Selection of Mill Cutter and Cutting Parameters through an Expert System

Transcription

1 Selection of Mill Cutter and Cutting Parameter through an Expert Sytem L. Rubio and M. De la Sen Abtract Thi paper dicue the election of tool in milling operation. An expert ytem hinged on numerical method ha been developed to carry out thi reearch. The knowledge bae i given by limitation in proce variable, which let u define the allowable cutting parameter pace. The mentioned proce variable caue intabilitie due to tool-work-piece interaction, knowing a chatter vibration, and the power available in the pindle motor. Then, a tool cot model i contrived. It i ued to chooe the uitable cutting tool, among a known et of candidate available cutter. Once the cutting tool i elected, the cutting parameter are calculated. For thi purpoe, other two cot function are deigned, which are depended on the time and frequency domain repone propertie. An example i preented to illutrate the method. I. INTRODUCTION Machining, in particular milling operation, i a broad term ued to define the proce of removing material from a work-piece. Furthermore, the milling operation proce i required, nowaday, to increae it productivity, reducing cot and improving the final product []. Thi paper bring forward the concept of electing an appropriate mill cutter, among a known et of candidate cutter, and obtaining the adequate cutting parameter for milling operation through an expert ytem. There are everal veratile approache for tool and/or cutting parameter election baed on the deign of expert ytem on manufacturing environment. Wong and Hamouda [2] developed an on-line fuzzy expert ytem. The ytem input, the tool type, the work-piece material hardne and the depth of cut and control the cutting parameter at the machine, a output. Cemar Cakir et al. [3] explained an expert ytem baed on experience rule for die and mold operation. In that paper, the geometry and material of the work-piece, tool material and condition and operation type are conidered a input. Then, the ytem provide recommendation about tool type, tool pecification, work-holding method, type of milling operation, direction of feed and offet value. Vidal et al. [4] focued on the problem of chooing the manufacturing route in metal removal proce. They elect the cutting parameter by optimizing the cot of the operation taking into account everal factor, uch a, material, geometry, roughne, machine and tool. Carpenter and Maropoulu [5] deigned a ytem, which L. Rubio and M. De la Sen are with the Intituto de Invetigación y Dearrollo de Proceo, Facultad de Ciencia y Tecnología, Campu de Leioa, Univeridad del Paí Vaco, Apartado 644, Bilbao, Spain ( {webrurol,webdepam}@lg.ehu.e). provide reliable tool election and cutting data for a range of milling operation. The method employ rule baed deciion logic and multiple regreion technique for a wide range of material. Here, the developed expert ytem conit of the relative compliance between the tool and the work-piece and it i predicted with analytical method. Moreover, milling proce imulation have been developed in the time and frequency domain, which are, then ued in the expert ytem definition. Firtly, the knowledge bae i explained. Baically, it define the allowable cutting parameter, which are known a cutting parameter pace, for a given toolwork-piece configuration. It i baed on the chatter vibration avoidance, which limit the productivity of the proce, and on a pindle power limitation criterion. On the other hand, a novel tool cot function i deigned. It ub-optimize a combination of everal effect of interet, namely, the pindle power conumption, the material remove rate (MRR), a well a, a tability criterion againt poible perturbation in the pindle peed variable ( N ). The MRR i a parameter which meaure the proce effectivene. It i required to be a large a poible. But, if MRR increae beyond certain limit, chatter vibration are appreciated and the proce become untable [6]. Other variable which limit the proce effectivene i the power available in the pindle motor ( P t ) [7]. A third parameter, N, taking part into the cot function i conidered to enure a well-poed behavior of the ytem if a perturbation in the pindle peed happened. In concluion, the propoed cot function i a meaure of how the milling proce i being carried out at certain operation condition. The larger the cot function i, the wort operation will be. Thu, the cutter which minimize the deigned cot function i elected. Once, the cutting tool i elected, the cutting parameter are obtained for a given tool configuration. A econd cot function i deigned. It i compoed by the above mentioned cot function for the input cutting pace parameter and the elected tool give the programmed cutting parameter. Then, the expert ytem conider tool characteritic, related tool-work-piece material parameter and milling operation a input and output the elected tool among the candidate and robut programmed cutting parameter.

