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Abstract

Nine kinds of carbide nose radius worn tools were used in turning of high-strength carbon-fiber-reinforced-plastics (CFRP) materials to study the cutting temperature of tip's surface. A new cutting temperature model using the variations of shear and friction plane areas occurring in tool nose wear situations are presented in this paper. The frictional forces and heat generated in the cutting process are calculated by using the measured cutting forces and the theoretical cutting analysis. The heat partition factor between the tip and chip is solved by using the inverse heat transfer analysis, which utilizes temperature on the K type carbide tip's surface measured by infrared as the input. The tip's surface temperature is determined by finite element analysis (FEA) and compared with temperatures obtained from experimental measurements. Good agreement demonstrates the proposed model.

Keywords

FEA Carbon-Fiber-Reinforced-Plastics (CFRP)Nose radius and temperature of CFRP

1. Introduction

Carbon-fiber-reinforced plastics (CFRP) are also widely used in the structures of aircraft, robots and other machines because of their high strength to weight ratio, and high clamping capacity. Konig et al.¹ presented in spite of the near net shape production technology available for the processing, molding and curing of fiber reinforced plastics (FRP); these materials have to be machined. 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 materials². Singamneni³ 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. The objective of this paper is to set up an oblique cutting CFRP model to study the cutting temperature for a nose radius worn tool with a chamfered main cutting edge.

2. Theoretical Analyses

Wang et al.⁴ illustrated that chip formation, cutting forces, and the surface morphology in edge trimming of unidirectional graphite/epoxy was highly dependent on fiber orientation. Bhatnagar et al.⁵ 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. Nakayama et al.⁶ and Chang⁷ investigated the relationship between the cutting forces, temperatures, surface roughness and BUE; the results indicated that the cutting forces were low when BUE was present. For the case of chamfered main cutting edge, must have not only nose radius R, worn depths d_B, cutting depth d, feed rate f, cutting speed V, back rake angle α_b, side cutting edge angle C_s, end side cutting edge angle C_e, negative side rake angle, α_s1 and positive rake angle α_s2 are used as shown in Figure 1 and Table 1 . In Figure 1 , the shear plane A includes the area A₁, A₂, A₃, A₄, A₅ and A_s. The friction plane Q includes Q₁, Q₂, and Q₃. In Figure 2 , geometrical wear of the cutting tool on the tool face is shown from the top view so as to define the type of wear on the tool edge: viz. a curve of radius R₃, a straight line and a curve of radii R₂, R₁ (R₁ = R₂). The measurable values (i.e. h₁, h₂, h₃, h₄, l₁, l₂, l₃, l₄, and l₅) can be obtained by amplifying the profile projector screen by drawing the circumference of the tool edge before the cut, and again drawing the change after wear has occurred and can be obtained by the following equations:

\begin{array}{l} D M = \sqrt{(h_{1}^{2} + I_{4}^{2})} \overset{_____}{M C} = \sqrt{(h_{2}^{2} + I_{3}^{2}),} \\ C N = \sqrt{(h_{3}^{2} + I_{2}^{2})} and N P = \sqrt{(h_{4}^{2} + I_{5}^{2})} \end{array}

(1)

\begin{array}{l} θ_{R 1} = \tan^{- 1} (I_{5} / h_{4}); θ_{R_{2}} = \tan^{- 1} (I_{2} / h_{3}), \\ θ_{R 3} = \tan^{- 1} (h_{1} / I_{4}); and θ_{M c} = \tan^{- 1} (I_{3} / h_{2}) \end{array}

(2)

\begin{array}{l} R_{1} = N P / (2 \sin θ_{R_{1}}); R_{2} = C N / (2 \sin θ_{R 2}) and \\ R_{3} = D M / (2 \sin θ_{R 3}); (R_{1} = R_{2}) \end{array}

(3)

\begin{array}{l} A = A_{1} + A_{2} + A_{3} + A_{4} + A_{5} + A_{s}; \\ A_{1} = 0.25 {[4 a_{1}^{2} n_{1}^{2} - {(a_{1}^{2} + n_{1}^{2} - c_{1}^{2})}^{2}]}^{1 / 2} \end{array}

(4)

\begin{array}{l} A_{2} = (1 / \cos η) \int_{0}^{2 θ_{R_{2}}} [f_{C D} - (h_{1} + h_{2}) + h_{3} \\ - R_{2} \sin (2 θ_{R_{2}} - Φ)] d_{s} \int_{0}^{2 θ_{R_{1}}} [f_{C D} - (h_{1} + h_{2} + h_{3}) \\ + R_{3} \sin (Φ)] d_{s} \end{array}

(5)

\begin{array}{l} A_{3} = \overset{_____}{M C} / 2 \cos η_{c}^{'} [2 (f_{C D} - h_{1}) - h_{2}] \\ \sin (η_{c}^{'} + θ_{M C}) c o n s t 1 \end{array}

