© Strojni{ki vestnik 50(2004)5,252-266 © Journal of Mechanical Engineering 50(2004)5,252-266 ISSN 0039-2480 ISSN 0039-2480 UDK 621.9.01:621.941 UDC 621.9.01:621.941 Izvirni znanstveni ~lanek (1.01) Original scientific paper (1.01) Dolo~evanje zna~ilnih tehnolo{kih in gospodarskih parametrov med postopkom odrezovanja A Determination of the Characteristic Technological and Economic Parameters during Metal Cutting Uro{ @uperl - Franci ^u{ V prispevku je predlagan nov nedeterministični optimizacijski postopek za zahtevno optimizacijo rezalnih parametrov pri odrezovanju. Ta postopek uporablja umetne nevronske mreže (ANN) za reševanje problema optimiranja rezalnih pogojev. Predlagan postopek temelji na kriteriju največje stopnje proizvodnje in vključuje štiri tehnološke omejitve. Z izbiro optimalnih rezalnih parametrov je mogoče doseči ugodno razmerje med nizkimi obdelovalnimi stroški in visoko produktivnostjo ob upoštevanju podanih omejitev postopka rezanja. Eksperimentalni rezultati kažejo, da je predlagani algoritem pri reševanju nelinearnih optimizacijskih problemov s postavljenimi omejitvami učinkovit in ga je mogoče vključiti v inteligentne obdelovalne sisteme. Najprej je oblikovan problem določitve optimalnih parametrov odrezovanja, kot večciljni optimizacijski problem. Nato so predlagane nevronske mreže za predstavitev proizvajalčevih prednostnih struktur. Za demonstracijo zmogljivosti predlaganega postopka je nadrobno obravnavan nazoren primer. © 2004 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: odrezovanje, pogoji rezanja, struženje, optimiranje, postopki nedeterministični) A new non-deterministic optimization approach to the complex optimization of cutting parameters during machining is proposed. It uses artificial neural networks to solve the cutting-conditions optimization problem. The developed approach is based on the “maximum production rate criterion” and incorporates four technological constraints. By selecting the optimum cutting conditions it is possible to reach a favourable ratio between low machining costs and high productivity, taking into account the given limitation of the cutting process. First, the problem of determining the optimum machining parameters is formulated as a multiple-objective optimization problem. Then, neural networks are proposed to represent manufacturers’ preference structures. The experimental results show that the proposed algorithm for solving the non-linear-constrained optimization problems is efficient and can be integrated into intelligent manufacturing systems. To demonstrate the performance of the proposed approach, an illustrative example is discussed in detail. © 2004 Journal of Mechanical Engineering. All rights reserved. (Keywords: machining, cutting parameters, turning, nondeterministic optimization) 0 UVOD Inteligentna proizvodnja dosega znatne denarne in časovne prihranke, če vključuje učinkovito avtomatično načrtovanje postopka. Načrtovanje postopka obsega določitev primernih strojev, odrezovalnih orodij in odrezovalnih parametrov pri določenih pogojih rezanja za vsako opravilo na danem obdelovancu. Optimalna izbira rezalnih pogojev pomembno prispeva k povečanju produktivnosti in zmanjšanju stroškov, zato je največji del pozornosti v tem prispevku posvečen prav temu problemu. Problem gospodarnosti 0 INTRODUCTION Intelligent manufacturing achieves substan-tial savings in terms of money and time if it integrates an efficient automated process-planning. Process planning involves a determination of the appropriate machines, the tools for machining parts and the machining parameters under certain cutting conditions for each operation of a given machined part. The optimum selection of the cutting conditions contributes significantly to an increase in productivity and a reduction of costs. For this reason a lot of attention is paid to this problem in this contribution. The