2 II. SYSTEM DESCRIPTION A model, which repreent the dynamic compliance between the tool and work-piece in milling procee, ha been developed. In thi cae, it i predicted with analytical method. The model aume the cutter to have two orthogonal degree of freedom and the workpiece to be rigid. The feed i along the x-axe (fig.). The milling cutter ha n t teeth, which are equally paced. The dynamic of the ytem i given by differential equation [8, 9]: Fig.. End part of the milling ytem: tool and work-piece. nt mx x+ cx x+ k x x = f x = 0 nt m y y+ c y y+ k y y = f y = 0 () t = f () t x () t = f () t y (,2) where m i, ci and ki are the ma, damping and tiffne of the tool, f x and f y are the component of the th cutting force that i applied by the tooth, which are obtained by proecting f into the two orthogonal axi. A imple model of the cutting force will be dicued here which expre the tangential cutting force to be proportional with the intantaneou chip thickne. Depite thi implicity, thi model capture the eence of the proce. Hence, ft = kt b h () 3 where k t i the pecific cutting force parameter, b i the axial depth of cut and h i the intantaneou chip thickne. In addition, the radial force may alo be expreed in term of the tangential force a, f r = kr ft ( 4 ) where kr i a proportional contant. Thi cutting force model ha been ued by everal author [6]. The mot critical variable in (3) i the chip thickne becaue it change not only with the geometry of cutting tool and cutting parameter, but alo with the uneven urface left by the previou pae of the cutting tool. Hence, after determining the chip thickne for an uncut freh urface, thi thickne mut be compared with the undulation left by the cutting tool during previou pae at the ame poition to obtain the intantaneou thickne of the material left to be removed. Thi proce i known a regenerative mechanim [6]. The chip thickne i meaured in the radial direction, with the coordinate tranformation, v = x in φ y coφ () 5 whereφ i the intantaneou angular immerion of tooth meaured clockwie from the normal Y axi (fig.). h ( φ ) [ φ + ( v v )] g( φ ) t o = in ( 6 ) where g( φ ) i a unit tep function which determine whether the tooth i in or out of cut, t i the feed rate per tooth, T i the tooth period and, if the pindle rotate N rad /, the immerion angle varie a at ( ) φ ( t) = N t, and φ ( t) = 0 if the -tooth i not engaged with the part [6]. th The 4 order Runge-Kutta method i employed to olve the differential equation () and (2) in the time domain [8, 9]. The tability lobe are obtained from the equation (3) and (4). Thi baic tudy ha been yet developed by the author in previou tudie, and there exit an extenive bibliographic to develop the ytem tability in the cutting parameter pace (ee for intance [, 6, 9]). In the next ection, ome mention to the mathematical formulae of the tability lobe will be made. The main purpoe of the preent paper i not to develop analytically the tability border line but to take it into account in the deign of the expert ytem. Therefore, the tability border line i uppoed known. For a good undertanding of the expert ytem, that will be preented in the ection 3, above mentioned reference can be ued. Figure 2 how the lobe char and the analytical time and frequency domain repone for a tool 2 ytem, which characteritic can be een in ection 5. The chatter tability lobe make up a pindle peed (frequency) dependent dividing line between table (down part line) and untable (up part line) depth of cut for a certain width of cut. The left place repone correpond to a table tate and the right place one correpond to untable tate. Stable tate correponded figure preent a delimit time repone, and the tooth paing frequency and it harmonic, frequency repone. Untable tate correponded figure preent a not delimit time repone, and the chatter frequency i appreciated.

