Author's Accepted Manuscript

A review on modelling and simulation of laserbeam machining

Pedram Parandoush, Altab Hossain

PII: S0890-6955(14)00085-6DOI: http://dx.doi.org/10.1016/j.ijmachtools.2014.05.008Reference: MTM2954

To appear in: International Journal of Machine Tools & Manufacture

Received date: 28 February 2014Revised date: 21 May 2014Accepted date: 27 May 2014

Cite this article as: Pedram Parandoush, Altab Hossain, A review on modellingand simulation of laser beam machining, International Journal of Machine Tools &Manufacture, http://dx.doi.org/10.1016/j.ijmachtools.2014.05.008

This is a PDF file of an unedited manuscript that has been accepted forpublication. As a service to our customers we are providing this early version ofthe manuscript. The manuscript will undergo copyediting, typesetting, andreview of the resulting galley proof before it is published in its final citable form.Please note that during the production process errors may be discovered whichcould affect the content, and all legal disclaimers that apply to the journalpertain.

www.elsevier.com/locate/ijmactool

A review on modelling and simulation of laser beam machining

Pedram Parandoush, Altab Hossain

Department of Mechanical Engineering, Faculty of Engineering,

University of Malaya, Kuala Lumpur, Malaysia

Corresponding Email: altab75@um.edu.my (A. Hossain)

A Review on Modelling and Simulation of Laser Beam Machining

3

Abstract—Laser Beam machining (LBM) is a widely used thermal advance machining process capable of high accuracy machining of almost any material with complex geometries. CO2 and Nd:YAG lasers are mostly used for industrial purposes. Drilling, cutting, grooving, turning and milling are the application of LBM with different material removal mechanism. Modelling and simulation of LBM process is indispensable for optimization purposes. Modelling can be done by implementing analytical, numerical, experimental and Artificial Intelligence based methods. This paper provide a review on the various methods used for modelling and simulation of laser beam machining process as well as key researches done in this field so far. Keywords—LBM, modelling, simulation, review

1. Introduction

Emerge of advanced engineering materials and requirement of precision in manufacturing made conventional machining unreliable in the modern industry. Therefore, Advanced Manufacturing Processes (AMP) introduced to obviate new industry requirements. Laser Beam Machining (LBM) is one of the AMP witch can shape almost all ranges of engineering materials from metallic alloys to non-metals as well as composite materials. Laser beam is widely used in Cutting, Drilling, Machining, Etching, Welding and Heat Treatment [1, 2]. Material removal in LBM is based on high heat flux generated by laser beam which melt and vaporize the workpiece material in the focused point. Unique privileges of LMB such as being a non-contact process, automation adaptability, cost reduction, Small Heat Affected Zone (HAZ) and resolving the need for finishing operations, made it famous in the manufacturing industry. The laser beam is generated by the phenomena so-called stimulated emission which caused when high energy photons strike the medium. These photons excite the electrons of the medium atoms into amplifying state which result to emission of photons with same wavelength of absorbed light from the medium, this light is a coherent and focused beam called laser [3, 4]. It was Einstein who discovered the stimulated emission concept [5] and the first laser created by Townes and Shawlow in 1957 using Ruby medium [6]. The lasing medium can be gas, liquid or solid, but in manufacturing processes CO2 and Neodymium Yttrium Aluminum Garnet (Nd:YAG) are motley used as medium. CO2 lasers have high beam power with good efficiency without sacrificing the quality of the beam. On the other hand, Nd:YAG lasers have shorter wavelength about 1μm which make them suitable for machining reflective materials due to higher light absorption compared to CO2 lasers. Although Nd:YAG lasers operate with low powers but they can be used in pulsed mode with high peak power to cut thicker materials. Thinner materials also can be cut by Nd:YAG lasers using short pulse duration. [2, 7].

Modeling and simulation of quality characteristics in LBM such as Material Removal Rate (MRR), Surface quality (roughness, morphology), mechanical properties (strength, hardness), metallurgical characteristics (HAZ, recast layer, dross inclusion), geometry of machined material (taper, hole diameter, kerf width, kerf angle, molten layer), temperature distribution, striation formation, etc. are reviewed in the present paper.

2. Material removal in LBM

Material removal in LBM consists of 3 stages: 1) melting 2) vaporization and 3) chemical degradation which involves braking the chemical bonds and degradation of the material. The thermal energy required for melting and vaporization is gained by absorption of high density laser beam which is focused on the work piece by means of lenses. A high pressure assisting gas may be used for removing molten, vaporized or chemically degraded materials from the machining area in order to have a clean cut with sharp edges [1].

4

In thermal processes like LBM, mechanical properties of workpiece material are not concerned, but thermal and optical properties such as thermal conductivity, thermal diffusivity, absorptivity, etc. has significant effect on the quality characteristics of the machining process. Hence, hard and brittle materials which represent suitable thermal properties like low thermal conductivity and diffusivity are beneficial in LBM process. Subsequently, there is no contact between tool and workpiece and material removal occurs without any mechanical force. Material Removal Rate (MRR) can be defined regardless of common constrains in conventional machining such as maximum tool force, tool chatter, and the formation of built up edge. Flexibility of LBM can be increased significantly by introducing multi-axis positioning systems or robots, which add various applications to a single machine [8]. The physical phenomena in the laser beam interaction with any substrate material can be categorized as reflection, absorption, scattering and transmission. However, induction any effect in the workpiece is only possible through absorption of the laser beam. The absorbed energy from the photons is dependent on wavelength of the laser, incident angle, surface roughness, temperature of the solid and the spectral absorptivity characteristics of the workpiece material. Reflection in the machined cavity called multiple reflection and is more complicated than the effect of reflection in the surface of the un-machined material. The multiple reflections in a machined cavity are schematically represented in the Figure 1. Where I0 is the incident laser energy, Ia1 ,Ia2 and Ia3 are the first, second and third absorptions, respectively, and Ir1, Ir2 and Ir3 are the first, second and third reflections, respectively. The absorbed energy after n reflection can be defined as:

naQ Q( r )= (1)

where Q is incident laser beam energy, r is angle-dependent reflection coefficient and n is number of multiple reflections. n 4π θ= (2)where θ is the angle of cavity wall with normal direction. [9, 10]

The laser beam can be approximated as Gaussian type in analysis for improved accuracy and lower complexity. The intensity of laser beam normal to the surface based on Gaussian distribution is given by:

( )2

2 200 2

RI( x, y,z ) I exp ( x y ) / R(z)

R ( z )= − + (3)

where 20 0I ( P R )π= is the beam power density at the center of the beam, P is laser power, 0R is the

radius of focused laser beam and R(z) is radius of the expanding laser beam given by:

20 2

0

W zR( z ) R 1 ( )Rπ λ+

= + (4)

where λ the laser is wave length and W is the distance between workpiece surface and focal plane of concentrating lens. [11, 12]

5

Laser beam machining is a thermal process and developing a mathematical model for the process requires implementing heat transfer equations and fluid mechanics laws for molten material at the cutting front. Although, all the laser machining processes are similar in nature but, some minor differences such as using fixed or stationery heat source for drilling and cutting

respectively and different behavior of materials in interaction with laser and presence of heat made these processes unique in terms of modelling. In this section drilling, cutting, grooving, turning and milling and their theoretical background will be discussed elaborately.

