Prediction of Surface Roughness in CNC Milling of ...

Mathematical Models and Computational Methods

Prediction of Surface Roughness in CNC Milling of Al7075 alloy: A case study of using 8mm slot mill cutter J. Kechagias, P. Kyratsis, K. Kitsakis and N. Mastorakis

interact with the environment due to their influence on mechanical properties [3]. Surface roughness or texture constitutes a measure for achieving finer surface irregularities in the finished product, while three components i.e., roughness, waviness, and form are required for its determination [4]. A number of methodologies investigating the relations of the cutting parameters with the produced surface quality are reported in literature. Response surface methodology (RSM) is one of the mostly used in order to build mathematical models based on the Taguchi theory [5]. Other researchers are combining the application of fuzzy logic with the Taguchi method and optimise the surface roughness achieved [6, 7]. The present paper deals with the effects of different process parameters: depth of cut (ap), cutting speed (Vc), and feed rate (f) on the surface quality, when slot milling Al7075 alloy workpieces. A set of experiments using design of experiments and Neural Networks modelling were used and the surface texture parameters measured during this study were the following: Ra (the arithmetic mean surface roughness) and Rz (the mean of 5 maximum peak-to-valley roughness depths in 5 successive sampling lengths), all measured in μm. Experimental results are used in order to train a feed forward back propagation neural network (FFBP-NN) and predict the surface texture parameters in finish slot milling of Al7075 alloy parts. The use of the FFBP-NN together with the performed experiments resulted in a successful way to model the process and predict the surface texture parameters when different cutting parameters apply.

Abstract—The current study investigates the surface roughness of slots produced using an 8mm slot mil cutter during milling of Al7075 alloy. Twenty seven slots were cut using all the different cutting conditions by a KC633M 8mm drill-slot end mill cutter. The three independent variables considered were the depth of cut (ap, mm), cutting speed (Vc, m/min), and feed rate (f, mm/rev); each one having three different levels. Process performance is estimated using the statistical surface texture parameters Ra, and Rz; both measured in microns. To predict the surface roughness within the limits of the parameters involved, an artificial feed forward back propagation neural network model was designed for the data obtained. Keywords—Face Milling, Neural Networks, Modelling, Surface Texture Parameters I. INTRODUCTION Aluminum alloys are extensively used as a main engineering material in various industries automotive and aerospace industries, the mould and die components manufacturers and every case in which weight is the most important factor [1]. Surface roughness has an important role in the performance of finished components. It refers to the third up to the sixth order deviation from the nominal surface and all different order deviations are superimposed and form the surface roughness profile [2]. Surface properties dominate the quality of the finished component, since they influence features like dimensional accuracy; tribological characteristics such as the friction coefficient and wear; post processing requirements; appearance and cost. Besides the obvious problems related to correct dimensions, one of the more significant problems is achieving the appropriate finish or surface smoothness on the workpiece. Surface quality is important for a number of reasons i.e. aesthetic (a smooth and free from scratches surface is more likely to give a favorable impression to the customer), surfaces affect safety and they

II. EXPERIMENTAL SETUP The material used for performing the experiments was Al 7075 (90% Al, 5.6% Zn, 2.5% Mg, 1.6% Cu, and 0.23% Cr). A two flute end mill cutter (KC633M) made by Kennametal was used to perform 27 slots upon three plates. The cutter diameter was 8mm, the length 63mm and the helix angle 30o (Fig. 1). Three Al7075 plates with a thickness of 12mm (150mm in length and 50mm in width) were used to cut the slots (Fig. 2). A four axis HAAS VF1 CNC machining center with continuous speed and feed control within their boundaries was used for twenty seven slotting operations (Fig. 3). During cutting operations an appropriate coolant fluid was used.

J. Kechagias is with Department of Mechanical Engineering, Technological Educational Institute of Thessaly, Larisa, Greece (e-mail: [email protected]). P. Kyratsis is with Department of Mechanical Engineering and Industrial Design, Technological Education Institution of Western Macedonia, Kila Kozani, Greece (e-mail: [email protected]). K. Kitsakis is with Department of Mechanical Engineering, Technological Educational Institute of Thessaly, Larisa, Greece (e-mail: [email protected]). N. Mastorakis is with Department of Industrial Engineering, Technical University of Sofia, Sofia, Bulgaria (e-mail: [email protected]).

