Vol. 27 No. 2 2025 3 EDITORIAL COUNCIL EDITORIAL BOARD EDITOR-IN-CHIEF: Anatoliy A. Bataev, D.Sc. (Engineering), Professor, Rector, Novosibirsk State Technical University, Novosibirsk, Russian Federation DEPUTIES EDITOR-IN-CHIEF: Vladimir V. Ivancivsky, D.Sc. (Engineering), Associate Professor, Department of Industrial Machinery Design, Novosibirsk State Technical University, Novosibirsk, Russian Federation Vadim Y. Skeeba, Ph.D. (Engineering), Associate Professor, Department of Industrial Machinery Design, Novosibirsk State Technical University, Novosibirsk, Russian Federation Editor of the English translation: Elena A. Lozhkina, Ph.D. (Engineering), Department of Material Science in Mechanical Engineering, Novosibirsk State Technical University, Novosibirsk, Russian Federation The journal is issued since 1999 Publication frequency – 4 numbers a year Data on the journal are published in «Ulrich's Periodical Directory» Journal “Obrabotka Metallov” (“Metal Working and Material Science”) has been Indexed in Clarivate Analytics Services. Novosibirsk State Technical University, Prospekt K. Marksa, 20, Novosibirsk, 630073, Russia Tel.: +7 (383) 346-17-75 http://journals.nstu.ru/obrabotka_metallov E-mail: metal_working@mail.ru; metal_working@corp.nstu.ru Journal “Obrabotka Metallov – Metal Working and Material Science” is indexed in the world's largest abstracting bibliographic and scientometric databases Web of Science and Scopus. Journal “Obrabotka Metallov” (“Metal Working & Material Science”) has entered into an electronic licensing relationship with EBSCO Publishing, the world's leading aggregator of full text journals, magazines and eBooks. The full text of JOURNAL can be found in the EBSCOhost™ databases.
OBRABOTKAMETALLOV Vol. 27 No. 2 2025 4 EDITORIAL COUNCIL EDITORIAL COUNCIL CHAIRMAN: Nikolai V. Pustovoy, D.Sc. (Engineering), Professor, President, Novosibirsk State Technical University, Novosibirsk, Russian Federation MEMBERS: The Federative Republic of Brazil: Alberto Moreira Jorge Junior, Dr.-Ing., Full Professor; Federal University of São Carlos, São Carlos The Federal Republic of Germany: Moniko Greif, Dr.-Ing., Professor, Hochschule RheinMain University of Applied Sciences, Russelsheim Florian Nürnberger, Dr.-Ing., Chief Engineer and Head of the Department “Technology of Materials”, Leibniz Universität Hannover, Garbsen; Thomas Hassel, Dr.-Ing., Head of Underwater Technology Center Hanover, Leibniz Universität Hannover, Garbsen The Spain: Andrey L. Chuvilin, Ph.D. (Physics and Mathematics), Ikerbasque Research Professor, Head of Electron Microscopy Laboratory “CIC nanoGUNE”, San Sebastian The Republic of Belarus: Fyodor I. Panteleenko, D.Sc. (Engineering), Professor, First Vice-Rector, Corresponding Member of National Academy of Sciences of Belarus, Belarusian National Technical University, Minsk The Ukraine: Sergiy V. Kovalevskyy, D.Sc. (Engineering), Professor, Vice Rector for Research and Academic Aff airs, Donbass State Engineering Academy, Kramatorsk The Russian Federation: Vladimir G. Atapin, D.Sc. (Engineering), Professor, Novosibirsk State Technical University, Novosibirsk; Victor P. Balkov, Deputy general director, Research and Development Tooling Institute “VNIIINSTRUMENT”, Moscow; Vladimir A. Bataev, D.Sc. (Engineering), Professor, Novosibirsk State Technical University, Novosibirsk; Vladimir G. Burov, D.Sc. (Engineering), Professor, Novosibirsk State Technical University, Novosibirsk; Aleksandr N. Korotkov, D.Sc. (Engineering), Professor, Kuzbass State Technical University, Kemerovo; Dmitry V. Lobanov, D.Sc. (Engineering), Associate Professor, I.N. Ulianov Chuvash State University, Cheboksary; Aleksey V. Makarov, D.Sc. (Engineering), Corresponding Member of RAS, Head of division, Head of laboratory (Laboratory of Mechanical Properties) M.N. Miheev Institute of Metal Physics, Russian Academy of Sciences (Ural Branch), Yekaterinburg; Aleksandr G. Ovcharenko, D.Sc. (Engineering), Professor, Biysk Technological Institute, Biysk; Yuriy N. Saraev, D.Sc. (Engineering), Professor, V.P. Larionov Institute of the Physical-Technical Problems of the North of the Siberian Branch of the RAS, Yakutsk; Alexander S. Yanyushkin, D.Sc. (Engineering), Professor, I.N. Ulianov Chuvash State University, Cheboksary