3 Figure 2: The milling ytem repreentation, tability char, force time repone and force frequency repone. The expert ytem, which i explained in the next ección, i obtained from the analytical prediction of the tool-work-piece ytem behavior preented above.. III. EXPERT SYSTEM The main obective of the expert ytem i to obtain a mill cutter, among the available one, which have an operating point or adequate cutting parameter, with maximum productivity (MRR), robutne tability againt pindle peed perturbation and minimum power conumption. For thi purpoe, the allowable cutting pace parameter, pindle peed, feed rate and axial depth of cut for a contant radial depth of cut, are conidered. The regenerative chatter intability and the power available in the pindle motor are taken into account. Then, a novel cot function i chemed. It i inverely proportional to MRR and a parameter determinate a tability againt pindle peed perturbation and proportional to power conumption. Each term of the cot function ha a proportional factor to have term of approximately imilar magnitude. Alo, a weight factor which meaure the importance of each term i incorporated. The weighting factor are intended to be programmed by the machine operator. A. Milling proce determination and preliminary rule In order to evaluate the ytem performance, a uitable tool and performance indice are needed. Milling procee, baically, conit of two phae roughing and finihing the urface. The main difference between thee operation i to decide the mot appropriate performance index for a given tool. The quality and geometric profile of the cutting urface i of paramount importance in milling finihing operation, wherea roughing -milling conit on removing a large amount of material from a blank. Thi paper deal with roughing milling operation. The rate at which the material i removed i called material removing rate (MRR). Thi parameter meaure the productivity of machining procee. In milling operation, MRR i defined a the multiplication between axial and radial depth of cut, and feed per tooth. MRR upper limit i given by chatter vibration and power deliver by the pindle motor. For certain combination of cutting parameter, uch a pindle peed, axial depth of cut and feed per tooth, either chatter vibration are ened, or the power available by the pindle motor i inufficient. Then, thee parameter bound the roughing-milling productivity. For thoe reaon, the input cutting parameter pace i given by the cutting parameter a a firt approximation, below the line at the table tability lobe char while the power conumption i le than the power available by the pindle motor. But, due to uncertaintie in the model, the lobe are contructed, not by replacing pure imaginary root into the characteritic equation, but adding a poitive real number to them. Furthermore, to have a robut ytem, it ha been taken into account a confine in a programmed maximum depth of cut. Then, the following algorithmic methodologie are ued, which are called preliminary rule: Rule: Stability margin etting to enure that the ytem play in a table region, depite the ytem model uncertaintie. Rule.: For calculating ecure tability lobe char, a mall tability margin i elected, i.e, it i uppoed that the chatter vibration happen at δ + i ω intead of at i ω c. The reaon i that the tability border line i calculated from a linear approximation. Then, i ωc i replaced byδ + i ωc, δ > 0, when the tability border line i calculated. Thi rule i applied to the equation (3). Rule.2: For improving the robutne of the ytem, a margin at the final expreion for chatter free axial depth of cut ha been taken into account, equation (8), i.e, blim = α blim,0 < α <. Thi rule let a better control capacity in the pindle peed. On the other hand, a better MRR election i lot becaue of the above deign implifying proce. Rule2: For earching the allowable input pace parameter, the et of pindle peed, N, axial depth of cut, b and feed rate, t the following rule are applied. Rule2.: Calculate the boundary point, pindle peed and axial depth of cut pair, which compoe the line between table and untable zone, atifying Rule. Thi rule i obtained by plotting the tability lobe char, which give the line between table and untable zone Rule2.2: Calculate the admiible input pace, Q : = (N, b, t ). The boundarie pindle peed and axial c

