A Finite Element Analysis of Orthogonal Machining Using Different Tool Edge Geometries

This paper summarizes the effects of edge preparation of the cutting tool in orthogonal cutting on the following variables: stress distributions at the tool rake face, cutting forces and tool-chip contact length. The Finite Element Method (FEM) is selected using the ANSYS /V4.5 code. Six models of cutting tools have been suggested having edge radii of (0.01, 0.05, 0.1, 0.15, 0.2, and 0.25) mm. The results obtained provide a fundamental understanding of the process mechanics for cutting with realistic cutting tool edge radius in order to assist in the optimization of tool edge design. The results show that the optimum edge radius from the six simulated models is (0.05) mm; this edge radius gives minimum value of effective stress. The results show also that the optimum edge radius that shows minimum tangential cutting and feed forces is (0.01) mm. The results investigated that the tool-chip contact length is increased, until reaching maximum value of (2.4) mm at (r=0.15mm), and minimum value of (0.75) mm at (r=0.01mm). The maximum relative difference between simulated results of this work and other previous paper results is (2% - 17%) for the tool effective stresses, (5%) for the tangential force, and (11%) for the feed force.


1-Introduction:
In metal cutting, the modification of the tool edge geometry is referred to as edge preparation, the purpose of edge radius preparation is to strengthen the cutting edge and prepare a surface for deposition of coatings.In addition, hone edges can reduce the initiation of notch wear, and are usually employed in finish cut [1].The objective effect of the cutting tool geometry is to establish a predictive theory that would enable to predict cutting performance.The models are mainly established to obtain a better understanding of the cutting mechanism itself due to the tremendous difficulties, which occur in attempting to measure temperatures, strain rates, stresses and other variable factors.The (FEM) can be applied to model and simulate the machining process.Furthermore, modeling of metal cutting processes can reveal useful information, which may not be measured directly during the cutting process itself.With a model, the interaction of the tool and the chip can be examined, if a valid model exists, the model can be used to vary certain material or process parameters.On one hand, this may help to design materials or tools which are more suitable for the machining operations, and also on the other hand, this procedure can be used to find new optimized tool geometries.Most of the early research work on the FEM modeling of orthogonal cutting was limited by the assumption of a perfectly sharp cutting edge which requires a predefined criterion for chip separation from the workpiece along the predefined parting line [1] showed that increased tool edge radius alters the temperature distribution of the tool and shifts the position of maximum temperature closer to the tool tip.Experimental results also indicated that cutting forces increase as the tool edge radius increases within the same limit in the simulated models.Shatla et al. (2000) [6] applied the Lagrangian formulation using FEM simulation to study the influence of edge preparation (hone/chamfer) on tool temperature and stress in orthogonal cutting of (H13) tool steel (46 HRC).Simulation results showed that the effective or normal stress of the tool reached a minimum value when using a moderate edge radius (0.1) mm.The tool with an excessive edge radius resulted in a significant increase in the tool stress and shifted the stress concentration close to the flank face.
In the same study, the effects of different chamfer geometries on the tool rake and flank temperatures were also summarized.Leopold (2000) [7] used new method Visioplasticity-FEA.This method reduces the gap between theory and practice.Suggestions for overcoming some practical difficulties and extending the scope of this visioplasticity based predictive modeling approach are also considered.He found relationships between edge radius with grooved tool radius, cutting forces, the coefficient of the chip contraction, and tool-chip contact length.Altan et al. (2002)[8] performed FEM simulation to investigate the effect of tool edge geometries honeded of (0.01, 0.05, 0.1) mm, and chamfered of(0.1mm×15˚,0.1mm×25˚,0.2mm×15˚, 0.2mm×25˚) upon chip formation, cutting forces and process variables (temperature, stress, and strain) in orthogonal cutting and compared the results with the available experimental data.The results showed that both force components increase with increasing edge radius.Also the degree of plastic deformation in the secondary shear zone on the machined surface increases considerably as the edge radius increases.It is also showed that the edge radius does not have a significant influence on the magnitude of both stress components.Ozel (2003)[9] studied the influence of edge preparation in (CBN) cutting tool on process parameters and tool performance using FEM simulations and experimental tests.A set of orthogonal cutting experiments using honed (0.02) mm and chamfered (0.1mm×25˚) tools were performed.The results showed that the zone of workpiece material is formed under the chamfer acting as an effective rake angle during cutting.Altan (2003) [10] performed FEM simulation to investigate the effect of tool edge geometries honed of (0.01, 0.05, 0.1, 0.2) mm, chamfered of (0.1mm×15˚, 0.1mm×25˚,0.2mm×15˚,0.2mm×25˚), and sharp edge upon cutting force, chip flow, temperature, and tool stress in orthogonal cutting.Altan and Yen (2004) [11] studied the influence of the cutting edge radius (9, 14, 18, 20 and 24) µm of coated tools on chip formation in orthogonal cutting of Alloy steel.The results showed that the optimum edge radius has been revealed so as to minimizing the effective stress in the cutting tool to be (r =14µm).