2.1. Material Removal in Laser Drilling   Laser drilling is a one-dimensional process in which high intensity laser beam focus on the workpiece and create

a molten layer that result in vaporization and drilling the hole into the material. The beam diameter may be more than the diameter of the drilled hole due to the various heat losses during laser drilling including heat conduction to the workpiece interior. Laser drilling gets lots of attention for being economically efficient in drilling large amount of closely located holes in structures. It is also suitable for high tolerance and micro scaled holes especially when pulsed mode laser is used. There are two types of laser drilling: percussion drilling which involve punching through the material while nozzle and workpiece are fixed as illustrated in Figure 2 and trepan drilling which cut the material in a circular path with desired diameter similar to laser cutting. trepan drilling is more suitable for larger diameter holes [6, 13].

In laser drilling laser the governing equations describing the heat conduction inside the material is given as 2Tc k T Q

tρ ∂

= ∇ +∂

(5)

where ρ is density, T is temperature, t is time, k is thermal conductivity and c is the volume specific heat. The essential boundary condition is at the surface of workpiece where conduction heat into the material, irradiation, vaporization and convection loss take place. It is given as

( )ig ik T h u h T Tρ ∞∇ = + − (6)

Fig. 1. Multiple reflections in a machined cavity [9]

6

where igh is heat of sublimation, iu is local velocity of the interface at the considered point, h is

convective heat transfer coefficient and aT is the ambient temperature. An important factor in analyzing laser drilling is the fact that matter removes by evaporation and position of the boundary condition changes with time, consequently. Various solutions for mentioned problem can be found in [14-16].  

Fig. 2. Schematic of laser beam percussion drilling [13]

7

2.2. Material Removal in Laser Cutting and Grooving The principle of material removal and energy loss in laser cutting are similar to those for laser drilling. Erosion front formation occur in the front of the laser beam and temperature field is mobile because of relative motion between the tool and workpiece. Laser cutting can be considered as a steady-state thermal process, workpiece temperature is independent of time and dependent on distance to erosion front. The accumulated molten material can be ejected by assisting gas through kerf or vaporize (Fig. 3). Laser cutting superiority can be seen by reviewing its unique advantages including high material utilization, material versatility, no tool wearing, flexibility and high accuracy with good edge quality. Laser grooving has found its application in marking a diverse range of materials with complex geometries. It requires less power in compared to laser cutting and is well suited for hard and brittle materials which cannot be marked with contact machining processes due to crack formation [1, 6].

Fig. 3. Laser cutting material removal mechanism [6]

Similar to laser drilling, in cutting and grooving heat conducting into the material causing material removal by melting and vaporization. The only difference is the relative velocity between workpiece and laser beam called scanning velocity. The process can be considered as a steady-state heat transfer problem by defining the laser beam as the origin of the coordinate system, otherwise, the problem whould be a transient heat transfer phenomena. Commonlly in analyzing laser cutting laser heat flux is assumed as a boundary condition as in many publication such as [17-20]. In that case the governing equation could be expressed as

2Tcu k Tx

ρ ∂= ∇

∂ (7)

where u is the scanning velocity and x is the direction of the laser beam movement. The necessary boundary condition at the vaporization region is given by

( )2 20 0 igI exp ( x y ) / R h(T T ) k T h uρ∞− + = − − ∇ − (8)

Similar to laser drilling an additional boundary condition needed for the vaporization regime due to the material removal changing the geometry of the boundary given as at T T∞= , z s( x, y )= (9)where s( x, y ) is the local depth of the groove. [12, 20]

2.3. Material Removal in Laser Beam Turning and Milling Three-dimensional material removal concept has been introduced in laser machining to adapt the process for bulk material removal. It requires two laser beams simultaneously in action for

machininmaterial considerisignificanin the gromachine efficient accurate yet, lasermilling asimilar towhich ex

ResearchmachiningroovingconcentraPham et which remmilling odecreasedon laser mvaporizatmilling wpositioneclose loowhich dis

3. Theor

Theorequation phenomestress, M

ng, each of thfrom workping tool expently higher tooves rather the whole mwhen combirepositionin

r milling is sand turning ao laser groovxplained prev

hers developeng ceramics bg to form a dation at grooal. [22] propmove the ma

of alumina ced efficiency milling of intion happens

when liquid fed crates andop CNC systestinguishing

retical Method

retical modelin order to d

ena and all thMRR, etc. The

Fig.

he beams creiece. It is moenses or weathan those fothan the bul

material needined with oth

ng made lasetill able to p

are shown inving, the theoviously.

ed novel desby fracture wesired path.

ove tips causposed a methaterial layer eramics undeof laser mill

ntractable mas instantly wformation is d second pasem to contro

g of laser ligh

ds for Modelli

lling of laserdevelop a mahe characteriere are two m

. 3. Three-dimensi

eate a blind ost suitable faring. The voor single bealk of the macded to be remher techniqur milling not

perform the en Figure 4. Soretical cons

sign and techwas proposeThen, an un

se fracture whod to use laby layer usier water donling in wateraterials indic

without formaunavoidables break bridg

ol laser millinht and the lig

ing

r cutting invathematical istics relatedmain categor

ional laser machin

groove and ifor machininolume of rem

am machininchined mate

moved [6]. Lues and usedt a practical

entire procesSince, the basiderations a

hniques in thd by Tsai an

nfocused lasewhich occursaser machinining chemicalne by Litao er compared tcated that quation of lique in which thges betweenng instead oght that form

volves using model capab

d to it such ary in theoret

ing (a) helical lase

intersection ng of complemoved materg, because thrial. Therefo

Laser millingas a finishinmethod for

ss [8]. Variosics of the la

are same as l

he field of land Chen [21]er heat the arin the direct

ng as a rapidl degradationet al. [23] shoto air. Koval

uality is signiuid state. Thehe first pass n them. Chanof conventionm plasma is s

physics prinble of descris temperaturtical modelli

er turning (b) ring

of two groovex shapes wirial per unit he machininore, there is ng in particulang operationentire machi

ous type of laaser milling laser groovin

aser milling. ] which usesrea in order ttion of the fod manufacturn. An investiowed increalenko et al. [ificantly bettey also suggecreate symm

ng & Tu [25]nal open loopsignificantly

nciples and eibing materiare distributioing: analytic

laser turning (c) la

ves remove ithout energy is

ng only tale pno need to

ar is more n. Difficulty ining procesaser beam and turning

ng and cuttin

A method fos laser beam to increase sormed crackring process igation on la

ased quality a[24] experimter when ested two ph

metrically ] designed a p control in easier.

energy balanal removal on, residual al solution b

aser milling [6]

8

the

place

in sses,

are ng

or for

stress ks.

aser and

ments

hase

nced

based

9

and numerical solution based models. Modelling based on analytical solution is usually centered on some assumptions and is not always able to solve the whole system in practical cases. On the other hand, numerical modelling is able to solve almost all types of laser matching problems by dividing the workpiece into small elements and nodes. However, that solution is approximated because exact values are only available at the nodes position. Numerical methods can be divided into mesh based methods such as finite element methods (FEM), boundary element methods (BEM) and finite difference methods (FDM) and mesh-free methods such as smoothed particle hydrodynamics (SPH). Hybrid methods also exist that combine two or more methods to achieve proper results. There are various aspects of laser beam machining that can be modelled with different methods in order to predicting the outcome which is essential for any manufacturing process [10]. This chapter provides a review on the theoretical modelling and simulation of the various laser machining processes as well as some artificial intelligence methods.