4 depth of cut, give the maximum pindle peed and axial depth of cut pair without chatter vibration (rule 2.). The time domain imulation i ued to obtain the applied force by the milling machine. A it will be then een in the next ection, the pindle power i force-dependent, which i pindle peed, axial depth of cut and feed rate dependent. Then, for a given pindle motor power available, the admiible input cutting parameter pace i obtained. B. Tool election In thi ection, an approach for tool election i uggeted. For thi purpoe, a tool cot model function i deigned. The deigned tool cot model i ued to elect the appropriate tool between the candidate though the optimization Rule, explained below. Then, the tudy require a given et of candidate milling cutter. Each one i characterized by the following propertie: R = ω, ω, ξ, ξ, k, k, n, D, β where i ( nxi nyi xi yi xi yi ti i i ) ( xi ω yi ) W ( ξ xi, ξ yi ) ξ i the tool damping ratio, ( k xi k yi ) K ω, i the tool natural frequency,, i the tool tatic tiffne, n ti i the tool number of teeth, Di i the tool diameter and βi i the tool helix angle. R i T, i =,2,.., N, where N i the number of tool and T i the et of tool available to the deigner. W i the et of tool natural frequencie, conformed by ω, for each tool, ξ i the et of tool the pair ( nx ω ny ) damping ratio, conformed by the pair ( ξ, ) x ξ y for each tool and tool tatic tiffne i conformed by k, for each tool. ( ) x k y C. Tool cot model definition To carry out the election of a uitable tool, a novel tool cot function ha been conceived. The tool cot model for a ingle milling proce can be calculated uing the equation (20). C( Pt, MRR, N ; R, c, c2 ) = c NF Pt + NF NF (20) + c 2 + c 3 2 MRR 3 N 3 with c =, T i i= MRR = a b t, N q N b, t and ( ) Q R, where Pt = V f t ( ) n t = φ, take it definition given below,,. Standardizing factor, NF i, are defined a follow, NF = P tav, where PtAv i the power available in the pindle motor, NF 2 = MRRmax, where MRRmax i the maximum MRR with the chatter vibration and pindle power retriction calculated among all the candidate cutter and NF3 = N,max where N, max i the maximum meaured value of thi variable among the candidate cutter. The tool cot function i deigned to be MRR, power conumption, and a range againt poible perturbation in tool rotational motion, dependent and inverely proportional to MRR and a range againt poible perturbation and directly to power conumption. Thee parameter have the following definition: Material or Metal -Removing Rate ( MRR ) MRR = a b t, being a the radial depth of cut, the axial depth of cut and t the linear feed rate. The MRR i a parameter, which compare, the efficiency of the milling proce. A larger MRR improve the proce productivity. Cutting power draw from the pindle motor ( P t ) The cutting power, P t, drawn from the pindle motor i found from, n t Pt = V f t = ( ) φ (2) being V = π D N the cutting peed and N the pindle peed. The tangential cutting force i given by: ( φ ) K b h( φ ) ft = t (22) where b i the axial depth of cut, K t i the cutting force coefficient, which are material dependent and i h φ i the chip evaluated from experiment, and ( ) thickne variation, which i feed rate t (mm/rev-tooth) dependent. Spindle peed ecurity change ( N ) An additional term, pindle peed ecurity change, i added to the cot function model to be ure that chatter vibration are avoided. The pindle peed ecurity change, N, meaure the nearet pindle peed at which chatter vibration happen to the uppoed pindle peed it will be operated. Thi fact allow having an error margin due to poible perturbation in thi variable. To calculate analytically, N, the following algorithmic methodologie are carried out. They are divided in two cae: Cae I: k = 0, thi cae correpond to pair, pindle peed, axial depth of cut, ituated below the firt lobe of the tability char. Then, there i no lobe in the right part of the point a it can be hown in figure 3. Suppoe that ( N I, b I ) i the point which N ha to be calculated: a) If bmin, cri > b, N = N, min, cri N, I ). b) If bmin, cri < b, N = ab( N, cri ( bi ) N I ). b min, cri i the minimum value of the axial depth of cut correponding to the border line, N, min, cri i it b i the left- correponding pindle peed, N, cri ( I ) proection of the point ( I b I ) N, into the nearet lobe.

