An Integrated Analytical Thermal Model for Orthogonal Cutting with Chamfered Tools

In this study, an analytical slip-line approach is utilized to investigate the friction factor at the tool-chip interface and dead metal zone phenomenon in orthogonal cutting with chamfered tools. Analytical thermal modeling of chamfered tools is also formulated and integrated into the model. Orthogonal cutting of AISI 4340 steel is performed. Measured forces are utilized in identifying the friction factors at the tool-interface. Comparison of predicted and measured forces indicates good agreements. The combined predictive model of forces and temperatures may offer distinct advantages in cutting tool design and process optimization. INTRODUCTION Chamfered tools with negative rake angle were first proposed by Hitomi [1961]. The negative rake angle helps trapping the work material in front on the chamfered edge. The trapped work material acts as a cutting edge, which protects tool from rapid tool wear and increases edge strength. This stable trapped work material zone was observed by many researchers such as Kita et al. [1982], Hirao et al. [1982], Jacobson and Wallen [1988], and Zhang et al. [1991], and named as dead metal zone (DMZ). It differs from built-up-edge (BUE) because it does not disappear with the increasing cutting speed [Zhang et al., 1991]. Early research on dead metal zone was mostly experimental towards classifying the types of dead metal zones under different cutting conditions and chamfered tool design. Recently, some analytical models have been proposed for better understanding of dead metal zone phenomena. Zhang et al. [1991] proposed a three-deformation zone cutting model and calculated the shear angle by utilizing the minimum energy method. They found that dead metal zone does not depend on cutting speed and chamfer angle. Ren and Altintas [2000] extended this model by applying the Oxley’s [1989] modeling approach, which relates the flow stresses in the primary and secondary shear zones to the strain and strain rates. Movaheddy et al. [2002] proposed a thermo-mechanical ALE finite element formulation to simulate chip formation process in orthogonal cutting with chamfered tools. The zone of stagnant material is identified from the velocity profile around the cutting edge. They concluded that chip formation is not affected by chamfer angle because of dead metal zone formed under the chamfer. Long and Huang [2005] extended the model previously used by Zhang et al. [1991] and Ren and Altintas [2000] by considering that the inclination of the dead metal zone under chamfer is not equal to the shear angle and using Johnson-Cook constitutive equation to calculate shear flow stress. Fang [2005] extended the Lee and Shaffer’s [1951] model to study the effect of large negative tool rake angle and cutting speed on the tool-chip friction and the geometry of stagnation zone and showed that the size of the stagnation zone decreases with increasing cutting speed. Recently, Fang and Wu [2005] proposed a slip-line model for chamfered tools without dead metal zone formation in front of the chamfer edge and validated their model on three different aluminum alloys. In this study, slip-line approach will be utilized to identify the tool-chip friction under different cutting conditions with the presence of dead metal zone in machining of AISI 4340 steel. There have been numerous studies on analytical thermal modeling of metal cutting starting from pioneering studies of Hahn [1951], Jaeger [1942] and many others. Recently, Komanduri and Hou [2000, 2001] predicted the temperature distributions in the chip, tool and workpiece by extending Hahn’s solution. An extensive literature survey on thermal modeling in machining can also be found in Komanduri and Hou [2000]. In this study, Komaduri and Hou’s work, which is proposed for sharp tools [Karpat and Özel, 2006a], will be extended for chamfered tools. SLIP-LINE MODEL FOR CHAMFERED TOOL WITH NEGATIVE RAKE ANGLE For the cutting tools with chamfered edge preparation, a three zone cutting model has been proposed by Zhang et al. [1991]. These deformation zones are the primary deformation zone, the tool-chip interface and the deformation zone under dead metal zone and illustrated in Fig. 1 with its associated hodograph in Fig. 2. The dead metal zone ABD is assumed to be extending from rake face for simplicity. The chip is assumed to be straight. The tool chip friction at BD and BC causes deformation zones BCK and DBG. The model includes two central fan regions as θ andδ . SC represents a stress free boundary, which makes 45° with SI. The shear angle is represented with (φ ), the inclination of GD by ( β ), and AD by (α ), respectively. The angle formed by the DMZ with the cutting direction is named DMZ angle (α ). FIGURE 1. SLIP-LINE MODEL In this model, the work material flow separates at point D. The work material above point D flows upward into the chip, the work material under point D flows downward into the workpiece. FIGURE 2. HODOGRAPH OF SLIP LINE MODEL In this slip-line model, cut chip thickness (tc), tool-chip contact length on the rake face (BC) and the chip velocity (Vch) are calculated according to given cutting velocity (V), uncut chip thickness (tu), tool-chip friction factors on BD, BC and AD, and tool geometry (height of the chamfer (h), rake angles ( 1 γ ) and ( 2 γ )). The friction factors on tool-chip interface (m1= / BD k τ ), (m2= / BC k τ ) and under dead metal zone (m3 = / AD k τ ) are used to find the slip-line angles ( 1 2 3 , , ζ ζ ζ ). The variables , BD BC τ τ and AD τ are shear stresses on BD, BC and AD. The following expressions can be written