machining-economics problem VBgfFMK stran 252 @uperl U., ^u{ F.: Dolo~evanje karakteristi~nih tehnolo{kih - A Detremination of Characteristic obdelave vključuje določitev karakterističnih parametrov postopka, in sicer običajno hitrosti rezanja, stopnje podajanja in globine rezanja, z namenom optimirati ciljno funkcijo. Vključene ciljne funkcije, s katerimi merimo optimalnost rezalnih pogojev, so: (1) najmanjši stroški na enoto, (2) največja stopnja proizvodnje, (3) utežna kombinacija večciljnih funkcij. Rezalne omejitve, ki bi jih morali upoštevati pri gospodarnosti obdelave vključujejo: omejitev obstojnosti, rezalne sile, moči, temperature odrezka in omejitev hrapavosti površine. Običajno so problem gospodarnosti obdelave reševali z uporabo optimizacijskih algoritmov, ki vsebujejo geometrično in stohastično programiranje [1], diferencialni račun [2], linearno programiranje [2] in računalniške simulacije [3]. Ti algoritmi so bili razviti ob upoštevanju samo enega cilja, to je npr. zmanjševanje stroškov, povečanje dobička, itn. Medtem ko večina dosedanjih raziskav temelji na enovariantni optimizaciji, obstaja nekaj uspelih poskusov tudi pri večvariantni optimizaciji. Philipson in Ravidran [2] uporabita ciljno programiranje za optimiranje postopka obdelave, Ghiassi [4] uporabi več ciljne tehnike linearnega programiranja in interaktivne tehnike. Raznolikost izdelkov in negotovost na tržišču povzročata, da so interaktivne metode načrtovanja postopka obdelave neučinkovite zaradi močnih in pogostih interakcij z izdelovalci pri načrtovanju postopkov obdelave. Bolj zaželena je metoda na podlagi prednostnega modela, npr. večatributna vrednostna funkcija, ki predstavlja izdelovalčevo celovito prednost. Optimiranje rezalnih parametrov je nelinearna optimizacija z omejitvami, zato je težko rešiti ta problem z nedeterminističnimi algoritmi. Zato so bile nedavno uporabljene nedeterministične tehnike reševanja različnih tipov optimizacijskih problemov pri odrezovanju. Lokalne iskalne tehnike vključujejo simulacijsko ohlajanje (SA) [5], genetske algoritme (GA) [6], algoritma UNM in PSO [7]. Nov postopek, ki omogoča učinkovito in hitro izbiro optimalnih rezalnih pogojev brez kršenja postavljenih rezalnih omejitev so umetne nevronske mreže (UNM - ANN). Algoritem deluje na podlagi usmerjenih in žarkovnih mrež ob hkratni uporabi novih sodobnih algoritmov učenja, ki se avtomatično prilagajajo trenutnim razmeram med postopkom učenja. Cilj raziskave je prikazati potencial nevronskih mrež pri optimiranju postopka odrezovanja. Gibalo študije je tudi predstaviti proizvajalčeve prednostne strukture z uporabo UNM. Glavni cilj prispevka je določiti takšne optimalne rezalne pogoje (rezalno hitrost, podajanje in globino reza), ki čim bolj povečajo obseg proizvodnje, zmanjšajo obdelovalne stroške in izboljšajo kakovost izdelka. consists of determining the characteristic process parameters, usually the cutting speed, the feed rate and the depth of cut, in order to optimize an objective func-tion. The included objective functions for measuring the optimality of the machining conditions are: (1) minimum unit-production cost, (2) maximum production rate, (3) maximum production rate and (4) a weighted combi-nation of several objective functions. The cutting con-straints that should be considered in machining eco-nomics include the following: tool-life constraint, cut-ting-force constraint, power, chip-tool interface-tempera-ture constraint, surface-finish constraint. Usually, the machining-economics problem has been solved using optimization algorithms, which include geometric and stochastic programming [1], differential calculus [2], linear programming [2], and computer simulating [3]. These algorithms were de-veloped by considering only a single objective, such as minimization of cost or maximization of profit, etc. While most of the research undertaken