JOliRNAL OF SCIENCE & TECHNOLOGV • No. 88 - 2012
DETERMINING THE OPTIMAL TECHNOLOGY PARAMETERS FOR CNC MILLING MACHINE USING THE ARTIFICIAL EVOLUTION
NEURAL NETWORK
XAC DINH Tl ! 6 N G S 6 C 6 N 0 N O H O T 6 1 U U KHI P H A Y TRfe&J MAY CNC B A N G PHU'ONG P H A P M A N G NO RON TlfiN H 6 A NHAN T^O
Nguyen Ngoc Kien, Vu Toan Thang Hanoi University of Science and Technology
Received Mareh 2. 2012; accepted May 8, 2012 ABSTRACT
This paper presents the mathematical method to determine the optimal technology parameters for satisfaction of the sudace mughness function on milting CNC. The artificial neural nelvmrk and the generate algorithm (artificial calculation) is used to determine the tetOinology parameters The artificial neural network method is used to determine the accurate empirical relationship between input- technology parameters and output-surtace mughness. The impmved generate algorithm for empirical relationship is used to determine the optimal empirical parameters. Thus, it can tie able to determine the technology parameters for the optimum mechanical manufacturing
Key word Roughness, Artificial Neural Network (ANN), Generate Algonthm (GA). chromosome, genes, population, mutation, hybridization, natural selection.
T6IVI TAT
Bdi bdo trinh bdy phuang phdp todn hgc xdc dinh cdc thdng sd cdng nghd tdi uu di thda mSn ydu ciu vi hdm dd nhip nhd bi mdt ti vl khi gia edng trdn mdy f^ay CNC. Su dung m^ng noron nhdn 190 kit hgp v&i gidi thudt tiin bOa (tri tui nhdn teo llnh todn) di xdc dinh cdc thdng sd cdng nghd tdi uv. Phuang phdp mang naron di xde dinh mdi quan hd thgc nghiem glCfa cdc yiu td diu vdo Id ehi dd cit vd diu ra Id dd nhip nhd bi mdt ti vl v&i dd chinh xdc cao. Tir mdi quan hd thgc nghidm dd dung gidi thudt tiin hodn cdi tiin tim bd dd lidu thgc nghidm tdi uu Id ca s& dd tim ra dugc bd thdng sd chi dd cBt tdi uv cho qud trinh gia cdng ca khi
• .INTRODUCTION Ihe optimum technology parameters on T- . .. L • 1 . u I manufacturing on CNC machine [11.
I oday, the meenanieal technology ° ^ '
develops towards precision manufacturing 2. FORMULATION OF THE direction. Manufacturing on the numerical MA FHEMATICAL MODEL
2.1 The mathematical model f o r artificial neural nel%\ork
control machine can be set up a flexible technology parameters to enhance the efficiency of equipment. That efficiency is the
best way to go with a optimum technology Based on Ihe neurons network of human parameters. The speed of technical calculation formulates a mathematical model to establish is developed and becomes a base for the the relationship between technology numerical solution. The artificial intelligence parameters (S.F.D) and surface roughness (RJ.
calculation is a good solution to determine the .^^^ ; , , .^^^^^^ ^^^ ^^ ^^^
opt.mum technology parameters on ; f ^„, m a n i i f a r l i i n n o nrnf*»ccino Thi» artiHr.,'! nt .i i r . i "^ r \ '• \ /• f manufacturing processing. The artificial neural
network (ANN) is enables to determine an (D). tool wearing, material hardness ...the . , . , . . , output layer includes one or more output:
exact relationship between input and output r u i. -u T- n ^, , ^ , ""'f^"' surface roughness, space roughness, vibration parameters. Based on that exact re ationship c ..- c ...- J • •._
J . . , . . , '-'<»i^"3i"H frequency, cutting force, cutting productivity...
