Jun－min XIAO

Department of Mechanical and Electrical Engineering，Zhongshan Polytechnic，Zhongshan 528404，China

Experimental study on milling tool life for SKD11 steel and optim ization of cutting parameters*

Jun－min XIAO?

Department of Mechanical and Electrical Engineering，Zhongshan Polytechnic，Zhongshan 528404，China

In order to improve tool life for hardened steel SKD11 during the m illing process，the related m illing experiments are carried out and the influence of cutting parameters on tool life is analyzed based on range method.It is found that the influence o f axia l cutting depth on toolwear is pretty strong，and the influence of radial cutting w idth on toolwear is very weak.Based on the m illing experiments，the mathematicalmodelof toolwear is established by using of regression analysis method.In order to solve the actualm illing problem，the cutting parameters are optim ized by using of SQP optim ization method based on MATLAB software.During the optim ization process，the machining efficiency and the tool wear quantity are set as the objective function.The optim ized cutting parameters could greatly improve the machining efficiency in the prem ise of ensuring smaller toolwear，and it provides the im portant theory evidence and case reference for NC machining enterprises to reduce com positive production costs.

Tools life，Wear，Machining efficiency，Mathematicalmodel，SKD11

*Project supported by Fostering Plan for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province(Yq2013195)

? Jun－min XIAO，Associate professor.E－mail:xiaojunmin517@163.com

1.Introduction

Tool life is not only an important indicator to evaluate the reliability and performance of cutting tool，but also is the basis for the optimization of cutting parameters and tool design，and makes the strategy of automatic tool change and tool requirement planning.Therefore，it is very necessary to predictand evaluate tool life reliably［1］.Many Chinese and foreign scholars have carried out scientific research about cutting tool life from different academic directions.For example，Alauddin studied the influence of cutting speed，feed rate and axial cutting depth on tool life by using the response surfacemethod，and established tool life formulas［2］.Tsai et al studied the effect of cutting parameters on tool life based on a new network proposed by Tsai.This network could automatically select the optimal number and node type by applying PSE criterion，and the prediction accuracy is much higher than the neural network［3］.LIXuanqi，et al carried out some related experimental study on tool wear for titanium alloy and analyzed the influence of tool geometry parameters on tool wear，and the conclusion was drawn as follows:the larger spiral angle is helpful to improve the tool life［4］.WANG Xiaoqin et al carried out the related research of tool life for Ti6Al4V material and constructed the tool life model.The optimized parameterswere obtained by drawing the curves of tool life and machining efficiency in the paper［5］.The hardened steel SKD11 has a very high hardness，and its hardness can reach HRC58－62.It is widely used in the field of plastic mold and die due to its good mechanical properties.Since the hardened steel SKD11 has relative high hardness，the cutting tool by using this kind ofmaterial is always subjected to high cutting stress and high temperature environment in the milling process，which will directly shorten the service life ofmilling cutters［6］.The rapid wear ofmilling tool will significantly increase the auxiliary production time and greatly improve the tool cost，so it is very important for milling hardened steel to improve tool life by optimizing cutting parameters.

2.Experimental conditions and results

The CNCmachining center of VMC650E type is used in milling experiments of tool wear.The workpiecematerial used in the experiments is the hardened steel SKD11，and the hardness is up to HRC58.The end－mill cutters of solid carbidewith TiAlN coating are adopted during the machining process，and the tooth number ofmilling cutter is 4 and tool diameter is 6 mm.The work－piece blank is the cube and the size is 100 ×100 ×30(mm3).The range of cutting parameters is as follows:The spindle speed is 2 500 r/min，the feed is200 ～300mm/min，the axial cutting depth is 0.1 ～0.3 mm and the radial cutting width is 3.0 ～4.2 mm.The ZIG－ZAG reciprocating cutting way is adopted in the milling process.Based on the four parameters of cutting speed，feed rate，axial cutting depth and radial cuttingwidth，the L9(34)orthogonal milling experiments are designed and carried out according Taguchimethod，and the experimental data as shown in Table 1 could be obtained［7］.

Table 1.The experimental data of toolwear

3.Analysis of experimental data

The analysis content about tool wear quantity Mas shown in Table 2 could be obtained based on the rangemethod.Ki(i=1，2，3)represents the sum of test resultswith the same level in each column.R is the range value of factors，and its expression is as follows:R=max(K1，K2，K3)－ min(K1，K2，K3).The range value in each column is different according to Table 2，and which means that the influence of different factors on test data is different.The bigger range value of one factor shows that it has greater influence on tool wear.According to the experimental data of Table 2，the conclusions could be drawn:the influence of axial cutting depth on tool wear is the strongest，and the influence of radial cuttingwidth on tool wear is the weakest.

