外文翻译--多目标优化激光切割工艺 英文版.pdf

Optics received in revised form 1 September 2007 accepted 7 September 2007 Abstract This paper presents a hybrid Taguchi method and response surface method TMRSM for the multi response optimisation of a laser beam cutting process The approach fi rst uses the Taguchi quality loss function to fi nd the optimum level of input cutting parameters such as assist gas pressure pulse width pulse frequency and cutting speed The optimum input parameter values are further used as the central values in the response surface method to develop and optimise the second order response model The two quality characteristics Kerf width KW and material removal rate MRR that are of different nature KW is of the smaller the better type while MRR is of the higher the better type have been selected for simultaneous optimisation The results show considerable improvement in both the quality characteristics when the hybrid approach is used as compared the results of a single approach r 2007 Elsevier Ltd All rights reserved Keywords Taguchi method Laser beam cutting Hybrid approach 1 Introduction The laser was invented in 1960s and has wide applica tions in the fi eld of fi ne cutting of sheet metals due to its precision and high intensity 1 2 Laser beam cutting LBC canbesuccessfullyusedforthecuttingof conductive and nonconductive diffi cult to cut advanced engineering materials such as refl ective metals plastics rubbers ceramics and composites Apart from cutting diffi cult to cut materials LBC is most widely used in industries to achieve complex shapes profi les with close tolerances for cutting of steel sheets 3 The most widely used industrial lasers for cutting of sheet metals are gaseous CO2and solid state Nd YAG There has been growing interest in recent years in the use of pulsed Nd YAG lasers for precision cutting of thin sheet metals because of its high intensity low mean beam power good focusing character istics and narrow heat affected zone HAZ LBC is a thermal energy based non conventional cutting method in which sheet material is cut mainly due to melting and vaporisation The molten material is ejected with the help of high pressure assist gas jet 4 The schematic of the LBCprocesshasbeenshowninFig 1 Sinceits introduction LBC has always been a major research area for getting the exceptionally good quality of cut The quality of cut solely depends on the setting of process parameters such as laser power type and pressure of assist gas sheet material thickness and its composition cutting speed and mode of operation continuous wave or pulsed mode A lot of experimental investigation has been undertaken with the aim of analysing the effect of process parameters on cut geometry and cut surface quality In most of the experimental investigations of the LBC process researchers have varied one factor at a time to analyse the effect of input process parameters on output qualitycharacteristicsorresponses 5 10 Butthis technique requires a large number of experimental runs because only one factor is varied in each run keeping all otherfactorsconstant Also inthistechnique the interaction effects among various input process parameters are not considered To overcome these problems some researchershaveincorporateddesignofexperiments methodologies such as the response surface methodology RSM and Taguchi methodology TM during experi mental study of LBC process Tam et al 11 applied the Taguchi method to study the laser cutting process for 4 5mm thick mild steel sheet The ARTICLE IN PRESS 0030 3992 see front matter r 2007 Elsevier Ltd All rights reserved doi 10 1016 j optlastec 2007 09 002 Corresponding author Tel 915322271812 fax 915322445101 E mail address avanishdubey A Kumar Dubey signal to noise S N ratio of overall fi gure of merit was considered as quality function This quality function integrates the weighted effects of quality characteristics Kerf width KW surface roughness micro hardness slope of cut edge and HAZ and cost components cutting speed oxygen pressure and beam power Lim et al 12 have applied the same approach for the study of the surface roughness obtained during high speed laser cutting of stainless steel sheets Li et al 13 have also applied Taguchi s robust design methodology to study the width of cut and HAZ during laser cutting of quad fl at no QFN lead packages using a diode pumped solid state laser DPSSL system The cutting parameters taken are laser current laser frequency and cutting speed Mathew et al 14 performed parametric studies on pulsed Nd YAG laser cutting of fi bre reinforced plastic composite sheet 2mm thick A central composite design CCD with uniform precision was used for experimental design and a second order response surface model for HAZ andKerftaperwasdeveloped Theinputprocess parameters were cutting speed pulse energy pulse dura tion pulse repetition rate and gas pressure Almeida et al 15 applied factorial design approach to determine the effects of pulse energy overlapping rate and type of assist gas on the surface roughness and dross formation edge irregularity during Nd YAG laser cutting of pure titanium and titanium alloy Ti6Al4V The design of experiments based studies on LBC process so far have been mainly aimed at