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Analysis and prediction of the impact of technological parameters on cutting force components in rough milling of AZ31 magnesium alloy

Analysis and prediction of the impact of technological parameters on cutting force components in... This paper presents the results of experimental study of the AZ31 magnesium alloy milling process. Dry milling was carried out under high-speed machining conditions. First, a stability lobe diagram was determined using CutPro software. Next, experimental studies were carried out to verify the stability lobe diagram. The tests were carried out for different feed per tooth and cutting speed values using two types of tools. During the experimental investigations, cutting forces in three direc- tions were recorded. The obtained time series were subjected to general analysis and analysis using composite multiscale entropy. Modelling and prediction were performed using Statistica Neural Network software, in which two types of neural networks were applied: multi-layered perceptron and radial basis function. It was observed that milling with high cutting speed values allows for component values of cutting force to be lowered as a result of the transition into the high-speed machining conditions range. In most cases, the highest values for the analysed parameters were recorded for the component F , whereas the lowest were recorded for F . Additionally, the paper shows that a prediction (with the use of artificial neural x y networks) of the components of cutting force can be made, both for the amplitudes of components of cutting force F and amp for root mean square F . rms Keywords High-speed dry milling · Cutting forces · Magnesium alloys · Entropy · Neural networks 1 Introduction which occur in the cutting process. A change in the cutting force components during the milling process may affect the The machining allowance can be removed by means of deformation of a workpiece. [1]. In addition, changes in the machining methods using high cutting speeds (HSM cutting force may affect phenomena such as adhesion and –High Speed Machining, HPC–High Performance Cut- accretion, leading to an additional decrease in surface qual- ting, HSC–High Speed Cutting), which allows for shorter ity, shape and dimensional accuracy. There are also stud- machine time, increased volumetric efficiency and reduced ies investigating power demand in the milling of different manufacturing costs. Parts for the machine-building and materials, including magnesium alloys. Compared to other aircraft industries are usually machined by milling. The so- metals [2], the milling of magnesium alloys can be done called “utility” indicators of machinability include forces (F) in an effective way due to the possibility of applying high values of the technological parameters of the milling process [3], both during the square shoulder milling and roughing plunge milling process [4]. For instance, unlike in the case * M. Kulisz m.kulisz@pollub.pl of Al-Si alloys, the cutting force generated in the milling of magnesium alloys is lower by approx. 50%. Given the low Department of Organisation of Enterprise, Management cutting resistance [5] and temperature [6] in this process, the Faculty, Lublin University of Technology, Lublin, Poland thermal and mechanical loads on the tools are low, too [7]. Department of Production Engineering, Mechanical Cutting speed has a significant impact on the efficiency Engineering Faculty, Lublin University of Technology, of milling processes. Given the ranges of cutting speed Lublin, Poland 3 v , milling processes are often divided into those per- Department of Applied Mechanics, Mechanical Engineering formed applying “conventional” parameters and those Faculty, Lublin University of Technology, Lublin, Poland Vol.:(0123456789) 1 3 1 Page 2 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 performed at higher values of v (characteristic of HSM). an increase in resistance, and as a consequence also an The moment of “transition” into a range of the parameters increase in temperature generated in the cutting zone. which are typical of HSM can be defined in the following In the study [12] an analysis was performed of, among way: ∂F/∂v < 0 (HSM) and ∂F/∂v > 0 (conventional mill- others, cutting forces that were obtained during the dry face c c ing) [8]. The distinction between conventional milling and milling operation of ZE41 magnesium alloy. The variable HSM is generally made when an increase in the cutting input parameters in the process were: spindle speed, feed speed v leads to a decrease in the cutting force. HSM is per tooth, depth of cut, and tool diameter. Based on studies defined as a highly efficient cutting method ensuring high conducted, it was observed that the cutting forces gradually surface quality (Ra—arithmetical mean roughness of the increased with an increase in input parameters. These cut- profile parameter is often lower than 1 µm). The use of ting forces are more closely linked with spindle speed than HSM helps eliminate finishing which is usually done by feed per tooth. The authors also concluded that both constant grinding. For instance, the use of HSM enables