Vol. 27 No. 2 2025 5 CONTENTS OBRABOTKAMETALLOV TECHNOLOGY Sundukov S.K., Nigmetzyanov R.I., Prikhodko V.M., Fatyukhin D.S., Koldyushov V.K. Comparison of ultrasonic surface treatment methods applied to additively manufactured Ti-6Al-4V alloy................................................................ 6 Kate N., Kulkarni A.P., Dama Y.B. A comparative evaluation of friction and wear in alternative materials for brake friction composites............................................................................................................................................................... 29 Naumov S.V., Panov D.O., Sokolovsky V.S., Chernichenko R.S., Salishchev G.A., Belinin D.S., Lukianov V.V. Microstructure and mechanical properties of Ti2AlNb-based alloy weld joints as a function of gas tungsten arc welding parameters............................................................................................................................................................................. 43 Jatti V.S., Singarajan V., SaiyathibrahimA., Jatti V.S., KrishnanM.R., Jatti S.V. Enhancement of EDM performance for NiTi, NiCu, and BeCu alloys using a multi-criteria approach based on utility function................................................ 57 Stelmakov V.A., Gimadeev M.R., Nikitenko A.V. Ensuring hole shape accuracy in fi nish machining using boring...... 89 EQUIPMENT. INSTRUMENTS Patil N., Agarwal S., Kulkarni A.P., Saraf A., Rane M., Dama Y.B. Experimental investigation of graphene oxide-based nano cutting fl uid in drilling of aluminum matrix composite reinforced with SiC particles under nano-MQL conditions............................................................................................................................................................................. 103 Gimadeev M.R., Stelmakov V.A., Nikitenko A.V., Uliskov M.V. Prediction of surface roughness in milling with a ball end tool using an artifi cial neural network................................................................................................................. 126 Osipovich K.O., Sidorov E.A., Chumaevskii A.V., Nikonov S.N., Kolubaev E.A. Manufacturing conditions of bimetallic samples based on iron and copper alloys by wire-feed electron beam additive manufacturing......................... 142 Babaev A.S., Savchenko N.L., Kozlov V.N., Semenov A.R., Grigoriev M.V. Performance of Y-TZP-Al2O3 composite ceramics in dry high-speed turning of thermally hardened steel 0.4 C-Cr (AISI 5135)...................................................... 159 MATERIAL SCIENCE Sokolov R.A., Muratov K.R., Mamadaliev R.A. Morphological changes of deformed structural steel surface in corrosive environment......................................................................................................................................................... 174 Chernichenko R.S., Panov D.O., Naumov S.V., Kudryavtsev E.A., Salishchev G.A., Pertsev A.S. Eff ect of heterogeneous structure on mechanical behavior of austenitic stainless steel subjected to novel thermomechanical processing............................................................................................................................................................................. 189 Panov D.O., Chernichenko R.S., Naumov S.V., Kudryavtsev E.A., Salishchev G.A., Pertsev A.S. Eff ect of cold radial forging on structure, texture and mechanical properties of lightweight austenitic steel................................................ 206 Deshpande A., Kulkarni A.P., Anerao P., Deshpande L., Somatkar A. Integrated numerical and experimental investigation of tribological performance of PTFE based composite material.................................................................... 219 Vorontsov A.V., Panfi lov A.O., Nikolaeva A.V., Cheremnov A.V., Knyazhev E.O. Eff ect of impact processing on the structure and properties of nickel alloy ZhS6U produced by casting and electron beam additive manufacturing........ 238 Misochenko A.A. Martensitic transformations in TiNi-based alloys during rolling with pulsed current........................... 255 EDITORIALMATERIALS 270 FOUNDERS MATERIALS 279 CONTENTS
