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SIMULATION OF END MILLING OPERATION FORPREDICTING CUTTING FORCES TO MINIMIZE TOOL

DEFLECTION BY GENETIC ALGORITHMR. Jalili Saffar

a& M. R. Razfar

a

aDepartment of Mechanical Engineering, Amirkabir University of Technology (Tehran

Polytechnic), Tehran, Iran

Published online: 11 Mar 2010.

To cite this article: R. Jalili Saffar & M. R. Razfar (2010) SIMULATION OF END MILLING OPERATION FOR PREDICTING CUTTINGFORCES TO MINIMIZE TOOL DEFLECTION BY GENETIC ALGORITHM, Machining Science and Technology: An International Journal,

14:1, 81-101, DOI: 10.1080/10910340903586483

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Machining Science and Technology, 14:81101Copyright 2010 Amirkabir University of TechnologyISSN: 1091-0344 print/1532-2483 onlineDOI: 10.1080/10910340903586483

SIMULATION OF END MILLING OPERATION FOR PREDICTING

CUTTING FORCES TO MINIMIZE TOOL DEFLECTIONBY GENETIC ALGORITHM

R. Jalili Saffar and M. R. Razfar

Department of Mechanical Engineering, Amirkabir University of Technology

(Tehran Polytechnic), Tehran, Iran

This paper presents a 3D simulation system which is employed in order to predict cutting

forces during end milling operation. Machining errors on the machined surface mostly arise

from tool deflection. Therefore, in this research an attempt is made to optimize the machining

parameters with the objective of minimization of the tool deflection using Genetic Algorithm

(GA). In contrast to other optimization methods, in which machining time and cost are defined

as the objective functions, this algorithm considers tool deflection as the objective function, while

surface roughness and tool life are the constraints. In order to verify the accuracy of the 3D

simulation and the optimization process, these results are compared with experimental results

obtained from the theoretical relationships. The agreement of these results with the experimental

results is compared. The obtained results indicate that the optimized parameters are capable of

machining the workpiece more accurately and with better surface finish.

Keywords cutting force, end milling, finite element method (FEM), geneticalgorithm, tool deflection

INTRODUCTION

The end milling operation is a metal cutting process using a rotatingcutter with several teeth. Figure 1 shows the model coordinate system

for end-milling operation. Chip formation is the essential phenomenonin the cutting process. The cutting force, cutting temperature, tool wear,chatter, burr, built-up-edge, chip curling and chip breakage are still thetopics of the current research. In the recent decades, with the emergenceof powerful computers and the development of numerical methods, suchas finite element method (FEM), finite difference method (FDM) andartificial intelligence (AI), these are widely used in the machining industry.

Address correspondence to R. Jalili Saffar, Department of Mechanical Engineering, AmirkabirUniversity of Technology (Tehran Polytechnic) 424-Hafez Ave., 15875-4413 Tehran, Iran. E-mail:[email protected]

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82 R. J. Saffar and M. R. Razfar

FIGURE 1 (a) Model coordinate system of end-milling operations and (b) axial and radial depthof cut.

Among these, finite element method has become a powerful tool in thesimulation of cutting process. Various parameters in the cutting process,

such as cutting force, cutting temperature, strain, strain rate, stress, etc.,can be predicted by simulation of the chip formation in metal cutting.Most of these parameters are very difficult to measure using experimentaltechniques. Therefore, development of a novel prediction method byintegration of the finite element method simulation of cutting process withmachining model seems advantageous.

