Numerical simulation of metal removal in laser drilling using radial point interpolation method

Abstract Prediction of penetration depth in metal laser drilling is done through a simple meshfree numerical model. 2D axisymmetric simplified model of transient metal laser drilling is proposed for continuous laser beam of Gaussian distribution with strong form of Radial Point Interpolation Method (RPIM) used for approximating the temperature field. The commonly used Multi-Quadrics (MQ) and Exponential (EXP) Radial Basis Functions (RBFs) are tested and compared with each other. The model logic is constructed in MATLAB code, while the results are compared with published numerical and experimental work. The simulation results give good agreement with the previous numerical and experimental work, showing the model reliability in predicting the penetration depth in such a physically complex process.

[1]  Wen Chen,et al.  Recent Advances in Radial Basis Function Collocation Methods , 2013 .

[2]  Aravinda Kar,et al.  Temperature‐dependent absorptivity and cutting capability of CO2, Nd:YAG and chemical oxygen–iodine lasers , 1997 .

[3]  Benedict D. Rogers,et al.  Understanding the behaviour of pulsed laser dry and wet micromachining processes by multi-phase smoothed particle hydrodynamics (SPH) modelling , 2013 .

[4]  B. Yilbas,et al.  Laser heating including the phase change process and thermal stress generation in relation to drilling , 2003 .

[5]  Alain J. Kassab,et al.  An Efficient Localized Radial Basis Function Meshless Method for Fluid Flow and Conjugate Heat Transfer , 2007 .

[6]  Yuwen Zhang,et al.  Vaporization, melting and heat conduction in the laser drilling process , 1999 .

[7]  Jcj Kees Verhoeven Modelling laser percussion drilling , 2004 .

[8]  J. Monaghan Smoothed particle hydrodynamics , 2005 .

[9]  E. Kansa MULTIQUADRICS--A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS-- II SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS , 1990 .

[10]  A. Faghri,et al.  A generalized thermal modeling for laser drilling process—I. Mathematical modeling and numerical methodology , 1997 .

[11]  Guirong Liu,et al.  On the optimal shape parameters of radial basis functions used for 2-D meshless methods , 2002 .

[12]  X. Ni,et al.  Modeling and simulation on long pulse laser drilling processing , 2014 .

[13]  Lin Li,et al.  An analytical model for laser drilling incorporating effects of exothermic reaction, pulse width and hole geometry , 2006 .

[14]  J. Mazumder,et al.  Laser material processing: Fourth edition , 2010 .

[15]  E. Kansa Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates , 1990 .

[16]  B. Šarler,et al.  Local radial basis function collocation method for linear thermoelasticity in two dimensions , 2015 .

[17]  Guirong Liu,et al.  A meshfree radial point interpolation method (RPIM) for three-dimensional solids , 2005 .

[18]  M. Kim Meshfree isoparametric finite point interpolation method (IFPIM) with weak and strong forms for evaporative laser drilling , 2012 .

[19]  Hua Li,et al.  Meshless Methods and Their Numerical Properties , 2013 .

[20]  A. M. Sifullah,et al.  A Fuzzy Logic-Based Prediction Model for Kerf Width in Laser Beam Machining , 2016 .

[21]  B. S. Yilbas,et al.  Laser Nanosecond Pulse Heating of Surfaces and Thermal Stresses , 2001 .

[22]  Eduardo Divo,et al.  A Localized Radial-Basis-Function Meshless Method Approach to Axisymmetric Thermo-Elasticity , 2006 .

[23]  Nukman Yusoff,et al.  Numerical and intelligent analysis of silicon nitride laser grooving , 2015 .

[24]  V. Yadava,et al.  Laser Beam MicroMachining (LBMM) – A review , 2015 .

[25]  Marc Duflot,et al.  Meshless methods: A review and computer implementation aspects , 2008, Math. Comput. Simul..

[26]  M. Gross Smooth particle hydrodynamics (SPH) modelling of laser cutting , 2008 .

[27]  Yusoff Nukman,et al.  Optimization of Prediction Error in CO2 Laser Cutting process by Taguchi Artificial Neural Network Hybrid with Genetic algorithm , 2013 .

[28]  W. Tao,et al.  Weighted Least-Squares Collocation Method (WLSCM) for 2-D and 3-D Heat Conduction Problems in Irregular Domains , 2011 .

[29]  David Bergström,et al.  The absorptance of steels to Nd:YLF and Nd:YAG laser light at room temperature , 2007 .

[30]  Pierre Gremaud,et al.  A simple model for laser drilling , 2011, Math. Comput. Simul..

[31]  Guirong Liu Mesh Free Methods: Moving Beyond the Finite Element Method , 2002 .

[32]  Guirong Liu,et al.  A point interpolation meshless method based on radial basis functions , 2002 .

[33]  Jian Lu,et al.  Numerical simulation of heat transfer and fluid flow in laser drilling of metals , 2015, Other Conferences.

[34]  Luca Vincenzo Ballestra,et al.  Computing the survival probability density function in jump-diffusion models: A new approach based on radial basis functions , 2011 .

[35]  A. Cheng Multiquadric and its shape parameter—A numerical investigation of error estimate, condition number, and round-off error by arbitrary precision computation , 2012 .

[36]  A. Kassab,et al.  A locally-integrated meshless (LIM) method applied to advection-diffusion problems , 2014 .

[37]  A. Kar,et al.  Two‐dimensional model for laser‐induced materials damage: Effects of assist gas and multiple reflections inside the cavity , 1992 .

[38]  J. Wertz,et al.  The role of the multiquadric shape parameters in solving elliptic partial differential equations , 2006, Comput. Math. Appl..

[39]  A. Cheng,et al.  Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method , 2007 .

[40]  M. Kim Meshfree isoparametric point interpolation method (IPIM) for evaporative laser drilling , 2011 .

[41]  Bengt Fornberg,et al.  On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere , 2008, J. Comput. Phys..

[42]  Amir Faghri,et al.  A generalized thermal modeling for laser drilling process—II. Numerical simulation and results , 1997 .