5 term enure that the cot function will be comparable among the different cutter. The, value are the weight of the cot function term. They c i, i =,2, 3 meaure the importance of the cot function term. The below optimization Rule 3 give a pattern to program the parameter c i. Fig. 3: Spindle peed ecurity change, ( N ), cae I. Cae II: k 0, in thi cae, the point,which N ha to be calculated, i ituated between two lobe in the table region. Suppoe that ( N II, b II ) i the mentioned point, then k uch that N, min, cri ( k) < N II < N,min, cri ( k + ), where k i the lobe number, k = 0,.. S, and S i the number of printed lobe, and N, min, cri ( k) i the pindle peed correponding to the axial depth of cut minimum value on the border line, bmin, cri ( k), for the k-lobe. Then: b k > b < b k a) If min, cri ( ) min, cri ( + ) ab N,min, cri ( k) N N = min ab N ( k + ) ( ), ( ),min, cri N b) If bmin, cri ( k) < b > bmin, cri ( k + ) ab( N, cri ( k) N ), N = min ab N ( k + ) N ( ), cri where N cri ( k) ( N II, b II ) into the k-lobe, and ( k ), i the left-proection of the point N, cri + i the right-proection into the k+-lobe. The cae under conideration i graphically repreented in figure 4. Note that, the expert ytem doe not take into account the proce damping non-linearity, then, other cae to calculate N have not been taken into conideration ince bmin ( k) = bmin ( k +, ) k. Furthermore, the other poible cae in the N calculation are not conidered, ince they are untable tate cae. On the other hand, the calculated N have been done taking into account Rule. and.2. Standardization factor, NF, are alo added to the cot i function to have term with the ame magnitude. Moreover, they make to have a relative term between all the candidate cutter involved. On the other hand, thee Fig. 4: Spindle peed ecurity change, ( N ), general cae. D. Optimization rule The above defined tool cot function i ued to elect the appropriate tool and cutting parameter, through the following optimization rule. Rule 3: Weight factor election The weight factor are intended to be programmed by the machine operator. An extended explanation of their meaning and their adequate election i given in thi ection To elect uitable value of c i, i =,..,3, their meaning ha to be perceived. The c -value meaure the importance of the pindle peed conumption. A larger c parameter i the more important to the pindle power conumption in the cot model function. The c2 meaure the machine productivity if the c 2 i near to one high productivity i required and if it i near to zero the productivity ha no importance. The ame reaoning i applied to the c 3, which meaure the tability againt poible perturbation in the pindle peed variable. It ha to be taken into account that the expert ytem, enure that the pindle power conumption i alway going to be maller than the power available in the pindle motor, through Rule. Alo, that the cutting parameter pace ha no ened chatter vibration through Rule 2. Then, a poible criterion leading to a proce with acceptable productivity, which i the main obective of the milling procee, c 2 about 0.75, and the other two contant will add 0.25, uitable value are c = 0. and c 2 = 0.5. Rule 4: Tool election criterion A imple tool election criterion for cutter election ha been developed. For a given value of c, c2, c3, and a

6 given tool characteritic, the cot function value i obtained for all the admiible input cutting parameter pace. The minimum value of the cot function i tored. The procedure i repeated for all the available cutter. Comparing the minimum value of the cot function for all available or candidate cutter, the correponding cutter to the minimum value of the minimum value of the cot function i the elected tool. The election criterion i, mathematically, expreed a: Compute, C ( P ( q ), MRR ( q ), N ( q ); R, c c ) t i 2 ; (23) for each R i T, i N, and N i the et of candidate tool and q ( N, b, t ) = {,.., } N p N p, where i a dicrete ub-pace of the cutting parameter pace where the cot function (20) i calculated. For obtaining the elected tool, ST, compute { C( P ( q ), MRR( q ), N ( q ); R, c c )} ST = arg min t i, 2 i N (24) with ST T, obtaining the appropriate tool according to the criterion. Following the rule, the expert ytem provide an appropriate cutter among the candidate. Note that the obective of the expert ytem are to obtain a tool which ha an operating point or adequate cutting parameter where the MRR will be higher than the other available tool, with a precribed tability robutne and without conumption more power than the available in the pindle motor. Hence, the tool cot model i deigned o a to minimize it. Furthermore, the power conumption will be minimum, and the MRR and tability robutne will be maximum, for a given value of, 2 c c, and c 3. The c i, i =,2, 3, are deigned by the machine operator. Rule 5: Cutting parameter election To obtain the cutting parameter a imple criterion, which conit of calculate the cutting parameter which correpond to the minimum value of the cot function above defined for a certain value of c, c2, c3. But, here, a new approach thought an auxiliary cot function i going to be applied. In thi cae, once the tool ha been elected, another novel and complete cot function i deigned in order to obtain the bet cutting parameter. It i compoed by the above defined cot function and other two, which are time and frequency domain