determines the optimum technology parameters
by using the generate algorithm (GA). Both The relationship between input and methods are good solution for determination of output parameters are described by the
JOURNAL OF SCIENCE & TECHNOLOGV * No. SS - 2012 relationship between input layer and output
layer. The active function fl^x) is used in this algorithm is the sigmoid function [2]:
y(u) = f{u) = -1 (1) u value between input layer and hidden layer is written by:
(/ = J]w,,.x,+fij=l ton(2) u value between hidden layer and output layer is written by:
''=Z^*/-^-'
k=l ton (3)Where:
m - number of input nodes; n-number of hidden nodes; k-number of output nodes; x- input value; v- calculation value at hidden nodes; w- weight value; 0- threshold.
The relationship between technology parameters and surface roughness is formulated by system of mathematical equations in which the weights can be changed to predict exactly the higher relationship.
[npui layer hidden layer S(uO
R„) is the function of weight and bias variables so the adjusting weight value has to make the error to go to minimize. The Gradient method is used for adjusting the weights.
The error function between the calculation value by ANN y, and the measured surface roughness R^, at the output order j is written by:
e, = R^-yj
Total error for the iteration n is written by:
Fig ! Artificial neural network model Back propagation algorithm (BPA) To determine a relationship between technology parameters and surface roughness is described by the system of the mathematical equations, we have lo determine the system of weights and wy and threshold Qy (bias). The weights and bias are determined from errors between the predicted value y, and measured surface roughness R^, by BPA. Total error (y,-
m=\t^,'{r'>\t(^-
y.) Where:Ry- measured surface roughness of training set.
yj-calculation value by ANN.
The weights w,j is adjusted to reduce the error value E. The neural has an input and output value, each value has a weight to estimate its effect.
Derivate the error function at the loop of n is written by:
dE(n) _ dEjn) de^jn) dy^jn) du^jn) 5w,j(«) &^(n) dy^in) du^{n) dWy(n)
£^-,(„).M!)-
»,(") /.(",("))
dvt (n) du.(n)'.(");
^ = . , W . ( - i ) . / > , W ) . . , W
The adjusting value for a weight:
dE{n)
Aw =-q- -ne,{nU-\).f{u,[r,)).x,(n) cHv,j(/j)
dE{n) _ dE{n) dc^(n) dyj{n)
^=^, ( " ) • / • ( " , ( " ) )
JOURNAL OF SCIENCE & TECHNOLOGY • No. 88 - 2012 Av/^^{n) = rjSj{n)jc,{n)
The new weight is written by;
Wy(n+1) w,,(n)iAW||
The result of ANN determines the weights for the relationship between S.i.v and R,. This system equations are used to appreciate the relationship. The ANN method is more exact prediction than the regression method.
The system equations are used for optimization Ihe technology parameters.
2.2 The malhemalical model for generating algorithm
The generate algorithm (GA) bases on the natural selection ofthe evolution theory by Darwin [3]. The ANN method predicts the relationship R,^ItS.F,D) so the optimum problem is written as:
Determining the vector u= (S.F.D) to Rt=
fl[S,F,D) is minimum
Subject Io: S™,„< S<Sn,„; F,nm<P<F„„;
Dn„n<D<Dm„. This problem finds a vector u=(S,F,D) in the feasible region of Ihe constrains. This paper presents the solution of actual generate algorithm. Vector u is a individual (chromosome), each value S.F.D is a gen, a population includes more individuaU The initialization population is created by random ofthe value S.F.D. The number ofthe population (m) should be not very large because it increases number of searching loop, and m should be not vcr\' small because of approaching to the local minimum. This solution chooses m=40 individuals.