the short- depth of cut and tool diameter are proportionally related to ening of milling time (by as much as four times) with- the cutting forces at increasing spindle speeds and feed per out decreasing surface quality and shape accuracy. The tooth, respectively. These forces should be kept under con- desired shape accuracy can be attained thanks to, among trol as they can impact the cutting tool. When the cutting others, a decrease in the cutting forces in high-speed mill- force is excessive, this also has a negative effect on the qual- ing. Among the high-speed machining methods, one can ity of a machined surface. With an increasing feed rate, the distinguish two highly efficient methods: high perfor- vibration in the machine-holder-workpiece-tool (MHWT) mance cutting (HPC), used for pre-treatment or forming, system increases, too. This is caused by the impact of exces- and high-speed cutting (HSC), which is used for finishing. sive cutting force [13]. One recent definition of HSC has introduced the concept Based on the above, it can be seen that the values of the of so-called limit cutting speed v which marks the range cutting force and of its components are influenced by many c-gr of high-speed milling [9]. factors associated with the machining process, including but Both when the milling process is performed by tools with not limited to the materials from which tool is made and the so-called “classical end mill geometry,” as well as when a material being machined, the tool geometry, and the machin- wave-shaped cutting edge is used, the cutting force compo- ing parameters. Of these, however, the most significant is the nents and their amplitudes are more affected by changing selection of appropriate machining parameters, as has been the feed per tooth f rather than by variations in the cut- demonstrated by researchers in work such as [14], while ting speed v . In the milling of AZ91HP alloy, the cutting others claim that the use of high cutting speeds, feed rates, force components are the highest when the tool with a PCD and cutting depths allows for an increase in machining effi- (polycrystalline diamond) end mill is used. The type of tool ciency. The relationships between the factors listed above are coating (e.g. TiB and TiAlCN) has a significant effect on frequently nonlinear in nature. An additional drawback may the cutting force, too. This can be particularly observed in be the process instability resulting from the translational the case of carbide end mills. The cutting force components motion of the end mill [15]. Moreover, during machining, (F —component of the cutting force in the x-axis direction, at specific combinations of cutting depth and spindle speed, F —component of the cutting force in the y-axis direction) the regenerative effect may arise. Under chatter conditions, in the milling process for EN AW-6082 alloy are the lowest the vibration developed is sometimes so strong that the when a TiB -coated tool is used. With a change in the value amplitude of the vibration between the tool and workpiece is of v , one can observe a characteristic point of “transition” larger than the chip thickness, so that the chip becomes dis- into an HSC machining range (at v = 450 ÷ 600  m/min) sected, and the machined surface is spoiled by chatter marks. c-gr [10]. This phenomenon is the so-called machining instability [16]. Additionally, the effects of tool wear on cutting perfor - The manufacturing industry requires quality machined sur- mance were investigated for milling of magnesium alloy faces, and so violent chatter or machining instability must within the cutting speed range of 1600–2000 m/min under therefore be avoided. dry conditions in studies by [11]. These mechanisms were A stability chart is commonly used to indicate stable dominantly categorized into adhesion wear, abrasion, and (chatter-free) cutting as a function of spindle speed and diffusion under dry conditions. Extensive flaking was the depth of cut [17]. It has long been recognized that sub- significant failure mode at the cutting speed of 1600 m/min, stantial gains in productivity can be achieved by exploit- while serious flank wear and gross fracture were mainly ing the lobed nature of the stability chart, particularly at responsible for failures at the cutting speeds of 1800 and high speeds. The stability lobe diagram (SLD) is used in 2000 m/min. An increase in power consumption may also the processing of various types of materials, those com- result in an increase in cutting force components and cause monly considered as difficult to process (titanium alloys, steel, nickel alloys), lightweight alloys (aluminium alloys, 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 3 of 19 1 magensium alloys), as well as various composite materials entropy method (MSE), defined as a measure of the degree [18]. In this paper, the authors additionally conducted statis- of disorder or uncertainty of a given signal, allowing for an tical, recurrence, and composite multiscale entropy analyses. assessment of the complexity of time series. This is based The authors performed a classic trial involving changing the on a granulation procedure conducted by averaging original spindle