repone related. Then, the firt new cot function tudie the temporal behavior of the input cutting parameter, and the econd one it frequency repone. The reultant cot function i ued to obtain the cutting parameter for the elected tool. E. Temporal repone cot model definition The temporal repone cot model i defined a the t maximum overhot ( ) p M and the ettling time ( ) dependent function. Thoe characteritic are typical in the tudy of the time domain repone of a ytem. Ct ( T Q, c c ) t,, tool t 2t = ct + c2t t,max M,max where t, max and M, max are the maximum ettling time and maximum overhot between the allowable input cutting pace parameter, Ttool i the elected tool according with the previou ection and 2 i= c =, c 0. it it a) Frequency repone cot model definition The frequency repone cot model i dependent on the relation between the firt and the econd harmonic frequencie through the function, R 2 h, and the relation between the firt harmonic frequency and the chatter frequency,. That i: C f R ch, 2 2, R h R h tool f 2 f = c f + c2 f R2h max R ch max ( T Q, c c ) where R 2h max and R2ch max are the maximum of thoe parameter between the allowable input pace cutting parameter, T i the electing tool according the tool previou ection, and c =, c 0. 2 if i= b) Total cot- function model The total cot function i, then, compoed by the defined above three cot function, the tool cot model, the temporal repone cot model and the frequency repone cot model. For thi cae, the cutting parameter are calculated following the algorithm: Creul tan t ( Ttool, Q, cr, c2r, c3r ) = cr C( Ttool, Q, c, c2, c3 ) + + c C T, Q, c, c + c C T, Q, c, c 2r t 3 i= ( ) ( ) tool t 2t 3r where c ir =, c ir 0, and Ttool f if tool Compute, reultant ( 2 3 ) M f 2 f i the elected tool. C T, Q, c, c, c ; q Q, tool r r r tool tool atifying the rule 2.2. Compute, ** q = arg min( Creul tan t ( Ttool, q, cr, c2r, c3r )) and q obtain the input cutting parameter for the elected tool. Rule6: Reultant cot function weight factor election.

7 To elect the value of cir it ha been taken into account the fact that the mot important term in Creul tan t i C by practical reaon. It i becaue C t and C r are corrected term. For thi reaon, it hould be taken the c r about 0.8, and c 2 r and c 3 r about 0. each one. The time and frequency domain weighting factor, c t, c2t, c f, c2 f are aumed to have the ame value or be very imilar. The analytical tet for mill cutter election wa conducted uing pindle peed with increment of 000 rpm, axial cutting depth tarted with it minimum value in the tability border line divided by ten, and it i increaed in tep of thi ame ize, for a given pindle peed. The operation contraint on the maximum feed per tooth i mm and the tep integration i elected to be The pindle power availability i w. The reultant tool i that leading to the minimum tool cot function value. In figure 6, it i hown the value of tool cot function a c -parameter varie, the c 3 -value ha been taken a a contant c 3 = and the c 2 follow the rule c 2 = c c 2. Finally, figure 5 how a cheme of the expert ytem. The developed expert ytem take the α and δ contant, the tool modal parameter uch a it natural frequency, damping ratio, tool tatic tiffne, the number of teeth, the radiu of the tool, the helix angle, and the cutting contant for the work material and cutter (tool characteritic), the pindle power available and the cot function weight factor, a input and output the appropriate tool among the candidate and robut programmed cutting parameter. IV. EXAMPLE Fig. 5: Schematic expert ytem repreentation. For the validation of thi method, the above tudy ha been applied for two practical traight cutter and a fullimmerion up-milling operation. The example conider the tool to have the following characteritic, according with the ection III.B notation, R = ( 603,666,3.9,3.5,5.59,5.75,3,30,0), and R 2 = ( ,9.65,.39,.38,0.879,0.97,2,2.7,0). The natural frequency i meaured in hertz, the tool damping i in %, the tool tiffne i in KN mm and the diameter of the tool i in mm. The work-piece i a rigid aluminum block whoe pecific cutting energy i 2 choen to be K,2 = 600KN mm and the proportionally factor i taken to be k r = 0. 3, for the tool one, and k r2 = 0.07 for the other one. Other deign expert ytem parameter are, the tability margin factor, δ = 0.05 and the tability margin factor for the axial depth of cut, α = Fig. 6: Minimum tool cot function v. c varie, with c 3 = Thi tudy ha been performed to illutrate the influence of the c i parameter in the tool cot function. It i oberved the tool R ha a better behavior repect to the tool R2 for all poible value of c and c 2, with c 3 = Analye with other value of c, c 2 and c3 have been carried out and the reult are imilar, and the tool R ha a better behavior. Then, a more general analyi how in figure 7, in which the minimum value of the tool cot function for all poible combination of c, c 2, c 3, with the retriction c+ c2 + c3 = i diplayed. The analyi ha revealed that the firt tool ha a better behavior than the econd one for all combination of the ci parameter. Thu the output of the expert ytem i the firt tool. For the cutting parameter election, two tep have been done. Firt, the cutting parameter correponding to the minimum of the tool cot function for the elected tool for value of c = 0. 2, c 2 = , c 3 = i obtained. * Thee value are = ( 5800,0.4924,0.2722) q.