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 2 5 Prediction of surface roughness in milling with a ball end tool using an artificial neural network Mikhail Gimadeev a, *, Vadim Stelmakov b, Aleksandr Nikitenko c, Maksim Uliskov d Pacific National University, 136 Tihookeanskaya St., Khabarovsk, 680035, Russian Federation a https://orcid.org/0000-0001-6685-519X, 009063@togudv.ru; b https://orcid.org/0000-0003-2763-1956, 009062@togudv.ru; c https://orcid.org/0000-0003-4729-5558, 005392@togudv.ru; d https://orcid.org/0009-0001-9858-423X, 2016104779@togudv.ru Obrabotka metallov - Metal Working and Material Science Journal homepage: http://journals.nstu.ru/obrabotka_metallov Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science. 2025 vol. 27 no. 2 pp. 126–141 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2025-27.2-126-141 ART I CLE I NFO Article history: Received: 30 January 2025 Revised: 01 March 2025 Accepted: 27 March 2025 Available online: 15 June 2025 Keywords: Milling Roughness Regression analysis Artificial intelligence Neural network Standard error Funding This work has funded by the Ministry of science and higher education of Russian Federation (project № FEME– 2024–0010). ABSTRACT Introduction. Milling stainless steel with a ball-end tool is a complex technological process that requires precise control of processing parameters to ensure high surface quality. In this regard, it is an urgent task to develop methods for predicting roughness parameters, such as Rz. The aim of this work is to develop a predictive neural network model that can estimate surface roughness when milling stainless steel using a ball-end tool. Method and methodology. The main focus is on error backpropagation and gradient descent methods, as well as hyperparameter tuning, which are necessary to prevent overfitting and underfitting of the model. Experimental studies include the analysis of both controlled variables, such as feed per tooth, angle of inclination and diameter of the tool, and uncontrolled, including coolant supply and tool wear. Results and discussions. The use of coolant for milling austenitic steel has reduced the roughness parameters Rz by an average of 14%. A strong negative correlation has been established between the dimensional wear of the tool and the parameter Rz (−0.95). At the same time, wear in the range of 2…4 μm affects an increase in the Rz parameter by 21% compared to the minimum values. The data obtained were used to train eight configurations of artificial neural networks, which were used to predict roughness using the Rz parameter. The results show that the 3-16-16-1 network configuration showed the lowest MSE (0.0313), followed by 3-20-14-1 (0.0470) and 3-64-64-1 (0.0481), respectively. In addition, these configurations also demonstrated the lowest average absolute error values, which demonstrate the average of the absolute differences between predicted and observed values (0.1014; 0.1251 and 0.1155, respectively), and the coefficient of determination, which is a statistical measure indicating the proportion of data variability explained by the model (0.9944; 0.9916; 0.9904). A comparison of the experimental data with the predictions of various models allowed us to determine the average value of the absolute differences for the models according to the parameter Ra ≈ 0.074. The study suggests approaches to training neural network models for accurate prediction of roughness parameters, which makes a significant contribution to the methods of modeling machining processes. For citation: Gimadeev M.R., Stelmakov V.A., Nikitenko A.V., Uliskov M.V. Prediction of surface roughness in milling with a ball end tool using an artificial neural network. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2025, vol. 27, no. 2, pp. 126–141. DOI: 10.17212/1994-6309-2025-27.2-126-141. (In Russian). ______ * Corresponding author Gimadeev Mikhail R., Ph.D. (Engineering), Associate Professor Pacific National University, 136 Tihookeanskaya st., 680035, Khabarovsk, Russian Federation Tel.: +7 924 216-31-39, e-mail: 009063@togudv.ru Introduction The quality of the machined surface plays a decisive role in ensuring the operational properties of machine parts [1]. Surface roughness (Rz and Ra) often serves as one of the main metrics for assessing the surface condition in the machining process [2]. Modeling methods for predicting Rz can be divided into three categories: experimental models, analytical models, and artificial intelligence (AI)-based models [3, 4]. In recent years, AI-driven models have become widely used among researchers to predict characteristics related to machining processes [5], and the use of artificial neural networks (ANN) is considered by the authors to predict surface roughness, tool wear, and other parameters in machining [6].