speed and observed the appearance of chatter vibra- points on the time series [30]. Unfortunately, with a large tions and signatures of intermittency. scale factor τ, the results may be skewed by an error which Thus, due to the complexity of the milling processes and can be eliminated by applying the concept of composite mul- their nonlinear nature as well as due to phenomena occur- tiscale entropy (CMSE) [31]. ring in the cutting zone, attempts are being more and more The aim of this paper is to analyse the impact of changes commonly made to model the machining processes using in technological parameters on the cutting force values in the mathematical analytical methods [4], semi-analytical tech- case of milling an AZ31 magnesium alloy with two differ - niques namely the Chebyshev collocation method and tem- ent tools. This alloy is relatively rarely analysed in milling poral finite element analysis (TFEA) [19] or using Artificial processing, to a much lesser extent than the AZ91D mag- Intelligence (AI) systems [20]. Apart from Danis et al. [4], nesium alloy. Carrying out investigations for two types of mathematical modelling was also employed by Fu et  al. cutting tools can reveal some differences in the course of [13], and Weremczuk et al. [21]. When the nature of a pro- milling process. analysis made use of courses of cutting cess is too complex to be described in mathematical terms forces obtained experimentally, based on which a statistical using equations, modelling is often performed using Neural analysis was conducted. The study also made use of compos- Network Toolbox [22] or Statistica software package [20]. ite multiscale entropy (CMSE) as a measure of disorder in Artificial neural networks are most often employed for this the time series of the cutting force signal. It is believed that purpose, which is confirmed in the works by Kilickap et al. it can be an extension of the analyses conducted on the basis [23] or Kazemi et al. [24] of commonly used indicators and provide additional infor- The main aim of the modelling of cutting processes is mation on the course of the cutting process. Additionally, the prediction of the course of the technological processes the use of neural networks was proposed to develop predic- which are of a nonlinear nature. This may serve to create tive models for the component values of total cutting force, systems supporting decision-making processes in a business, and the values of the amplitudes of cutting forces F and amp for example when selecting technological machining param- root mean square F for the TiAlN-coated tool. The input rms eters. For the modelling and simulation of cutting force com- parameters for modelling were the technological parameters ponents, neural networks can be used, such as RBF (Radial of the process (cutting speed and feed per tooth). An analysis Basis Function) and MLP (Multi-Layered Perceptron). of the literature shows that no such modelling has been so The authors of one study [25] presented a model for the far conducted. prediction of components of cutting force for an AZ91HP alloy with two inputs, namely the machining parameters (cutting speed and feed per tooth). Other materials which 2 Experimental set‑up have been studied by other researchers using simulations of cutting force components include aluminium alloy (input The main aim of the study was to investigate the effect of parameters: spindle speed, feed per tool, radial depth and parameters such as cutting speed v and feed per tooth f on c z axial depth) [26], 7050 aluminium alloy (input parameters: the dynamics of a system during milling. The experimental spindle speed, feed per tooth, milling width) [27], Inconel investigations were conducted on AZ31 magnesium alloy 718 (input parameters: tool wear, feed per tooth, cutting specimens cut on an AVIA VMC 800HS machining cen- depth, cutting width, cutting speed) [28], and also AZ31 tre. Chemical composition and mechanical properties of the magnesium alloys with a PCD tool (cutting speed range machined magnesium alloy are shown in the Table 1. and feed per tooth as input parameters) [10]. The models The tools used in the study were 16 mm end mills (z = 2), developed allow for the testing of different configurations one carbide TiAlN-coated (Fenes) and the other with a PCD of input parameters (machining parameters) without having end mill (Guhring). On the basis of the conducted literature to simultaneously conduct experimental tests. The results of review, it was observed that these tools enable achieving our experiments show that the measured results and simu- favourable machining effects during the milling of magne - lated results correspond well with each other. Modelling sium alloys. These tools are frequently employed in mill- and simulation can also be used to predict the influence of ing of various lightweight alloys, a carbide TiAlN-coated technological parameters on other indicators, e.g. the surface tool is relatively cheap and yields good machining effects, quality [29] achieved by machining processes. whereas a PCD tool enables to achieve high quality of the Additionally, it is becoming increasingly common in surface, comparable to grinding Ra ≤ 0.16 