8 manufactured for each tool in order to minimize the change of tool. Finally, apart from being a cheep method, the expert ytem could be eaily ued by an inexpert human operator. Fig. 7: Minimum tool cot function veru c, c2, c3 varie It can be a well-done firt approximation. For a more appropriate olution, taking into account the time and frequency domain ytem repone, the total cot function, C reult ha been calculated for the allowable cutting pace parameter. The minimum value i aved for c t = c2 t = 0. 5, c f = c2 f = 0. 5, and c r = 0. 8, c 2 r = 0., c 3 r = 0. the reulted programmed cutting ** parameter are = ( 5680,0.457,0.265) q. Fig. 8: Situation of the point q** in the tability diagram and tool diplacement and power conumption time domain repone for the elected tool. Figure 8 how the ituation for the tability lobe of the programmed point q **, the tool diplacement and the power conumption. It i oberved that the point i robutly table and the power conumption i le than the power availability in the pindle motor, while the MRR meaure become acceptable. Thi method can alo be applied to any number of elected tool generating in automatic tak the bet one to be ued in the ytem. Moreover, the method can be ued to chedule the relative compliance between the available tool and the ued work-piece material. On the other hand, the expert ytem can be ued to optimize the manufacturing proce, in the ene of planning the adequate equence of work-piece to be V. CONCLUSION An efficient approach for mill cutter election ha been developed through the deign of an expert ytem. Such an expert ytem i intructed with the characteritic of the available candidate tool, a well a with the tability margin and contrain of operation, uch a, power availability and robut. Furthermore, a tool cot model function, built from the expert ytem preliminary rule, i propoed to evaluate the poible achievable performance by each candidate tool in the milling proce. Thi performance index i then ued to elect an appropriate tool and cutting parameter for the operation which lead to the maximum productivity, while repecting tool tability and power conumption margin though optimization rule. A imulation example, which how the behavior of the ytem, i preented. ACKNOWLEDGMENT The Author are very grateful to MCYT by it partial upport through grant and to the UPV/EHU through Proect 9/UPV 00I06.I /2003. REFERENCES [] S. Y. Liang, R. L. Hecker and R. G: Lander, Machining Proce Monitoring and Control: The State of the Art, in Journal of Manufacturing Science and Engineering, vol. 26, 2004, pp [2] S. V. Wong and A. M. S. Hamouda, The development of an online knowledge-baed expert ytem for machinability data election, Knowledge-Baed Sytem, Vol.6, pp , [3] M. C. Cakir, O. Irfan and K. Cavdar, An expert ytem for die and mold making operation, Robotic and Computer-Integrated Manufacturing, Vol.2, pp , [4] A. Vidal, M. Alberti, J. Ciurana and M. Caadeú, A deciion upport ytem for optimizing the election of parameter when planning milling operation, International Journal of Machine Tool and Manufacture, Vol.45, pp , [5] I. D. Carpenter and P. G. Maropoulo, A flexible tool election deciion upport ytem for milling operation, Journal of Material Proceing Technology, Vol.07, pp , [6] Y. Altinta, Manufacturing Automation, Cambridge Univerity Pre, [7] O. Maeda, Y. Cao and Y. Altinta, Expert pindle deign ytem, International Journal of Machine Tool and Manufacture, Vol.45, pp , [8] H. Li and X. Li, Modeling and imulation of chatter in milling uing a predictive force model, International Journal of Machine Tool and Manufacture, Vol.40, pp , [9] L.Rubio and M. De la Sen, Analytical procedure for chatter in milling, Redicover 2004, June 4-6, 2004, Cavtat, Croatia.