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 2 2025 To function effectively, neural models use a vast network of simple computing processors known as “neurons.” Neural networks are often used to solve complex problems in which the behavior of variables is not well known. One of their fundamental characteristics is the ability to learn from examples and apply this knowledge in a generalized way, which allows the creation of nonlinear models. This ability makes the use of ANN in multicriteria analysis very effective [7, 8]. The configuration of a neural network requires the definition of several important parameters: the number of nodes in the input layer, the number of hidden layers, the number of neurons in each hidden layer, and the number of neurons in the output layer. The state of neuron k is determined by the equation: 1 ( ) i = , n k i ki k S x w b where xi is the output signal calculated by a neuron i; wki is the synaptic weight between i and bk neurons; k is a weight associated with a constant, non–zero value known as the neuron’s bias. To use ANN, it is necessary to calculate synaptic weights and biases. The process of determining these parameters is called training and occurs iteratively, where the initial parameters are updated until the process reaches sufficient convergence. The activation function f describes how the internal input and the current activation state influence the determination of the next state of the block. The most commonly used types of activation functions can be identified as follows: Threshold function: 1, 0 ( ) . 0, 0 k k k if S f S if S A unit step function, or threshold function, is a mathematical function that takes the value 1 if its argument is greater than or equal to some threshold, and 0 otherwise. Piecewise linear function, an example of which can be represented as: , ; ( ) , , k k k k k aS d if S c f S eS g if S c where a, c, d, e, g are constants. A piecewise linear function consists of several linear sections, each defined on its own interval. The linear sections are connected to form a continuous function, although the derivative of such a function may be discontinuous at the junctions between sections. Sigmoidal function: 1 ( ) , 1 exp( ) k f S aµ where a is the slope parameter of the sigmoidal function. This function is the most commonly used and is characterized as an increasing function that balances linear and nonlinear behavior while maintaining its value within the range from 0 to 1. The choice of activation function can significantly impact network performance. The rectified linear unit (ReLU), defined as ReLU(X) = max{X, 0}, is currently the most widely used activation function and is popular in neural networks due to its non-saturation and non-linearity [9]. Compared to activation functions that exhibit saturation, such as the sigmoidal function, ReLU combined with gradient descent has superior performance. Gradient descent is a method used to minimize the loss function by adjusting the weights. In neural network training, the objective function is the output error of the network. The minima of the function form troughs, and the maxima form hills [10, 11].
