OPTIMIZATION OF TURNING PROCESS USING A NEURO-FUZZY CONTROLLER

Transcription

1 Sixteenth National Convention of Mechanical Engineers and All India Seminar on Future Trends in Mechanical Engineering, Research and Development, Deptt. Of Mech. & Ind. Engg., U.O.R., Roorkee, Sept , 2000 OPTIMIZATION OF TURNING PROCESS USING A NEURO-FUZZY CONTROLLER J. H. Panchal, R. Khanna and U. S. Dixit Department of Mechanical Engineering, Indian Institute of Technology, Guwahati ABSTRACT The selection of proper machining-parameters viz. feed, speed and depth of cut is an important task for obtaining the desired performance in the turning process. This work proposes a neuro-fuzzy control scheme for the selection of feed and speed in a single pass turning. The scheme provides the manufacturer a flexibility of specifying the objectives in linguistic terms. The scheme is dependent on the sensory feedback by force and vibration sensors. A well-trained neural network predicts the surface roughness and dimensional deviation, which in combination determine the quality of the work-piece. A fuzzy set model is developed to give quantitative assessment of the total machining performance encompassing surface finish, dimensional accuracy, cost of production and metal removal rate. The first technique models the inverse process dynamics using feed forward neural network with one hidden layer similar to the work of Azouzi and Guillot (1998), and the second technique uses genetic algorithm for obtaining global optimum solution. It has been found that genetic algorithm offers advantage over the former optimization technique. Obtained results have also been compared by traditional optimization method in metal cutting and relative advantages of the present scheme have been discussed. INTRODUCTION Finding out the proper machining parameters is a difficult task and has attracted the attention of a number of researchers. The objective is minimum production cost per piece, minimum production time, maximum profit rate or any weighted combination of these. Abulnaga and El- Dardiry (1984) have formulated the general optimization problem in metal cutting and carried out a comprehensive study of the available computer codes. They assume the availability of a detailed process model along with various process constants. The problem with the mathematical models of machining is that they overlook the significant variation in metal cutting conditions as the part is machined. Hence, the programmer of these machines is left with no choice but to choose a conservative parameter set so as to minimize machining vibrations and tool breakage. A better strategy is to monitor the process condition on-line and accordingly alter the machining parameters in order to obtain best machining performance. Cutting force and vibrations are relatively easy to measure parameters, which have potential to predict job quality. However, dependence of surface roughness and dimensional deviation on feed, depth of cut, speed, force and vibration is ly complex and non-linear in nature and may vary from machine to machine. Artificial neural networks, which are being developed in an attempt to mimic the computational architecture of the brain, seem to make better choice for on-line prediction of job quality in terms of dimensional deviation and surface finish. A neural network is trained by providing a number of inputoutput data sets. After training is over, the network is able to predict the output for an input to a fair degree of accuracy. The initial attempt to apply neural networks in machining was made by Rangwala and Dornfeld (1989). After that they have been used in a number of machining processes, by various researchers (Jammu and Danai, 1993; Liao and Chen, 1994; Tarng et al., 1994; Li et al., 1998; Ko and Cho, 1998; to name a few). Recently, Azouzi and Guillot (1998) presented a feed back neurocontrol scheme for turning, in which on-line adjustment of feed and cutting speed is carried out to maximize an index encompassing surface roughness, dimensional deviation and material removal rate. Cost of machining and subjectivity of