µm (elimination the analysis of dynamic processes to use the multiscale of additional machining processes). A constant radial depth 1 3 1 Page 4 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 Table 1 Chemical composition and mechanical properties of AZ31 magnesium alloy [32] Chemical composition Al Mn Zn Cu Others Mg 2.5–3.5 0.1–0.2 0.7–1.3 0.05 0.04 Rest Mechanical properties R (MPa) R (MPa) E (GPa) A (%) HB ρ (g/cm ) m p0.2 5 250–290 150–220 ~ 45 12–21 46–73 1.78 of cut a = 14 mm, axial depth of cut a = 6  mm, and the lobe diagram (SLD). The modal hammer is used to excite the e p following technological parameter ranges were applied: tool and then the resulting vibrations are measured by the v = 200–1200 m/min and f = 0.05–0.30 mm/tooth, as shown low mass accelerometer mounted at the tool tip. Next, the c z in Table 2. The technological parameter ranges v and f were modal parameters in the form of frequency response func- c z selected on the basis of the previous studies on magnesium tion (FRF) are implemented to CutPro9 software, which alloys, which can be found in other available publications calculates and plots SLD for three different values of feed as well as on the basis of the previous own studies and lit- per tooth f (Fig. 2). In the second step of the experiment, a erature review. In addition, v was obtained via studies and verification of unstable lobes is performed for series of spin- analyses of HSM; however, it is limited by the technological dle speeds and the depths of cut presented as black points capacity of the machining device (maximum spindle speed in the SLD. Experimental verification of stability lobes is of 24,000 rpm). frequently employed during the experimental studies of the Figure 1 shows a plan of the experiments and a schematic machining processes. The parameters, based on which the diagram of the experimental set-up. The experimental set- CutPro software determines the stability curves, are static. up is composed of two subsystems: a modal analysis system However, these parameters may change during processing and a dynamometer system. The former is used to meas- and thus change the location of stability lobes. ure tool-holder stiffness and damping coefficient (modal SLD was prepared only for a carbide TiAlN-coated tool. parameters). It consists of the modal hammer PCB 086C03, In the case of PCD tool, creation of SLD would be risky, accelerometer PCB 352B10, data acquisition card (DAQ) because a relatively brittle part of the tool made of poly- NI9234 and CutPro software. The latter is used to measure crystalline diamond should be struck with a modal hammer, the cutting force components (F , F and F ) by means of a which could result in its damage. x y z Kistler 9257B piezoelectric dynamometer connected to a The location of SLD curves affects the rigidity and vibra - Kistler 5017B signal conditioner and a SCADAS Mobile tion damping of the system. Diameter and free length of the LMS analyser. Both experimental rigs are integrated in the tool were the same in both cases; thus, the system rigidity computer system. Measurements are conducted in two steps. did not change. The influence of blade shape and the type In the first, the impact test is done to get data for the stability of coating affect the MHWT system rigidity to a minimal Table 2 Technological Cutting tool Cutting speed Feed per tooth Axial depth of cut a (mm) Radial depth of cut a (mm) p e parameters with which the v (m/min) f (mm/tooth) c z milling process was carried out PCD, TiAlN 200 0.15 6 14 800 0.05 0.10 0.15 0.20 0.25 0.30 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 5 of 19 1 Fig. 1 Design of the: a experiment and b schematic diagram of the experimental set-up c schematics of the artificial neural network with the analysed process parameters degree. Thus, it can be concluded and assumed with high the highest positive value of the signal. The F amplitude amp degree of probability that the SLD curves are similar for is the highest deviation from equilibrium. Higher values F amp both tools (or even identical). than F result from the signal asymmetry (shifted towards max The cutting forces generated on the workpiece during the bottom). In the presented case, F is approximately max the machining were measured by a dynamometer mounted equal to 400 N, while F is about 900 N. amp on the milling machine underneath the workpiece. The cor- An additional aim of this study was to verify whether it is responding force signals from the dynamometer were first possible to predict the impact of technological parameters (f transmitted to the charge amplifier, next to the analyser and, and v ) on the maximum values of the components of total finally, to the computer system. The sampling rate of data cutting force and on the values of the amplitudes of cut- recorded during the test was set to 1 kHz. ting forces F and the root mean square F when rough amp rms A typical, experimentally obtained time series is pre- milling an AZ31 magnesium alloy using a carbide TiAlN- sented in Fig. 3. In the paper, the maximum value F is coated tool. Thus, a simulation of selected components of max 1 3 1 Page 6 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 