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 2 5 Multilayer perceptrons (MLP) are recognized as the most widely used ANN models. A MLP consists of several layers: an input layer that receives raw data; one or more hidden layers that process the data by applying weights and activation functions; and an output layer that produces the final output or prediction based on the processed data. Neurons in each layer are connected only to neurons in the next layer, with no feedback or connections between neurons within the same layer. Additionally, a typical feature of MLP is the full connectivity between layers. An example of a network structure consisting of four layers: input layer, two hidden layers, and output layer, is shown in Fig. 1. Fig. 1. Neural network structure for predicting the roughness parameter Rz In this structure (Fig. 1), the input layer has 8 nodes, each hidden layer has 8 nodes, and the output layer has 1 node. The nodes in the input layer represent the following factors: feed per tooth (fz, mm/tooth), angle of inclination (γ, °), tool diameter (D, mm), cutting speed (V, mm/min), cutting depth (ap, mm), side step (ae, mm), coolant supply (W, l/min), and tool wear (r, mm). The node in the output layer represents the predicted surface roughness parameter (Rz, μm). The network shown is fully connected, meaning that each neuron in any layer is connected to all neurons in the previous layer. Signal flow through the network is from left to right, layer by layer. Considering a multilayer network with j and k nodes in each hidden layer, the example structure shown in Fig. 1 can be described by an 8–j–k–1 configuration. In general, the operation of this type of network is described by two main phases: forward propagation and back propagation. The process of training MLP networks using the back propagation (BP) method follows the sequence: Forward Propagation → Loss Calculation → Back Propagation → Weight Update. An essential feature of MLP networks is the nonlinearity of neuron outputs, achieved by using the activation function. Successfully building an ANN model based on the Rz response requires multi-factor experimentation and tuning. Although many researchers have applied ANN for modeling in various fields such as machine learning [12–14], there is still no clear guideline for building a predictive model. This study examines elements that can affect model performance and the Rz response using the capabilities of the TensorFlow Python library to reduce uncertainty and improve prediction quality. Four performance indicators (metrics) were selected to evaluate the accuracy of models for predicting surface roughness [15]. These metrics include the coefficient of determination (R²), mean absolute error (MAE), mean squared error (MSE), and root mean squared error (RMSE). The coefficient of determination
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 2 2025 (R²) shows what proportion of the variance of the dependent variable is explained by the independent variables of the model: 2 2 1 2 1 . n i i i n i i i Y Y R Y Y where n is the number of data; Yi is the observed values; Ŷ is the predicted values; Ȳ is the mean value of Y. Despite its usefulness, R² has limitations: it does not account for the number of predictors and can be biased by outliers. MAE is a measure of the absolute error | | Y Y between predicted and actual values: 1 0 1 . n i i i MAE Y Y n MAE is less sensitive to large errors than MSE and RMSE because it uses absolute error values. MSE and RMSE are characterized by the mean square error and its square root, respectively: 1 2 0 1 , n i i MSE Y i Y n 1 2 0 1 . n i i RMSE Y i Y n MSE is sensitive to large errors because squared differences increase with large deviations. Since RMSE is measured in the same units as the data itself, it is easier to interpret than MSE. However, like MSE, RMSE is also sensitive to large errors. Analysis of these metrics is critical for a comprehensive assessment of predictive performance [15, 16]. When comparing these metrics, special attention is paid to MSE, which has the advantage of detecting and accounting large errors, making it useful in machine learning tasks where minimizing large deviations is important.Additionally, MSE is smooth and differentiable, simplifying gradient computation in optimization methods such as gradient descent. Therefore, MSE is often a more suitable choice for accuracy assessment. Furthermore, the coefficient of determination R², with values close to 1, is considered most favorable. A preliminary data analysis is also performed before using machine learning models. This includes checking for normality and identifying/removing outliers that can significantly affect model accuracy. Model optimization is an important step for effective solutions. Configuring hyperparameters ensures the best performance estimated from validation datasets within the selected algorithm. Hyperparameters play a significant role in controlling the learning process and significantly affect predictive accuracy. Proper setting of hyperparameters also helps reduce overfitting and underfitting, improving accuracy. Dropout is a method to prevent overfitting by randomly excluding neurons during training, preventing coadaptation [14]. The aim of this work is to develop a predictive neural network model for assessing surface roughness when milling stainless steel with a ball-end tool. To achieve this aim, the following tasks were addressed: – study of predicting surface roughness parameter Rz when milling with a ball-end tool, including optimizing ANN architecture, selecting number of layers, and tuning model parameters to improve prediction accuracy. – analysis of the influence of various input parameters, including tool tilt angle, on roughness prediction accuracy, and development of an approach to minimize input data without loss of model effectiveness, as well as study of model applicability with limited training sets. – final testing of the developed model, assessment of accuracy using MSE, RMSE, MAE, and R² metrics, and evaluation of effectiveness through comparison of predicted and experimental data.