According to a comprehensive survey conducted by the CIRP WorkingGroup on Modeling of Machining Operations during 19961997 (VanLuttervelt et al., 1998), among the 55 major research groups active in

modeling, 43% were active in empirical modeling, 34% in analyticalmodeling and 23% in numerical modeling, in which finite elementmodeling techniques are used as the dominant tool. In recent years,application of finite element analysis in metal cutting has rapidly grown.Finite element method has been used to simulate machining by Klamecki(1973), Okushima and Kakino (1971), and Tay et al. (1974). With thedevelopment of faster processors with larger memory, model limitations andcomputational difficulty have been overcome to some extent. Comparedto empirical and analytical methods, finite element methods used in the

analysis of chip formation have several advantages as follows: Material properties can be handled as functions of strain, strain rate and

temperature; The interaction between chip and tool can be modeled as sticking and

sliding; Non-linear geometric boundaries, such as the free surface of the chip,

can be represented and used; In addition to the global variables, such as cutting force, feed force and

chip geometry, the local stress, temperature distributions, etc., can alsobe obtained.

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3D Simulation to Predict Cutting Forces 83

The current research also reports on a new error compensationapproach in the machined surfaces with small diameter tools. Thedetermination of optimal cutting parameters, such as axial depth of cut,radial depth of cut and feed rate, are vital modules in process planningfor the increased accuracy of machined surfaces. One of the purposes ofthis paper is to investigate the optimal cutting parameters to minimize

tool deflection for error compensation on the machined surface whilemaintaining material removal rate and stability of the cutting process. Themain parameters in end milling which affect tool deflection and surfacefinish are axial depth of cut, radial depth of cut and feed rate. The optimalcutting parameters are subject to an objective function of tool deflectionwith the feasible range of cutting parameters. The user of the machine toolmust know how to choose cutting parameters in order to minimize cuttingtime, cutting force and produce better surface finish (surface roughness)under stable conditions. Normally, feed rate, axial depth of cut and radial

depth of cut immersion are chosen according to the technical guidance.But these parameters are strongly dependent on the static and dynamicproperties of the tool. In order to obtain better surface roughness, theproper setting of cutting parameters is crucial.

This paper introduces a computer algorithm developed to optimizethe cutting parameters to minimize tool deflection, improve tool life andsurface roughness for a constant material removal rate. The system ismainly based on a powerful artificial intelligence (AI) tool, called geneticalgorithms (GA). The use of the impact and the power of AI techniques

have been reflected on the performance of the optimization system.The methodology of the developed optimization system is illustrated bypractical examples throughout the paper. Optimization of the machiningparameters increases product quality to a great extent.

CUTTING FORCE MODELING OF END-MILLING OPERATION

Conventional Cutting Force Model

Tlusty and MacNeils (1975) cutting force model is developed forconventional end-milling operations according to the below equations.

Fx = Fu[(e s) Pf(sin2 e sin

2 s) 05(sin2e sin2s)] (1)

Fy = Fu[Pf(e s) + (sin2 e sin2 s) 05Pf(sin2e sin2s)] (2)

where Fu is unit force (N) and Fu = Kmrft/ tan /2,Fx is normal directioncutting force (N), Fy is feed direction cutting force (N), r is toolradius(mm), Km is material coefficient (N/mm2), ft is feed per tooth(mm/tooth), s is integrating start angle (Rad), e is integrating end angle

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(Rad), also according to the experimental data, the proportional factor Pfis usually selected as 0.3.

SIMULATION OF END MILLING OPERATION (FEM)

The implementation of cutting process simulation is based on

numerical technique. Several approaches are supplied for numericalmodeling: (a) Lagrangian, (b) Eulerian and (c) Arbitrary LagrangianEulerian (ALE).

In Eulerian approach, the mesh is fixed spatially and the materialflows through the mesh. Eulerian approach is suitable for analysis of thesteady state of the cutting process. In Lagrangian approach, the meshfollows the material. Because the deformation of the free surface of thechip can be automatically treated by elastic-plastic material deformation,Lagrangian approach can be used to simulate from initial to steady statecutting process. Arbitrary Lagrangian Eulerian (ALE) approach combinesthe features of pure Lagrangian and Eulerian approach, in which the meshis allowed to move independently of the material. It is an effective toolfor improving mesh quality in the analysis of large deformation problems.Many commercial FE codes introduce ALE approach by adjusting meshbased on different criteria adaptively. The adaptive meshing techniquethat is used in this model belongs to ALE approach. It can be employedto analyze not only the Lagrangian problem but also Eulerian problem.By giving suitable mesh control parameters, the whole process from theinitial to steady state can be simulated without the need of chip separationcriterion or any chip geometry data from experiment.