the optimisation of the single quality characteristic at a time It has been found that the optimum parameter settings for one quality characteristic may deteriorate other quality characteristics As the aim of a manufacturing process is always to improve the overall quality of a product it is necessary to optimisethemultiplequalitycharacteristicssimulta neously Antony 16 has demonstrated a Taguchi quality loss function based multi objective optimisation technique for manufacturing processes taking an example of electro nic assembly problem He has found considerable im provementinmultiplequalitycharacteristics in comparison to single quality characteristics Different hybrid approaches have recently been used for the optimisation of different machining processes Taguchi method with fuzzy logic 17 or with grey relational analysis 18 has been used to optimise the electrical discharge machining process a non conventional thermal based machining process with multiple machining performance Chiadamrong 19 has suggested a sequential integration approach of TM and RSM to optimise the quality characteristics in manufacturing system He demonstrated the hybrid methodology by taking a case study of printed circuit board manufacturing plant and found a signifi cant reduction in quality loss The hybrid approach of TM and RSM has yet not been applied in the study of LBC process with single or multiple performance measures In the present paper a hybrid Taguchi method and response surface method TMRSM approach has been used to develop the response models and to optimise the ARTICLE IN PRESS Nomenclature b regression coeffi cient Dcomposite desirability dindividual desirability knumber of responses or quality characteristics Lijthe quality loss for the ith quality characteristic at the jth trial condition or run Li maximum quality loss for the ith quality characteristic among all the experimental runs mMean of multiple S N ratios of all experimental runs nnumber of experimental runs pnumber of control factors or input process parameters wiweighting factor assigned to ith response or quality characteristic xiith input process parameter or control factor Yjtotal normalised quality loss value in jth experimental run yiresponse or observed quality value in ith experimental run yijnormalised quality loss value for ith experi mental run and jth quality characteristic ZS N ratio Zopredicted multiple S N ratio at optimum parameter levels Ze j multiple S N ratio of jth trial condition or experimental run GAS JET DRAG LINES MELTING OR SLAG NOZZLE GAS FOCUSING OPTICS LASER BEAM CUTTING EDGE ON WORKPIECE Fig 1 Schematic of laser beam cutting A Kumar Dubey V Yadava Optics MSD 1 n X n i 1 y2 i 3 For HB type MSD 1 n X n i 1 1 y2 i 4 where yiis the observed response or quality value at the ith trial or experimental run and n is the number of trials at same parameter level In multi objective optimisation a single overall S N ratio for all quality characteristics is computed in place of separate S N ratios for each of the quality characteristic This overall S N ratio is known with the name of multiple S N ratio MSNR The MSNR for jth trial Ze j is computed as given below 16 Ze j 10log10 Yj 5 Yj X k i 1 wiyij 6 yij Lij Li 7 where Yjis the total normalised quality loss in jth trial wi representstheweightingfactorfortheithquality characteristic k is the total number of quality character istics and yijis the normalised quality loss associated with the ith quality characteristic at the jth trial condition and it varies from a minimum of zero to a maximum of 1 Lijis the quality loss or MSD for the ith quality characteristic at the jth trial and Li is the maximum quality loss for the ith quality characteristic among all the experimental runs 2 2 Response surface method RSM is a collection of statistical and mathematical methods that are useful for the modelling and optimisation of the engineering science problems In this technique the main objective is to optimise the responses that are infl uenced by various input process parameters RSM also quantifi es the relationship between the controllable input parameters and the obtained responses In modelling and optimisation of manufacturing processes using RSM the suffi cient data is collected through designed experimentation In general a second order regression model is developed because fi rst order models often give lack of fi t 23 According to RSM all the input process parameters are assumed to be measurable the corresponding responses can be expressed as follows y f x1 x2 xp 8 where x1 x2 y xpare input process parameters and y is the response which is required to be optimised Here it is assumed that the independent variables input process ARTICLE IN PRESS A Kumar Dubey V Yadava Optics 0 0 a 0 0 a 0 0 0 a 0 0 a 0 0 0 a 0 0 a Here the value of code a is equal to 2p 1 4 and it is introduced to provide the orthogonal property to array The coded level 0 represents the central value of input process parameters It is important for a second order model to provide optimum prediction about the process behaviour within the specifi ed range of all input process parameters So the model should have a reasonably consistent and stable prediction of responses at