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 2 5 Research methodology Milling operations were performed on a DMG MORI DMU 50 universal milling machine with 9 kW power and maximum rotation speed nmax = 8,000 min −1. The workpiece was made of austenitic stainless steel AISI 321 with chemical composition,wt. %: C ≤ 0.12; Si ≤ 0.8; Mn ≤ 2.0; P ≤ 0.035; S ≤ 0.02; Ni 9–11; Cr 17–19; Ti < 0,8; Fe – bal. The cutting tool was a hard alloy with multilayer (TiN and TiNAl) PVD coating and fine-grained base, with diameters of 6, 8, 10, and 12 mm from Sandvik Coromant. During the experiments, measurements of tool radius wear (r, mm) by levels were obtained using a TT140 contact sensor from Heidenhain. Surface roughness after milling was measured using a SURFCOM 1800D profilometer; for this device, the error according to the standard is 3 %. Filter – 50 % Gaussian. The parameter of the basic length (step cutoff) was chosen to be 0.8 mm (ISO 4288:1996) for all measurements, since the expected range should be 0.5 < Rz ≤ 10. Tracing was performed three times in the direction of tool feed. Experimental design included controlled factors: ap, fz, γ, D, V, and uncontrolled factors: W and r. The response parameter was surface roughness Rz. After experiments, ANN models were built using Python with TensorFlow and Keras libraries for neural network creation, training, and regularization, NumPy for array operations, and Scikit-learn for data preprocessing. Experimental data were divided into training and test sets that went through a process of standardization and normalization, accounting for 70 % and 30 % of the total number of experiments performed, corresponding to 28 training attempts and 12 testing attempts. The neural network training algorithm used is the back propagation (BP) method. This method calculates the gradient of the loss function with respect to the weights of the neural network. During forward propagation, the input data passes through the network, generating an output prediction. The error of this prediction is then calculated and propagated back through the network, from the output layer through all hidden layers to the input layer. At each layer, the gradient of the error with respect to the weights is calculated. Hyperparameter values were tested and best values for the models are presented in Table 1. The optimizer (Adam) updates weights according to computed gradients. These steps are repeated for each training epoch, allowing iterative improvement of predictions. Results and discussion One of the most important distributions in statistics is the normal distribution, which describes typical behavior of many phenomena. To determine the distribution of Rz, measured data after mechanical processing of 512 surfaces with coolant were analyzed. For all surfaces, technological parameters were ap = 0.2 mm, ae = 0.4 mm. Roughness results (Rz) are shown in Fig. 2. Ta b l e 1 Hyperparameters for the BPNN model Model Hyperparameters Indicator Sequential Activation hidden layers Leaky ReLU Kernel_regularizer l1=0,0001, l2=0,0001 Dropout 0.01 Optmizer Adam Learning_rate 0.001 Loss mean_squared_error Metrics MSE, RMSE, MAE Batch size 16 Epochs 500
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 2 2025 Pearson goodness-of-fit test showed no basis for rejecting the hypothesis of normal distribution when conditions f > 100 and p > 0.05 are met. The sample Rz data deviate from the mathematical expectation of 5.357 μm by 0.389 μm on average. The data follow a normal distribution according to the 2σ rule with a probability of 0.9873. For neural network modeling, outliers were removed because they can distort results and reduce model ability to identify data patterns effectively [17]. For further experiments, depth and lateral pitch were kept constant at ap = 0.2 mm and ae = 0.4 mm [18], reducing the number of variable input parameters to three. Variable W is often considered stochastic and uncontrollable, introducing unexplained variance independent of explanatory variables and the model. Typically, W and r are treated as integral components of variability; their influence on Rz was considered fz = 0.4 mm/tooth, γ = 50°, D = 6 mm, z = 2. Results are shown in Fig. 3. Rational use of