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Fig. 1: Cutting tool main dimensions

Fig. 2: Machined specimens of Al7075 alloy Fig. 4: Surface texture parameters

Fig. 5: Machined specimen and surface tester

The main cutting parameters (depth of cut - ap, in mm; cutting speed - Vc, in m/min; and feed rate - f, mm/rev) were assigned on a standard orthogonal array in order to explore the entire parametric space with a limited number of experiments. Three levels were specified for each of the three cutting parameters (Table 1, 2).

Fig. 3: HAAS VF1CNC machine centre (7500 rpm, 15 KW)

Surface roughness is a widely used index characterising a product’s quality, and is measured off-line, when the component is already machined. The surface texture parameters measured during this study were the following (Fig.4): • Ra(μm): the arithmetic average height of roughness irregularities measured from a mean line within the evaluation length (L) [Ra=(y1+y2+...yn)/n] • Rz(μm): the mean of 5 maximum peak-to-valley roughness depths in 5 successive sampling lengths [Rz=(Ry1+Ry2+Ry3+Ry4+Ry5)/5]

Table 1: Parameter design.

Νο 1 2 3

Levels 1 2 0.5 1 50 100 0.05 0.08

3 1.5 150 0.11

Table 2: Matrix of experiments

Surface roughness measurements were taken using a RUGOserf tester. For the purposes of the current research, a full factorial experiment plan was used [8, 9, 12, 13].

ISBN: 978-1-61804-350-4

Process Parameters Depth of cut (ap, mm) Cutting Speed (Vc, m/min) Feed Rate (f, mm/rev)

111

Ex. No.

ap mm

Vc m/min

f mm/rev

Ra μm

Rz μm

1 2 3 4

0.5 0.5 0.5 0.5

50 50 50 100

0.05 0.08 0.11 0.05

0.247 0.717 1.080 0.335

2.167 3.067 4.933 2.033


5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

0.5 0.5 0.5 0.5 0.5 1 1 1 1 1 1 1 1 1 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

100 100 150 150 150 50 50 50 100 100 100 150 150 150 50 50 50 100 100 100 150 150 150

0.08 0.11 0.05 0.08 0.11 0.05 0.08 0.11 0.05 0.08 0.11 0.05 0.08 0.11 0.05 0.08 0.11 0.05 0.08 0.11 0.05 0.08 0.11

0.427 0.813 0.250 0.377 0.423 0.307 0.557 0.867 0.387 0.693 1.017 0.447 0.617 0.907 0.307 0.497 0.773 0.343 0.620 0.853 0.657 0.567 0.990

networks have an input layer of X inputs, one or more hidden layers with several neurons and an output layer of Y outputs. In the selected ANN, the transfer function of the hidden layer is hyperbolic tangent sigmoid, while for the output layer a linear transfer function was used. The input vector consists of the three process parameters of Table 1 and the constant value one (1). The output layer consists of the performance measures, namely the Ra and Rz surface texture parameters. According to ANN theory FFBP-NNs one hidden layer is appropriate to model each mapping between process parameters and performance measures in engineering problems [16]. In the present work, five trials using FFBP-NNs with one hidden layer were tested having 5, 6, 7, 8, and 9 neurons each (Fig. 6). The one with 6 neurons on the hidden layer gave the best performance, as indicated from the results tabulated in Table 3. The one-hidden-layer 6-neurons FFBB-NN was trained using the Levenberg-Marquardt algorithm (TRAINLM) and the mean square error (MSE) was used as the objective function. The data used were randomly divided into three subsets, namely the training, the validation and the testing samples. Back-propagation ANNs are prone to the overtraining problem that could limit their generalization capability [15]. Overtraining usually occurs in ANNs with a lot of degrees of freedom [16, 17] and after a number of learning loops, in which the performance of the training data set increases, while the performance of the validation data set decreases. Mean squared error (MSE) is the average squared difference between network output values and target values. Lower values are better. Zero means no error. The best validation performance is equal to 0.306 at epoch 2 (Fig. 7).

