324 CHAPTER 10 FINITE ELEMENT SIMULATION OF CUTTING PROCESSES 10.1 INTRODUCTION This chapter deals with the Finite-Element Method (FEM) of machining and simulation. Results about the influence of working conditions and tool geometry (cutting-edge finishing) on tool forces, temperatures, stresses, strain and velocity when machining Al7075-T6 are presented. The aim of the chapter is to demonstrate the possibilities of FEM for understanding the chip formation process in machining and to show its capabilities in areas like tool insert design. There have been numerous applications of FEM in chip formation processes. Initially, custom-made codes and later, basically with general- purpose software like Abaqus TM , ALGOR TM (metal forming), DEFORM- 3D TM , MARC TM , LS DYNA TM , and FLUENT TM . In addition, two specific commercial software programs seemed on the market during the last decade: AdvantEdge™ and DEFORM™. Advant- Edge and DEFORM-2D/-3D both programs provide an interface to the end user, in order to ease the introduction of process parameters and in a way make transparent those subjects dealing with the mathematical theory of the finite-element method. DEFORM is software specialized in modeling machining operations in 2D and 3D based on an
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324
CHAPTER 10
FINITE ELEMENT SIMULATION OF
CUTTING PROCESSES
10.1 INTRODUCTION
This chapter deals with the Finite-Element Method (FEM) of
machining and simulation. Results about the influence of working conditions
and tool geometry (cutting-edge finishing) on tool forces, temperatures,
stresses, strain and velocity when machining Al7075-T6 are presented. The
aim of the chapter is to demonstrate the possibilities of FEM for
understanding the chip formation process in machining and to show its
capabilities in areas like tool insert design.
There have been numerous applications of FEM in chip formation
processes. Initially, custom-made codes and later, basically with general-
purpose software like AbaqusTM, ALGORTM (metal forming), DEFORM-
3DTM, MARCTM, LS DYNATM, and FLUENTTM. In addition, two specific
commercial software programs seemed on the market during the last decade:
AdvantEdge™ and DEFORM™.
Advant- Edge and DEFORM-2D/-3D both programs provide an
interface to the end user, in order to ease the introduction of process
parameters and in a way make transparent those subjects dealing with the
mathematical theory of the finite-element method. DEFORM is software
specialized in modeling machining operations in 2D and 3D based on an
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implicit integration method, with fully coupled thermo-mechanical analysis.
Since the formulation is Lagrangian, an adaptive remeshing technique is used
to reduce the mesh distortions when the chip is formed. Several material
constitutive laws can be used to model the material behavior (Oxley’s
equation, Johnson–Cook equation, among others). A material database can be
found in this software, both for tool and workpiece materials. For modeling
the contact at the tool–chip interface, a constant shear factor friction law or
Coulomb friction law can be employed. Workpiece and tool geometries
should be configured by the user, both in terms of the external dimensions and
those of the mesh of the two parts. However, coating layers can be
implemented in the tool. Also remarkable is the availability of loading some
existing geometries of tools and tool holders from a database incorporated in
the program.
The objective of this work is to set up two FEM reference models
to study two dimensional and three-dimensional cutting operations. In order
to reduce the experimental costs, FEM of machining can be employed to
qualitatively predict tool forces, stress, temperature, strain, strain rate and
velocity fields.
10.2 CONSTITUTIVE MODELS FOR WORK MATERIAL FLOW
STRESS
The flow stress or instantaneous yield strength at which work
material starts to plastically deform or flow is mostly influenced by
temperature, strain, strain rate, and other factors. Accurate and reliable flow
stress models are considered highly necessary to represent work material
constitutive behavior under high-speed cutting conditions especially for a
(new) material. Therefore, semi-empirical constitutive models are widely
utilized. The constitutive model proposed by Johnson and Cook (Johnson
&Cook 1983) describes the flow stress of a material with the product of
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strain, strain rate and temperature effects that are individually determined as
given in Equation (10.1). In order to reduce the number of experiments
constitutive material laws are needed. The constitutive material law has to
describe the plastic behaviour in dependence for a wide range of strain, strain
rate and temperature. For the simulation several material models have been
developed, which consider strain hardening, strain rate hardening and thermal
softening. Most of material laws are of empirical nature. Empirical material
laws ( Flow stressdf ( , ,T)dt
) describe the flow stress as a function of strain,
strain rate and temperature. Empirical material laws contain specific material
constants, which will be determined by regression analyses or by the least
squares method based on the experimental measured flow stress curves.
m
n room
0 melt room
T TA B .(1 Cln( )). 1T T
(10.1)
0
(1 Cln( )) viscous damping,m
room
melt room
T T1T T
, temperature
function, Material constants: A, B, n, C, m,Reference velocity: 0 ,Room
temperature: roomT ,Melting temperature: meltT .In the Johnson–Cook (JC)
model, the parameter A is in fact the initial yield strength of the material at
room temperature and a strain rate of 1s-1 and represents the plastic
equivalent strain. The strain rate is normalized with a reference strain rate 0.
