**4.3 Finite element model and simulation results**

The corresponding mesh is refined in some region as severe plastic deformation may be induced under material surface which is shown in figure 5. The most fundamental and crucial characteristic of metal cutting process lies in the formation of chip. In reality, the chip is not exactly "cut" but "sheared" away from the work material which forms a clear distinction between machining plastic metal and other materials. Figure 6 shows the chip formation process during precision machining of titanium alloy. Chip formed with the tool approaching the material from the right side and the chip flow in curved fashion. When the original chip thickness or feed rate or depth of cut is compared with the chip thickness after cutting, the deformation can be clearly observed. This deformation is fundamental for the


Table 1. FEM simulation parameters

Fig. 5. FE simulation model

Analysis Precision Machining Process Using Finite Element Method 119

and rake face of cutting tool; the third plastic deformation region where the tribology behavior is generated between materials machined surface and the clear face of cutting tool. With the cutting in of tool, the elastic deformation is initially induced at the contact interface between cutting tool and materials. After that the titanium alloy becomes going into yield state with the further successively feeding of cutting tool and the plastic deformation region gradually comes into being ahead of cutting tool. The successive feeding of cutting tool results in the contraction of the elastic deformation and expansion of plastic deformation. The full contact between cutting tool and workpiece comes into being and the elastic-plastic deformation is generated. The simulation results show that fairly concentrated shear separates the nearly unstrained work materials from the fully strained chip. But no obvious region of secondary deformation is generated close to the rake face of tool. The contact length between rake face of cutting tool and the bottom is very small which also justifies

0 100 200 300 400 500 600

Cutting Force in X Direction

Time Step

Chip thickness

III

Metal cutting process at nanometer scale involves plastic deformation in small localized regions where opposing surface contact or in the interior of workpiece materials. As for chip formation, the single-shear plane model and practically all its "basic mechanics" have been

I

II

most of the cutting process are accomplished by the local tool tip.

2.5

2.0

1.5

Cutting Force (N)

1.0

0.5

Depth of cut

Fig. 7. Simulation results of cutting force

Fig. 8. Deformation area in the metal cutting

Fig. 6. FE simulation of precision machining of titanium alloy

metal cutting process and involves large deformations of materials with very large strains and very high strain rates. The produced chip is in contact with the tool face in a highly pressurized zone causing sticking friction which transforms to sliding friction further up on the tool face. A large amount of heat is generated in the cutting zone as a result of plastic work and friction causing temperature rise in the tool and chip.

There are three main plastic deformation areas in this precision machining process as shown in figure 6, namely, the first plastic deformation region, which dominates the kind and the morphology of the chip and generated large amount of heat, the degree of plastic deformation is closely related with materials stress-strain relationship; the second plastic deformation region where the intense tribology process is generated between bottom of chip

(*a*) Timestep: 90 (*b*) Timestep: 180

(*c*) Timestep: 270 (*d*) Timestep: 360

Fig. 6. FE simulation of precision machining of titanium alloy

work and friction causing temperature rise in the tool and chip.

metal cutting process and involves large deformations of materials with very large strains and very high strain rates. The produced chip is in contact with the tool face in a highly pressurized zone causing sticking friction which transforms to sliding friction further up on the tool face. A large amount of heat is generated in the cutting zone as a result of plastic

(*e*) Timestep: 450 (*f*) Timestep: 540

There are three main plastic deformation areas in this precision machining process as shown in figure 6, namely, the first plastic deformation region, which dominates the kind and the morphology of the chip and generated large amount of heat, the degree of plastic deformation is closely related with materials stress-strain relationship; the second plastic deformation region where the intense tribology process is generated between bottom of chip and rake face of cutting tool; the third plastic deformation region where the tribology behavior is generated between materials machined surface and the clear face of cutting tool. With the cutting in of tool, the elastic deformation is initially induced at the contact interface between cutting tool and materials. After that the titanium alloy becomes going into yield state with the further successively feeding of cutting tool and the plastic deformation region gradually comes into being ahead of cutting tool. The successive feeding of cutting tool results in the contraction of the elastic deformation and expansion of plastic deformation. The full contact between cutting tool and workpiece comes into being and the elastic-plastic deformation is generated. The simulation results show that fairly concentrated shear separates the nearly unstrained work materials from the fully strained chip. But no obvious region of secondary deformation is generated close to the rake face of tool. The contact length between rake face of cutting tool and the bottom is very small which also justifies most of the cutting process are accomplished by the local tool tip.

Fig. 7. Simulation results of cutting force

Fig. 8. Deformation area in the metal cutting

Metal cutting process at nanometer scale involves plastic deformation in small localized regions where opposing surface contact or in the interior of workpiece materials. As for chip formation, the single-shear plane model and practically all its "basic mechanics" have been

Analysis Precision Machining Process Using Finite Element Method 121

tensile. It is also tensile along the surface of chip which has moved out of the contact with

Presently, the hypotheses propounded by various researchers to explain the curvature of the chip include (i) The cutting moment causes the chip to bend; (ii) The 'crushing' of chip in the secondary shear zone and the resultant acceleration of the work material in moving through the secondary shear zone causes the chip to lengthen along this side (the front side). This can also results in a curvature of the chip which is similar to the curvature of a bimetallic strip; (iii) The shear plane is curved in such a way that the shear plane angle is smaller near the exit of shear plane. Thus the chip velocity on the back side is smaller than the average

The bending moment on the chip considered as a beam would result in compressive stress along the free surface (back) of the chip if hypothesis (i) was true. Crushing of the chip in the

Only a curved shear plane would result in a stress distribution similar to that given by the finite element analysis, while simultaneously accounting for curl of the chip. It should be noted that though the chip does accelerate (due to secondary shear) as it flows along the rake face of tool, this is just an accessory to chip curl and not the cause of chip curl. The reason for the curvature of the shear plane can be found from a detailed analysis of the stress distribution in the zone of plastic deformation. Work in this direction is in progress.