Calculation of adaptation for each individual: K, «1-Pt. P,- selection probability for cach individual ith: E =
Z(«.-),
The minimum problem P, is the smaller the better (K, is larger). The fitness probability as: qi-'K/A. A^^K,; number hybridization individual mi.=rr.m with r is probabiliiy hybridization. The hybridization individuals are replaced by the parent individual. The parent one has high fitness at iteration uh as u,, Uwto generate two crossbreeds uv u'.
w\, =a.u^ +(\-a)J4/,n, =04/^+(I-a)j/„
(a - genetic probability)
Checking for the fitness of two crossbreeds, if the crossbreed has the small fitness, it will be eliminated to continue hybridization to get the belter crossbreed. The crossbreeds of the new population is better Ihan old one.
If there are only hybridization and selection it often goes to the local minimum point. Thus it needs lo generate some mutation individuals to go out of the local minimum point. Mutation enhances probability for determination the global minimum poinL
Mutation probability is b lo generate number of mutation individuals mjb^b.m
To select random the one of individuals in the population u«-(S,..V„.[„) after mutated u»MS„.V„.i,) cach the genes S„-S«-Mi-S -S ). l-unction Mt.S,„„-S„„„)=
f^iiiiv-S,,,,,,).! 1-1 " '1 uhcrcT-total iteration
Begin Initialization population
I
Mutation ^ —-Calculate fitness
1
-
population "^
f0r(R,)n„n'?
1
Hybridization Selection
l-'ig 2 Diagram generate algorithm
JOURNAL OF SCIENCE & TECHNOLOGY * No. 88 - 2012
(max age), t-mutation iteration (age of population), r-mutation probability of genes, b- system parameier. 1ft is small while GA do not find the local minimum point to increase value A, so the mutation individual has high value to go out o f t h e local minimum region. 1ft is big enough to reduce value A so the population Is stable to go to the global minimum point.
Table I. Experimental and results
Fig 3. Global minimum point 3. EXPERIMENTAL AND RESULTS 3.1 Experimental
Experimental is done at BKCNC centre.
BIO building-Hanoi University of Science and Technology, Viet Nam. Steel alloy S355JO is used with face milling on MIXKON 600-CNC machine fixim Switzerland, measuring the surfiice roughness by SJ400 machine from Japan. The face milling tool has Diameter of D=80mm, 6 teeth-Mitsubishi, tip cut JH VP15TF Mitsubishi Carbide. Experimental with speed S(m/min): from 136 to 304, federate F(mm/tooth): from 0.I3I to 0.468, Depth of cut D(mm): from 0.1226 to 2.477. Implementing with 47 cutting regimes (S,F,D) on 141 specimens. Using ANN to determine the relationship between S,F,D and R^. Result is illustrate in table 1.
3.2 Determination the o p t i m u m technology parameters by GA
Based on the system of equations to determine the relationship between S.F.D and R; by ANN is input to GA. The processing for 1000 iterations determines the optimum parameters as: SDP=316.8 (m/min); Fop=O.I49 (mm/tooth); Dop=O.I2 (mm); RHn,„=3.49jim.
Manufacturing on machine at (Sop,F'.p.Dop)=(316.8,0149,0.l2) to achieve with Rz=3.58(im. The error is 2 . 5 1 % compare Rz=3.58|im with Rzn„n=3.49[iin.