for training the network were the machining parameters v = 200–1200  m/min and f = 0.05–0.30  mm/tooth, while c z the output neuron for modelling a given networks was the cutting force component/amplitude of component F /root mean square of the component F . Therefore, modelling was performed for 4 different networks. Two types of network were used for modelling, an MLP (multi-layered Perceptron) network and an RBF (Radial Basis Function) network. The set of training and verification data was divided in a propor - tion of 75% (training set) to 25% (verification set). The test data set was omitted due to the small number of input data for training the network [21]. With the MLP network, linear, logistic, exponential, tanh and sinus activation functions were applied, while with the RBF network, Gaussian (hidden neurons) and linear (output neurons) functions were applied. The networks were mod- elled with a single layer of hidden neurons within a range of 2–9. The number of epochs fluctuated from 150 to 500. For each model, 100 networks were constructed and the best of these was selected based on training and verification qual- ity as well as on errors in these sets. Errors were calculated Fig. 2 Stability lobe diagram for milling processes using a carbide using the least squares method. TiAlN-coated (Fenes) tool 3 Experimental test results In the following study, the statistical analysis waveform forces were produced by experimental investigations. The bar charts show the results of the forces in three directions for two different tools (a PCD and a TiAlN-coated tool). The tests were carried out for six parameters, and are shown in the stability lobe diagram as points from 1 to 6 (Fig. 2). 3.1 Influence of cutting speed First, the impact of the cutting speed v was investigated. Figure 4a shows the change in the maximum cutting forces F in relation to the cutting speed. In the case of both tools, max the highest values of maximum forces F were observed max in the x direction (feed direction), the smallest in the z direc- tion. Similar relations are visible when analysing the ampli- tudes of cutting forces F (Fig. 4b). In the case of cutting amp speed v = 800 m/min, a significant difference in the value of the cutting force amplitudes F was observed for both amp Fig. 3 Time series for PCD tool (f = 0.05 mm/tooth) tools in the feed direction. The highest values of standard deviations F (Fig. 5b) and root mean square F (Fig. 5a) std rms cutting force (F and F ) and amplitude of the component were observed at the cutting speed of v = 600 m/min. x y c F as well as the root mean square for the component F was From the experimental tests carried out for the AZ31 x x conducted. The component F was selected because it has alloy, it can be concluded that with the increase of the the greatest impact on the total cutting force. cutting speed v to 600 m/min, all the components of the To conduct the simulation, the Statistica 13 Neural Net- cutting forces increase (most components in the feed direc- works software package was used, and input data comprised tion). At the same time, above v = 800 m/min a significant the results of experimental studies. The input neurons reduction in cutting forces was observed for both tools. 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 7 of 19 1 Fig. 4 The effect of change in cutting speed v on the value of cutting forces for f = 0.15 mm/tooth a maximum F and b amplitude F in the c z max amp milling of AZ31 magnesium alloys using different tools Fig. 5 The effect of change in cutting speed v on the value of cutting forces for f = 0.15 mm/tooth a root mean square F and b standard devia- c z rms tion F in the milling of AZ31 magnesium alloys using different tools std This is due to the characteristic transition to HSM machin- the TiAlN-coated tool. In the case of effective value F rms ing for higher cutting speeds. Significantly, lower maxi- and standard deviation F , the highest values were again std mum cutting forces F were observed when cutting using obtained for the component F . The lowest values of indi- max x the PCD tool. However, when analysing the amplitude of cators when milling at low cutting speeds were noted for cutting forces F , smaller values were obtained using amp 1 3 1 Page 8 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 component F , though after achieving a cutting speed of be concluded that the waveforms obtained during cutting v = 800 m/min the lowest values were seen for F . with the PCD tool show greater variability. This is evi- c y The dramatic increases in values which are repeated denced by the much higher F (Fig. 6b), F (Fig. 7a) amp rms in the case of all analysed indicators, particularly visible and F (Fig. 7b) values for the F component in the case std x for the cutting speed range of v = 400–800  m/min, can be of the PCD tool. associated with the course of stability curves. Rotational The use of a carbide tool with a TiAlN coating provides speeds equivalent to cutting speeds of v = 400  m/min and greater stability of the milling process at a wide range of v = 800 m/min were determined based on stability curves feed per tooth. As in the case of changes in cutting speed, to be