3.1. Analytical Solution Based Modelling expanded the body of heat conduction solutions in order to include scanning velocity of

continuous wave and pulsed mode Gaussian laser and developed a mathematical model for prediction of groove depth in evaporative cutting of semi-infinite body for continuous wave lasers which can be found in ref [20]. In this simple model which has been solved analytically phase change of the medium from solid to gas assumed to happen in one step. This assumptions as well as constant absorptivity and neglecting multiple reflection was the issues that authors suggested to be solved in the future works. Aloke et al. [26] expressed a model for predicting the dimensional accuracy in trepan laser drilling of thin mild steel plates. In this model it is assumed that residual stress formed by laser is high enough to deform steel plate and determined that it playing key role in achieving good dimensional accuracies for cutting smaller kerf widths. This model found to be more accurate in drilling holes with smaller diameters. The results of their analysis indicated that for thicker sheet metals three-dimensional (3D) models provide more precise predictions. Di pietro and Yao [27] developed a technique to predict the surface roughness in laser cutting process for the first time by analyzing the dynamic phenomena that happens within cutting front. The output variable of this model was striation formation frequency and periodic structure depth. Authors suggested that this model can be used in conjunction with previously developed models due to the several mechanism that exist for forming striations and changing the cutting condition can change these mechanisms. Thermal analysis of CO2 assisting gas jet has been done by Yilbas and Kar [28] in order to developed a prediction model for molten layer thickness and approximate heat absorption magnitude by considering momentum effect and shear stress at gas-liquid interface. Man et al. [29] focused on gas jet modelling and predicted pressure, momentum, gas density distribution and existence of shock waves. Their Analysis concluded that supersonic gas jet flow characteristics are superior to conical nozzles gas jets. Optimum cutting speed in laser cutting of decorative ceramic tiles has been described in a model developed by Black [30, 31]. De Graaf and Meijer [32] studied on laser cutting of metal laminates and their model worked well in predicting aluminum layers quality but it underestimated the damaged zone in the synthetic layers. Kaebernick et al. [33] established a model for predicting the kerf width by considering the reaction of oxygen with molten layer for pulsed lasers. They developed this model by considering infinitesimal point heat sources and analyzing the surface inside the cutting zone. Another analytical solution for prediction kerf width proposed by Sheng et al. [34] as a function of erosion front dimensions. Erosion front has been defined by the frequency of resonant which induced by high pressure assisting gas waves. Jiang et al. [35] predicted the depth of grooves in sheet metal cutting with pulsed Nd:YAG laser.

10

Cenna and Mathew [36] used energy balance equation to predict lase cutting quality parameters in composite materials such as transmitted energy loss through the kerf and kerf breadth at inlet, outlet and angle of cut surface. The energy balance equation is expressed as

b cond vapE ( x, y )dxdy E ( x, y )dA E (x, y)dxdy= + (10)where bE is the laser beam energy, condE is the conduction energy and vapE is the vaporization energy component for the infinitesimal control surface. Figure 5 presents some comparison between model prediction and experiments in kerf width with various cutting speed for Glass Fiber Reinforced Plastics (GFRP) and Aramid Fiber Reinforced Plastics (AFRP).

Fig. 5. Comparison of theoretical and experimental results of kerf width variations with cutting speed for 4 mm thick (a) GFRP and (b) AFRP for 800 W CV CO2 laser [36]

Yilbas [37] developed a prediction model for kerf width based on scaling laws and oxidation reaction from gas jet has been taken into the account. Li et al. [38] proposed a theoretical model for cutting speed of mild steel sheets at which striation free cutting occurs. A lumped parameter model for relating cutting parameters (laser power, spot size a cutting speed) and material properties to cut depth has been develop by li et al. [39] in order to increase previous model and make them applicable to wide set of parameters ranging from slow to fast cutting speeds and low to high laser powers. Melt geometry in laser cutting of steels has been modelled in the Mathematical model of Tani et al [40]. Film thickness and velocity relationship with kerf depth in the cutting plate is determined based on energy balance within the kerf. Minimum acceptable value of melt ejection speed from bottom of the kerf and kerf occlusion caused by excess of

11

molten material in the boundary layer at the kerf width were two mechanism considered responsible for dross formation. They also proposed a model [41] for prediction of striation and dross formation. Their model successfully predicted the effect of high pressure assisting gas and allowed transition from single slope at low cutting speeds to double slope at high speeds. Wee et al. [42] proposed a two-dimensional analytical model by focusing on power, scan speed and spot size for predicting power absorption over the cut front, oxidation effect and melt thickness. Yinzhou et al. [43] proposed a model for predicting the operating window for nano-second pulsed laser striation-free cutting of alumina. The effect of gas type, gas pressure, nozzle stand of distance (SOF), cutting speed, average laser power and pulse frequency considered in their study. They have extended the existed theories for continuous wave (CW) to striation-free pulsed laser cutting of ceramics.

3.2. Numerical Modelling and Simulation Numerical simulation and modelling usually is based on fewer assumptions compared to

analytical solutions but may need more computing power compared to modelling based on exact solution. This leads researchers to work mostly on numerical modelling recently as the computing powers increase for achieving more accurate solutions. Modest and Michael [44] developed a three-dimensional conduction model for computing temperature distribution and groove shape cause by evaporation. The method used was finite difference method (FDM) for simulation. This model expands the application of previous models from CW to various conditions such as pulsed mode and Q switch. They developed another model [45] for prediction of transient temperature distribution in a finite thickness slab for CW or pulsed mode lasers. These models are presented for the materials that ablate or decompose by laser irradiation. An integrated analytical and numerical two-dimensional model was proposed by Sheng and Joshi [46] to estimate the HAZ extent and kerf shape. The aim was to develop a computationally efficient model compared to 3D FEM models. Yu [47] used ANSYS codes for 3D thermal analysis of laser cutting and drilling and considered change in phase and boundary as well as loading conditions in simulation. Di Pietro and Yao [48] investigated the cutting front mobility in CO2 laser cutting without neglecting the CNC axis acceleration. This 2D numerical model analyze the effect of various velocities on cutting front temperature. Based on the results, it was evident that laser movement with acceleration cause significantly better beam coupling. Pieteo et al [49] performed a quality optimization by developing a transient heat-transfer model. Their inspections revealed that machining front has a dynamic behavior which is not neglectable in determination of temperature distribution. Kim and Zhang [19] simulated pulsed laser cutting process with their FE model and analyzed the amount of material removal and groove smoothness with different laser powers and pulse numbers. Their analysis led to a threshold curve which determine acceptance region for a quality cut pulsed laser cutting which is shown in Figure 6. Later on Kim [17, 18] developed two numerical model with BEM which considered an unsteady heat-transfer phenomena in evaporative laser cutting. Groove shape and temperature distribution in these two models compared with previous FEM based models and showed a good agreement with those as mentioned in Figure 7.

12

Fig. 6. A threshold curve for material removal in laser power (LP) and number of pulses (NPS) [19]

Fig. 7. Maximum groove depth comparison between BEM and FEM [18]

A simple yet accurate heat conduction loss model developed by Prusa et al. [50] in order to estimate characteristics of HAZ such as thickness and optimized cutting speed as well as resultant temperature field was determined. The key result of their research was correlation between dimensionless rate of conduction loss and Peclet number known as dimensionless cutting speed (PE) which is

* 0.686condQ 3.20Pe+= for 0.20 Pe 10≤ ≤ (11)

where *cond condQ Q kd T= Δ is dimensionless conduction heat transfer loss, condQ is rate of conduction

heat loss, d is the thickness of the workpiece and Pe is Peclet number represents the ration of convection to thermal diffusion speeds. Kheloufi and Amara [11] developed a transient numerical model to determine the effect of process parameters on temperature, velocity distribution and kerf shape. Physical phenomena in the gas-liquid surface such as pressure and friction force exerted by gas jet and the absorbed heat by the surface are incorporated into the numerical model. Scintilla and Tricarico [51] estimated the difference between cutting front temperature in CO2 and disk laser beam fusion cutting in their numerical model. The error in this model does not exceed 10% unless for the thickness greater than 8mm due to the huge recast layer. The results indicated that conduction loss is higher in CO2 laser compare to disk laser. It causes higher temperature in cutting front which leads to lower viscosity with ease of ejection from cut kerf. It justifies the better edge quality in CO2 lasers. Determining thermal stress and residual stress distribution is essential in designing every laser machining process, therefor, predicting it numerically can be a great help to manufacturers. Arif et al. [52] analyzed residual stress with finite element analysis in thick sheet metal laser cutting and found out that temperature field and resultant von Mises stress significantly rise in the

13

direction normal to the scanning speed. Initially laser power heat the cutting path and as process continues cutting path cools down result in residual stress developed by change in temperature gradient. Yilbas and Akhtar [53] developed a 3D model similar to the previous model and concluded when temperature is less than melting temperature and temperature gradient are high, considerable stress will be formed. Yilbas et al. [54] used ABAQUS codes to develop a model for stress analyzing of hole cutting of Ti-6Al-4V alloy.