With the increasing of high quality and accuracy of modern automated machining technology, numerical simulation of machining technology such as FEM is starting to emerge. The FEM based virtual machining simulation has the capability of calculating the results of process variables about the precision machining process used for optimization the cutting process thus providing many benefits to the metal cutting application. Presently, FEM is mainly of use to mechanical and materials engineering, as a tool to support process understanding, materials machinability development and tool design. The research efforts show that the model used in FEM of precision metal cutting process should be adequate to the process. But the concept of FE model should be broadened in order to embrace important facets physics including uncertainty, which has been axiomatized out of modern cutting research. Breakthrough in these directions will have considerable impact by making metal cutting simulation useful for practical optimization of various metalworking operations including the cutting and machine tools, the metal working fluids and fixtures

[2] T.L. Anderson, Fracture Mechanics – Fundamentals and Applications, CRC Press, New

[3] J. Chaskalovic, Finite Element Methods for Engineering Sciences, Springer-Verlag, 2008

[1] M.C. Shaw, Metal Cutting Principles, Oxford Science, Oxford, 1984

*yy* in the middle of the chip is compressive. Such a

*yy* in the front (underside) of the chip.

distribution of stress is the critical factor to develop initial formation of chip.

the tool rake face (front) while the

chip velocity which causes the chip to curl.

**5. Conclusion** 

and so on.

**6. References** 

York, 1995

secondary shear zone will result in compressive

known since nineteenth century and referred as the Merchant (or Ernst-Merchant model) model[1]. This model has been the basis for most of the present metal cutting analysis. The first orthogonal model was brought forward in 1937 by Piispanen[1] and termed as card model. In this model, the material cut is assumed as a deck of cards inclined to the cutting direction which is shown in figure 9. Merchant assumed the chip to be formed over an infinite thin plane called shear plane. This shear plane starts from the cutting edge of the tool and crosses the chip on an angle with the cutting direction, which is termed as shear angle. When the chip passes the shear plane it is sheared away from the workpiece and increases in thickness. In this simulation, no single shear plane is observed in the whole precision machining process. On the other case, there some maximum stress band is continuously generated in front of cutting tool. This shear band possesses irregular geometry shape which extends from first deformation region to third deformation region.

Fig. 9. Card of cutting process

A zone of plastic deformation extends underneath the machined surface. This subsurface deformation will result in compressive stresses in the machined surface. Though the stress patterns are those with the load applied by the tool still present, elastic recovery caused by the unloading of the tool is not expected to significantly change the stress distribution close to the free surface. So the stress in the machined surface sufficiently far away from the tool can be taken to be the residual stress. The location of the nodes along the machined surface when compared with the location of tool cutting edge yields information about the elastic recovery of the machined surface after it passes under the tool. The elastic spring-back of the machined surface is found to be far less than the radius curvature of cutting edge which justify that most of the material in front of the rounded cutting edge is actually pushed ahead of the tool and not into the machined surface.

The simulation results also shows that the continuous internal curling chip is generated under current working conditions. At the beginning, part of chip adjacent to the tool tip begins to curl and form helix circle with small radius. After that, the larger helix circle surround the previous small one is gradually formed with the feeding of the cutting tool. The deformation coefficients ( *<sup>c</sup> u t t* ) is gradually increased in this process which result in the increasing of cutting force (figure 7). The stress along the free surface (back) of chip is tensile. It is also tensile along the surface of chip which has moved out of the contact with the tool rake face (front) while the *yy* in the middle of the chip is compressive. Such a distribution of stress is the critical factor to develop initial formation of chip.

Presently, the hypotheses propounded by various researchers to explain the curvature of the chip include (i) The cutting moment causes the chip to bend; (ii) The 'crushing' of chip in the secondary shear zone and the resultant acceleration of the work material in moving through the secondary shear zone causes the chip to lengthen along this side (the front side). This can also results in a curvature of the chip which is similar to the curvature of a bimetallic strip; (iii) The shear plane is curved in such a way that the shear plane angle is smaller near the exit of shear plane. Thus the chip velocity on the back side is smaller than the average chip velocity which causes the chip to curl.

The bending moment on the chip considered as a beam would result in compressive stress along the free surface (back) of the chip if hypothesis (i) was true. Crushing of the chip in the secondary shear zone will result in compressive *yy* in the front (underside) of the chip. Only a curved shear plane would result in a stress distribution similar to that given by the finite element analysis, while simultaneously accounting for curl of the chip. It should be noted that though the chip does accelerate (due to secondary shear) as it flows along the rake face of tool, this is just an accessory to chip curl and not the cause of chip curl. The reason for the curvature of the shear plane can be found from a detailed analysis of the stress distribution in the zone of plastic deformation. Work in this direction is in progress.