so far has been based on single-objective optimization, there have been some successful attempts at multi-objective optimi-zation. Philipson and Ravidran [2] apply goal-programming techniques for machining-process optimizations, Ghiassi [4] applies multi-objective linear-programming tech-niques and interactive techniques. The diversity of prod-uct mix and the uncertainty of market value make interactive approaches to machining-process planning inefficient owing to the extensive and frequent interactions with manu-facturers for planning the machining process. A global approach based on a preference model, such as a multiattribute value function that represents a manufacturer’s overall preference, is more desirable. The optimization of machining parameters is a non-linear optimization with constraints, so it is dif-ficult for non-deterministic optimization algorithms to solve this problem. Consequently, non-deterministic techniques have recently been applied to solve vari-ous types of optimization problems in machining. Lo-cal search techniques include the simulated annealing (SA) algorithm [5], the genetic algorithm (GA) approach [6], the ANN approach and the PSO algorithm [7]. The new approach, which ensures efficient and fast selection of the optimum cutting conditions, without violating any imposed cutting constraints, is the artificial neural network (ANN). The algorithm works on the basis of feedforward and radial basis networks with the simultaneous use of a new, advanced learning algorithm, which automatically adapts to cur-rent conditions during the training process. The purpose of this study is to demonstrate the potential of neural networks for machining-process opti-mization. The motivation of this study is also to represent the manufacturer ’s preference structures using ANNs. The main objective of the paper is to determine the optimal machining parameters (cutting speed, feedrate, depth of cut) that maximize the extent of production, reduce the manufacturing costs and improve the product quality. | lgfinHi(s)bJ][M]lfi[j;?n 04-5_____ stran 253 I^BSSIfTMlGC @uperl U., ^u{ F.: Dolo~evanje karakteristi~nih tehnolo{kih - A Detremination of Characteristic Prispevek je oblikovan takole. V poglavju 1 je oblikovano opravilo struženja kot večciljni optimizacijski problem s tremi neprimerljivimi in nasprotujočimi si cilji. V poglavju 1 je predlagana nevronska mreža, da pridemo do izdelovalčeve posredne večatributne vrednostne funkcije. Nato je opisan nevronski algoritem za optimiranje rezalnih parametrov. V poglavju 4 so obravnavani rezultati izračunov, ki kažejo razlike med različnimi metodami. 1 TEORETIČNI POSTOPEK K REŠEVANJA PROBLEMA OPTIMIRANJA Naloga optimizacije je določiti takšen niz rezalnih pogojev v (rezalna hitrost), f (podajanje), a (globina rezanja), ki zadosti omejitvenim enačbam in uravnoteži nasprotujoče si ciljne dejavnike. Opravilo struženja je oblikovano kot večvariantni optimizacijski problem z omejitvenimi neenačbami ter s tremi nasprotujočimi si cilji (stopnja proizvodnje, stroški opravila, kakovost obdelave). Rezalni parametri morajo biti tako izbrani, da je stroj čim bolj izkoriščen in obstojnost orodja čim daljša. V splošnem izbira lažjih delovnih razmer ni gospodarsko upravičena. Z zmanjševanjem rezalne hitrosti, podajanja in globine rezanja se zmanjša delovni učinek in podaljša obstojnost orodja. Tako se sicer prihrani pri orodjih in zmanjša stroške za menjavo orodij, vendar se povečajo stroški delovnega mesta. Nasprotno tudi velja, da ni vedno namen izdelati čim več v najkraj šem mogočem času. Pri izbiri optimalnih rezalnih pogojev za dano strojno opravilo naredimo kompromis med največjo stopnjo odvzemanja materiala in najmanjšo obrabo orodja. 