Ceramics show different behavior in laser beam machining. However, modelling the material removal phenomena for ceramic workpieces cannot be exactly same with metallic materials. A crack free cutting is a challenge for thick ceramic sheets due to the brittle characteristics and catastrophic breakdowns often happens as the result of these cracks. Solution is to understand the transient temperature that affect thermal stress distribution [55]. Li and Sheng [56] proposed a hybrid model for ceramic cutting with CO2 laser in which temperature and stress distribution are determined through numerical simulation and kerf geometry obtained using analytical solution. Yan et al. [55] used three-dimensional FEM to investigate crack formation in laser cutting of thick-section alumina (Al2O3) ceramics and optimized the process to obtain a crack free cut by considering the effect of four parameters i.e. feed rate, laser peak power, and pulse duration and repetition rate on temperature and stress distribution and potential crack formations. Yan et al. [57] also optimized the same process with CO2 laser to overcome low process efficiency of the close-piercing lapping (CPL) method and compared the results with those obtained by fiber laser in ref [55]. The comparisons between two laser modes are illustrated in Table 1.

Table 1. Comparison of optimized parameter between co2 and fiber laser cutting of 6mm thick alumina (Al2O3) [57]

Process parameters CO2 laser crack‐free 

cutting 

Fiber crack‐free 

laser cutting 

Peak power (w)  3500  1000 

Pulse duration (ms)  2.8  5 

Pulse frequency  18  30 

Cutting speed (mm/min) 

90 (straight line cutting) 

80 (profile cutting) 90 

Assist gas  O2  O2 

Gas pressure (bar)  4  5 

Nozzle diameter (mm) 

1.5  1.5 

Nozzle standoff distance (mm) 

1  1 

Focused spot size (µm) 

100  50 

Powers density (W/cm2) 

4.46×107  5.10×107 

Rayleigh length (mm) 

0.74  1.82 

Absorptivity  100 %  20.6 % 

14

Since laser machining is not limited by material selection, the need for modeling and optimization for diverse range of materials motivated researchers to develop models for almost any materials such as glass, plastics, composites or even organic materials like stones. Negarestani et al. [58] develop a 3D transient numerical model for carbon-fiber reinforced composite on a heterogeneous fiber-matrix mesh for the first time. This model is able to predict transient temperature field and HAZ dimensions. Based on their findings higher scanning speed and double-line processing yield better machining qualities and it was suggested to use fiber-matrix interface in similar materials. Lee et al. [59] developed a model for laser cutting of the current collectors of lithium-ion batteries which is commonly pure copper or aluminum. Numerical simulation of this model showed that aluminum cutting is highly dependent on laser intensity rather than interaction time while cutting of copper is dependent on both mentioned parameters. Laser cutting of glasses also became very popular due to its effectiveness in cutting brittle materials and its non-contact nature. Several numerical models such as [60-62] has been developed for laser glass cutting which mostly use controlled fracture method with the purpose of having crack free cutting and smooth surface quality. Yang et al. [61] concluded in their research that YAG laser possessed better quality and uniform temperature distribution and is able to do multi-layer glass cutting simultaneously. Nisar et al. [60, 62] numerical models investigated various parameter effects in laser glass cutting, such as pulsed and CW laser, workpiece thickness, laser power and scanning velocity.

Assisting gas can has a great influence on the laser machining process, Yilbas and Shahin [63] studied on the reaction between oxygen assisting gas and molten metal in CO2 laser cutting by laminar boundary approach. Mai and Lin [64] modeled flow structure caused by supersonic impinging jet around an inclined substrate during laser cutting using FLUENT which is a finite element method. This model simulate shock wave phenomena induced by impinging jet with varying nozzle angles and suggested that angle of incident dramatically affect flow structure. While Most of the model describing gas dynamics are highly simplified and neglect most of the important mechanical mechanisms, Gross [65] simulated the whole process including assisting gas dynamics with a 3D fully coupled model and found out that simplifications like dimension reduction are not admissible for a complete investigation on the process. However, the proposed numerical model was unable to produce results in an ordinary hardware due to the high processing demand. Gou et al. [66] developed a model able to predict the mass flow rate and axial trust affected by various standoff distances and exit Mach number. They have conclude that suitable standoff distance is the key factor in high quality laser cutting rather than nozzle type. Kovalev et al. [67] developed a mathematical model to analyze viscous compressive gas in the groove channel and solved it numerically with 3D full Navier-Stock equation. The results showed that gas flow aerodynamics has significant effect on striation characteristics over the cutting depth. Using super-sonic nuzzle seems to be more cost efficient in cutting the tick sheet materials and greater beam diameter is essential in order to ensure a quality cut with good scavenging in addition to laser power and gas inlet pressure.

Laser drilling modelling needs unique approach and cannot be treated as a steady-state heat transfer phenomena unlike laser cutting process. Ganesh et al. [68] proposed a general model for drilling metals which include heat transfer, fluid dynamics of melt expulsion and tracking all the interfaces between gas, liquid and solid in a 2D axisymmetric coordinate. Later on Ganesh et al. [69, 70] made some improvements on their previous model by using a fixed grid system for temperature transforming model. A theoretical model using FDM developed by Yue et al. [16] to analyze ultra-sonic aided laser drilling which is a combination of ultra-sonic and laser machining for improved quality. Developed model is able to predict the shape of the drilled hole and thickness of the recast layer. Cheng et al. [14] developed a model using finite difference method

15

(FDM) for fine hole drilling of the carbon-fiber composites in order to predict hole dimensions. They found out that HAZ around the holes cause swelling about 50% in diameter. Collins and Gremaud [15] proposed a simple and effective model assuming laser drilling an axi-symmetry process based on one-dimensional formulation and cross-sectional averaging. The purpose of this model was development of a computationally cheap model without sacrificing the accuracy. Leintz et al. [71] presented a numerical finite volume multi-phase simulation model for short pulsed laser drilling. This model showed that ablation mechanism is dependent on pulse duration and phase of the drilling process. Percussion drilling of thick-section alumina was the concern of Yan et al. [72] study for drilling holes with low taper and low spatter deposition. Kim [73] used meshfree isoparametric finite point interpolation method (IFPIM) for developing a model for evaporative laser drilling. The presented method possessed weak form on the boundary and single strong form on the domain. Finally he compared the results with those from FEM and BEM in term of groove shape which illustrated in Figure 8. Eppes and Milanovic [74] Released a MATLAB-based utility named DREAM for analyzing, estimating and modeling variety of laser drilling process outcomes. The aim was to overcome the absence of sophisticated software to utilize theoretical models.