Run
1 2 3 4 5 6 7 8 9 HI 11 i:
13 14 IS 16 17 IS
\9 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
S
169 81 369 79 169 81 2 6 9 79 16981 16981 269,79 135 65 303 7 2198 2198 2198 2198 219 8 269 79 I3S6S 169 81 169 81 169 81 169 81 186 39 190 16 190 16 202 97
2198 2198 2198 2198 2198 2198 2198 236 38 249 44 249 44 249 44 253.21 269 79 269 79 269 79 269 79 269 79 269 79 303 7 316 76
F
02 02 0.4 0.4 02 04 0,4 03 0,3 0 13 047 0.3 03 0.3 0-2 03 02 04 0 2 04 023 0 36 0 24 0 27 04 03 013 0 47 0 3 03 0 25 0 33 0 36 0 24 0 18 0 37 02 03 02 02 -04 0 4 03 0 07
D
060 060 0.60 0.60 2 0 0 2 0 0 2 0 0 1 3 0 130 130 130 012 2,48 130 200 130 2 0 0 2 0 0 0 60 0 60 0 83 0 88 0 88 1 0 7 105 2 0 0 1 3 0 1 3 0 0 1 : 2 4 8 1 5 0 1 5 3 0 88 0 88 1 72 1 77 3 00 0 ID 010 060 0 60 2 00 1 30 0 50
Rzi (^m)
871 7 39 7 9 7 6 3 2 7,47 5,64 5 7 2 10 33 5 9 6 S34 6 14 7 57 6 19 7 24 4 96 10 03 7 47 5 64 8 71 7 97 966 8 43 9 78 8 88 58 5 48 8 34 6 14 7 57 619 9 23 7 89 6 22 738 8 32 7 66 4 96 6 36 5 89 7 39 6 32 5 72 5 96 6 16
"
8 85 7 14 79 6 35 7S6__|
5 6 8 5 41 10 12 6 2 6 831 642 7 53 5 51 7 6 9 5 IS 10 12 7 56 5 68 8 85 79 9 39 7 82 9 48 94 6 43 5 72 8 31 6.42 7 53 551 8 9 8 651 6 57 7(il 7 6 8 6 3 5 5 18 56 604 7 14 6 3 5 5 9 3 6 26 6 23
Error (%)
1 65 341 0,92 041 I 15 07 351 2(15 5 08 04 4 54 0 56 1094 62 444
oes
1 15 0 7 1 6 5 0 9 2 2 8 4 7 25 3 0 6 5 8 7 10.93 4 3 2 04 454 0 5 6 10 9 4 2 73 17 55 24 3 05 7 63 17 1 4 4 4 1 1 9 8 2 4 7 341 041 3 61 5 08 1 IS
The average error is 9mc'=4.21%
.lOllltNAl, OF SCIENCr. & TECIWOLOGY * So. 88 - 2012
4. CONCLUSION 136 to 304, federale F(mm/tooth): from 0,131 The artinci.1 neural network melhod is ' " » f ' • "fP* "J <="' °('""!>^ f™™ O-'^^' » used to determine the empirieai relationship ITn^'^?^^ ^"^ r T T!Z , . . , . .ri. . (S,F,D) on 141 Specimens, using GA with 1000 between input and output parameters, fhe exact . . ^ j „ -. ^^ •.
ANN is higher than exact regression method so "•"•«»'°"' *^f" ""<^ R«.i«- 3.49Mm with optimum determine optimum parameters Is the more parame ers.
precise. GA method solving Ihe optimum (S^.F„p.Dop)''(316.8,0I49.0.l2) problem is combined ANN. Both methods arc -,, „... , . . - - , . .
powerful tool for the optimum empirical design. , ^^'f "'""^ °*^«his result >s 2.51% compare The experimental with speed S(m/min): from ' ° '^' ^^^' "lanufaclunng condition.
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2. R.Battili, Firsi-and second-order mclhod for learning: between steepest descent and Newton's method. Neural Compulation 4(1992)141-166.
3. D.C.Liu, J.Nocedal, On the L-BFGS method for large scale optimization. Mathematical Programming 45( 1989)503-528.
4. J.Nocedal, J.S.Wright, Numerical Optimization, Springer, Beriin,I999.
5. T.P.VogI, J.K.Mangis. J.K.RIgler, W.T.Zink. D.L.Alkon, Accelerating the convergence of Ihe back-propagation melhod. Biological Cybernetics 59(1998)257-263.
Authors address: Nguyen Ngoe Kien - Tel: (+84)986.333.357, Email: kiennn-clm (?mail.hul.edu.v Hanoi University of Science and Technology
No. I Dai Co Viet Sir., Ha Noi, Viet Nam