1.1 Izoblikovanje ciljnih funkcij 1. Stopnja proizvodnje Stopnjo proizvodnje običajno merimo s celotnim časom, ki je potreben za izdelavo enega izdelka (T). Je funkcija stopnje odvzemanja kovine (SOK - MRR) in obstojnosti orodja; Tp=Ts+Vx kjer so = T, T, Ti in V pripravljalni čas orodja, čas menjave orodja, čas ko orodje ne reže in prostornina odvzetega materiala. V določenih opravilih so Ts, T, T in V stalnice, od koder izhaja, da je T funkcija SOK in T. - Stopnja odvzemanja kovin (SOK). SOK lahko z analitično izpeljavo izrazimo kot zmnožek rezalne hitrosti, podajanja in globine reza: The paper is organised as follows. In sec-tion 2, a turning operation is formulated as a con-strained multi-objective optimisation problem with three non-commensurate and conflicting objectives. In Section 3, a neural network is proposed for ac-cessing a manufacturer’s implicit multi-attribute value function. Then a neural algorithm for cutting-param-eter optimization is described. In Section 5, computa-tional results are discussed to show the differences between the various approaches. 1 THEORETICAL APPROACH TO SOLVING THE OPTIMIZATION PROBLEM The purpose of the optimization is to determine such a set of cutting conditions – v (cutting speed), f (feedrate), a (depth of cut) – that satisfies the limitation equations and balances the conflicting objectives. The operation of turning is defined as a multiple-objective optimization problem with limitation non-equations and with three conflicting objectives (production rate, operation cost, quality of machining). The cutting parameters must be selected so that the machine is utilised to the maximum possible extent and that the tool-life is as long as possible. In general, the selection of the easier operating conditions is not economically justified. If the cutting speed, feeding and cutting depth are de-creased, the work efficiency is reduced and the tool resistance to is wear prolonged. In this way the tools are saved and the cost of the tool replacement is re-duced, but the labor costs are increased. Conversely, it is not always our aim to produce as much as possible within the shortest possible time. When selecting the optimum cutting conditions for some machine operation we make a compromise between the extent of re-moval of the material and the minimum tool wear. 1.1 Formulation of objective functions 1. Production rate The production rate is usually measured as the entire time necessary for the manufacture of a prod-uct (Tp). It is a function of the metal removal rate (MRR) and the the tool-life; Tc (1+ ) T MRR +T (1), where Ts, Tc, Ti and V are the tool set-up time, the tool change time, the time during which the tool does not cut and the volume of the removed metal. In some operations the Ts, Tc, Ti and V are con-stants, so that Tp is a function of MRR and T. - The metal removal rate (MRR). MRR can be expressed by analytical derivation as the product of the cutting speed, the feeding rate and the cutting depth: MRR =1000-v-f-a (2) VBgfFMK stran 254 @uperl U., ^u{ F.: Dolo~evanje karakteristi~nih tehnolo{kih - A Detremination of Characteristic - Obstojnost orodja (T). Obstojnost orodja je merjena kot povprečen čas med menjavami ali ostrenjem orodja. Zveza med dobo trajanja orodja in parametri je podana z dobro znanim Taylorjevim obrazcem: T = - a f Tool-life (T). The tool-life is measured as the av-erage time between tool changes or tool sharpenings. The relation between the tool life and the parameters is expressed with the well-known Taylor’s formula: 3 (3), kjer so kT, a1, a2 in a3, vedno pozitivni stalni parametri, določeni statistično [8]. 2. Stroški opravila Stroške obdelave lahko izrazimo kot stroške na izdelek (C ). Pri stroških opravila ločimo dve veličini, povezani z rezalnimi parametri (T, T) [5]: where kT, a1, a2 and a3, which are always positive constant parameters, are determined statistically [8]. 