2 optimization goals have not been incorporated by the authors. The present work proposes a technique for optimization of turning parameters based on the online sensory measurement of cutting force and vibration in order to predict job quality. The objectives considered are minimum cost of production, maximum production rate and maximum job quality. One way to satisfy these objectives, is to take weighted-combinations of these objectives. However, in the present work, a fuzzy set based approach has been used to find out the overall machining performance index, because of two main reasons. Firstly, the most of manufacturers may find it difficult to specify an objective measure in the form of weights. It is more convenient to specify the relative preference for various goals in terms of linguistic parameters, such as very production rate, low cost and moderate job quality. The fuzzy sets are conveniently used to compute with such type of linguistic variables. Secondly, various goals are incommensurate and hence, need to be converted into non-dimensional form judicially for combining them. This difficulty is automatically eliminated in fuzzy set approach, as preference for each goal can be expressed in terms of membership grade. There have been some attempts to use fuzzy sets in machining (Fang and Jawahir, 1994; Lee et al., 1999). NEURO-FUZZY CONTROLLER The block diagram shown in Fig. 1 illustrates the working of the proposed neuro-fuzzy controller. The feedback about the machining process is obtained by means of force and vibration sensors. A neural network having eight neurons in the hidden layer is used to predict the surface roughness and dimensional deviation from feed, depth of cut, cutting speed, force and vibration as input to the network. The training data for turning of a job of 200-mm length and 30 mm diameter has been taken from the paper of Azouzi and Guillot (1998). Out of 25 available data sets, 21 data sets were used for training and 4 data sets were used for testing. It was observed that the overall error minimized by taking eight neurons in the hidden layer. The cost model gives the approximate cost of production per piece for a given feed and depth of cut. The cost of production C p in a machining operation is given by: TmTs Tm C p = Cu Tm + Th + + Ce (1) T T where C u is the cost of operating the machine per minute, C e is the tool change cost, T m, T h, T s are machining time, job handling time, tool setting time in minutes respectively and T is the tool life in minutes. The machining time T m is calculated from the expression: π D L T m = (2) 1000 f v where D is the job diameter in mm, L is the length of job in mm, f is the feed in mm/rev and v is the cutting speed in m/min.. Tool life depends can be determined by Taylor s equation: n n1 v T f = c (3) Parameters n, n1 and c are dependent on tool work combination and their values have large variation. These can be taken as fuzzy number and tool life (and hence cost of production) can be obtained as fuzzy number. Since in the optimization procedure, costs of production have to be compared for different process parameters, they have to be defuzzified. This has been done by Panchal et al. (2000). However, it has been observed, in the present work, that estimation of cost of production by crisp arithmetic, taking the average values of n, n1 and c provides values, fairly close (within 2%) to those obtained by fuzzy arithmetic procedure. Hence, in order to save computation time, the cost of production has been calculated by crisp arithmetic, here. The performance index evaluation module gives an overall index of the turning performance depending on the subjective requirement of the manufacturer. The procedure for obtaining performance index involves determination of individual membership grades for each objectives viz. job quality, cost of production and material removal rate. For each objective, three categories have been defined in terms of linguistic variables. The material removal rate can be very, or average. The production cost can be very low, low or average. Job quality can be very good, good or average. The machine operate has to specify his requirement in terms of these linguistic variables. For a particular machining parameters, material removal rate and cost of production are calculated by standard formulae and dimensional deviation and surface roughness are predicted by neural network model. Depending on operator s objective, membership grades for various conflicting goals are 2

3 Sensor Data on Force and Vibration Material Removal Rate Feed Velocity Depth of cut QUALITY MODEL Surface Finish Dimensional Deviation PERFORMANCE INDEX EVALUATION MODULE Overall Performance Index Feed Velocity COST MODEL Cost of Production Desired Objective Fig. 1. Neuro-fuzzy controller block diagram found. (The procedure of finding membership grades will be discussed in detail in the subsequent section.) The performance index is found by fuzzy intersection operation i.e. by taking minimum of the membership grades for cost of production, material removal rate, dimensional deviation and surface roughness. (Note that dimensional deviation and surface roughness together comprise the job quality). The procedure of finding the performance index is based on the noncompensating strategy in which the overall performance is decided by the most poorly performing attribute. The feed and cutting speed, which maximize the performance index can be found either by inverse neural network, as done by Azouzi and Guillot (1998) or by Genetic Algorithm. The optimization procedure will be discussed in a further section. The optimal feed and cutting speed data can be then supplied to the electronic control of the machine. If there is sudden variation in the force or vibration data, it will be captured by the neural network model to modify the dimensional deviation and surface roughness values. Accordingly, the overall performance index gets changed and no longer remains optimal. Hence, the feed and cutting speed values are changed to restore the optimality of performance index. Thus, the proposed neuro-fuzzy control can provide adaptive control of the turning process. CONSTRUCTION OF MEMBERSHIP FUNCTIONS The construction of the membership functions is subjective, but there are some considerations while selecting the membership functions. These are discussed in the following subsections. Membership Functions for Cost of Production Three categories of cost of production are defined: very low cost, low cost and average cost. The membership functions of these can be constructed in a number of ways. A simple way to construct the membership function of low cost is, to calculate approximate minimum machining cost from classical economics of machining theory (Rs. 200 in the example taken in this paper) and assign to all costs lower than minimum cost of production, a membership grade value equal to 1. The 1.25 times the minimum cost is assigned a membership value equal to 0.5 on the ground that more than 25% of the minimum cost of production will not be treated low cost. A straight line can be drawn from the membership grade of 1 at Rs. 200 up to membership grade of 0.5 at Rs. 250 and can be extended till it becomes zero at Rs The membership grade of very low cost is the square of membership grade of low cost and the membership grade of average cost is the square root of the membership grade of low cost. Membership Functions for Quality 3