Fig. 8. Comparison of groove shapes with IFPIM (Q9, Q9-LI, and Q9-DI-LI), Q5 [73], BEM and FEM [18]

4. Artificial Intelligence (AI) Based Modelling and Simulation

Engineering problems which involve complexity and non-linearity have been benefited from AI methods which can develop system for applications require human intelligence. Artificial Neural Network (ANN), FUZZY expert systems (FES), Genetic Algorithm (GL) are common in laser beam machining models. AI methods mostly use experimental data to generate models.

4.1. Artificial Neural Network (ANN) Modeling ANN based models have pragmatic natures and are able to precisely solve problems that can better be understood through experiment. Neutrals in ANN perform non-linear weighted summations of the applied inputs. Once the applied input signals ix ( i 1,2,3,..., p )= received by neurons, they are modified by interconnection ijw which represents the interconnection weight between input ix and neuron j . In every particular neuron, the weighted inputs are summed along with a bias weight j0w in order to provide a single result iju . The output of neuron j is given by

Tjy f (W( n ) X ( n ))= (12)

16

where jy is the output from neuron j , W( n ) is the interconnection weight vector, T is the transpose, X( n ) is the vector of input signals for iteration n and function f is nonlinear activation, or transfer, function given by

a(.)

1f (.)1 e−=+

(13)

Each neuron is able to perform a simple logic or mathematic operation. Complex cases i.e. laser machining modelling requires a multi-layer neural network structure consist of simple neurons and experience training and operation phases. An example of the ANN model is shown in Figure 8. In the training phase neurons in the first layer are fed with input signals and each neuron computes an output using interconnection weights. These outputs play the role of input signals for the next layer, and so on until the output layer which the results of it will be compared with the desired output value. Naturally, these values are not same and results in the generation of an error signal will be generated. Back propagation through the network updates interconnection weights. This weight adaptation process carries on until obtaining set of weights and biases that satisfies all input-output pairs [75-77]. Yousef et al. [77] implemented multi-layered neural network in order to develop a prediction model for nonlinear laser cutting process. The predicted variable was groove geometry (Depth & Diameter) as a function of laser power density and it was suggested by authors that adaptive properties of this network may be beneficial due to the condition change caused by deterioration from age and use. Madić and Radovanović [78] used experimental data suggested by Taguchi method for training the artificial neural network in order to develop a model for optimizing HAZ in the CO2 laser cutting process of stainless steel. After final simulation the average predicting error was found to be 6.46 %. The ANN model used in their study is presented in Figure 9. Tsai et al. [79] performed a the Multiple Regression Analysis (MRA) and developed an Artificial Neural Network (ANN) model which involved more input parameters in the model such as current, the frequency and the cutting speed. Depths of the cut, widths of heat affected zone (HAZ) and cutting line in epoxy and copper-compounded epoxy were predicted parameters in this model. At the end, a genetic algorithm (GA) is implemented to optimize the parameters for fastest cutting speed and least HAZ. The results of predicted HAZ width by ANN model is compared with experimental data In Figure 10. Dhupal et al. [80] studied on modeling and optimization of Nd:YAG laser turning using a feed-forward ANN technique. Solving the model has been done by multi-objective genetic algorithm (GA). Considered parameters of Laser turning was lamp current, pulse frequency, pulse width, cutting speed and assist gas pressure in order to predict their effect on the laser turned micro-grooves. Ciurana et al. [81] applied ANN in Pulsed Laser Micromachining (milling) of Hardened AISI H13 Steel. Their model output was surface roughness and geometrical features.

4.2. FES b

fuzzinessnon-lineainformatiinferencefuzzifiedwords, linpresentedTHEN” rtwo inpuRule 1: IFRule 1: IF. . . Rule n: IF

Fig. 9.

Fig.

FUZZbased modelss. It uses the ar and compion [82]. FEe and 3) defud by assigninnguistic varid in Figure 1rules which c

uts and one oF x1 is A1 anF x1 is A2 an

F x1 is An an

The ANN Model

10. Comparison b

ZY Expert s can develoconventiona

lex system sS commonly

uzzification. ng various miables conve11. In the neconsist inpu

output can bend x2 is B1 Tnd x2 is B2 T

nd x2 is Bn T

with four inputs a

between perdition a

System (Fop approximaal mathematsuch as machy consist threIn fuzzificaembership fu

ert into fuzzyext step fuzzyts and outpu

e expressed aTHEN y is CTHEN y is C2

THEN y is Cn

and one output for

and experimental d

FES) ated solutiontical tools to hining proceee main proc

ation stage linfunctions throy variables. Ay rule base i

uts. As an exas 1 ELSE, 2 ELSE,

n.

predicting HAZ w

data for laser cutti

ns by manipuovercome c

esses and is acesses: 1) funguistic variough variouA typical meis generated

xample one ru

with four inputs [78

ing of Epoxy [79]

ulating tolercomplicationable to modeuzzification, iables (input

us fuzzy princembership fuin the form ule for a log

8]

ances for ns in analyzinel vague 2) fuzzy

t & outputs) ciples. In othunction is of “IF and

gic system w

17

ng

are her

with

where AiµB(i) and machininlaser powetc. In thfuzzy momembers

AB( x ,y ) mμ =

The analywhere the

A( x ) Aμ μ=

Implicatithe outpuabsolute

*

A

xy

μμ

= ∑∑

where y icentroidsFigure 1

Pandedevelopinsides. Onmost subDuralumroughnesSyn et al

i, Bi and Ci aµC(i). x1, x2 an

ng process thwer, pulse rate next step e

odel is a simpship of fuzzy

A( x ) B(min ,μ μ⎡⎣yze of implie output of e

A( x1 ) A( x2 )μ μ+ +

ion and aggrut in the fuzzvalue. CentrA( x )

A( x )

μ

is the crisp vs [83]. An ex2. ey and Dubeng a FES bane of the mosbstantial facto

min followed ss and dross . [85]. Figur

are the fuzzynd y are fuzz

he inputs of tte, etc. The oeach rule hasple and mos

y sets in the fy ) ⎤⎦ cation result

each rule aggA( x3 ) A...μ μ+ +

regation proczy form is obroid method

value of the oxample of a F

ey [84] appliased model fost important or in laser cuby frequencinclusion in

re 12 presen

y subsets defzy values ofthe fuzzy mooutputs can bs to be evalust widely usefollowing fo

ts is the nextgregate into ( xn ) cesses combbtained and dis the most

output and xFUZZY logi

ied FUZZY for reducing k

conclusion utting of higcy of the puls cutting of In

nts the structu

Fig. 11. A mem

fined by corrf fuzzy sets Aodel is inputbe surface q

uated throughed fuzzy systorm

(14)t step which a single fuzz

(15)ined are catedefuzzificatipopular for t

(16)

x* is the singlic model for

logic theorykerf width aof this publi

ghly reflectivses. Anotherncoloy alloyure on Syn e

mbership function

responding mA, B and C, rt parameters quality, groovh implicationtem [82] whi

is done throzy set in the

egorized as fion is requirethis purpose

leton value or laser cutting

y in laser cuttand kerf deviication is indve and thermr FES modely 800 with Cet al. FES mo

plot [84]

membership respectivelysuch as scan

ve depth andn process. Mich consider

ough aggregafollowing fo

fuzzy inferened in order t

e and is can b

of each memg process is

ting of Duraiations at topdicating gas

mally conductl for predicti

CO2 laser wasodel.