Temperature term in the JC model reduces the flow stress to zero at the
melting temperature of the work material, leaving the constitutive model with
no temperature effect. In general, the parameters A, B, C, n and m of the
model are fitted to the data obtained by several material tests conducted at
low strains and strain rates. The JC model provides a good fit for strain-
327
hardening behavior of metals and it is numerically robust and can easily be
used in finite element simulation models (Jaspers &Dautzenberg 2002).
10.3 TWO-DIMENSIONALFINITE ELEMENT SIMULATION
OF CUTTING PROCESSES
Machining operations such as orthogonal metal cutting are complex
nonlinear and coupled thermomechanical processes. The complexities are due
to large strain and high strain-rate in the primary shear zone and due to the
contact and friction between the chip and tool along the secondary shear zone.
In addition to the above, complexities are also caused by local heat generated
through the conversion of plastic work in the chip during.
Chip formation and the frictional work between the tool and chip.
An undesired byproduct of the metal cutting process is the creation of residual
stresses and strains in the freshly cut workpiece, which is known to affect the
integrity of the newly finished surface, including shortened creep and fatigue
lives of the machined component under service loads. Hence a careful
assessment of the residual stress and strain fields in the workpiece is
necessary for optimizing the cutting process and for safeguarding against the
premature failure of machined parts under creep and fatigue loading
conditions.
A simulation procedure has been developed through the use of
several advanced modeling options in the general-purpose code deform 2D.
An updated Lagrangian formulation suitable for large strain deformations is
employed. Plane strain conditions are assumed. Strain-rate effects are
included with an overstress viscoplastic constitutive model. Frictional contact
along the tool-chip interface is made to obey a modified moulombfriction law.
Adiabatic heating conditions are used to account for temperature rise due to
local heating induced by plasticity and friction. Chip separation from the
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workpiece is modeled using a stress-based chip separation criterion.
Temperature-dependent material properties are considered. This investigation
provides a detailed exposition of stress, strain, temperature, velocity and
cutting force field evolution at different stages after cutting, and of the
formation of residual stresses and strains near the finished surface of the
workpiece.
This two-dimensional finite element simulation of cutting processes
investigates the effect of nose radius, cutting speed, cutting feed with a
constant depth of cut.
The material properties (Mechanical Properties, Thermal Properties),
cutting tool properties and material constants for the process simulation is as
The 3D simulations were run as per design matrix and simulation
example output results are shown below the Figures 10.11 -10.16.
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Figure 10.11 Example of cutting force obtained from 3D FEA model
Figure 10.12 An example of Effective strain obtained from 3D FEA model
Figure 10.13An example of effective stress obtained from 3D FEA model
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Figure 10.14 An example of velocity obtained from 3D FEA model
Figure 10.15 An example of cuttingtemperature obtained from 3D FEA model
Figure 10.16 An example of cutting tool insert temperature obtained from 3D FEA model
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This regression model procedure is explained in detail in Chapter 4
in Section 4.3.1.
10.6 RESULTS AND DISCUSSION 3D FEA MODEL
The developed mathematical model was used to predict responses
by substituting the respective values of the process parameters. The influence
of the machining parameters on responses was studied using the developed
model.
10.6.1 Direct Effects of Machining Parameter on Response
The direct effect of process parameters was studied by keeping all
the machining parameters at the middle level except the parameter whose
direct effect was studied.
10.6.1.1 Effect of machining parameter on cutting force
Figure 10.17 (a) shows the effect of cutting speed on resultant
cutting force. From Figure 10.17 (a) it is clear that as the cutting speed
increases, resultant cutting force firstly decreases approaching value at cutting
speed 190m/min then it marginally increases. Figure 10.17 (b) shows the
effect of cutting feed on resultant cutting force. From figure 10.17 (b) it is
clear that as the cutting feed increases, resultant cutting force firstly decreases
approaching value at cutting feed 0.8mm/tooth then it increases. Figure 10.17
(c) shows the effect of depth of cut on resultant cutting force. From the figure,
it can be inferred that the increase in depth of cut resulted in increasing trend
all levels of forces.
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Figure 10.17 Main effects plot for response (Resultant cutting force)
10.6.1.2 Effect of machining parameter on cutting temperature
Figure 10.18 (a) shows the effect of cutting speed on cutting zone
interface temperature. From the figure, it can be inferred that the increase in
cutting speed resulted in increasing trend all levels of forces. Figure 10.18 (b)
shows the effect of cutting feed on cutting zone interface temperature. From
Figure 10.18 (b) it is clear that as the cutting feed increases, cutting zone
interface temperature firstly decreases approaching value at cutting feed
0.8mm/tooth then it increases. Figure 10.18 (c) shows the effect of depth of cut
on cutting zone interface temperature. From the figure, it can be inferred that the
increase in depth of cut resulted in increasing trend all levels of forces.
