Chatter Stability Boundary Analysis Using Neural Network

INSTRUCTION A more important focus on chatter is the stability boundary analysis that is more practical and realistic in the sense that this analysis shows the chatter boundary region in all available cutting condition and the chatter state for the machinist in field to get the insight easily to avoid the chatter problem. Considering this points, a new method to get the chatter stability boundary is mainly discussed in this study. Present study about these kind of chatter stability boundary is the results of Kim and Yoon in the scope of basic knowledge[1-4]. Their study also have its roots on the study of Altintas[5]. There is some problem that cannot exactly discriminate the condition for specific cutting coefficient between that of half immersion and full immersion endmilling. Also in real calculation, the specific coefficient of different end-milling is considered as same. So it has some unreliable limitation in their results for concrete propose. However, the RBNN stability lobe analysis that is suggested in this study is more realistic than the conventional method in the means that this method uses the real experimental data as an input. So, it can represent the end-milling more realistic. In this study, the conventional FFT or time series spectrum is used for discriminating the chatter. After deciding the state of chatter in all condition, The state was coded and used as an input in all region with respect to an axial depth of cut and spindle revolution in the end-milling. In this paper, it was suggested to discriminate the chatter region by using the RBNN stability lobe algorithm. And it was verified that the output of the RBNN stability lobe also consists with the conventional stability lobe method. Further more it has some merit to represent the stability lobe considering experimental data using concrete data. NEURAL NETWORK A new RBNN stability lobe method is proposed and compared with the conventional stability lobe analysis[2,3] in this paper. This new method has the advantage of a fast convergence and a less error than other BP (back propagation) learning algorithm. The proposed radial basis neural network has two hidden layer. One of them uses the radial basis function and the other does linear function as a transfer function. The output vector can be acquired by learning algorithm considering the weights and the bias. In RBNN algorithm, the dependent output parameter, a, can be obtained by multiplying the weights w to input vector p and by adding the bias. The output, a, become a new input in second hidden layer and a new output can be obtained with the same procedure. Fig.1 shows this architecture of RBNN algorithm. The left side of this figure shows the radial basis layer and the right side shows the linear layer. Fig. 2 shows the total architecture of the neural network. It has an input of two units, two hidden layer of seven units and an output of three units.