functions µAy. in the lasernning speed d width, HAZ

Mamdani typr minimum

ation processorm

nce. As the rto compute tbe expressed

mbership illustrated in

alumin sheet p and bottompressure as ttive materialing surface s proposed b

18

A(i), r , Z, e

s

result he

d in

n

for m the l like

by

4.3. Genet

the advanbe define1) Start w2) Calcul3) Perfor

popula4) Replac5) Recom

Sanjaythis modebeen usedsimultaneand desigimplemenreview be

5. Concl

LBM iCutting, Gsimulation discussion

1) Thermdisadv

2) There laser ptype orecast laser msimulathroug

Fig

Genetic algorithmntage of finded in the follwith a randomllation of fitnesrming the threeation. cing the new p

mputing fitness

y et al. [87] pel is reliabled for optimizeous optimizgn of experimnted with othefore in this

lusions

is one of the Grooving, Turn

of laser beam:

mal nature of vantage of bein

are variety of power, laser waof assisting gas

layer, micro cmachining pheation in LBM cgh analytical or

g. 12. The structure

etic Algorim (GA) is actding global olowing stepsly generated pos function H o

e stages of sele

population withs H from step 2

presented a e estimating ozation purpozation of kerment methodher method paper and c

most powerfuning and Milli

m machining ha

the LBM madng low energy ef parameters relavelength, mods and its pressucracks and droenomena is escan provide relr AI based mod

e of the FUZZY ex

ithm (GL)ting accordinoptimum poi [79]:

opulation of ‘nf every of ‘x’ cection, crossov

h the current on2 followed by s

model basedof recast layoses in this prf taper and sds. As mentisimultaneou

can be found

ul Advanced Ming, amongst as been done i

de it most suefficient in termlated to laser, wde of operationure, etc. Favorass adherence a

ssential for havliable predictiodelling. Optimu

xpert system for a

) based Mng to the meint [86]. The

’ m-bit chromochromosomes i

ver and mutatio

ne. step 3 and 4 un

d on GA for yer at exit anpaper. Kumasurface rougioned in this usly to develod in [79, 80].

Manufacturing other non-conin the presente

uitable for harms of productioworkpiece mat

n, material typeable quality chas well as smoving an accuraon of these quaum range of pa

typical laser cuttin

Modeling chanics of th

e mechanism

osomes in the populatioon in order to g

ntil reaching the

laser trepan nd entrance oar Pandey anghness with t

section genop a hybrid

Methods whintact methods. ed work and th

rd and brittle on rate. terial and proce and thickness

haracteristics ofooth surface rouate and high qality characteriarameters can b

ng process [85]

he natural gem of the gene

on. generate ‘n’ of

e termination c

drilling. Thof the drilledd Kumar Duthe aid of geetic algorithmethod whi

ich found appA review on

he following is

materials. Co

cess affecting Ls, feed rate, enf LBM are minughness. Therequality machinistics for rangebe obtained as

enerics and hric algorithm

ffspring from c

criterion

he main featud hole that haubey [86] doenetic algorithm can also bch has been

plication in Drn the modellins conclusions o

nversely, it h

LMB quality suergy, pulse durnimized HAZ, efore, understaning. Modelline of input paramthe result.

19

has m can

current

ure of as one a thm be

rilling, ng and of this

as the

uch as ration, taper,

anding ng and meters

20

3) There are three main methods for developing a prediction model for laser beam machining process: (1) Theoretical, (2) Experimental and (3) Artificial intelligence methods. Each method has its own benefit and limitation and selection of the method should be based on the nature of the work. However, experimental method has not been reviewed in presented work.

4) Theoretical modelling of the laser machining process involves using physics principles and energy balanced equations where material removal tale place in the workpiece. These equations can be solved analytically or numerically. Analytical solutions are based on some simplifying assumptions whereas numerical solutions are based on approximation. Numerical methods such as FEM, FDM, BEM and SPH can deal with more complex real-world situations which results in more accurate simulation.

5) Artificial Intelligence (AI) methods such as ANN, FES and GA has become popular in the engineering, recently and manufacturing processes modelling has been benefited from these method for developing intelligence models. AI methods can solve non-linear and complex cases with reasonable computational cost and good accuracy. They also can be used for developing hybrid models with other AI, theoretical or experimental methods to improve the accuracy of each method and taking more parameters into account.

6. Future Works

The authors propose to develop the modeling and simulation of laser beam machining by using hybrid intelligent approach such as Adaptive Neuro-Fuzzy Inference system (ANFIS) and the research is ongoing. Since, ANFIS integrate principles of Neural Networks and Fuzzy expert, it can capture the advantage of both respective methods in one model. In ANFIS an intelligence neural network is implemented in order to determine fuzzy inference membership functions or fuzzy rules from the training data [88].

ACKNOWLEDGEMENTS

The authors are grateful to the University of Malaya for providing the support under the grants RP010C-13AET and Faculty of Engineering.

REFERENCES [1] A. K. Dubey and V. Yadava, "Laser beam machining—a review," International Journal of Machine Tools and

Manufacture, vol. 48, pp. 609-628, 2008. [2] J. Meijer, "Laser beam machining (LBM), state of the art and new opportunities," Journal of Materials Processing

Technology, vol. 149, pp. 2-17, 2004. [3] A. Kuar, B. Doloi, and B. Bhattacharyya, "Modelling and analysis of pulsed Nd: YAG laser machining characteristics

during micro-drilling of zirconia (ZrO2)," International Journal of Machine Tools and Manufacture, vol. 46, pp. 1301-1310, 2006.

[4] C. Bagger and F. O. Olsen, "Pulsed mode laser cutting of sheets for tailored blanks," Journal of materials processing technology, vol. 115, pp. 131-135, 2001.

[5] J. D. Majumdar and I. Manna, "Laser processing of materials," Sadhana, vol. 28, pp. 495-562, 2003. [6] G. Chryssolouris, "Laser machining-theory and practice," 1991. [7] N. Tabata, S. Yagi, and M. Hishii, "Present and future of lasers for fine cutting of metal plate," Journal of materials

processing technology, vol. 62, pp. 309-314, 1996. [8] D. Pham, S. Dimov, and P. Petkov, "Laser milling of ceramic components," International journal of machine tools and

manufacture, vol. 47, pp. 618-626, 2007. [9] A. N. Samant and N. B. Dahotre, "Laser machining of structural ceramics—a review," Journal of the European

Ceramic Society, vol. 29, pp. 969-993, 2009. [10] P. Schaaf, Laser Processing of Materials: Fundamentals, Applications and Developments vol. 139: Springer, 2010. [11] K. Kheloufi and E. H. Amara, "Numerical Investigation of the Effect of Some Parameters on Temperature Field and

Kerf Width in Laser Cutting Process," Physics Procedia, vol. 39, pp. 872-880, 2012. [12] M. Kim, Z. Chen, and P. Majumdar, "Finite element modelling of the laser cutting process," Computers & structures,

vol. 49, pp. 231-241, 1993. [13] W. Schulz, U. Eppelt, and R. Poprawe, "Review on laser drilling I. Fundamentals, modeling, and simulation," Journal

of Laser Applications, vol. 25, p. 012006, 2013. [14] C. Cheng, Y. Tsui, and T. Clyne, "Application of a three-dimensional heat flow model to treat laser drilling of carbon

fibre composites," Acta materialia, vol. 46, pp. 4273-4285, 1998. [15] J. Collins and P. Gremaud, "A simple model for laser drilling," Mathematics and Computers in Simulation, vol. 81, pp.

1541-1552, 2011. [16] T. Yue, T. Chan, H. Man, and W. Lau, "Analysis of ultrasonic-aided laser drilling using finite element method," CIRP

Annals-Manufacturing Technology, vol. 45, pp. 169-172, 1996.

21

[17] M. J. Kim, "Transient evaporative laser-cutting with boundary element method," Applied Mathematical Modelling, vol. 25, pp. 25-39, 2000.

[18] M. J. Kim, "Transient evaporative laser cutting with moving laser by boundary element method," Applied Mathematical Modelling, vol. 28, pp. 891-910, 2004.