(6)

A_{4} = \int_{0}^{2 θ_{R_{3}}} [(f_{C D} + R_{3} \cos Φ - R_{3}) / \cos η_{c} n] d_{s}

(7)

A_{5} = 1 / [2 (i_{1} + k_{1}) j_{1} c o n s t 1]

(8)

\begin{array}{l} A_{s} = (W_{e}^{2} \cos^{2} α_{S 1} \tan C_{s}) / (2 \sin ϕ_{e} \cos α_{b}) (19); \\ Q = Q_{1} + Q_{2} + Q_{3} \end{array}

(9)

\begin{array}{l} Q_{1} = [d / \cos C_{s} + (h_{1} + h_{2}) \tan C_{s}] f_{C D} \\ + 0.5 (I_{1} h_{2} + I_{2} h_{3} - I_{3} h_{1} - I_{3} h_{2}) \\ + (I_{2} h_{4} - I_{1} h_{4} - I_{3} h_{1}) - R_{1}^{2} (2 θ_{R 1} + 0.5 f_{C D}^{2} \tan C_{s}) \\ - 0.5 [R_{2}^{2} (2 θ_{R 2} - \sin 2 θ_{R 2}) \\ + 0.5 R_{3}^{2} (2 θ_{R 3} - \sin 2 θ_{R 3}) - [I_{1} - I_{2} + 0.5 \\ (f_{C D} - h_{1} - h_{2} - h_{3} - h_{4}) \tan C_{s}] \\ (f_{C D} - h_{1} - h_{2} - h_{3} - h_{4}) \end{array}

(10)

\begin{array}{l} Q_{2} = W_{e} \cos α_{S_{1}} (d / \cos C_{s}) \\ - W_{e} \cos α_{S 1} \tan C_{s} / \cos α_{b} \end{array}

(11)

and Q_{3} = W_{e}^{2} \cos α_{S 1} \tan C_{s} / 2 \cos α_{b}

(12)

Figure 1

Model of the chamfered main cutting edge nose radius tool with wear f > R, (R ≠ 0)

Figure 2

Specifications of nose radius with wear

Table 1

Tool geometries specifications (chamfered edge)

Lead angle C_s	Tool no	Positive and negative rake angle: α_s1, α_s2	Nose radius worn tools: (R)
20°	1	10°, −10°	0.1, 0.3, 0.5, 1.0
20°	2	20°, −20°	0.1, 0.3, 0.5, 1.0
20°	3	30°, −30°	0.1, 0.3, 0.5, 1.0
30°	4	10°, −10°	0.1, 0.3, 0.5, 1.0
30°	5	20°, −20°	0.1, 0.3, 0.5, 1.0
30°	6	30°, −30°	0.1, 0.3, 0.5, 1.0
40°	7	10°, −10°	0.1, 0.3, 0.5, 1.0
40°	8	20°, −20°	0.1, 0.3, 0.5, 1.0
40°	9	30°, −30°	0.1, 0.3, 0.5, 1.0
tips

Cutting Forces Calculation

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 Eqs. (14) and (15)

N_{S} = F_{c} \sin θ + F_{t} \cos θ

(13)

F_{c} = t_{0} A_{0} \frac{\cos (β - r)}{\sin θ \cos (θ + β - r)}

(14)

F_{t} = τ_{0} A_{0} \frac{\cos (β - r)}{\sin θ \cos (θ + β - r)}

(15)

τ_{s} = τ_{c o m p o s i t e} = τ_{f i b e r} V_{f}^{8}

(16)

f_{1} = τ_{s} t_{1} \sin β / \cos (ϕ + β - α) \sin ϕ

(17)

Where the area of unreformed chip is (A₀), β is the mean friction angle, r is the rake angle. By knowing the shear area A₀ of the undeformed chip, the shear strength τ₀ was calculated⁹. The shear energy per unit time (U_s) and the friction energy per unit time (U_f) were proposed as:

\begin{array}{l} U_{s} = F_{s} V_{s} = τ_{s} A V \cos α_{e} / \cos (ϕ_{e} - α_{e}), \\ F_{s} = F_{c} \cos θ + F_{t} \sin θ; and \\ V_{s} = V \cos α_{e} / \cos (ϕ_{e} - α_{e}) \end{array}

(18)

\begin{matrix} U_{f} = F_{t} V_{c} = f_{t} \int^{B_{1}} 0^{d_{b} V_{c}} = τ_{s} \sin β V \cos α_{e} Q / \\ [\cos (ϕ_{e} + β - α_{e}) \cos (ϕ_{e} - α_{e})], \\ U = U_{s} + U_{f} = V {(F_{H})}_{U \min} \end{matrix}