Mechanical Aspects

The development of metal cutting theory helps engineers to get betterunderstanding of the mechanical aspects of cutting process, includingcontact and friction, material property, chip separation, etc. The modeling

of these aspects discussed below influences the accuracy of cutting processsimulation.

Contact Law. In a metal cutting process, due to high stresses, strainrates and temperatures, a high mechanical power is dissipated in thetoolchip interface, thus leading to many structural modifications of thecontacting pieces. Shih and Yang (1993) have shown that no universalcontact law exists that can predict friction forces among a wide range ofcutting conditions. Childs and Maekawa (1990) have indicated that stickand slip zones along the inter-facial zone between the chip and the tooldepend on cutting conditions, pressure, temperature, etc.

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In this model, a classical Coulomb friction law is assumed to model thetoolchip and the toolworkpiece contact zones. The contacting bodies areassumed to stick together ifTt < |Tn| and in a relative motion ifTt =|Tn| with Tn and Tt representing the normal and tangential componentsof the surface traction at the interface and , the friction coefficient,assumed as a constant depending on the nature of the contacting bodies.

A value of = 032 is assumed here; this has been determined from aspecific friction test (Joyot et al., 1993).

Material Constitutive Model. Numerical simulation of chip formationrequires a thermo-visco-plastic law (Meslin and Hamann, 2003). In thecase of large plastic deformations and large strain rates, several researchershave proposed specific flow stress expressions; the well known Johnsonand Cook (1983) formulation is often used. This material model, given inEquation (3), was developed in the 1980s to study impacts, penetrationsand explosives (Zouhar and Piska, 2008).

The main workpiece material used in this research is mild carbon steel,AISI 1045. To describe the material property of AISI 1045, the JohnsonCook constitutive equation is used:

= (Bn)

1 + Cln

1000

Tmelt T

Tmelt Troom

+ ae000005(T700)

2

(3)

where B = 9961, C = 0097, n = 0168, a = 0275, Tmelt = 1480C and isthe effective stress in MPa, is the strain, is the strain rate (s1) and T

is temperature in C (Koppka et al., 2001).The JohnsonCook model is a well-accepted and numerically robustconstitutive material model and is highly utilized in modeling and simu-lation studies. The JohnsonCook (JC) model assumes that the slope of theflow stress curve is independently affected by strain hardening, strain ratesensitivity and thermal softening behaviors. Each of these sets is representedby the brackets in the constitutive equation (zel and Zeren, 2006).

Chip Separation

Chip Separation Criterion. The chip separation criteria used byresearchers can be categorized as two types: geometrical and physical(Huang and Black, 1996).

Model Realization. There are several methods to model chip separationin a finite element mesh. These are dependent on the software used insimulation. Some of these are explained below:

1) Element removal (Ceretti et al., 1996);2) Node debond (Shi et al., 2003; Shet and Deng, 2000, 2003);

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3) Node splitting (Shet and Deng, 2000);4) Adaptive mesh (Arrazola et al., 2002), which is the method used in this

paper.

Chip Formation Modeling for End Milling Operation

In milling operations, both cutting action and the chip produced arediscontinuous. In every milling cycle, the produced chip will separate fromthe newly produced workpiece surface without any connection when thecutting tool disengages from the workpiece. Hence the adaptive meshingtechnique in ABAQUS/Explicit cannot be used as a chip separationmethod any more. In this method, chip separation is realized by definingshear failure criterion. The shear failure model is based on the value of theequivalent plastic strain at element integration points; when the equivalentplastic strain reaches the strain at failure plf , then the damage parameter w

exceeds 1, and material failure takes place. If at all the integration pointsmaterial failure takes place, the element is removed from the mesh. Thedamage parameter, w, is defined as

w =pl

pl

f

(4)

where pl is an increment of the equivalent plastic strain. The summationis performed over all increments in the analysis. There are two methods

to define the strain at failure. For the JohnsonCook plasticity model, thestrain at failure is given by Equation (5).

