closely with the experimental values 
• 
From Fig. 8, it proved that the distribution
of chamfered main cutting edge tool’s temperature was close the Fig.
10 
CONCLUSIONS
A series of preliminary tests were conducted to asses the effect of tool geometries
of K type of chamfered main cutting edge carbide tool. Chamfered cutting edge
sharp worn tools with C_{S} = 20°, the conditions f = 0.24 mm rev^{1},
α_{S1}(α_{S2}) = 10°(10°) and nose radius
R = 0.3 mm, produce the lower cutting forces and lower cutting temperature.
Good correlations between predicted values and experimental results of forces
and temperatures during machining with sharp worn tools in cutting CFRP. The
FEM and Inverse heat transfer solution in tool temperature in CFRP turning is
obtained and compared with experimental measurements. The good agreement demonstrates
the proposed model.
APPENDIX A
Coefficients of the tool have a sharp corner (R = 0) without tool wear:
APPENDIX B
Coefficients of the tool have a sharp corner (R = 0) with tool wear:
ACKNOWLEDGMENT
This work was supported by National Science Council, Taiwan, R.O.C. under grant number NSC 20092622E197001CC3