[19] M. J. Kim and J. Zhang, "Finite element analysis of evaporative cutting with a moving high energy pulsed laser," Applied Mathematical Modelling, vol. 25, pp. 203-220, 2001.

[20] M. Modest and H. Abakians, "Evaporative cutting of a semi-infinite body with a moving CW laser," Journal of heat transfer, vol. 108, pp. 602-607, 1986.

[21] C.-H. Tsai and H.-W. Chen, "Laser milling of cavity in ceramic substrate by fracture-machining element technique," Journal of materials processing technology, vol. 136, pp. 158-165, 2003.

[22] D. Pham, S. Dimov, C. Ji, P. Petkov, and T. Dobrev, "Laser milling as a ‘rapid’micromanufacturing process," Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 218, pp. 1-7, 2004.

[23] Q. Litao, W. Yang, and Y. Lijun, "Study of Nd: YAG pulsed laser milling Al2O3 ceramic in water and air condition," 2006.

[24] V. Kovalenko, J. Yao, Q. Zhang, M. Nayebi, M. Anyakin, R. Zhuk, et al., "Laser Milling of the Intractable Materials," Procedia CIRP, vol. 6, pp. 505-510, 2013.

[25] G. Chang and Y. Tu, "Closed-loop control in ultrafast laser milling process using laser triggered plasma," International Journal of Machine Tools and Manufacture, vol. 60, pp. 35-39, 2012.

[26] R. Aloke, V. Girish, R. Scrutton, and P. Molian, "A model for prediction of dimensional tolerances of laser cut holes in mild steel thin plates," International Journal of Machine Tools and Manufacture, vol. 37, pp. 1069-1078, 1997.

[27] P. Di Pietro and Y. Yao, "A new technique to characterize and predict laser cut striations," International Journal of Machine Tools and Manufacture, vol. 35, pp. 993-1002, 1995.

[28] B. Yilbas and A. Kar, "Thermal and efficiency analysis of CO2 laser cutting process," Optics and lasers in engineering, vol. 29, pp. 17-32, 1998.

[29] H. Man, J. Duan, and T. Yue, "Dynamic characteristics of gas jets from subsonic and supersonic nozzles for high pressure gas laser cutting," Optics & Laser Technology, vol. 30, pp. 497-509, 1998.

[30] I. Black, "Determining cutting speeds for the CO2 laser machining of decorative ceramic tile," The International Journal of Advanced Manufacturing Technology, vol. 14, pp. 651-655, 1998.

[31] I. Black, "Laser cutting speeds for ceramic tile: a theoretical–empirical comparison," Optics & Laser Technology, vol. 30, pp. 95-101, 1998.

[32] R. De Graaf and J. Meijer, "Laser cutting of metal laminates: analysis and experimental validation," Journal of Materials Processing Technology, vol. 103, pp. 23-28, 2000.

[33] H. Kaebernick, D. Bicleanu, and M. Brandt, "Theoretical and experimental investigation of pulsed laser cutting," CIRP Annals-Manufacturing Technology, vol. 48, pp. 163-166, 1999.

[34] P. Sheng and G. Chryssolouris, "Investigation of acoustic sensing for laser machining processes Part 2: Laser grooving and cutting," Journal of materials processing technology, vol. 43, pp. 145-163, 1994.

[35] C. Jiang, W. Lau, T. Yue, and L. Chiang, "On the maximum depth and profile of cut in pulsed Nd: YAG laser machining," CIRP Annals-Manufacturing Technology, vol. 42, pp. 223-226, 1993.

[36] A. Cenna and P. Mathew, "Analysis and prediction of laser cutting parameters of fibre reinforced plastics (FRP) composite materials," International Journal of Machine Tools and Manufacture, vol. 42, pp. 105-113, 2002.

[37] B. Yilbas, "Laser cutting quality assessment and thermal efficiency analysis," Journal of Materials Processing Technology, vol. 155, pp. 2106-2115, 2004.

[38] L. Li, M. Sobih, and P. Crouse, "Striation-free laser cutting of mild steel sheets," CIRP Annals-Manufacturing Technology, vol. 56, pp. 193-196, 2007.

[39] Y. Li, W. P. Latham, and A. Kar, "Lumped parameter model for multimode laser cutting," Optics and lasers in engineering, vol. 35, pp. 371-386, 2001.

[40] G. Tani, L. Tomesani, and G. Campana, "Prediction of melt geometry in laser cutting," Applied Surface Science, vol. 208, pp. 142-147, 2003.

[41] G. Tani, L. Tomesani, G. Campana, and A. Fortunato, "Quality factors assessed by analytical modelling in laser cutting," Thin solid films, vol. 453, pp. 486-491, 2004.

[42] L. M. Wee and L. Li, "An analytical model for striation formation in laser cutting," Applied surface science, vol. 247, pp. 277-284, 2005.

[43] Y. Yan, L. Li, K. Sezer, D. Whitehead, L. Ji, Y. Bao, et al., "Nano-second pulsed DPSS Nd: YAG laser striation-free cutting of alumina sheets," International Journal of Machine Tools and Manufacture, vol. 53, pp. 15-26, 2012.

[44] M. F. Modest, "Three-dimensional, transient model for laser machining of ablating/decomposing materials," International journal of heat and mass transfer, vol. 39, pp. 221-234, 1996.

[45] M. F. Modest, "Laser through‐cutting and drilling models for ablating/decomposing materials," Journal of Laser Applications, vol. 9, p. 137, 1997.

[46] P. S. Sheng and V. S. Joshi, "Analysis of heat-affected zone formation for laser cutting of stainless steel," Journal of materials processing technology, vol. 53, pp. 879-892, 1995.

[47] L. Yu, "Three-dimensional finite element modelling of laser cutting," Journal of materials processing technology, vol. 63, pp. 637-639, 1997.

22

[48] P. Di Pietro and Y. Yao, "A numerical investigation into cutting front mobility in C0< sub> 2</sub> laser cutting," International Journal of Machine Tools and Manufacture, vol. 35, pp. 673-688, 1995.

[49] P. D. Pietro, Y. Yao, and A. Jeromin, "Quality optimisation for laser machining under transient conditions," Journal of Materials Processing Technology, vol. 97, pp. 158-167, 2000.

[50] J. M. Prusa, G. Venkitachalam, and P. A. Molian, "Estimation of heat conduction losses in laser cutting," International Journal of Machine Tools and Manufacture, vol. 39, pp. 431-458, 1999.

[51] L. Scintilla and L. Tricarico, "Estimating cutting front temperature difference in disk and CO2 laser beam fusion cutting " Optics & Laser Technology, vol. 44, pp. 1468-1479, 2012.

[52] A. Arif, B. Yilbas, and B. Aleem, "Laser cutting of thick sheet metals: residual stress analysis," Optics & Laser Technology, vol. 41, pp. 224-232, 2009.

[53] B. S. Yilbas and S. Akhtar, "Laser cutting of alloy steel: Three-dimensional modeling of temperature and stress fields," Materials and Manufacturing Processes, vol. 26, pp. 104-112, 2011.

[54] B. S. Yilbas, S. Akhtar, and C. Karatas, "Laser hole cutting into Ti-6Al-4V alloy and thermal stress analysis," The International Journal of Advanced Manufacturing Technology, vol. 59, pp. 997-1008, 2012.

[55] Y. Yan, L. Li, K. Sezer, D. Whitehead, L. Ji, Y. Bao, et al., "Experimental and theoretical investigation of fibre laser crack-free cutting of thick-section alumina," International Journal of Machine Tools and Manufacture, vol. 51, pp. 859-870, 2011.