pl

f =

d1 + d2 exp

d3

p

q

1 + d4 ln

pl

0

1 + d5

(5)

where strain at failure, plf , is dependent on a nondimensional plastic strain

rate, pl

/0; a dimensionless pressure-deviatoric stress ratio, P/q (wherep is the pressure stress and q is the Mises stress); and a nondimensionaltemperature, . Strain at failure is evaluated by defining the failureparameters d1 d5.

The cutting condition is given in Table 1. Figure 2 shows the initialgeometry, mesh and assembly of the workpiece and the cutting tool. Theworkpiece is discrete, with a mesh composed of C3D8R elements, and localfine mesh is given along the moving path of the cutting edge due to veryhigh gradients of variables in this area, such as stress, etc.

The cutting tool is modeled as a rigid body and workpiece is modeledas a deformable body in order to obtain all the necessary cutting processvariables for study on machining force. The chip formation process is

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TABLE 1 Cutting Conditions

Cutting type Work material Tool material Tool geometry Cutting parameters

End milling,Dry cutting

AISI 1045 HSS Table 3 Table 2

treated as a Lagrangian problem. Every boundary segment of workpieceis defined as a Lagrangian boundary region. There are different waysto assign shear failure criterion to form different shapes of chips. Nget al. (2002) designed two different kinds of shear failure criteria, onecriterion is assigned to a line of element along the moving path of thecutting edge to separate the chip from the workpiece; another criterionis assigned to part of the chip material to generate cracks in order tosimulate serrated chips (Ng et al., 2002). Bacaria et al. (2000) defined

only one material shear failure model for the whole workpiece material. Inthe model, the shear failure criterion is integrated with a material modeldesigned specially for the workpiece material AISI 1045 and assigned tothe whole workpiece.

OPTIMIZATION

Working Principle of GA

The genetic algorithm (GA) is a population-based search optimizationtechnique (Zarei et al., 2009). In general, the fittest individuals ofany population tend to reproduce and survive to the next generation,

FIGURE 2 Initial geometry, mesh and assembly of the tool and the work piece in chip formation

analysis for b = 3mm, a = 15mm and f = 25 mm/min, diameter of tool = 3mm.

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thus improving successive generations. However, inferior individuals can,by chance, survive and also reproduce. Genetic algorithms have beenshown to solve linear and nonlinear problems by exploring all regionsof the state space and exponentially exploiting promising areas throughmutation, crossover, and selection operations applied to individuals in thepopulation. The use of a genetic algorithm requires the determination

of six fundamental issues: chromosome representation, selection function,the genetic operators making up the reproduction function, the creationof the initial population, termination criteria, and the evaluation function.

Implementation of GA

Coding. In order to use GAs to solve the problem, variables (in thispaper a, b and ft) are first coded in some string structures (chromosomes).Binary-coded strings of ones and zeros are primarily used. The length of

the string is usually determined by the desired solution accuracy. In orderto solve this problem using GA, binary coding is chosen to represent thevariables a, b and ft. In the calculation here, 8 bits are chosen for a, b andft thereby making a total string length of 24. With the coding, the solutionaccuracy obtained in the given interval for ft, a and b are 0.001 mm/tooth,0.01 mm and 0.01 mm, respectively.

Fitness Function. GAs mimic the survival of the fittest principle.So, naturally they are suitable for solving maximization problems.Maximization problems are usually transformed to minimization problems

by some suitable transformation. A fitness function, F(x), is derived fromthe objective function f(x), and is used in successive genetic operations.For maximization problems, fitness function can be considered the sameas the objective function. The minimization problem is an equivalentmaximization problem such that the optimum point remains unchanged.A number of such transformations are possible. The fitness function oftenused is

F(x) =1

(1 + f(x))(6)

where F(x) is the fitness function and f(x) is the objective function. Theindependent variables for optimal cutting parameters have been identifiedas follows: tool diameters and length, spindle speed, and feed per tooth.