speeds which generated instability during the machin- the highest values of the analysed indicators were noted for ing process. Despite the fact that the machining process was component F , while the lowest were noted for F . x z conducted with all remaining values of technological param- eters within the unstable machining zones of the stability curves, clear increases in these values were not observed. This may be associated with the feed per tooth value of 4 Multiscale entropy analysis f = 0.15 mm/tooth which the sample millings were con- ducted at, as the stability curves were generated for feed per In further analysis of the cutting forces, the composite tooth of f = 0.05 mm/tooth and f = 0.30 mm/tooth. multiscale entropy (CMSE) method was used [31]. In this z z method, τ is the scale factor. The original time series is 3.2 Influence of feed per tooth divided into non-overlapping windows of length τ and the data points inside each window are averaged. In the next step, the influence of the feed per tooth f was i=j+k−1 1 N investigated. The change of the feed per tooth was car- () y = x ,1 ≤ j ≤ ,1 ≤ k ≤ , (1) k,j ried out in the range f = 0.05–0.30 mm/tooth in six steps. i=(j−1)+k Together with the increase of the feed per tooth, all compo- where N—length of data series, x—time series. nents of the cutting forces increase; this is visible for the F At each scale factor τ, the composite multiscale entropy component (feed direction) for both tools (Fig. 6 and Fig. 7). calculation is based on the averaged time series {y} and In the case of cutting with the TiAlN-coated tool, higher reads as values of maximum forces F for the F component were max x observed. However, observing the other indicators, it can Fig. 6 The effect of change in feed per tooth f on the value of cutting forces for v = 800  m/min a maximum F and b amplitude F in the z c max amp milling of AZ31 magnesium alloys using different tools 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 9 of 19 1 Fig. 7 The effect of change in feed per tooth f on the value of cutting forces for v = 800 m/min a root mean square F and b standard deviation z c rms F in the milling of AZ31 magnesium alloys using different tools std Fig. 8 The composite multiscale entropy analysis for measured cutting force components a F and b F signals for two different values of the x y cutting speed and f = 0.15 mm/tooth where m = 2 is the pattern length and r is the similarity crite- () CMSE(x, , m, r) = SampEn(y , m, r), (2) rion, which is usually equal to 10% of the standard deviation k=1 of the original time series {x} used. 1 3 1 Page 10 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 Fig. 9 The maps of composite multiscale entropy against cutting speed and scale factor τ at f = 0.15 mm/tooth for the TiAlN-coated tool a F , b z x F and for PCD tool c F , d F y x y Next, the method of composite multiscale entropy was impacted the change in the level of entropy when using the used to analyse the experimental cutting forces. Figure 8 TiAlN-coated tool. Similar behaviour was observed for the shows the composite multiscale entropy for two values entropy levels of component F (Fig. 8b). of cutting speed (v = 200  m/min and v = 1200  m/min— The change in multiscale entropy of the component sig- c c points 1 and 6 on Fig.  2) and two different tools. In the nals F and F dependent on the change in cutting speed is x y case of component F , a considerable increase in entropy also presented in the form of maps for the TiAlN-coated was observed for milling using the PCD tool at a speed of tool (Fig. 9a, b) and the PCD tool (Fig. 9c, d). The high- v = 200  m/min (Fig. 8a). Change in speed only slightly est levels of entropy when milling with the TiAlN-coated 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 11 of 19 1 Fig. 10 The composite multiscale entropy analysis for measured cutting force components a F and b F signals for two different values of feed x y per tooth and v = 800 m/min tool occurred for cutting speed of v = 800  m/min, which increases, then gradually decreases, particularly in the coincide with dramatic rises in the values of cutting force case of the PCD tool. The character of changes in entropy components and which may be the result of machining in is maintained for both tools throughout the full range of the unstable SLD area. In the case of component F , the changes in feed per tooth. A decrease in the level of entropy level of entropy increases for successive values of the scale of both cutting force components can only be seen when factor τ, and this effect subsides along with an increase milling with the TiAlN-coated tool at the highest feed per in cutting speed. The level of entropy for component F tooth of f = 0.30 mm/tooth. y z is characterized by considerably greater variability. This effect occurs regardless of the type of cutting tool used. Figure  10 shows the composite multiscale entropy 5 Simulation results for two values of feed per tooth (f = 0.05  mm/tooth and f = 0.30 mm/tooth) and two different tools. In the case of Based on the results of the modelling process conducted feed direction (Fig. 10a), it was observed that for the feed for selected maximum cutting force