OPTIMAL CONTROL OF CNC CUTTING PROCESS

jixiegongcheng990104CHINESE OURANLOF田ChinanfoMECHANICAL科技期刊。ENGINEERINGWANFANG DATAV olume 12 Number 11999OPTIMAL C ONTROL OFCNC CUTTING PROCESS①Wang QiyiGao GuoliW ang RendeNortheastern U niversityAbstract The itelligent optimizing method of cutting parameters and thecutting stable districts searching method are set up. The cutting parameters of eachcutting pass could be optimized automatically, the cutting chatter is predictedthrough setting up the dynamic cutting force AR(2) model on-line, the spindlerotation speed is adjusted according to the predicting results so as to ensurethecutting system work in stable district.Key words: Optimal control Cutting parameters optimizing Stalble districtssearching0 INTRODUCTIONWith the rapid development of electronic technology and computer technology, theintelligence of metal cutting system is becoming higher and higher. In spite of these, theexperience selecting method of cutting parameters and cutting chatter exist in the cuttingprocedure extensively[ 1~5] , which reduce the working efficiency and impair the workingquality, sometimes even cause seriously economical losts. In order to make the most of the highefficiency and the great cutting capacity of the CNC cutting system, optimizing the cuttingparameters, monitoring the cutting process and adjusting the cutting parameters on-line,restraining the cutting chatter, improving the stability of C NC cutting system have been the mainproblems which can't be dodged in modern manufacturing industry[4~5] . In this paper, theintelligent optimizing method of cutting parameters and thecutting stabledistricts searchingmethod are set up, through which the high productivity and the low production costscan beobtained at the same time.1 INTELLIGENT OPTIMIZING METHOD OFCUTTIN中国煤化王RS"MYHCNMH GIt is impossible that each cutting tool is reliable, assume that the cutting tool is changed.fle///E/ Vqkjxgcxb- ejgxg9/jxg991990104.htm (第1/ 7页) 2010-3-23 1:46.:34jixiegongcheng990104when the cutting time is tr, and thereliability of the cutting tool isr. Each unordinary damageofcutting tool beforetp will resultsin a wasteworkpiece, and the cutting tool should bemust bereplaced at once. It is possible that the cutting tool should be damaged at any time of the cuttingprocess. In order to simplify the analyzing process, suppose that the damage of the cutting tool isfound after the cutting process, and there is only one cutting pass in the cutting process. Thecutting time and cutting costs of each qualified workpiececan be expressed as[3]Cc=C/{t,g+t,) [ 1+(1-r)/P ] +(Crt,a+Ct(2-r)/P+CMU1-r)/P+Ctp[ 1+(1-)/P ](1)t=(to+t,) [ 1+(-)/P ] +t,a(2-)/P+tp[1+(1-)/P]where C- -C osts of aqualified workpiecet一-C utting time of a qualified workpieceC- - -Running costs of unit timeP=t/tp .tp-- -Time of one cutting pass .tp=π DL/( 100v0)(on normal cutting condition,tp tp) .D--Diameter of theworkpieceL一 -Length of the workpieceV--C utting speed-Feeding speedCw-- =C osts of thesemifinished workpieceC一- C osts of the cutting toolt,一-Time of install and remove theworkpiecet,g -Time of feed and quit the cutting toolt a- -Time of change and adjust the cutting toolNeglected the high range infinity small items from Eq.( 1),the optimizing object function ofone cutting pass can be expressed asf(Cc,t)=A0+A1tp/t+tp(2)Where A0=t,q+t,rA1=(,q+t,)(1-n)+t,a(2-r)+K [ C(2-n)+CW(1-r) ]/Cr中国煤化工MHCNMH GIn Eq.(2), when K=0, the optimizing object is cutting eficiency, when K=1, the optimizing.fle///E/ Vqkjxgcxb- ejgxg9/jxg991990104.htm (第2/ 7页) 2010-3-23 1:46.:34jixiegngcheng9909104object is cutting costs, when 0Z , the optimizing resultsmust be adjusted, and itcan be defined that the optimal cutting passes are N or N-1. The cutting parameters whichneeded to be optimized areap1na2... ,api;V1,V2, .... , V;,fr,f2, .. , f(i=N or N- 1),then thefinal optimizing object of multi-cutting pass can be expressed asf(Cct)=f(Cct)+f2(C+t)+... +f(Cc+t+... +f(Cot)(4)2 PREDICTING METHOD OF CUTTING CHATTERThe AR(2) model of the dynamic cutting forcecan be expressed asφ_xx中,1Xt-1-Y 2Xt-2=ε t(5)where Xt, Xt-1 , Xt2-- -System outputs中中-AR(2) model cofficients of dynamic cutting force-Fitting residualThe general resolution of Eq.(5) can be expressed as中国煤化工r, = A1+ A2λ2+ 2三(型+型”)。)er-sMHCNM HGsm0\ λ1- λ2(6).fle///E/ Vqkjxgcxb- ejgxg9/jxg991990104.htm (第3/ 7页) 2010-3-23 1:46.:34jixiegngcheng990104whereh1,2=(中+√幅+ 4幢>)/2Because the dynamic force is continues and the damping ratio of the cutting system is farless than 1, so the scopeof中1 and中2 can be expressed as0<ψ2<1 .φ→中x<1(7)The cutting chatter can be predicted according to Eq.