Table 2.The range analysis of toolwear

4.Construction of prediction model

The prediction model of tool wear as shown in Eq.1 could be constructed in the premise of considering the four factors of cutting speed，feed rate，axial cutting depth and radial cutting width.Themeaning of parameters in Eq.1 are as follows:M represents the tool wear quantity(Units:μm)，K represents comprehensive coefficient ofmilling conditions，v represents cutting linear velocity(Units:m/min)，fzrepresents feed rate per tool－tooth(Units:mm/tooth)，aprepresents axial cutting depth(Units:mm)，aerepresents radial cutting width(Units:mm).Since the equation as shown in Eq.1 is a typical nonlinear function，it is necessary to convert Eq.1 into linear function as shown in Eq.2.If y=Log M，C0=log(K)，x1=log v，x2=log fz，x3=log apand x4=log ae，then the complex linear equation as shown in Eq.2 could be converted into the equation as shown in Eq.3.Based on the experimental data as shown in Table 1，the corresponding coefficients in Eq.3 could be solved through multiple linear regression，and the value of corresponding coefficients in Eq.3 are as follows:C0=9.743 7，C1= －0.144 8，C2=3.883 5，C3=0.655 6，C4= － 0.179 3.Therefore，the model of tool wear for hardened steel SKD11 as shown in Eq.4 could be obtained.

In order to evaluate the fitting degree of the prediction model of toolwear，the significance testing for the regression equation as shown in Eq.4 should be carried out by using of statistic F.The law of significance testing of statistic F is as follows:n represents the number of experiments，m represents the number of variables，the significant level is set as 0. 05;if F ＜F0.05(m，n － m －1)，then the regression equation can not be trusted;if F ＞ F0.05(m，n －m －1)，then the regression equation can be trusted.In this paper，m is 4 and n is 9，the value of F0.05(4，4)can be obtained by consulting F distribution table，and it is 6.39.Based on the equation as shown in Eq.5，the F value of the prediction model could be obtained according to experiments data，and it is43.38.Because F ＞ F0.05(4，4)，so the predictionmodel of toolwear in this paper is very significant，and it can predict the tool wear accuracy in the machining process.The meaning of parameters in Eq.5 is as follows:SArepresents regression sum of squares，SErepresents the residual sum of squares.

5.Cutting parameters optim ization

5.1.Objective function

In order to improve themachining efficiency and reduce tool wear in milling process，the material removal rate is set as objective function f1(Y)and the toolwear quantity is set as objective function f2(Y).Based on function f1(Y)and function f2(Y)，one new objective function f(Y)could be constructed by using unified objective function method，and multiobject function can be converted to a single objective model［8］.If theweight coefficient of function f1(Y)isω1and the weight coefficient of function f2(Y)is ω2，then the unified objective function as shown in Eq.6 can be obtained.The material removal rate as shown in Eq.7 can be obtained according to cutting material volume per unit time.The meaning of parameters in Eq.7 is as follows:C representsmaterial removal rate(Units:mm3/min)，z represents the number of cutter tooth，D represents tool diameter.The objective function f(Y)as shown in Eq.6 can be converted into a new objective function as shown in Eq.8.On the basis of experience，the value ofω1is set as0.8 and the value ofω2is set as0.2 in Eq.8.

5.2.Constraint conditions

In order to ensure the rigidity of themilling cutters，the axial cutting depth has a certain range;due to the limit of the performance ofmilling cutters，the feed rate per tool－tooth must has a scope limitation;according to cutting experience，the radial cutting width generally should not exceed 85 percent of tool diameter.On the basis of the above analysis，the constraint conditions as shown in Table 3 could be obtained.

Table 3.The constraint conditions for Eq.8

5.3.Solution of optim ized cutting parameters

At present，there aremany optimizationmethods for solving constrained nonlinear minimization problems with multiple variables，such as sequential quadratic programming(SQP)，genetic algorithm(GA)，particle swarm optimization(PSO)，artificial neural nets(ANN)［9－10］.Genetic algorithm is a random algorithm，and it can not obtain certain solutions;particle swarm optimization is easy to fall into local solution，and most likely it can not obtain the optimal solution;artificial neural nets algorithm requires a large number of sample data，and its solution is not very reliable.Because the solution results based on SQP are very reliable and the programming of SQP is simpler than other optimization methods［11］，the SQP is adopted for solving the optimized cutting parameters in this paper.The programming of SQP has three steps and they are as follows:(1)update Hessian matrix of Lagrange function，(2)solve quadratic programming problem，(3)search target and calculate objective function.Based on MATLAB software，the computer program for solving theminimization problem is written，and the solution results could obtained as follows:Cutting velocity v=75 m/min;feed rate fz=0.014 mm/tooth;axial cutting depth ap=0.3 mm and radial cutting width ae=5 mm.Based on Eq.4 and Eq.7，the toolwear quantity and machining efficiency could be obtained by using the above optimized cutting parameters，and which are 63.7 μm and 334.4mm3/min.In order to better reflect the effectof optimization，comparison of parameters optimization about tool wear quantity and machining efficiency as shown in Table 4 are obtained in this paper.