3.500 5.400 1.933 3.467 3.933 2.100 3.567 4.267 2.500 3.567 4.800 3.133 3.700 5.000 2.133 3.433 4.467 2.600 3.867 5.000 4.400 3.667 4.467

III. NEURAL NETWORK ARCHITECTURE Aiming in the prediction of the produced surface roughness parameters (Ra, and Rz) during slot milling of an AL7075 alloy, a NN model has been developed. The three factors studied were used as input parameters of the NN model, together with the constant value one (1). Previous studies indicate that by using DoE methods, a structured method of NN parameter-setting can be implemented [14]. It identifies NN and training parameter settings, resulting in enhanced NN performance. Training samples are presented to the NN during training, and the network is adjusted according to its error. The twenty seven (27) experimental data samples (Table 2), were separated into three groups, namely the training, the validation and the testing samples (70%, 15%, and 15% respectively). Training samples were presented to the network during training and the network was adjusted according to its error. Validation samples were used to measure network generalization and to halt training, when generalization stopped improving. Testing samples have no effect on training and so they provide an independent measure of network performance during and after training (confirmation runs). In general, a standard procedure for calculating the proper number of hidden layers and neurons does not exist. For complicated systems the theorem of Kolmogorov or the Widrow rule can be used for calculating the number of hidden neurons [15]. In this work, the feed-forward with backpropagation learning (FFBP) architecture has been selected to analyze the surface texture parameters. These types of ISBN: 978-1-61804-350-4

Fig. 6: The selected ANN architecture (feed-forward with backpropagation learning). Table 3. Best performance of ANN architecture. ANN Architecture 4x5x2 4x7x2 4x8x2 4x6x2 0.997 0.998 0.996 Training 0.993 0.794 0.580 0.767 Validation 0.821 0.897 0.784 0.705 Test 0.791 0.896 0.883 0.881 All 0.919 Best val. 0.612 1.584 2.0541 0.306

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4x9x2 0.996 0.705 0.691 0.827 1.774


epoch

3

2

6

4

3

Fig. 7: The selected ANN architecture (feed-forward with backpropagation learning).

Fig. 10: Regression plots-Test

Another performance measure for the network efficiency is the regression (R) (Figs 8-11). Regression values measure the correlation between output values and targets. The acquired results show a good correlation between output values and targets during training (R=0.993), validation (R=0.821), and testing procedure (R=0.791). The trained ANN model can be used for the optimization of the cutting parameters during slot milling of Al7075 alloy. This can be done by testing the behavior of the response variable (Ra and Rz) under different variations in the values of depth of cut (ap), cutting speed (Vc), and feed rate (f) (Fig. 1213).

Fig. 11: Regression plots-Validation

Fig. 8: Regression plots-Training Fig. 12: Ra vs. feed rate and cutting speed (ap=1.5mm)

Fig. 9: Regression plots-Validation

Fig. 13: Rz vs. feed rate and cutting speed (ap=1.5mm) ISBN: 978-1-61804-350-4

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IV. CONCLUSIONS The surface texture parameters (Ra and Rz) of Al7075 parts during slot milling were measured according to an orthogonal matrix of experiments. The results were used to train a feed forward back propagation neural network with a topology of 4X6X3 neurons. The proposed NN can be used to predict the surface texture parameters as well as to optimize the process according to each one of the surface texture parameters. As a future work, authors plan to improve the performance of FFBP-NN incorporating more experiments as well as investigate the performance of alternatives training algorithms. In addition, a comparison among other approaches such as regression and additive modeling will be performed. Using the extracted NN, the surface response of Ra and Rz can be drawn and the effects of process parameters can be estimated inside the experimental region in which the designed experiments were conducted. This methodology could be easily applied to different materials and initial conditions for optimization of other material removal processes.

[12] [13]

[14]

[15]

[16] [17]

ACKNOWLEDGMENT The authors express special thanks to Mr Konstantinos Sirgkanis for their support during the developed laboratory activities. REFERENCES [1]

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