Genetic Operators

Reproduction. Reproduction is the first operator applied on apopulation. In this process individual strings are copied into a separatestring called the mating pool according to their fitness values, i.e., the

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strings with a higher fitness value have a higher probability of contributingto one or more offspring in the next generation.

Crossover. After reproduction, the population is enriched with goodstrings from the previous generation but lacking any new string. Acrossover operator is applied to the population to hopefully create betterstrings.

Mutation. Mutation, as in the case of simple GA, is the occasionalrandom alteration of the value of a string position. This means changing 0to 1 or vice versa on a bit by bit basis and with a small mutation probabilityof 0.001 to 0.05.

After applying the GA operators, a new set of population is created.Then, they are decoded and objective function values are calculated.This completes one generation of GA. Such iterations are continued tillthe termination criterion is achieved. The above process is simulated

by a computer program with a population size of 25, iterated for 200generations and crossover and mutation probability are selected to be 0.9and 0.001, respectively.

Objective Function

Tool Deflection. The main objective of the static analysis is to determinethe deflection of end mills under milling forces. For static deflectionanalysis and simulation of end mills, the tool holder is assumed to be

rigid and the cantilever beam model is used. The loading and boundaryconditions of the end mill used in the model are shown in Figure 3, where

D1 is the mill diameter, D2 is the shank diameter, L1 is the flute length, L2is the overall length, Fx is the point load. Kivanc and Budak (2004) definedEquation (7) to predict deflections of tools for given geometric parametersand density:

f(x) = deflectionmax = CFx

E

L13

D14+

(L23 L13)D24

N(7)

FIGURE 3 Loading and boundary conditions of tool.

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where Fx is the applied force and E is the modulus of elasticity (MPa) ofthe tool material. The geometric properties of the end mill are in mm.The constant C is 9.05, 8.30 and 7.93 and constant N is 0.950, 0.965 and0.974 for 4-flute, 3-flute and 2-flute cutters, respectively. These parametersused for this investigation are given in Table 2.

Constraints

Surface Roughness. Ra is the most commonly used parameter to describethe average surface roughness and is defined as an integral of the absolutevalue of the roughness profile measured over an evaluation length as:

Ra = (1/l)l

0|Z(x)|dx (8)

where Z(x) is the height of each peak and l is the length of workpiece that

is machined. The average roughness is the total absolute area of the peaksand valleys divided by the evaluation length; it is expressed in m. Thevalue of surface roughness in end milling can be represented by (Kivancand Budak, 2004):

Ra = 318(f2t )/(4d) (9)

where ft is feed per tooth (mm/tooth) and d cutter diameter (mm).

Tool Life. Tool life TL(min) can be defined as a tools useful life until itno longer produces satisfactory parts. An improved empirical formula forthe practical tool life TL(min) of a cutting tool to be used in end millingoperations has been proposed by Tolouei-Rad and Bidhendi (1997):

TL =

60Q

C(G/5)g

V(A)w

1m

(10)

where m is 0.15 for HSS tools, while it reaches a maximum of 0.30 for thecarbide tools, C is 33.98 for HSS tools and 100.05 for the carbide tools, Q

is the contact proportion of cutting edge with workpiece per revolution,G is slenderness ratio. given as G = b/ft, and A is chip cross-sectional

TABLE 2 Specifications of Tools

Mill diameter (D1),Shank diameter (D2)

Flute(C,N)

Flutelength (L1)

Overalllength (L2)

3 mm, 6 mm (HSS) 4 (9.05, 0.95) 11 mm 56 mm6 mm, 6 mm (HSS) 3 (8.30, 0.965) 22 mm 59 mm

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area, given as A = bft, g = 014 and w = 028 (Tolouei-Rad and Bidhendi,1997).