2-Finite Element modeling
The FEM provides a systematic procedure for the derivation of the approximation functions over subregions of the domain.In FEM desecrates a structure into several elements (pieces of the structure).
Then reconnects elements at nodes as if nodes were pins or drops of glue that hold elements together.This process results in set simultaneous algebraic equations.For a general linear and/or nonlinear static problem the equations for a Finite Element analysis are expressed as: {F}=[K] {U} where: F is the vector matrix for the forces on the element, K is the stiffness matrix, and U is the vector of nodal displacements to be determined The model shown in Fig.
( 1) is built as a general orthogonal cutting model.The length of the workpiece is assumed to be 30mm.The uncut chip thickness (or depth of cut) is (0.5) mm while the height of workpiece is assumed to be (10) mm.The cutting tool was modeled with rake angle (γ) equal to (10˚) and the clearance angle (α) is assumed to be (5˚).Six models of cutting tools have been suggested having edge radius of (0.01, 0.05, 0.1, 0.15, 0.2, and 0.25)mm.The minimum one (edge radius of 0.01 mm) is supposed to be sharp.Modeling geometry and dimensions is done using the Cartesian coordinate, 2-D model.Both the workpiece and the tool are modeled with nonlinear quadrilateral elements.The tool was modeled with a fine mesh near the cutting tool tip and the other portion far from the tip was modeled coarsely.The model was divided into three parts with Lagrangian solid elements chosen to be (plane42) (four-nodes) this solid element is used for cutting tool modeling, while Lagrangian solid element is chosen (visco106) (fournodes), this element is used for chip and workpiece modeling.The solid elements (contac48), is chosen between tool and workpiece and between tool and the chip.The initial geometry and mesh are presented in Fig. (1), which consists of the following nodes and elements.
• 333 nodes (128 nodes for modeling of plane 42 and 205 nodes for modeling of visco106) • 283 element (173 visco elements and 110 plane elements).The mesh density for the chip was meshed more carefully specially on the line of contact between the chip and workpiece, where most be correspondent in mesh density in order to allowing chip separation take place, while the remain lines of the workpiece was defined to be free because the workpiece is out of our concern for this analysis.The boundary conditions are also shown in Fig. (1), the workpiece is fixed in all directions, and the tool is allowed to move towards the workpiece.The tool is considered to be rigid and moving at a constant cutting speed (V c ) in negative x direction.For this model, the cutting speed is assumed to be constant (150) m/min.Constraints were placed on the tool allowing movement only in the x direction.The cutting conditions are reported in table (1), the coefficients of friction between chip and tool and between

A Finite Element Analysis of Orthogonal
Machining Using Different Tool Edge Geometries 573 chip and workpiece was assumed to be constant (µ=0.5).

3-Modifying the ANSYS code for Metal Cutting Process
Joining between nodes is extremely useful in modeling and can be used successfully to simulate the metal cutting process.To simulate the chip separation, the workpiece is tied with chip segment by constant force in negative y direction.This force makes the chip and workpiece seem to be as one part till the chip formation process takes place.In this model it is required to select multiple pairs of nodes to be joined during the analysis and are therefore defined, when the failure criteria is adopted, the node pair is removed from the join, and the node motion is computed for the separation of nodes.The join ceases to exit, when all pairs of the join have failed, after which all the nodes of the join are treated as separate nodes.A tying force was included between the part of the workpiece that, is removed during the cutting (chip), and the remaining material (workpiece).When the joining force reaches certain critical value (chip separation criterion is reached), debond of the node pair in this region takes place and the two nodes move in different directions, which depends mainly on the assumed edge radius.The ANSYS code in this study is selected using Lagrange technique, which needs an overall view on material properties to get accurate results.The path for separating the chip from the workpiece is predetermined, as shown in Fig. (2), showing the initial contact and the start of separation and the steady state condition.

