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Modelling of Thrust Forces in Drilling of AISI 316 Stainless Steel Using Artificial Neural Network and Multiple Regression Analysis

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(1)Strojniški vestnik - Journal of Mechanical Engineering 58(2012)7-8, 492-498 DOI:10.5545/sv-jme.2011.297. Paper received: 2011-12-30, paper accepted: 2012-04-05 © 2012 Journal of Mechanical Engineering. All rights reserved.. Modelling of Thrust Forces in Drilling of AISI 316 Stainless Steel Using Artificial Neural Network and Multiple Regression Analysis Çiçek, A. 87˜ 6H  šŒH8• ›H •

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(14) 6. In this study, the effects of cutting parameters (i.e., cutting speed, feed rate) and deep cryogenic treatment on thrust force (Ff) have been investigated in the drilling of AISI 316 stainless steel. To observe the effects of deep cryogenic treatment on thrust forces, M35 HSS twist drills were cryogenically treated at –196 °C for 24 h and tempered at 200 °C for 2 h after conventional heat treatment. The experimental results showed that the lowest thrust forces were measured with the cryogenically treated and tempered drills. In addition, artificial neural networks (ANNs) and multiple regression analysis were used to model the thrust force. The scaled conjugate gradient (SCG) learning algorithm with the logistic sigmoid transfer function was used to train and test the ANNs. The ANN results showed that the SCG learning algorithm with five neurons in the hidden layer produced the coefficient of determinations (R2) of 0.999907 and 0.999871 for the training and testing data, respectively. In addition, the root mean square error (RMSE) was 0.00769 and 0.009066, and the mean error percentage (MEP) was 0.725947 and 0.930127 for the training and testing data, respectively. Keywords: artificial neural networks, regression analysis, cryogenic treatment, machining, thrust force, predictive modelling. 0 INTRODUCTION        ;;

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(199) Strojniški vestnik - Journal of Mechanical Engineering 58(2012)7-8, 492-498.   

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(456) == . Modelling of Thrust Forces in Drilling of AISI 316 Stainless Steel Using Artificial Neural Network and Multiple Regression Analysis. 493.

(457) Strojniški vestnik - Journal of Mechanical Engineering 58(2012)7-8, 492-498.  =  

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(531)   = ;H 2 DISCUSSION AND RESULTS 2.1 The Effects of Heat Treatments and Cutting Parameters on the Thrust Forces 6  

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(551) . Fig. 2. The variations in thrust force depending on the heat treatment, feed rate and cutting speed. 494. ⎞ ⎟⎟ ,  ⎠. {| }~€` }

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(553) Strojniški vestnik - Journal of Mechanical Engineering 58(2012)7-8, 492-498.  

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(736) = H. Table 3. Analysis of variance for thrust force Source Model Cutting Tools Cutting Speed Feed rate Error Total. Degrees of freedom 3 1 1 1 32 35. Sum of square 260238.04 5017.04 605 254616 2010.85 262248.89. Mean square 86746 5.017 605 254616 62.8 -. F value 1380.449 79.8396 9.6278 4051.880 <.0001 -. Pr > F <.0001 <.0001 0.0040 <.0001 -. Modelling of Thrust Forces in Drilling of AISI 316 Stainless Steel Using Artificial Neural Network and Multiple Regression Analysis. Contribution % 1.91 0.23 97.08 0.78 -. 495.

(737) Strojniški vestnik - Journal of Mechanical Engineering 58(2012)7-8, 492-498. Fig. 3. Comparison of experimental and residual thrust forces with thrust forces predicted by regression analysis.  ; 

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(792) = %. b). 1 ⎛ Ff = ⎜ − ( 3.2694× F1 + 3.0517× F2 + 3.7990× F3 − 7.7062× F4 + 0.0511× F5 + 0.9165 ) ⎝ 1+ e ×950,. ⎞ ⎟× ⎠. *0+.  Fi *i ´  3 HHH /  4+      

(793) I H*'+%. c) Fig. 4. Comparison of the actual and predicted thrust forces; a) 0.08 mm/rev, b) 0.1 mm/rev, c) 0.12 mm/rev. 496. {| }~€` }

(794) ‚ƒ }{„†. Fi =. 1 , 1 + e − Ei. *'+.

(795) Strojniški vestnik - Journal of Mechanical Engineering 58(2012)7-8, 492-498. Table 4. Statistical evaluation for the thrust force Goal. Learning algorithm. Number of neurons. Ff. SCG. 5. RMSE 0.00769. Training data R2 0.999907.  Ei

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(806)  

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(810)  6 4H. MEP 0.725947. RMSE 0.009066. Testing data R2 0.999871. MEP 0.930127.   =        ;

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(814) =   [[H Table 5. The weights between the input and hidden layers i 1 2 3 4 5. Ei = w1x(Ct/6) + w2x(V/60) + w3x(fx4) + i w1 w2 w3 -6.7500 -4.4407 -6.8930 -2.3814 -6.5059 -4.7796 -9.1133 -4.9393 6.0572 0.0480 0.1832 -6.4262 3.3620 -8.5526 -2.2916. i 11.7137 11.8331 -2.7930 3.7340 8.9342. 3 CONCLUSIONS  

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