Optimization of laser percussion drilling by using neural network For stainless steel 304

Transcription

1 Optimization of laser percussion drilling by using neural network For stainless steel 304 O.B.NAKHJAVANI 1, M.GHOREISHI 2, S.AGHANAJAFI 3 1-Department of Mechanical Engineering, IAzad University of Technology Science and Research Branch. PO BOX: , Tehran 16579, IRAN 2,3- Department of Mechanical Engineering, KNT University of Technology PO BOX: , Tehran 16579, IRAN Abstract: This research is focused on laser percussion drilling optimization through integrating the neural network method with the Lonberg-Marcoitte(L-M). To begin with, optimum input parameters of the process were obtained in order to optimize every single output parameters (responses) ANN method was used to create an experimental model of the process based on the experimental results. Then optimum input parameters (peak power, pulse width, pulse frequency, number of pulses, assist gas pressure and focal plane position) were determined by (L-M). The output parameters include the hole entrance diameter, circularity of hole entrance and hole exit circularity, and hole taper. The tests were conducted on Stainless steel 304 sheets, with 2.5 mm thickness. The sheets were drilled by a 400 w pulsed Nd: YAG laser emitting at 1.06 µm wave length. Oxygen was used as assist gas. With regards to the accuracy of the optimum numerical results and the high capability of the neural network in modeling, this method is reliable and precise and confirms the qualitative results in the previous studies. Keywords: optimization, laser drilling, neural network ١

2 1 Introduction: Inappropriate results in all conditions will ensue from simplification in developing mathematical models for the laser percussion drilling. Yilbas [1], to create a model similar to the physical model of the process, produced a statistical model. For this purpose, he used single pulse laser to make holes on Nimonic 75 and analyzed geometry of the resulting holes. To estimate the linear coefficients of the model, Yilbas [2] applied full factorial design to find effective laser drilling parameters. In the other study [3], he tested the effect of single pulse laser on process outputs (hole entrance diameter, circularity of hole entrance and hole exit, and hole taper). In another article [4], he tried laser drilling on three other materials (stainless steel, nickel and titanium). Since single-pulse laser was used in the experiments, the effect of the other factors such as the number of the pulses and the pulse frequency, which are important factors, were not discussed and tested. Tam et al [5] optimized depth of holes in laser drilling with Taguchi method by minimizing the drilling time. In that study, single-, double- and triplepulse laser were studied. Kamalu and Byrd [6] analyzed the effect of focal distance, the plane position, surface roughness of the material and the laser energy on the process. French et al [7] applied Nd: YAG laser in laser drilling and came across effective factors. They discussed the main and interaction effects of the 17 proposed factors on the quality of laser drilling. Ghoreishi et al [8-10] employed Central Composite Design (CCD) and Response Surface Method (RSM) to observe the effect of six input parameters on the process. They drilled mild steel and stainless steel work piece materials with laser drilling and analyzed the process parameters effects on the diameter of the hole entrance and hole exit, hole taper and circularity of the hole entrance and hole exist. In these researches [8-10] no certain numerical value has been achieved for the input and the output parameters which have not been optimized. 2 Method of Experiment: Laser drilling experiments were conducted by a Nd:YAG laser machine with wavelength of 1.06 µm on Stainless steel 304 sheets, 2.5 mm thick, using oxygen as assist gas. Diameter of the laser spot was 600 µm. In all experiments holes were drilled and each experiment was repeated five times and an average value was obtained as an output parameters. As the experiments were conducted in random order not only minor errors decreased in the observations, but the effects of environmental factors of the experiment were reduced. However, the output parameters of the system were not affected. Different methods are used to train neural networks, which will be pinpointed in the next section. In general, the network type developed by different methods lead to different yields. However, often the Lonberg- Marcoitte (L-M) method, which is the fastest method for training of the neural network, is mainly used to develop neural network. Significant decrease of error in the hidden layer neurons of the trained networks is the crucial feature of this method. MATLAB software has been used to develop neural ٢