2. Operation cost The operation cost can be expressed as the cost per product (Cp). In the cost of the operation two val-ues connected with the cutting parameters (T , T p ) [5] are distinguished: C C tp-\T +cl + c0 (4), kjer so Ct, Cl in C0 orodni stroški, stroški dela in režijski stroški. V določenih operacijah so C, Cl in C0 neodvisni od rezalnih parametrov. 3. Kakovost obdelave Najpomembnejše merilo za oceno kakovosti površine je hrapavost, izračunana po: kjer so x1, x2, x3 in k stalnice, ki pripadajo specifični kombinaciji orodje - obdelovanec. Na sliki 1 je na temelju zgornje razprave prikazana hierarhična struktura ciljev, prilastkov in rezalnih parametrov. Da bi lahko ovrednotili medsebojne vplive in učinke med dejavniki ter dobili celostni pregled nad vrednostnim sistemom podjetja, je priporočljivo določiti večprilastno funkcijo proizvajalca (y) [5], ki pomeni zmožnost podjetja - proizvajalca. Večprilastna vrednostna funkcija je definirana kot funkcija z dejanskimi vrednostmi, ki priredi dejansko vrednost vsaki večprilastni alternativi, tako da je bolj zaželena alternativa povezana z večjo vrednostjo indeksa kakor manj zaželena alternativa. Izbrana je naslednja večprilastna vrednostna funkcija proizvajalca [5]. where Ct, Cl and C0 are the tool cost, the labour cost and the overhead cost respectively. In some operations Ct, Cl and C0 are independent of the cutting parameters. 3. Cutting quality The most important criterion for the assessment of the surface quality is roughness, which is calcu-lated according to: ¦fx (5), where x1, x2, x3 and k are the constants relevant to a specific tool-workpiece combination. Based on the above discussion, a hierarchi-cal structure of the objectives, attributes and cutting parameters is depicted in Figure 1. In order to ensure an evaluation of the mutual influences and the effects between the objectives, and to be able to obtain an overall survey of the manufactur-er’s value system it is recommendable to determine the multi-attribute function of the manufacturer (y) [5] rep-resenting the company’s (or manufacturer ’s) overall preference. A multi-attribute value function is defined as a real-valued function that assigns a real value to each multi-attribute alternative, in such a way that a more preferable alternative is associated with a larger value index than a less preferable alternative. The following manufacturer’s implicit value function [5] is selected: 0,42-e (-0,22Tp) 0,36-e (-0,32Cp) 0,17-e' (-0,26Ra) 0, 05 (1 + 1,22-Tp-Cp-Ra) (6). Celostni postopek določevanja najprimernejših rezalnih parametrov je postopek z največjo večprilastne posredne funkcije proizvajalca. Natančneje, zanima nas modeliranje večprilastnih vrednostnih funkcij z nevronskimi mrežami. Vsak proizvajalec ima svojo obliko funkcije (y); to pomeni, da ima tudi svoje drugačne optimalne rezalne pogoje. One global approach to determining the most desirable cutting parameters is by maximising the manufacturer’s implicit multi-atttribute function. Specifically, we are interested in modelling a manu-facturer’s implicit multi-attribute value functions by neural networks. Every manufacturer has its own form of the function (y); it means that it also has its own different optimum cutting conditions. | IgfinHŽslbJlIMlIgiCšD I stran 255 glTMDDC k T @uperl U., ^u{ F.: Dolo~evanje karakteristi~nih tehnolo{kih - A Detremination of Characteristic 0?(UNM / ANN)[ Cilji Objectives Prilastki Attributes Rezalni pogoji Cutting conditions Sl. 1. Prikaz hierarhične strukture dejavnikov, prialstkov in rezalnih parametrov Fig. 1. A hierarchical structure of the objectives, attributes and cutting parameters 1. 2 Določitev omejitev Obstaja več dejavnikov, ki omejujejo rezalne parametre. Ti dejavniki običajno izvirajo iz tehnoloških in organizacijskih specifikacij. Upoštevane so naslednje omejitve: 1. Dovoljeno območje rezalnih pogojev Zaradi omejitev na stroju in rezalnem orodju ter varnosti pri obdelavi so rezalni parametri omejeni z spodnjo in zgornjo dopustno mejo: vin