coolant is an important factor in increasing metal processing productivity. When using coolant, the roughness parameter Rz decreased by an average of 14 %. The dissipation rate depends significantly on cutting speed Vc (m/min) and material removal volume Q (cm³/min): , 1000 zj c S fzn z Q where: nc is the rotation frequency min –1; S zj is the cross-sectional area during milling with a ball-end tool, mm2: 2 1 2 1 1 2 cos 1 2 2 2 2 sin 2 2 sin tan 2 2 4 2 cos 1 2 2 2 2 sin 2 p p p zj p a R R R a a S fz a R R . The effect of coolant depends on rational choice of cutting conditions, tool wear, and tool/workpiece materials [19]. Coolant use and cutting speed of at least 75 m/min are necessary to achieve minimum roughness Rz, beyond which W has little impact on model performance. Surface roughness also depends on tool wear degree [20], with a strong negative correlation R = −0.95. As the number of machined workpiece surfaces (i, pcs) increases, dimensional tool wear occurs, typically within the range of 2 to 4 μm. This wear leads to an approximate 21 % increase in the Rz parameter relative to its minimum observed values. Fig. 2. Distribution of surface roughness parameter Rz
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 2 5 Fig. 3. Dependence of surface roughness parameter Rz on cutting speed, coolant and tool wear An experiment with three factors at two levels each (Table 2) was conducted. Full factorial design yields 8 combinations (k = 23 = 8). Based on theoretical factor influence on roughness, the model considered was: Y(Rz) = a + bfzXfz + + bγXγ + bDXD Here are the calculated natural regression coefficients: a = 3.00; bfz = 2.77; bγ = –0.55; bD = –1.08. The parameters of the regression equation were estimated using the ordinary least squares method. Standardized β-coefficients: βfz = 0.17; βγ = –3.33; βD = –1.01. Comparison of the modules of the values of the standardized regression coefficients β allows us to conclude that γ (the angle of inclination of the ball-end tool) is the most influential factor in the formation of the roughness parameter Rz. When the fz factor is fixed, the remaining factors show negative standardized β coefficients (βγ = –0,54; βD = –1,09), indicating a decrease in the response value Rz. The value R 2 = 0.14 indicates that fz plays an important role in explaining Rz, and fixing it significantly reduces the explanatory power of the model. When γ is fixed, the standardized β coefficients (βfz = 2.77; βD = –1.09) show that fz has a strong positive contribution and D has a strong negative contribution. The high R2 = 0.84 indicates that even when γ is fixed, fz and D remain important in explaining Rz. When D is fixed, the standardized coefficients βfz = 2.76, βD = –0.54. This means that when D is fixed, an increase in fz leads to an increase in Rz, while an increase in γ leads to a decrease. The value R2 = 0.75 also indicates that the model with fixed D explains the variation in Rz well, and the factors fz and γ remain important in explaining Rz. The regression model (RM), obtained after conducting an experiment on processing free form surface with a ball-end tool, characterizing the relationship between the roughness value, feed per tooth, diameter and angle of inclination of the tool, expressed by a normalized model has the following form: Rz(RM) = 3 + 2.77fz – 0.55γ – 1.08D – 0.51fzγ – 1fzD + 0.22γD + 0.2 fzγD. Ta b l e 2 Experimental data values No. fz γ D fz∙γ fz∙D γ∙D fz∙γ∙D Rz 1 0.5 50 12 1 1 1 1 3.05 2 0.1 50 12 –1 –1 1 –1 0.13 3 0.1 10 12 1 –1 –1 1 0.18 4 0.1 10 6 1 1 1 –1 0.37 5 0.5 10 12 –1 1 –1 –1 4.33 6 0.5 50 6 1 –1 –1 –1 6.38 7 0.1 50 6 –1 1 –1 1 0.26 8 0.5 10 6 –1 –1 1 1 9.32
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 2 2025 In this study, we examine the effect of activation function on the performance of eight neural network models in predicting Rz (Fig. 4). Loss function reflects model training efficiency. The ReLU activation speeds training but requires monitoring of both Train Loss and Validation Loss. Low training loss with high validation loss indicates Fig. 4. Learning rates of various configurations