(19)

\begin{array}{l} F_{H} = {(F_{H})}_{U_{\min}} = U_{\min} / V = \\ {τ_{s} \cos α_{e} A / \cos (ϕ_{e} - α_{e}) + \\ τ_{s} \sin β \cos α_{e} Q / \cos (ϕ_{e} + β - α_{e}) \\ \cos (ϕ_{e} - α_{e})]} \end{array}

(20)

\begin{array}{l} {(F_{H})}_{U_{\min}} = {(R_{t})}_{H} = \\ (F_{t}) U_{\min} \sin α_{e} + N_{t} \cos α_{a} \cos α_{r 2} \end{array}

(21)

\begin{array}{l} F_{t} = τ_{s} \sin β \cos α_{e} Q / \\ \cos (ϕ_{e} + β - α_{e}) \sin ϕ_{e} \end{array}

(22)

N_{t} = [(F_{H}) - (F_{t}) U_{\min}] \sin α_{e}] / \cos α_{a} \cos α_{r 2}

(23)

F_{V} = - N_{t} \sin α_{r 2} + F_{t} (\cos α_{r 2} \cos η_{c})

(24)

\begin{array}{l} F_{T} = - N_{t} \sin α_{a} \cos α_{r 2} + F_{t} (\cos α_{a} \sin η_{c}) \\ - \sin α_{a} \sin α_{r 2} \cos η_{c} \end{array}

(25)

σ_{y} = H B / π

(26)

\begin{array}{l} (F_{T}) M = F_{T} + σ_{y} d_{B} \overset{_____}{M C} \cos (θ_{M C} - C_{s}) / 2 \cos α_{r 2} \\ σ_{y} [(L_{P 1} + V_{B 2}) + L_{P 2} V_{B 3}] \end{array}

(27)

τ_{y} = σ_{y} / 2

(28)

\begin{array}{l} {(F_{V})}_{M} = F_{V} + τ_{y} [d_{B} \overset{____}{M C}] \\ \cos (θ_{M C} - C_{S}) / 2 \cos α_{r 2} \\ + τ_{y} (L_{P 1} V_{B 2} + L_{P 2} V_{B 3}) \end{array}

(29)

F_{H H} = {(F_{H})}_{M} = (F_{H}) U_{\min}

(30)

F_{V V} = {(F_{V})}_{M} \cos C_{S} - {(F_{T})}_{M} \sin C_{s}

(31)

F_{T T} = {(F_{T})}_{M} \cos C_{S} + {(F_{V})}_{M} \sin C_{s}

(32)

Solid Modeling of Carbide Tip

To develop a 3D FEM model for thermal analysis, the tip cross-section profile perpendicular to the cutting edge was measured using a microscope, Solid Works™, was used to generate the tip body by sweeping the PCMD along the main cutting edge, as shown in Figure 2 .

Finite Element Model

The Abaqus™ is used in this study. The finite element mesh of the carbide tip is shown in Figure 4 , which was modeled by 58,000 four-node hexahedral elements. As shown in the top view of Figure 4 , 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.

Figure 3

Flow chart of heat calculate

Figure 4

Solid model of cutting tool

Modified Carbide Tip Temperature Model

Magnitude of the tip's load is shown in the following Eqs. (33) and (34)

K = U_{f} / A^{'}

(33)

A^{'} = L_{ρ} (d + w_{e} + V_{b})

(34)

Where the area of friction force action is A', U_f is the friction energy, L_f is the contact length between the cutting edge and the workpiece, as in Equ. (35), L_p is the projected contact length between the tool and the workpiece, as referred to in Figure 5 , and can be determined by Equ. (36)

\begin{array}{l} L_{f} = p h + h j + (j o k + d g) \cos α_{s 2} = \\ \begin{array}{l} (d - R) / \cos C_{S} + R (0.5 π - C_{s} + C_{e}) / \\ \cos α_{s 2} + f_{1} \cos C_{s} / [\cos (C_{e} + C_{s}) \end{array} \\ \cos α_{s 2}] - R \tan C_{e} / \cos α_{s 2} \end{array}

(35)

\begin{array}{l} L_{p} = [(d - R) / \cos C_{s} + R \tan C_{s}] \sin C_{s} + 0.5 R \\ (0.5 π - C_{s} + C_{e}) \sec α_{s 2} \cos (0.5 π - C_{s}) \\ + {f_{1} \cos C_{s} / [\cos (C_{e} - C_{s}) \cos α_{s 2}] \\ - R \tan C_{s} / \cos α_{s 2}} \cos C_{e} \end{array}

(36)

ρ c \frac{\partial T}{\partial T} = K \frac{\partial^{2} T}{\partial x^{2}} + k \frac{\partial^{2} T}{\partial y^{2}} + k \frac{\partial^{2} T}{\partial Z^{2}}