Table 4.Com parison of parameters optim ization

6.Conclusion

Based on the range analysis of experimental data，the conclusions are drawn as follows:the strongest influence on toolwear is axial cutting depth，followed by feed rate，cutting velocity and radial cutting width.Therefore，in order to reduce toolwear，smaller axial cutting depth and feed rate should be adopted in a machining process.Based on cutting experiments，the prediction model of tool wear for SKD11 steel has been constructed by using of regression method.It has been confirmed that the prediction model as shown in Eq.4 has very high credibility through the significance testing of regression equation.A unified objective function could be constructed based on machining efficiency and tool wear quantity，and by which the optimized cutting parameters could be solved based on the SQP optimization method and MATLAB software.Optimized cutting parameters obtained in this paper could greatly improve the machining efficiency in the premise of ensuring smaller toolwear.

［1］ PAN Yongzhi，AIXing，WAN Yi.Development of an Off－ line Tool－life Prediction and Management System［J］.Journal of Manufacturing Technology＆ Machine Tool，2008，15(8):114 －117.

［2］ Alauddin M，Baradie M A.EI.，HashmiM SJ.Prediction of tool life in end milling by response surfacemethodology［J］.Journal of Materials Processing Technology，1997，71:456－465.

［3］ Tsai M K，Lee B Y，Yu S F.A predicted modeling of tool life of high－speed milling for SKD61 tool steel［J］.Intermational Journal of Advanced Manufacturing Technology，2005，26:711－717.

［4］ LIXuanqi，F(xiàn)ANWei，YANGGang.Experimental study on milling toolwear of titanium alloy［J］.Journal ofMECHANICAL ENGINEER，2008(5):56－57.

［5］ WANG Xiao－qin，AI Xing，ZHAO Jun.Research on Tool Life in Ti6Al4V Milling with Coated Carbides and Cutting Parameter Optimization［J］.JOURNAL OFWUHAN UNIVERSITY OF TECHNOLOGYl， 2008，30(10):109－112.

［6］ Jing Lulu，Shen Zhong，Chen Ming.Experiment on Surface Integrity of Milling Tool for Hardened Steel SKD11［J］.Journal of Transactions of Nanjing University of Aeronautics＆ Astronautics，2007，24(2):157－163.

［7］ ZHANGMianhao.Research on Cutting Parameters Optimization based on Tool Life［J］.Journal of NEW TECHNOLOGY ＆ NEW PROCESS，2011(9):70－73.

［8］ SHUIYongbo，DINGWeiping，YANG Mingliang.Multiple Objectives Optimization Design of Suspension Parameters of a Certain Car［J］.Journal of Machinery Design＆Manufacture，2013(7):56－59.

［9］ ZHANG Gang，ZHU Mingbo，CHEN Yu.3D Trajectory Optimization of the SAR Imaging Seeker Based on SQP［J］.Journal of COMPUTER ENGINEERING ＆ SCIENCE，2012，34(4):145－150.

［10］ WU Liang－h(huán)ong，WANG Yao－nan.Research on Differential Evolution Algorithm for MOPs［J］.Journal of Journal of Hunan University:Naturnal Science，2009，36(2):53－57.

［11］ MA Li.Mathematical Experiments and Construction［M］.Beijing:Tsinghua University Press，2010.

SKD11銑削刀具壽命試驗(yàn)研究及工藝參數(shù)優(yōu)化*

肖軍民?

中山職業(yè)技術(shù)學(xué)院機(jī)電工程學(xué)院，中山 528404

為提高SKD11模具鋼銑削刀具的壽命，對(duì)SKD11模具鋼進(jìn)行了刀具壽命銑削試驗(yàn)，基于極差方法分析了各工藝參數(shù)對(duì)刀具壽命的影響規(guī)律?；诘毒邏勖娤髟囼?yàn)，利用多元線性回歸方法，推導(dǎo)并求解出了SKD11模具鋼銑削刀具磨損的數(shù)學(xué)模型。利用最優(yōu)化設(shè)計(jì)方法和MATLAB優(yōu)化工具箱，以加工效率和刀具磨損為目標(biāo)函數(shù)，針對(duì)實(shí)際的銑削問題優(yōu)選了工藝參數(shù)。優(yōu)化的工藝參數(shù)能兼顧刀具壽命和加工效率，為加工企業(yè)降低綜合生產(chǎn)成本提供了重要的理論依據(jù)和案例參考。

刀具壽命;磨損;加工效率;數(shù)學(xué)模型;SKD11

TG 714;TG54

10.3969/j.issn.1001－3881.2014.18.022

2014－05－13