Model of Dependence Between the Parameters of Surface Roughness and the Parameters of Form and Location During the Machining by Drills with the use of Artificial Neural Networks


 This paper presents a model of dependence between the parameters of surface roughness and the parameters of cylindricity and eccentricity in drilling operation for the enhancing steel EN 42CrMo4, hardness 28 HRC, with twist drills DIN 338 made of high-speed steel EN HS6-5-2, with normal blade. The quality of machining, besides the accuracy of measures, completely determined with the values of the parameters of the surface roughness and the parameters of form and location, hence this paper is oriented to the creating models between parameters of the quality of a machined surface and parameters of deviations from form and position. By the developing models based on artificial neural networks and using experimental results, it is possible to analyse the quality of machining on the basis of parameters of a surface roughness.


Introduction
In making products, regarding the aspect of the quality of machining, a special attention is devoted to their dimensional accuracy and the quality of machined surfaces, hence the measurement of both roughness parameters and accuracy parameters is especially important. The accuracy of machining comprises a precision of measures, accuracy of shapes of surfaces and accuracy of mutual relationships of two or more surfaces, while the quality of a machined surface is most often determined through a surface roughness. Since the quality of machining, besides the accuracy of measures, is completely determined by the values of parameters of the quality of a surface roughness and the parameters of form and location, this paper is oriented to the establishment of a model between parameters of quality of machined surface and parameters of form and position deviations. By the development of models based on neural networks by using experimental results, it is possible to analyse the quality of machining on the basis of the parameters of a surface roughness.
Krivokapić, Z., et al [1], give the application of a multiple regression and arti cial neural networks (ANNs), and this paper describes the development of models for the predicting a surface roughness, linking an arithmetic mean deviation of a surface roughness to a torque as an input variable, in the process of drilling.
Paper Vučurević, R., et al [2] presents the models for prediction of an arithmetic mean deviation of a surface roughness using arti cial neural networks, developed on the basis of parameters of drilling process and an axial force obtained for different values of blunting twist drills, based on the experimental results by using Taguchi design of experiment.
Peper Vučurević, R., et al [3] presents a comparative analysis of the models for the predicting a surface roughness developed by the application of a multiple regression and arti cial neural networks. These models were developed using experimental data for an arithmetical mean deviation of a surface roughness and the axial cutting force obtained by implementing the Taguchi design of experiment.
Paper by Spaić, O., at al [4] presents the prediction of a tool condition by applying a family of arti cial neural networks.
Çiçek, A., Kivak, T. and Samtaş, G. [13], by the application of Taguchi design of experiment, have found an optimal combination of the process parameters from the aspect of a surface roughness, while drilling an austenite stainless AISI 316 by twist drills of high-speed steel (HSS), in conventionally and cryogenically processes, varying a feed f [mm/o] and a cutting speed v [m/min] on two levels.
Raghunandan, B.V., Bhandarkar, S.L. and Pankaj, K.S. [14] also used a regression analysis to obtain a surface roughness model, while machining EN-19 material by turning with cemented carbide inserts.
Kumar, P.J. and Packiaraj, P. [15] used Tacuchi design of experiment, regression analysis and the analysis of a variance for the purposes of the researching the impact of drilling parameters such as a cutting speed v [m/min], feed f [mm/o] and a diameter of a twist drill d [mm], on a surface roughness and deviation of a hole diameter from rated values for drilling OHNS material, tool steel that is widely used in the production of tools, by twist drills made of high-speed steel (HSS).
Xu, Y., et al [16] present a very interesting paper related to the application of a back propagation wavelet neural network based prediction of a drill wear from thrust force and cutting torque signals.

Processing Quality Parameters
Mechanical machining yields micro-geometrical deviations of a machined surfaces in comparison to an ideal surface. These micro-geometric deviations, which characterise the quality of a machined surface, are called a surface roughness that have big impacts on the functional characteristics of machine parts [17]. Surface roughness, whose basic terms are prescribed by ISO 4287 standard [18], can be traced through several amplitude parameters of a roughness pro le such as maximum pro le height R p , maximum pro le valley depth R v , maximum height of the pro le R z , arithmetical mean deviation of assessed pro le R a (Figure 1).
Based on standard ISO 4287, a maximum pro le height R p is the largest pro le peak height within on the sampling length l r , while a maximum pro le valley depth R v is largest pro le valley depth within on the same length. A maximal height of the pro le is the sum of height of the largest pro le peak height and the largest pro le valley depth within a sampling length l r .
According to this standard, an arithmetical mean deviation of the assessed pro le R a is arithmetic mean of the absolute ordinate values Z(x) within a sampling length l r : An arithmetical mean deviation of the pro le is the most often used of all the standardized parameters for the measuring a surface roughness R a [19].
When making holes during the machining by drilling, the deviations of form and sizes of holes occur and it represents a geometrical difference between a hole given on the drawing and a real hole during the very development [20]. The most common parameters of form and location which are applied during making openings, holes and parts of a circular crosssection are roundness, cylindricity, and concentricity, and, besides the mentioned parameters, a tilting of a hole axis in relation to an ideal axis given by the drawing (eccentricity) can be traced as an additional parameter.
For the roundness, a tolerated circumferential line must lie into a round ring of a given tolerated width, while for cylindricity the tolerated cylindrical surface must lie between two coaxial cylinders, given the tolerated radial distance. For concentricity, an axis of tolerated part must lie inside a cylinder of given tolerated diameter whose axis coincides with the axis of a referent element [21].