4 The job quality comprises of surface finish and dimensional deviation. Separate membership functions are given for both. The overall membership function for quality is the minimum membership function among the two. For surface finish, it was decided to assign N6 (0.8 microns) and lower roughness values, the membership grade of 1 in the set of good surface quality and a grade of 0 to surface roughness N12 (50 microns). When a linear membership function is constructed as a function of roughness grade, a logarithmic function is obtained for the membership grade as a function of roughness value in microns. As a result, the following function is obtained for good surface finish: 1 Ra < 0.8 micron 100 ln µ = 0.15 Ra good Ra 50 ln 2 (4) 0 Ra > 50 Similar to the previous subsection the membership grades for very good surface finish and average surface finish are given by µ = µ and µ = (5) very good good average µ good For dimensional deviation, the membership grade of 1 is assigned to zero deviation and zero membership grade is assigned to maximum permissible deviation (here, it was taken as 0.3 mm). A linear membership function is taken for good dimensional quality, a square function for very good quality and square root function for average quality, between these bound. The function for good dimensional quality is given by δ 1 δ δ max µ = δ good max (6) 0 δ max > δ where δ denotes absolute standard deviation. The membership functions for very good and average dimensional quality are given by equation (5). Membership Functions for Metal Removal Rate The material removal rate is defined as the product of feed, cutting speed and depth of cut. By observing the experimental data, it is seen that taking maximum values for feed, velocity and depth of cut, a metal removal rate of 545 mm 3 /min is obtained. Hence, a membership grade of 1 is given to this maximum value and a grade of 0 is assigned to metal removal rate of 0. A linear membership function is used between these two extreme values. The membership grade values for very good production rate and average production rate are respectively the square and square root of the membership function of good production rate. OPTIMIZATION METHODOLOGY The performance index can be optimized in two ways- by inverse process model (Azouzi and Guillot, 1998) or by Genetic Algorithm. The basic principle of inverse process model is that the controller starts from some initial set of operating conditions. In an iterative manner, the controller tries to shift from current operating point to a operating point having er performance index. In the present work, a total of 1215 exemplers were generated by direct process network for training the inverse process network, by taking various sets of operating points. The number of neurons in hidden layer of inverse process network is 14. The error converged in about 10,000 epochs. In Genetic algorithm approach, the feed and cutting speed are the parameters of optimization that have been encoded in the form of binary string of 16 bits with 8 bits dedicated to each parameter. The number of members selected in each generation is 10. It is seen that for all the objectives, solution converges to optimum in about 400 generations of Genetic Algorithm. GA provides many solutions out of which the solution, for which the product of membership grades is the maximum, is chosen. This is based on the compensating strategy where one objective compensates for other. GA takes slightly more time than inverse process model, but the overall performance index is slightly er because of the ability of GA to find global optimum. EXAMPLES The computer simulations were carried out for a job of 200-mm length and 30 mm diameter being turned at a depth of cut of 1 mm. Figure 2 shows the results obtained when the objective is to have very low cost, very good quality and very production rate. Optimization has been carried out by inverse neural model. It is observed that steady state is obtained in about 20 iterations of the optimization process. The overall performance index 4