3 networks. Bayesian Regularization has been applied to improve the L-M method results. Peak power, Pulse time, Pulse frequency, Number of pulses, Gas pressure, and Focal plane position are the input parameters used in the research. The parameters variation range is shown in Table 1: The four output parameters (a) the hole entrance diameter, (b) the ratio of maximum to minimum Feret diameter for hole entrance (hole entrance circularity), (c) and for hole exit (hole exit circularity) and (d) hole taper were selected to achieve optimum input parameter settings in both single criterion and multicriteria optimization procedure. 3 Concepts of the Neural Networks: Actually the neural system follows optimization methods and focuses on an unknown structure, adjusting the parameters of the unknown model in order to minimize model errors. There is an appropriate network named feed forward back propagation neural network for approximation of complex performance [14]. In this type of network, the parameters in question are actually in the form of weight functions, which relate each input to a node. The node is formed by applying a stimulus function on the algebraic sum of the output values, multiplied by the related weight values (Fig. 1). The common method for training of the neural network is mainly in the form of gradient methods (local optimization method), divided into 4 categories in global optimization method [15]. Gradient methods include: 1. Steepest descent; 2. Conjugate gradient methods; 3. Newtonian methods; 4. Improved Newtonian methods. 4 Structure of the Neural Network: The network after receiving necessary training can be applied on an untrained input in order to get an appropriate output. This takes place through mechanism of decision making an interpolation process. To design a neural network, the following actions are required: Determination of the type of neural network; Determination of the proper size of the network and the type of stimulus functions. Once the network is designed, the network accuracy will be examined in response to inputs which are not applied in the training in order to determine the network accuracy to predict system performance. The neural network designed in this study is Feed Forward type with three hidden layers and an output layer. With this model, process output parameters can be developed for input parameters on which no experiments have been conducted before, so as to avoid timeconsuming and costly experiments. This model enjoys a prominent advantage, that is, high speed of finding process responses, which, as mentioned above, are very precise, compared to the experimental results. Four nodes have been considered in output layer, including hole entrance diameter, circularity of hole entrance, circularity of hole exit and hole taper angle (Fig. 1). The number of nodes in hidden layers has been selected 10, 7 and 8 respectively by try and error (Fig. 1). Stimulus functions in the first, second and third hidden layers are chosen sigmoid hyperbolic type and in the fourth layer, (process output layer) is selected linear type. ٣

4 By using the mentioned structure, the behavior of the process model (trained network) is checked and is presented in figures 2 to 6. Figures 2 to 5 indicate the value of input parameters in two cases of approximated modes and the laboratory results. As it is observed in the figures, the performance of the model is acceptable. [4]- B.S. Yilbas, Parametric study to improve laser hole drilling process, J. Mat Proc. Tech. 70, 1997, PP [5]- S.C. Tam, C.Y. Yeo, M.W.S. Lau, E.N. Lim, L.J. Yang, Y. Norr, Optimisation of laser deep-hole drilling of Inconel 718 using taguchi method, J. Mat. Proc. Tech. 37,1993, 5 Conclusions: As it can be seen from the figures 2 to 6, modeling with neural network has a considerable capability for approximation of the process performance. Accordingly, this method is preferred for modeling compared to the other methods of modeling approximation such as Response Surface Method (RSM). PP [6]- J. Kamalu, J.P. Byrd, Statistical design of laser drilling experiments, Proc. ICALEO 98, Sect. B,1998, PP [7]- P.W. French, D.P. Hand, C. Peters, G.J. Shannon, P.Byrd, K. Watkins, W.M. Steen, and Investigation of Nd: YAG laser References: [1]- B.S. Yilbas, Z. Yilbas, Parameters affecting whole geometry in laser drilling of Nimonic 75, SPIE 744, 1987, PP [2]- B.S. Yilbas, Study of affecting parameters in laser hole drilling of sheet metals, Trans. ASME: J. Eng. Mat. Tech. 109, 1978, PP [3]- B.S. Yilbas, Investigation into drilling speed during laser drilling of metals, Opt, Laser Tech.20 (1),1988, PP percussion drilling process using factorial experimental desings, Proc. ICALEO 99, Sect. C,1999,PP [8]- M.Ghoreishi, D.K.Y. Low, L.Li, Statistical modelling of laser percussion drilling for hole taper and circularity control, ImechE Part B:J. Eng. Manufact. Vol 216 Part B J Engineering Manufacture (2002) PP [9]- M. Ghoreishi, D.K.Y Low, L. Li, Comparative Statistical analysis of hole taper ٤

5 and circularity in laser percussion drilling International Journal of Machine Tools and Manufacture 42 (2002). PP [10]- L.Li, D.K.Y.Low.M. Ghoreshi, Hole Taper Characterisation and Control in Laser Percussion Drilling, Annals of the CIRP, Vol.51,1,2002 PP [11]- N. Chaiyaratana, A.M.S. Zalzala Hybridisation of Neural Networks and a Genetic Algorithm for Friction Compensation, congress on Evolutionary computation, Vol 1,2, 2000 [12]-Uros Zuperl. Franci Cus, Optimization neural networks, Robotics and Computer Integrated Manufacturing 2003 [13]- S.L. Mok, C, K, Kwong and W.S.Lau, a Hybrid Neural Network and Genetic Algorithm Approach to the Determination of Initial Process Parameters for Injection Molding. Advance Manufacturing Technology, 2001 [14]- Irwin,G.W., Warwick,K. and Hunt.K.J., Neural Network Application In Control, I.EEE., Michael Faraday House,U.K, [15]- Neural Network Toolbox-3.0 for use with MATLAB, Math work, of Cutting Conditions during Cutting by using ٥

6 Tables: Table 1: Range of parameters variation Inputs Parameters Min Max peak power [kw] 3 7 Pulse time [ms] Pulse frequency [Hz] Number of pulses 2 6 Gas pressure [bar] 2 6 Focal plane position [mm] Table 1: ٦

7 Figures: Figure 1: Structure of neural network (ANN) Figure 2: Plot of base model and neural network model for taper angle Figure 3: Plot of base model and neural network model for enter diameter Figure 4: Plot of base model and neural network model for enter circularity Figure 5: Plot of base model and neural network model for exit circularity Figure 6: Plot of sum square to reach an optimum model ٧

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