4-Material Modeling:
The material used for the workpiece is (AISI 1006 Steel), its mechanical and thermal properties are shown in table (2).The initial temperature is assumed to be (25ºC).A Von-Mises yield criterion is assumed, and isotropic strain hardening rule is applied.The tool is assumed to be (cemented carbide WC), whose mechanical properties are given in Table (3), the tool material has a hardness of (1700HV).

5-Results and Discussion: 5-1 Effect of Edge Radius on the Cutting Tool Stresses:
The shear stress distributions for the various edge radii, under identical machining conditions, are shown in Fig. (3).The shear stress was found to be maximum near the cutting edge due to high pressure caused by plastic deformation of the chip layers near the cutting edge in addition to the effect of sticking friction that affects the behaviors of contacting area resulting in high values of shear stresses at this region.It is clear also from Fig. (3) that the maximum value for the shear stress when using tool with edge radius within the range of (0.01-0.15) mm is increased within the limit of (237-550) MPa.But when using tool edge radius within (0.2-0.25) mm, the maximum shear stress is decreased from (373 to 295)MPa.This may be due to the increasing area of contact, which is more effective than the contact length.
The effective stress distributions for the six edge radii are shown in  4) shows that when using tool with edge radius within the range of (0.05-0.2) mm, the maximum effective stress is increased within the limit of (619 -3690) MPa and then decreased when using edge radius of (0.25) mm in order to reach the value of (3140) MPa, while when using tool with edge radius of (0.01) mm the effective stress is (3250) MPa..More details for stress distribution contours at the various tool edge values for the simulated tests are shown in the Appendix (A&B).These results show that the edge radius has a complex influence on the magnitude of both stress components (shear stress and effective stress).It is clear from the simulated results for the six edge radii, which are shown in Fig. (

5-2 Effect of Edge Radius on
Cutting Forces: shows that both forces increase as the edge radius increases from (0.01 to 0.25) mm.A comparison was made between predicted, experimental and simulated results from previous paper, showed good results.Apparently, this increase in forces is due to the increase of the cutting edge radius.In addition, the increase in chip thickness leads to a larger shear plane angle in the deformation zone, which increases the cutting forces.The predicted values of (F c and F t ) are in good agreement with experimental and numerical measured values from previous published papers.A comparison was made between predicted, experimental and simulated results from previous paper [10], showed good results.Apparently, this increase in forces is due to the increase of the cutting edge radius, which requires larger forces for material shearing.The predicted values of (F c and F t ) are in good agreement with experimental and numerical measured values from previous published papers.The maximum difference between cutting forces from this work and cutting forces from previous published paper [17] is less than (5%) for the tangential force and (11%) for the thrust force, this may be due to uncertainties in the material properties or due to some difference in the cutting conditions.7), that the contact length (L c ) increases as the edge radius increases within a range of (0.01-0.15) mm.The large normal contact pressure near the edge of the tool causes sticking and sliding friction between the chip and the rake face of the tool.Therefore, the material near the edge radius continues to deform and the temperature can be very high locally in some areas of the chip, resulting in further thermal softening.This thermal softening reduces the materials strainhardening capacity, so the instability takes place in a narrow band and finally forms an intense shear band [14].

6-Conclusions:
The main conclusions, which can be deduced from the present work, can be summarized as follows: 1.The results show that the optimum edge radius from the six models simulated is (0.05) mm; this edge radius gives minimum value of effective stress.2. The optimum edge radius for minimum tangential cutting and feed forces is (0.01) mm. 3. The results show that the toolchip contact length is increased, until reaching maximum value of (2.4) mm at (r = 0.15mm), and minimum value of (0.75) mm at (r = 0.01mm).4. The maximum relative difference between simulated results of this work and previous paper results is (5%) for the tangential forces, (11%) for the thrust force, and (2% -7%) for the tool effective stresses. A Eng. & Technology, Vol.25, No.4, 2007 A Finite Element Analysis of Orthogonal Machining Using Different Tool Edge Geometries 572 Eng. & Technology, Vol.25, No.4, 2007 Fig. (4), the maximum effective stress occurs at the tool tip, due to the existence of the sticking zone.Sliding takes place beyond the sticking region Eng.& Technology, Vol.25, No.4, 2007 A Finite Element Analysis of Orthogonal Machining Using Different Tool Edge Geometries 574 and therefore, one can observe that the effective stress decreases to zero at the point where chip leaves the tool face.Fig.( It is clear from Fig.(