5 is 0.23, indicating that this objective is cannot be fulfilled properly as the performance index is quite low Iteration Iteration Iteration Fig.2. Optimization results for the objective of very low cost, very good quality and very production rate Table 1 compares the results obtained from inverse neural model for various objectives. The simulation 3 gives overall performance index of 0.54, indicating that this objective is more achievable compared to simulations 1, 2 and 4. Reason is that the requirement on dimensional deviation and surface finish is less stringent, and consequently the controller could provide er feed. Table 2 compares the overall performance index obtained by Genetic Algorithm and inverse neural model. In the case of GA, the overall performance index is slightly er. This is because GA finds global optimum, whereas the neural network model has tendency to find local optimum. The computational time requirement is more in GA. Comparison with Traditional Model If the feed and speed are computed by traditional method for minimum cost, by partial differentiation of expression (1) with respect to feed and speed, the minimum cost of machining comes out to be Rs. 198 (Rs. 200 by fuzzy arithmetic), with feed and speed value of 0.6 mm/rev and 39 m/min respectively. Tool life parameters n, n1 and c are 0.3, 0.31 and 75 respectively. Handling and setting times are 3 and 2 minutes respectively and C u and C e are Rs. 50/min and Rs. 51. It is seen from Table 1 that when the requirement on job quality is not stringent, cost of manufacturing comes equal to minimum cost (simulation 3). When the requirement on quality is very stringent (simulation 1), the cost of manufacture increases, since in order to maintain better surface finish, feed has to be decreased. Traditional method does not have provision to incorporate quality. It also is unsuitable for adaptive control where based on sensor data, the process parameters have to be changed. CONCLUSIONS A neuro-fuzzy approach for optimization of single pass turning process has been proposed. The optimization model is capable of incorporating human knowledge, experience and view point of a decision-maker in the solutions. The optimum solutions can be obtained by inverse neural model or GA. GA is found to be more effective, even though it requires more computational time. The model can be easily extended to multiple pass turning and other machining operations. Experimental work is needed in order to fine -tune the proposed methodology. REFERENCES Abulenaga, A.M., and El-Dardiry (1984) Optimization Methods for Metal Cutting, Int. Jl. Mach. Tools Des. Res., Vol. 24, pp Azouzi, R., and Guillot, M. (1998) On Line Optimization of Turning Process Using Inverse Process Neuro Controller, ASME Jl. of Manuf. Sci. and Engng, Vol. 120, pp Table 1 Comparison of Results Obtained from Inverse Neural Model for Various Objectives 5

6 Simulat -ion no. 1 low 2 low 3 low 4 Average Cost Quality Production rate good Good Dimensional deviation (mm) Average Good Feed (mm/re) Speed (m/min) Cost (Rs.) MRR (mm 3 /s) Ra micron Overall perform ance index (µ) Table 2 Comparison of Results by Inverse Neural Model and GA Simulation no. Overall performance index (by Inverse neural model) Overall performance index (by GA) Fang, X.D., and Jawahir, I.S., (1994) Predicting Total Machining Performance in Finish Turning Using Integrated Fuzzy Set Models of Machinability Parameters, Int. Jl. Prod. Res., Vol. 32, pp Jammu, V.B., and Danai, K. (1993) Unsupervised Neural Network for Tool Breakage Detection in Turning, Annals of CIRP, Vol. 42, pp Ko, T.J., and Cho, D.W. (1998) Adaptive Optimization of Face Milling Operations Using Neural Networks, ASME Jl. of Manuf. Sci. and Engng, Vol. 120, pp Rangwala, S.S. and Dornfeld, D.A. (1989) Learning and Optimization of Machining Operations Using Computing Abilities of Neural Networks, IEEE Trans. System, Man & Cybernatics, Vol. 19, pp Tarng, Y.S., Hseigh, Y.H., and Hway, S.T. (1994) Sensing Tool Breakage in Face Milling with Neural Networks, Int. Jl. Mach. Tools. Manuf., Vol. 34, pp Li, X.Q., Wong, Y.S., and Nee, A.Y.C. (1998) A Comprehensive Identification of Tool Failure and Chatter Using a Parallel Multi Art-2 Neural Network. ASME Jl. of Manuf. Sci. and Engng, Vol. 120, pp Liao, T.W. and Chen L.J.(1993) A Neural Network Approach for Grinding Process: Modeling and Optimization, Int. J. Mach. Tools Manuf., Vol. 34, pp Panchal, J.H., Khanna, R., and Dixit, U.S. (2000) Optimization of Turning Process Using Genetic Algorithm Based Neuro-Fuzzy Controller, Proc. Optimization Techniques in Manufacturing Processes (OTMP), KCT, Coimbatore, India. 6