(37)

q_{t o o l} = K_{q f} L i and {shih}^{10}

(38)

where ρ is the density, c is the thermal conductivity, and k is the heat capacity. 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:

Figure 5

Calculation of the contact length (a) L_f and (b) L_p

Inverse Heat Transfer Solution and Validation

The flowchart for inverse heat transfer solution of K was obtained by the Abaqus™ software and is summarized in Figure 3 . The inverse heat transfer method is applied to solve K by minimizing an energy function on the tip surface determined by Eqs. (38) and (39), and finite element modeled temperature at specific infrared locations, as shown in Figure 4 on the tip face. The discrepancy between the experimentally measured temperature by infrared pyrometer, j at time t_i, T_j^ti |_exp and finite element estimated temperature at the same infrared location and time, T_j^ti|_exp determines the value of the objective function.

o b j (k) = {\sum_{i = 1}^{n i} \sum_{j = 1}^{n j} (T_{j}^{t i} |_{\exp} - T_{j}^{t i} |_{e s t})}^{2} 10

(39)

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.

3. Experimental Procedures

Experimental set up is shown in Figure 6. Table 2 shows some of the physical and mechanical properties of CFRP¹¹. The cutting tools used in the experiments are Sandvik H1P (K type)¹². Tool composition: WC 85.5%, TiC 7.5%, Ta (Nb)C 1% and Co 6 %, HV = 1740, density = 10.3g/cm³, thermal conductivity = 23 W/m–°K and heat capacity = 200 (J/Kg – °K). The tool geometries showed in Table 1 .

Figure 6

Experimental set-up

Table 2

Properties of the work materials (roving continuous strand, hardness, HS: 55–60)¹¹

Density g/cm³	Thermal conductivity kCal/hr°C	Fiber contain	Thermal expansion (10⁻⁶/°C)	Tensile strength (kg/cm²)	Compressive strength (kg/cm²)	Shear strength (kg/cm²)	Modulus tensile (kg/cm²)
1.7–1.9	0,21–0.28	75%	2–9	3.5–4	3.5–3.9	1.5–2	235–400

4. Results and Discussion

The Cutting Forces

Chang demonstrated in turning of CFRP with chamfered main cutting edge nose radius tools, the resultant cutting force, Fr, is about 15% less than that for unchamfered main cutting edge nose radius tools^13–15. As well as in the case of turning CFRP with chamfered main cutting nose radius worn tools, it shows the theoretical cutting forces are good agreement with the experimental values, Figure 7 .

Figure 7

The theoretical resultant cutting force, Fr (N) with K type chamfered nose radius worn tools vs. C_S(°) for different values of α_s1 and α_s2 (°) at d = 3 mm, f = .457 mm/rev and V = 252 m/min (CFRP)

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. An infrared (IR) pyrometer system with an optical fiber was developed for measuring the temperature of a chamfered main cutting edge tool during turning. Based on Li and Albert¹¹, according to Eqs. (38) to (39), the flowchart for inverse heat transfer solution of K is described in Figure 3 . After finding the value of K, the finite element model can be applied to calculate temperature at tips, the results are shown in Figures 8–9.

Figure 8

Cutting temperatures versus cutting time for different values α_s1 and α_s2 with unchamfered and chamfered nose radius worn tools at d = 3.0 mm, f = 0.33 mm/rev, V = 252 m/min and C_s = 30° (CFRP)

Figure 9

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, and V = 252 m/min (CFRP)

From Figures 8–9, it proved that the cutting edge temperature of the chamfered main edge nose radius worn tools were lower than unchamfered main cutting edge nose radius won tools.

According to Figures 8–9, the tip's surface temperatures of chamfered main cutting edge nose radius worn tools were not high and the inverse (calculated) data correlates closely with the experimental values.

From Figure 8 , the cutting temperatures of chamfered main cutting edge nose radius worn tool is the lowest, when C_S = 20°, α_s1(α_s2) = −10°(10°) and the temperature is not exceed 360°C.

From Figure 8 , it proved that the distribution of chamfered main cutting edge nose radius worn tool's temperature was close the Figure 9 .

5. Conclusions

The test investigated the cutting forces and cutting temperature during the turning of CFRP. Chamfered main cutting edge nose radius worn tools with C_S equals to 20°, 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 nose radius 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 accuracy of proposed model.

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A Study of Cutting Temperatures in Turning Carbon-Fiber-Reinforced-Plastic (CRFP) Composites with Nose Radius Worn Tools

Abstract

Keywords

1. Introduction

2. Theoretical Analyses

Cutting Forces Calculation

Solid Modeling of Carbide Tip

Finite Element Model

Modified Carbide Tip Temperature Model

Inverse Heat Transfer Solution and Validation

The Cutting Forces

Temperature of Surface of Tip

References