Cutting Force

The cutting force equations derived from the model in the x and ydirections are given as Equations (1) and (2).

EXPERIMENTAL RESULTS

The milling operation was carried out on a universal milling machineon steel AISI 1045 workpiece material using two HSS tools, (Table 2). AKistler dynamometer was used for determining cutting forces during endmilling. The force measurements were sampled at 2000 points/second,

and then digitally low-pass filtered at a cut-off frequency of 200Hz toeliminate the high-frequency components resulting from the machinetool dynamics and electrical noise. The purpose of the experiment is tovalidate the predicted cutting forces obtained from simulation and theoptimized parameters during an end milling operation. The experimentalsetup is shown in Figure 4. The test conditions were selected according tothe Machinerys Handbook and limitations of milling machine (Table 3).These conditions were used for simulation of operation too.

COMPARISON BETWEEN SIMULATION METHOD ANDEMPIRICAL METHOD

The cutting force is predicted using the simulation based on finiteelement method by implementation of the cutting process variables. Acomparison of the advantages and disadvantages of the empirical andsimulation method is made in Table 4.

FIGURE 4 Experimental set up (end milling).

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TABLE 3 Cutting Parameters for Experiments

Diameter oftool (mm)

Cutting speed(m/min)

Feed rate(mm/min)

Axial depthof cut (mm)

Radial depthof cut (mm)

6 47.12 8, 16, 20, 40 4 2.56 47.12 8, 16, 20, 40 5 2.56 47.12 8, 16, 20, 40 6 2.5

6 47.12 8, 16, 20, 40 7.5 2.53 23.56 8, 16, 25, 40, 50 1.5 1.53 23.56 8, 16, 25, 40, 50 3 1.53 23.56 8, 16, 25, 40, 50 4.5 1.53 23.56 8, 16, 25, 40, 50 5 1.5

RESULTS AND DISCUSSION

With presented simulation program, cutting forces have beencalculated. The cutting conditions which have been implemented in thesimulation are reported in Table 3. The solid line in Figure 5 showsthe cutting force (Fx) curve obtained from simulation under the cuttingcondition: b = 4mm, a = 25mm, feed rate = 8 mm/min, cutting speed =4712m/min and diameter of tool = 6mm. The dotted line in Figure 5shows the cutting force (Fx) curve obtained from the experiment underthe same cutting condition.

Also, Figure 6 shows the cutting force (Fx) curve obtained fromEquation (1) under the same cutting condition. It is found that thecalculated cutting force from Equation (1) is larger than experimentalone, whilst there is a good agreement between the cutting force obtainedfrom simulation and experiment. The comparison of the tool deflectionsobtained from Equation (7) and measured value for above conditions ispresented in Table 5.

TABLE 4 Comparison between FEM Method and Empirical Method

Compared aspects Empirical method FEM method

Environment requirement Special machine, tool, workpiece,personnel for cutting tests

Powerful computer, cutting forcemodel and FEM code

Procedure of calculatingcutting force

Cutting tests and regressiveanalysis

Running the program withcutting force models undernew cutting conditions

Application under newcutting conditions

New experiments haveto be carried out

If only cutting force model isupdated according to newcutting conditions, theprogram can be used again

Application at present Used in the real production For research and education

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FIGURE 5 Comparison between simulation and experimental curves for cutting force, Fx (undercutting condition: b = 4mm, a = 25mm, feed rate = 8mm/min, cutting speed = 4712 m/min, and

diameter of tool = 6mm).

The solid line in Figure 7 shows the cutting force (Fx) curveobtained from simulation under the cutting condition: b = 4mm,a = 15 mm, feed rate = 50 mm/min, cutting speed = 2356 m/min anddiameter of tool = 3mm. The dotted line in Figure 7 shows the cuttingforce (Fx) curve obtained from experiment tests under the same cutting

FIGURE 6 Cutting force (Fx) obtained from Equation (1), per revolution of tool (RAD) (undercutting condition: b = 4mm, a = 25mm, feed rate = 8 mm/min, cutting speed = 4712m/min anddiameter of tool = 6mm).