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 2 5 overfitting, meaning the model memorizes training data instead of generalizing. Fig. 3 shows 3–32–16–1 and 3–6–6–1 models remembered the training data too well, but cope poorly with new data. According to results and based on MSE (Table 3), best network configurations are 3–64–64–1 (MSE = 0.0481), 3–20–14–1 (0.0470), and 3–16–16–1 (0.0313). These also have low RMSE (0.2174, 0.2135, 0.1770) and MAE (0.1155, 0.1251, 0.1014). RMSE is interpreted as error in the same units as data. A design with k = 12 experiments was used to test the best models with factors fz ∈ {0.4; 0.5}, γ ∈ {10, 15, 20, 30, 40, 50}, D ∈ {6}, distributed randomly. Table 4 and Fig. 5 present data showing the relationship between the values obtained during the experiment, calculated based on the developed regression model and the predicted BPNN responses. Ta b l e 3 Predictive performance of the neural network Metrics 3-6464-1 3-6432-1 3-3232-1 3-3216-1 3-2014-1 3-1616-1 3-66-1 3-99-1 MSE 0.0481 0.0621 0.0572 0.0685 0.0470 0.0313 0.0415 0.0603 RMSE 0.2174 0.2492 0.2391 0.2617 0.2135 0.1770 0.2037 0.2456 MAE 0.1155 0.1228 0.1656 0.1361 0.1251 0.1014 0.1306 0.1447 R2 0.9904 0.9889 0.9898 0.9878 0.9916 0.9944 0.9926 0.9862 Ta b l e 4 Predicted (Y(Rz)) and experimental (Rz) values for selected configurations, at k = 12 fz γ D Rz Rz(RM) Y(Rz) 3-64-64-1 3-20-14-1 3-16-16-1 0.4 10 6 6.945 7.090 6.680 6.277 6.491 0.4 50 4.610 4.840 4.938 5.025 5.116 0.4 20 6.108 6.528 6.037 6.469 6.303 0.4 40 5.400 5.403 5.357 5.503 5.261 0.5 20 8.341 8.590 7.923 8.372 7.875 0.4 15 6.614 6.809 6.426 6.495 6.330 0.5 10 9.163 9.330 8.272 8.402 8.925 0.4 30 5.826 5.965 6.067 5.987 6.307 0.5 15 8.786 8.960 8.463 8.590 8.072 0.5 40 6.992 7.110 7.035 6.977 7.407 0.5 30 7.694 7.850 7.792 7.443 7.896 0.5 50 6.024 6.370 6.548 6.745 6.541 MSE 0.049 0.136 0.167 0.175 RMSE 0.221 0.369 0.408 0.418 MAE(Rz) 0.195 0.286 0.317 0.384 MAE(Ra) 0.049 0.072 0.081 0.095 R2 0.973 0.924 0.907 0.903
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 2 2025 Fig. 5. Predicted and Experimental values for selected classifications When evaluating Table 4 and Fig. 5, one can conclude that the models under consideration showed predicted values (Y(Rz)) close to the actual ones (Rz). The coefficient of determination R2 was 0.973 for the regression model and 0.924, 0.907, 0.903, respectively, for the considered configurations. For all configurations, MAE ≈ 0.2955 μm means that, on average, model predictions deviate from actual Rz values by 0.2955 μm. The Rz parameter correlates strongly with Ra (correlation coefficient 0.91) [21–23]. Statistical processing shows the relationship: Ra = (Rz – 0.391) / 4.022. Comparison of experimental data with model predictions shows MAE for Ra ≈ 0.049 μm, which is negligible in surface roughness context, indicating close agreement between observations and true mean values. Thus, errors found do not significantly affect result accuracy, confirming data compliance. Conclusion This paper discusses the development of an artificial neural network model to predict surface roughness when milling with a ball-end tool. The tuning process of ANN architecture, especially the selection of number of layers and neurons, is described to improve prediction accuracy. The concept of parameter selection based on the significance of the contribution to the accuracy of surface roughness prediction Rz is considered to reduce the input factors to the minimum possible. The results show that it is possible to obtain accurate predictions of surface roughness even when taking into account a small number of input parameters with relatively small training sets. Selecting the correct network configuration and input parameters is important to ensure accurate prediction. In addition, the study highlights the importance of considering the inclination angle of the ballend tool (10° to 50°) in training the ANN models, and the increase in the angle affects the decrease in the magnitude of the roughness parameters. The final tests conducted to check the adequacy of the proposed model showed that the model works well with reasonable accuracy under the given set of parameters. In conclusion, it can be said that this study contributes significantly to machining process modeling by milling.
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