(7).3 CUTTING STABLE DISTRICTS SEARCHING METHODThe nonlinear equation of cutting process can be expressed as[6]x(t)+2ai(t)+ w2x(t)=0a=[hw2+ ki bNw2 + 3k1bc2NA2w(p2 - 1+ 2M)/4]/(2wk)(8)w2 = w2[1 + 3β2A2/4+ k;bM/k + 3k[bczA2M(μ2-1 + 2M)/(4k)]where a 一.System decay coefficientw eq--System equivalent vibration frequencyh-- System damping constantW n-- -Systemnatural frequency-C utting stiffness-C utting widthN=μ sinw t_Overlapping coefficientt- Cutting time between two continuecuttingC2一-Nonlinear coefficient of cutting forceA-- -V ibration amplitudeM=1-μ coswt-Systemvibration frequencyk一System stiffnessβ 2- System nonlinear coefficientFig.1 is thevarying curve of the system critical cutting width bc with the spindlespeed, the中国煤化工lowest points of the curve is the absolutelimited cutting width bp. In FiE(ni;NiHCNMHG+1 are the ith and the i+ 1th critical spindlespeed), use O n as the searching scope, the spindlespeed in the stable district can be achieved. O n can be expressed as。fle//E/ Vqkjxgcxb- e/gxg9/jxg9901/990104.htm (第4/ 7页) 2010-3-23 1:46:34jixiegongcheng99010460wimπi=0,1,2, .On=n:-”"+1F (;2+ i)x2 + (2i + 1FarcsG + rcc(9)G=[(1+3c2A2/2)-/(1+3c2A2/2)- 18(c2A*p)2 ]/(6czA2)where w lim--C ritical vibration frequency↓1.辛1.21.An0.wwA350450550650950- -Spindle speed n/《r●min~")Fig.1 V anying curve of the system citical cutting width with the spindle speedThrough analyzing we can obtain that when the searching step isO n/5, the ratio that thesystem can obtain the stable district is 80 percent and through five times searching the system canreach thestable district. W hen the searching step isequal to O n/15, the ratio that the system canobtain the stable district is 93 percent, and through thirty times searching the stable district can beattained. The time of each searching process is 30 ms. H ence the total searching time cost on thirtysearching process is0.9s, and the growing time of cutting chatteris1s~ 2s, so thestable districtcan be obtained before thecutting chatter occurs. H ence△n/5 is used as the biggest searchingstep and O n/15 is used as the least searching step.In the cutting process, the monitoring systemwill sample the cutting force successivly,according to the sampling data, define if the system works in the stable district. If the system worksin the stable district, go on monitoring the dynamic cutting force. If thesystemworksin theunstable district, useO n/5j(j=1,2,3) as thesearching step length, search the spindle speed which isin the stalble district. If the spindle speed in the stable district can't be found, increasejtoj+1, goon searching thestable district.中国煤化工4 EXPERIMENTSAND DISC USSIONMHCNM HGThe experiment results arein T ablewherey is the ratio of thevibration amplitude before.。fle///E/ Vqkjxgcxb- ejgxg9/jxg991990104.htm (第5/ 7页) 2010-3-23 1:46.:34jixiegngcheng9909104and after cutting stable districts searching control.Table Results of cutting experiment| Beginingspindle speed Feeding speed Cutting depth Ratio of the vibration amplitudenp/(rmin-1)f/(mmir1)ap/mmY5000.0816.46005.17004.9Fig.2 is thevarying curve of the spindle speed. At first thesystemwas stable, after3s~ 4s, thecutting chatter was predicted, the control system adjusted the spindlespeed automatically,searching the stable district, when the searching step length wasO n/5, thesystemcouldn' tfindthe spindle speed which was in the stable district. SeeAB in Fig.2, then, thesearching step lengthwas decreased to△n/10, the spindle speed which was in the stable district was obtained, see BCin Fig.2.: 540-上520-一Cg 500-480-分460182430一Time t/sFig.2 Spindle speed varying curve中国煤化工MHCNM HG.fle///E/ Vqkjxgcxb- ejgxg9/jxg991990104.htm (第6/ 7页) 2010-3-23 1:46.:34jixiegngcheng99091045 CONCLUSIONS(1) Throughcutting parameters itelligent optimizing method, the higher cutting eficiencyand lower cutting costs can be obtained. For multi-cutting pass, the optimal cutting pass andoptimal cutting parameters of each cutting pass can be achieved through itelligent optimizingmethod.(2) Thestability of cutting process can be expressed through the cofficients of dynamiccutting forceAR(2) model, according to these coefficients the cutting chatter can be predictedprecisely. The stable districts searching method can assure that the cutting systemwork in thestable district.①This project is supported by National Natural Science Foundation of China. Manuscriptreceived on March 18, 1998References1 H induja. C alculation of optimum cutting condition for turning operations. ProC. Instn.Mech. Engrs., 1985, 199(B2) : 81~ 922 ArsecularatneA. Optimum cutting condition for turned components. Proc. Instn. Mech.Engrs, 1992, 206(B2) : 15~ 313李兆前,邓建新,田志仁.基于刀具可靠性的切削用量优化.机械工程学报, 1995 ,31(6) : 6~ 104于骏一,韩相吉，吴博达.变速切削的研究.机械工程学报, 1988, 24(4) : 56~ 625 Rahman. In- process detection of chatter threshold. Trans. ASME., 1988,110(2) : 44~ 506高国利,王启义.简化非线性切削颤振数学模型.东北大学学报(自然科学版) , 1995 ,16(2) : 190~ 193revised manuscript September 9, 1998中国煤化工MHCNM HG.fle///E Vqkjxgcxb- ejgxg9/jxg991990104.htm (第7/ 7页) 2010-3-23 1:46.:34