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TABLE 5 Tool Deflection Results (under cutting condition: b = 4mm,a = 25mm, feed rate = 8 mm/min, cutting speed = 4712m/min anddiameter of tool = 6mm)

Mill diameter (D1), Deflection (mm) Deflection (mm)Shank diameter (D2) By theory (Equation 7) Measured value

6 mm, 6 mm (HSS) 0.6609 0.7663

condition. Also, Figure 8 shows the cutting force (Fx) curve obtained fromEquation (1) under the same cutting condition. The comparisons of thetool deflections obtained from Equation (7) and measured value for aboveconditions are shown in Table 6.

The solid line in Figure 9 shows the cutting force (Fx) curveobtained from simulation under the cutting condition: b = 3mm,

a = 15 mm, feed rate = 25 mm/min, cutting speed = 2356 m/min anddiameter of tool = 3mm. The dotted line in Figure 9 shows the cuttingforce (Fx) curve obtained from experiment tests under the same cuttingcondition. Also, Figure 10 shows the cutting force (Fx) curve obtainedfrom Equation (1) under the same cutting condition. In Table 7, the tooldeflections obtained from Equation (7) and measured value for aboveconditions are compared.

According to Figures 510, there is a good agreement between thecutting forces obtained from simulation and experiments. The simulation

FIGURE 7 Comparison between simulation and experimental curves for cutting force, Fx (undercutting condition: b = 4mm, a = 15 mm, feed rate = 50 mm/min, cutting speed = 2356m/minand diameter of tool = 3mm).

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FIGURE 8 Cutting force (Fx) obtained from Equation (1), per revolution of tool (RAD) (undercutting condition: b = 4mm, a = 15 mm, feed rate = 50 mm/min, cutting speed = 2356m/minand diameter of tool = 3mm).

TABLE 6 Tool Deflection Results (under cutting condition: b = 4mm,a = 15mm, feed rate = 50 mm/min, cutting speed = 2356m/min anddiameter of tool = 3mm)


3 mm, 6 mm (HSS) 0.3186 0.338

FIGURE 9 Comparison between simulation and experimental curves for cutting force, Fx (undercutting condition: b = 3mm, a = 15mm, feed rate = 25mm/min, cutting speed = 2356 m/min and

diameter of tool = 3mm).

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FIGURE 10 Cutting force (Fx) obtained from Equation (1), per revolution of tool (RAD) (undercutting condition: b = 3mm, a = 15 mm, feed rate = 25mm/min, cutting speed = 2356 m/min anddiameter of tool = 3mm).

results and measured cutting forces clearly demonstrate that the accuracyof the simulation is higher than theoretical relationships. Also, accordingto Tables 57, there are good agreements between Equation (7) andmeasured tool deflections. These tables demonstrate the accuracy of

Equation (7) that has been used in optimization of cutting parameters.Optimization has been performed using GA to decide the best possiblecombination of feed rate, axial depth of cut and radial depth of cut bysatisfying constraints, including tool deflection, cutting force, tool life andsurface roughness. Figure 11 shows the effect of tool deflection on themachined surface. In this work, the error of the tool deflection on themachined surface has been computed using genetic algorithm.

The ranges of cutting parameters are given in Table 3. In this table,feed rates and depths of cut are changed but the cutting speed is

considered as constant, because the cutting speed has lesser effect on

TABLE 7 Tool deflection results (under cutting condition: b = 3mm,a = 15mm, feed rate = 25mm/min, cutting speed = 2356m/min anddiameter of tool = 3mm)


3 mm, 6 mm (HSS) 0.0531 0.056

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FIGURE 11 Error compensation (perpendicularly).

the cutting force and tool deflection. Table 8 shows the GA results foroptimized cutting parameters in the x direction for machining of mildsteel material (AISI 1045), but because of the limitation of the millingmachine, Table 9 has been used for cutting operation. Table 10 shows

the comparison of GA results and measured parameters versus optimizedmachining parameters for machining of mild steel material. The goodagreement between the GA results and measured parameters clearlydemonstrates the accuracy and effectiveness of the model presented andprogram developed.