points of interest xi This can be achieved by CCRD According to CCRD methodology standard error is kept same for all points that are at the same distance from the centre of the region This can be stated mathematically as follows 20 x2 1 x 2 2 x 2 p constant 10 CCRD requires minimum fi ve levels of all factors for the calculation of regression coeffi cients In this situation the total number of combinations or runs required becomes 2p 2p more than one runs at centre In present case of four control factors an standard CCRD matrix with 7 central point runs has been selected 20 The developed response model is used for fi nding optimum level of input process parameters This is obtained by location of stationary points that will lead to a point of maximum or minimum response 23 3 Experimental procedure and operating parameters The experimental studies were performed on a 200W pulsed Nd YAG laser beam machining system with CNC work table The oxygen is used as an assist gas The variable input process parameters or control factors taken are assist gas pressure pulse width pulse frequency and cutting speed Focal length of lens used is 50 0mm Nozzle diameter 1 0mm nozzle tip distance 1 0mm and sheet material thickness 0 5mm were kept constant throughout the experimentation The two quality char acteristics analysed are KW and MRR The grain oriented high silicon alloy steel sheet a magnetic material sheet used in transformer cores was used in the experiments as sheet material Two cuts each of 15mm length were obtained in each experimental run The KW was measured using the Tool Makers Microscope Model RTM 900 RADICAL Instruments India at 10 magnifi cation The KW mm taken is the mathematical average of two cuts corresponding to same experimental run KW of each cut has been measured at three different places at the top of the sheet Average of these three measurements represents the KW of each cut The MRR mg min is calculated by using the following formula MRR Loss of mass during each cut cutting speed length of cut 11 The MRR calculated is also taken as average of two cuts The loss of mass was obtained by weighing the specimen before and after the cutting using Electronic Balance Model A 120 Shimandzu Corporation Japan Thecontrolfactorstakenarethegaspressure 1 5 3 5kg cm2 pulsewidthorpulseduration 1 0 1 4ms pulse frequency 20 28Hz and cutting speed 25 75mm min The numerical values of factors at different levels are shown in Table 1 An exhaustive pilot experimentation is done to decide the parameter range for quality cut Here the quality cut basically represents the complete through and dross free cutting without any burning effect as per visual inspection through naked eye For example the minimum pulse width maximum cutting speed and gas pressure were found to be 0 6ms 125mm min and 4 5kg cm2 respectively for complete through cutting but below the pulse width of 1 0ms and beyond the cutting speed of 75mm min and gas pressure of 3 5kg cm2 the cutting was not free from burning effect and or dross adhesion to the bottom surface of the sheet The quality characteristics measured are KW and MRR The initial setting of input parameters is gas pressure 1 5kg cm2 pulse width 1 0ms pulse frequency 20Hz and cutting speed 25mm min In present case of four parameters at three different levels assuming no interaction between factors the dof has ARTICLE IN PRESS Table 1 Control factors and their levels used in OA design matrix SymbolFactorsUnitLevel 1Level 2Level 3 AGas pressurekg cm21 52 53 5 BPulse widthms1 01 21 4 CPulse frequencyHz202428 DCutting speedmm min255075 A Kumar Dubey V Yadava Optics d individual desirability Hi highest parameter values Lo lowest parameter values Cur current or optimum values oxygen p gas oxygen pressure Pulse wi pulse width Pulse fr pulse frequency cutting cutting speed Kerf wid Kerf width Table 12 Comparison of results of Taguchi approach and hybrid approach Quality characteristics Optimization technique Taguchi approachHybrid approach KW mm 0 37330 3267 MRR mg min 124 1095169 1667 A Kumar Dubey V Yadava Optics 1991 2 Steen WM Laser material processing New York Springer 1991 3 Luxon JT Parker DE Industrial lasers and their applications Englewood Cliffs NJ Prentice Hall 1985 4 Majumdar JD Manna I Laser processing of materials Sadhana 2003 28 3168 438 47 6 Lamikiz A Lacalle LNL Sanchez JA Pozo D Etayo JM Lopez JM CO2laser cutting of advanced high strength steels AHSS Appl Surf Sci 2005 242 362 8 7 Chen SL The effects of high pressure assistant gas fl ow on high power CO2laser cutting J Mater Process Technol 1999 88 57 66 8 Rajaram N Ahmad JS Cheraghi SH CO2laser cut quality of 4130 steel Int J Mach Tools Manuf 2003 43 351 8 9 Karatas C Keles O Uslan I Usta Y Laser cutting of steel sheets infl uence of workpiece thickness and beam waist position on Kerf size and stria formation J Mater Process Technol 2006 172 22 9 10 Tuersley IP Hoult TP Tony P Pashby IR Nd YAG laser machining of SiC fi bre borosilicate glass composites Part II The effect of process variables Composites Part A 1998 29A 955 64 11 Tam SC Lim LEN Quek KY Application of Taguchi method in the optimization of the laser cutting process J Mater Process Technol 1992 29 63 74 12 Lim SH Lee CM Chung