Experimental Results
The experimental results were obtained by measuring values of an arithmetical mean deviation of the pro le, as parameters of the surface roughness and the parameters of form and location conducting the experiment by a Taguchi orthogonal experimental plan, with varying factors of experiment (d -diameter of twist drill, n -speed, f -feed, ε -angle of installation of the workpiece) on three levels.
In this paper, the Taguchi orthogonal experiment plan L 9 [22], given in Table 1, with nine combinations of machining process parameters, was used. The experiment was carried out by drilling holes with a depth of l=3d in a test tube made of enhancement steel , hardness 28 HRC, using twist drills DIN 338 of high speed steel EN HS6-5-2 with normal blade.
The measurement of a surface roughness was done by measuring an arithmetical mean deviation (R a ) in a characteristic moments by rotating test tube for an angle of 90 o and measuring roughness at four characteristic positins, where a mean value of the measured values was taken as valid.
Before the start of the measurement, a validation of measuring device SURTRONIC 25 was carried out using a reference panel type 112/1534, with a value of arithmetical mean deviation of a surface roughness R a = 6 μm. Figure 2 presents the results of validation.
The measurement of form and location deviation, cylindricity (c) and eccentricity (e), was carried out in characteristic moments during drilling by twist drills, with normal blade in a test tube whose hardness is 28 HRC.
Before the start of the measurement, a quali cation of the stylus for measurement three-coordinate measurement device CONTURA G2 AKTIV manufactured by CARL ZEISS, measurement range 700x700x600 mm, with a CALYPSO measurement software, using a reference sphere and stylus for the quali cation was executed. Figure 3 gives the results of the quali cation.
The overview of the results of the measurement of an arithmetical mean deviation of pro le (R a ), cylindricity (c) and eccentricity (e), for different wear values on back surface of a twist drill (VB), is presented in Table 2.

Correlational Interdependences
With the goal to determine the existence of a correlational interdependence between an arithmetical mean deviation of the pro le and a cylindricity and eccentricity as parameters of form and location of a hole, the application of a scatter diagram on the data obtained for drilling by twist drills with normal blade in test tube with hardness of 28 HRC was carried out. The scatter diagram of roughness -cylindricity (Figure 4), was created by using data for arithmetical mean deviation of the pro le (R a ) and cylindricity (c) measured in characteristic moments, at the beginning of the process (VB=0 mm), at the moment a mean bluntness of the tool (VB=0,02 d) as well as at the moment of a bluntness of the tool (VB=0,04 d).
Based on the same principle, by using data both for arithmetical mean deviation of the pro le (R a ) and eccentricity (e), measured in characteristic moments, a scatter diagram of roughness -eccentricity was created ( Figure 5).
Based on the comparative analysis of given scatter diagrams with characteristic scatter diagrams [23], it can be noticed that there is no correlational interdependence between an arithmetical mean deviation of the pro le and a cylindricity and eccentricity, as the form and location parameters.

Arti cial Neaural Networks (ann) Design
When a correlational interdependence cannot be established, then using of arti cial neural networks (ANN) is recommended [24]. The creation of the model based on arti cial neural networks for the wear values on back surfaces of twist drills VB=0 mm and VB=0,04d was carried out Using MATLAB software package, based on the experimental results.
The creation of the model with several inputs and one output was done using Backpropagation arti cial neural network with two hidden layers with a sigmoidal transfer function and a linear transfer function in the output layer. The least errors in training, validation and testing were achieved by a neuron network of 15 neurons in the rst hidden layer, 10 neurons in the second hidden layer, and the learning function LEARNGDM.
The input data, used for training of the ANN for the prediction of cylindricity, were; diameter of twist drill, speed, feed, angle of installation of the workpiece and an arithmetical mean deviation of surface roughness, while a cylindricity was used as an output. Figure 6 presents the arti cial neural network architecture which yielded a cylindricity as the output through two hidden layers with ve inputs. The data used for training were the data obtained by the experiment for VB=0 mm and VB=0,04d and calculated for VB=0,01d and VB=0,03d.
The network for the predicting eccentricity cannot be established by previous analogy, hence an approach from paper [4] was used in this paper. Therefore, a cylindricity was introduced as the sixth input what provided an acceptable convergence of the network and only then it yielded the results. Figure 7 presents the architecture of arti cial neural network which yielded an eccentricity as the output through two hidden layers with six inputs.
The simulation of both networks was carried out for data obtained by the experiment for h=0,02d, and the results are given on Figure 8a for cylindricity and on 8b for eccentricity.
Based on the comparative analysis of the results obtained in the experiment and the result of arti cial neural networks, it is possible to prove that a mean error for cylindricity is 15,29%, while it is 13,57% for eccentricity.

Conclusions
Based on the experimental results, it can be seen that the value of an arithmetical mean deviation of the pro le as a parameter of surface roughness rises with tool wear, while the parameters of form and location, cylindricity and eccentricity have no such a trend. The check of a correlational interdependence between an arithmetical mean deviation, as well as the parameters of the surface roughness, and cylindricity and eccentricity, as the parameters of form and location, leads to the conclusion that the parameters of the surface roughness are not in a correlational interdependence with the parameters of form and location.
Therefore, this paper is oriented to the establishing a model between the parameters of the surface roughness and form and location parameters. By developing models based on arti cial neural networks and using experimental data it is possible to estimate the quality of machining on the basis of surface roughness parameters.
Based on the comparative analysis of the results obtained by the experiment and simulation of neural networks, it can be established that a mean error for cylindricity is 15,29%, while it is 13,57% for eccentricity.