Figure 10.18 Main effects plot for response (cutting zone interface temperature)
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10.6.1.3 Effect of machining parameter on effective strain
Figure 10.19 (a) shows the effect of cutting speed on effective
strain. From Figure 10.19 (a) it is clear that as the cutting speed increases,
effective strain firstly decreases approaching value at cutting speed 160m/min
then it increases. Figure 10.19 (b) shows the effect of cutting feed on effective
strain. From the figureit is clear that as the cutting feed increases, effective
strain firstly increases approaching value at cutting feed 0.08mm/tooth then it
decreases. Figure 10.19 (c) shows the effect of depth of cut on effective strain.
From Figure 10.19 (c) it is clear that as the depth of cut increases, effective
strain firstly increases approaching value at depth of cut 1.5mm then it
decreases.
Figure 10.19 Main effects plot for response (Effective strain)
10.6.1.4 Effect of machining parameter on effective stress
Figure 10.20 (a) shows the effect of cutting speed on effective
stress. From the figure, it can be inferred that the increase in cutting speed
resulted in increasing trend all levels of effective stress. Figure 10.20 (b)
shows the effect of cutting feed on effective stress. From Figure 10.20 (b) it is
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clear that as the cutting feed increases, effective stress firstly decreases
approaching value at cutting feed 0.09mm/tooth then it increases.
Figure 10.20 (c) shows the effect of depth of cut on effective stress. From the
figure it is clear that as the depth of cut increases, effective stress firstly
decreases approaching value at a depth of cut 2mm then it increases.
Figure 10.20 Main effects plot for response (Effective stress)
10.6.1.5 Effect of machining parameter on velocity
Figure 10.21 (a) shows the effect of cutting speed on velocity. From
Figure 10.21 (a) it is clear that as the cutting speed increases, velocity firstly
increases approaching value at cutting speed 190m/min then it decreases.
Figure 10.21 (b) shows the effect of cutting feed on velocity. From figure.
10.21 (b) it is clear that as the cutting feed increases, velocity firstly increases
approaching value at cutting feed 0.09mm/tooth then it decreases.
Figure 10.21 (c) shows the effect of depth of cut on velocity. From
Figure 10.21 (c) it is clear that as the depth of cut increases, velocity firstly
increases approaching value at depth of cut 1.5mm and then it decreases.
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Figure 10.21Main effects plot for response (Velocity)
10.6.1.6 Effect of response on cutting tool insert temperature
Figure 10.22 (a) shows the effect of cutting speed on cutting tool insert temperature. From Figure 10.22 (a) it is clear that as the cutting speed increases, cutting tool insert temperature firstly decreases approaching value at cutting speed 160m/min then it increases. Figure 10.22 (b) shows the effect of cutting feed on cutting tool insert temperature. From the figure, it can be inferred that the increase in cutting feed resulted in increasing trend all levels of cutting tool insert temperature. Figure 10.22 (c) shows the effect of depth of cut on cutting tool insert temperature. From Figure 10.22 (c) it is clear that as the depth of increases, cutting tool insert temperature firstly increases approaching value at a depth of cut 2mm then it decreases.
Figure 10.22 Main effects plot for response (cutting tool insert temperature)
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10.7 CONCLUSION
The experiments were carried out to estimate response (cutting force, cutting zone interface temperature, effective strain, effective stress, velocity and cutting tool insert temperature) and to gauge the effect of machining parameters such as cutting speed, cutting feed rate and depth of cut on AL7075-T6 aluminum alloy in FEA cutting processes. The following conclusions were derived after the investigation.
1. The cutting force, cutting zone interface temperature, effective strain, effective stress, velocity and cutting tool insert temperature of an AL7075-T6 aluminum alloy can be computed efficiently through FEA model developed in this work.
2. The direct effects of process parameters on cutting force, cutting zone interface temperature, effective strain, effective stress, velocity and cutting tool insert temperature within the range of investigation can be studied with ease from the central composite design.
3. FEM can give quite interesting qualitative values about the influence of input parameters on the results like temperature, stresses, velocity, etc. that are fairly difficult to be measured experimentally. 2D &3D modeling would be needed to meet industrial requirements regarding stresses, tool wear, etc.
4. This research is limited to one type of tool insert and one type of workpiece material. Enlarging this system to include more cutting tools and materials for workpieces could provide a better position for this study to be adopted into industrial use.
5. This system can accurately predict the contact time, Interface pressure, folding angle, chip morphology (chip thickness) within a wide range of machining parameters, and has practical potential application in industry.