[56] K. Li and P. Sheng, "Plane stress model for fracture of ceramics during laser cutting," International Journal of Machine Tools and Manufacture, vol. 35, pp. 1493-1506, 1995.

[57] Y. Yan, L. Ji, Y. Bao, X. Chen, and Y. Jiang, "CO2 laser high-speed crack-free cutting of thick-section alumina based on close-piercing lapping technique," The International Journal of Advanced Manufacturing Technology, vol. 64, pp. 1611-1624, 2013.

[58] R. Negarestani, M. Sundar, M. Sheikh, P. Mativenga, L. Li, Z. Li, et al., "Numerical simulation of laser machining of carbon-fibre-reinforced composites," Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 224, pp. 1017-1027, 2010.

[59] D. Lee, R. Patwa, H. Herfurth, and J. Mazumder, "Computational and experimental studies of laser cutting of the current collectors for lithium-ion batteries," Journal of Power Sources, vol. 210, pp. 327-338, 2012.

[60] S. Nisar, L. Li, M. A. Sheikh, and A. J. Pinkerton, "The effect of continuous and pulsed beam modes on cut path deviation in diode laser cutting of glass," The International Journal of Advanced Manufacturing Technology, vol. 49, pp. 167-175, 2010.

[61] L. Yang, Y. Wang, Z. Tian, and N. Cai, "YAG laser cutting soda-lime glass with controlled fracture and volumetric heat absorption," International Journal of Machine Tools and Manufacture, vol. 50, pp. 849-859, 2010.

[62] S. Nisar, M. Sheikh, L. Li, and S. Safdar, "The effect of material thickness, laser power and cutting speed on cut path deviation in high-power diode laser chip-free cutting of glass," Optics & Laser Technology, vol. 42, pp. 1022-1031, 2010.

[63] B. Yilbas and A. Sahin, "Oxygen assisted laser cutting mechanism—a laminar boundary layer approach including the combustion process," Optics & Laser Technology, vol. 27, pp. 175-184, 1995.

[64] C.-C. Mai and J. Lin, "Flow structures around an inclined substrate subjected to a supersonic impinging jet in laser cutting," Optics & Laser Technology, vol. 34, pp. 479-486, 2002.

[65] M. S. Gross, "On gas dynamic effects in the modelling of laser cutting processes," Applied mathematical modelling, vol. 30, pp. 307-318, 2006.

[66] S. Guo, H. Jun, L. Lei, and Z. Yao, "Numerical analysis of supersonic gas-dynamic characteristic in laser cutting," Optics and Lasers in Engineering, vol. 47, pp. 103-110, 2009.

[67] O. Kovalev, P. Yudin, and A. Zaitsev, "Modeling of flow separation of assist gas as applied to laser cutting of thick sheet metal," Applied Mathematical Modelling, vol. 33, pp. 3730-3745, 2009.

[68] R. K. Ganesh, W. W. Bowley, R. R. Bellantone, and Y. Hahn, "A model for laser hole drilling in metals," Journal of Computational Physics, vol. 125, pp. 161-176, 1996.

[69] R. Ganesh, A. Faghri, and Y. Hahn, "A generalized thermal modeling for laser drilling process—I. Mathematical modeling and numerical methodology," International journal of heat and mass transfer, vol. 40, pp. 3351-3360, 1997.

[70] R. Ganesh, A. Faghri, and Y. Hahn, "A generalized thermal modeling for laser drilling process (II): Numerical simulation and results [J]," International Journal of Heat and Mass Transfer, vol. 40, pp. 3361-3373, 1997.

[71] K.-H. Leitz, H. Koch, A. Otto, and M. Schmidt, "Numerical simulation of process dynamics during laser beam drilling with short pulses," Applied Physics A, vol. 106, pp. 885-891, 2012.

[72] Y. Yan, L. Ji, Y. Bao, and Y. Jiang, "An experimental and numerical study on laser percussion drilling of thick-section alumina," Journal of Materials Processing Technology, vol. 212, pp. 1257-1270, 2012.

[73] M. J. Kim, "Meshfree isoparametric finite point interpolation method (IFPIM) with weak and strong forms for evaporative laser drilling," Applied Mathematical Modelling, vol. 36, pp. 1615-1625, 2012.

[74] T. A. Eppes, I. M. Milanovic, and D. Shetty, "Laser percussion drilling modeling utility," Journal of Laser Applications, vol. 21, p. 102, 2009.

[75] I. Basheer and M. Hajmeer, "Artificial neural networks: fundamentals, computing, design, and application," Journal of microbiological methods, vol. 43, pp. 3-31, 2000.

[76] S. Haykin, Neural networks: a comprehensive foundation: Prentice Hall PTR, 1994.

23

[77] B. F. Yousef, G. K. Knopf, E. V. Bordatchev, and S. K. Nikumb, "Neural network modeling and analysis of the material removal process during laser machining," The International Journal of Advanced Manufacturing Technology, vol. 22, pp. 41-53, 2003.

[78] M. J. Madić and M. R. Radovanović, "Analysis of the heat affected zone in CO2 laser cutting of stainless steel," Thermal Science, vol. 16, 2012.

[79] M.-J. Tsai, C.-H. Li, and C.-C. Chen, "Optimal laser-cutting parameters for QFN packages by utilizing artificial neural networks and genetic algorithm," Journal of Materials Processing Technology, vol. 208, pp. 270-283, 2008.

[80] D. Dhupal, B. Doloi, and B. Bhattacharyya, "Modeling and optimization on Nd: YAG laser turned micro-grooving of cylindrical ceramic material," Optics and Lasers in Engineering, vol. 47, pp. 917-925, 2009.

[81] J. Ciurana, G. Arias, and T. Ozel, "Neural network modeling and particle swarm optimization (PSO) of process parameters in pulsed laser micromachining of hardened AISI H13 steel," Materials and Manufacturing Processes, vol. 24, pp. 358-368, 2009.

[82] A. K. Pandey and A. K. Dubey, "Fuzzy expert system for prediction of kerf qualities in pulsed laser cutting of titanium alloy sheet," Machining Science and Technology, vol. 17, pp. 545-574, 2013.

[83] K. GEORGE J and Y. Bo, "Fuzzy sets and fuzzy logic, theory and applications," -, 2008. [84] A. K. Pandey and A. K. Dubey, "Taguchi based fuzzy logic optimization of multiple quality characteristics in laser

cutting of Duralumin sheet," Optics and Lasers in Engineering, vol. 50, pp. 328-335, 2012. [85] C. Z. Syn, M. Mokhtar, C. J. Feng, and Y. H. Manurung, "Approach to prediction of laser cutting quality by employing

fuzzy expert system," Expert Systems with Applications, vol. 38, pp. 7558-7568, 2011. [86] A. Kumar Pandey and A. Kumar Dubey, "Simultaneous optimization of multiple quality characteristics in laser cutting

of titanium alloy sheet," Optics & Laser Technology, vol. 44, pp. 1858-1865, 2012. [87] S. Kumar, A. K. Dubey, and A. K. Pandey, "Computer-aided genetic algorithm based multi-objective optimization of

laser trepan drilling," International Journal of Precision Engineering and Manufacturing, vol. 14, pp. 1119-1125, 2013.

[88] A. Abraham, "Adaptation of fuzzy inference system using neural learning," in Fuzzy Systems Engineering, ed: Springer, 2005, pp. 53-83.

24

• Material removal mechanism and the theory of heat transfer in laser Beam Machining.

• Benefits and limitations of various methods in modelling laser beam machining.

• Review on modelling with analytical, numerical and artificial intelligence methods.

• The theory of artificial intelligence methods.

• A hybrid method for modelling has been proposed for future works.