Figure 12 shows that in practice with optimized cutting parameters(Table 9) the effect of tool deflection on the machined surface can bereduced. These results verify that the projection of tool deflection onthe machined surface has been eliminated by using GA results (Table 9).

Also, metal cutting has been performed using other cutting parameters(Table 3). Figure 13 shows the effect of tool deflection on the machinedsurface without using GA results. As can be seen, there is error in thesesurfaces.

TABLE 8 GA Results Values for the Optimized CuttingParameters for Minimizing Tool Deflection

Diameter ofend mill

Feedrate

Axial depthof cut

Radial depthof cut

3 mm (HSS) 22 mm/min 2.925 mm 1.42 mm

TABLE 9 GA Results Values for the Optimized CuttingParameters for Minimizing Tool Deflection in Practice

Diameter ofend mill

Feedrate

Axial depthof cut

Radial depthof cut

3 mm (HSS) 20 mm/min 3 mm 1.5 mm

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TA

BLE

10

ComparisonofGA

ResultsandExperimentalValuesfo

rtheOptimizedCuttingParameters

GA

results

Measur

edvalues

Cu

tting

spe

ed

(m

/min)

Feed

rate

(mm/min)

Axial

de

pthof

cut

(mm

)

Radial

depthof

cut(mm

)

Roughness

(

m

)

Tool

deflection

(mm

)

Cu

tting

force

Fx

(N)

Roughness

(m

)

T

ool

defl

ection

(m

m)

Cutting

force

Fx

(N)

23.5

6

25

3

1.5

1.6

0.0

531

19

2

0.0

56

10

98

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FIGURE 12 Compensated surface (perpendicularly) by using GA results in Table 8.

CONCLUSION

This paper shows that with simulation of the end milling operationby finite element method, based on the JohnsonCook theory, thecutting forces can be predicted well, and these values can be used forpredicting the tool deflection. The results of the simulation and theoreticalequations are compared with those of the experiments. Higher accuracyof simulation results compared to the theoretical relationships may beattributed to the following:

Material properties in the simulations are defined based on theJohnsonCook theory, i.e. they are functions of strain, strain rate,and workpiece temperature, whereas in the theoretical relationships,properties are simply defined using the constant material coefficient.

In simulation, non-linear geometric boundaries such as the free surfaceof the chip, can be represented and used whilst theoretical relationshipsare based on linear geometric boundaries.

FIGURE 13 Effect of tool deflection on the machined surface without using GA results (a),b = 3mm, a = 15mm, cutting speed = 2356m/min, feed rate = 16mm/min (b), b = 3mm, a =

15mm, cutting speed = 2356m/min, feed rate = 40mm/min (c), b = 3mm, a = 15mm, cuttingspeed = 2356 m/min, feed rate = 50 mm/min.

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Machining parameters are typically adjusted according to theinstructions in the tool catalogues and/or handbooks without consideringroughness requirements and geometrical tolerances of the surface to bemachined. Incorrect adjustment of the machining parameters, feed rateand depth of cut, lead to tool deflection and consequently reduced surfacequality. With increasing feed rate and depth of cut, the tool deflection

is increased. Optimization of machining parameters using GeneticAlgorithm leads to minimal machining errors. By defining maximumsurface roughness of 63 m as the constraint, surface roughness of16 m is obtained with the optimized parameters. With the GA-basedoptimization system developed in this work, it is possible to increasemachining accuracy (surface roughness and geometrical tolerances) usingoptimal cutting parameters.

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