components (F and f = 0.30 mm/tooth, the value of entropy is reduced. Sig- F ), amplitude of component F , and root mean square z y x nificantly lower values are observed when cutting with the for component F for each model a network with the best x, TiAlN coating tool. Similar results were observed in the y indicators was selected, for which the quality of training direction (Fig.  10b), but the value of entropy was higher and verification was the highest, and for which the errors than the x direction. Moreover, the difference in the obtained in training and verification were the lowest. The character - values (Frms/Fstd and entropy) confirms that the applica- istics of these networks are described in Table 3. The best tion of an additional index, i.e. composite multiscale entropy results were obtained for component F for the network enables observing the process from a different point of view. MLP 2-2-1 with two neurons obtained in 315 iterations, A map of changes in multiscale entropy of component while for component F the best results were obtained for signals F and F for the TiAlN-coated tool (Fig. 11a, b) and a network with six neurons (MLP 2-6-1) obtained in 438 x y PCD tool (Fig. 11c, d), also presented in relation to changes iterations. In the case of modelling of the amplitude of in feed per tooth. cutting force component F , the best network was obtained In the case of component F , the course of entropy dis- in 356 iterations, having 9 neurons in the hidden layer plays considerable variability, while for component F the (MLP 2-9-1). For these three models, the best models were level of entropy in the initial range of the scale coefficient obtained for the MLP network, while only in the case of 1 3 1 Page 12 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 Fig. 11 Maps of composite multiscale entropy against of feed per tooth and scale factor τ at v = 800 m/min for TiAlN-coated tool a F , b F and c x y for PCD tool c F , d F x y root mean square of cutting force component F were bet- component F , Fig. 12c for the amplitude of cutting force x y ter parameters obtained for the RBF 2-9-1 network. component F , and Fig. 12d) for the root mean square of The numerical results for the modelled parameters cutting force component F . These are the results of a sim- are presented below. Figure 12a) presents results for the ulation obtained after entering the assumed input param- cutting force component F , Fig.  12b) for cutting force eters v , f for each of the generated networks. x c z 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 13 of 19 1 Table 3 Characteristics of Network Network Quality Quality Error Error Activation Activation selected networks: cutting No Name (Training, %) (Validation, %) (Training) (Validation) (Hidden) (Output) force components (F and F ), x y amplitude of component F , and x Cutting force component F root mean square for component  1 MLP 2-2-1 97.35 99.98 1934.4 4222.3 Tanh Sinus Cutting force component F  2 MLP 2-6-1 99.95 99.74 10.1 467.8 Tanh Linear Amplitude of cutting force component F (F ) x x_amp  3 MLP 2-9-1 99.12 99.99 1956.5 2365.9 Logistic Linear Root mean square of cutting force component F (F ) x x_rms  4 RBF 2-9-1 99.73 99.95 74.2 263.8 Gaussian Linear Table 4 presents the R correlation coefficients and sen- During processing, these parameters may change as a result sitivity analysis of input parameters (f and v ) of the ana- of the occurrence of dynamic phenomena, which affects the z c lysed networks. It can be seen that neural networks are an location of stability lobes. Then, the cutting force signals appropriate tool to predict assumed values, and that both were subjected to a thorough analysis. Apart from the clas- input parameters have a significant impact on these values. sic and commonly employed approach, a dynamic analy- Moreover, the charts presented in Fig. 13 show this correla- sis was performed using multiscale entropy and numerical tion (between experimental results and those obtained in the simulations using artificial neural networks. The obtained simulation). The charts present a correlation for networks results confirm the appropriateness of the proposed research which are presented in a visual form in Fig. 12. approach. The analysis using dynamic indices enables to Based on the charts presented above, it can be stated that analyse both the limit values of measured forces and the sig- the networks obtained show satisfactory predictive capacity. nal complexity, which significantly contributes to the quality All obtained correlation coefficients are higher than 0.95. of the performed studies. Thus, it can be stated that neural networks may be an effec- Based on the studies conducted, it can be stated that: tive tool for the simulation of, for example, cutting force components and their amplitudes or their root mean square. 1) Increasing the cutting speed at low ranges of values Neural networks may be effectively used for the numerical causes an increase in cutting force in all directions. modelling of machining processes. 2) Performance of the machining process with high cut- ting speed values allows for component values of cutting force to be lowered as a result of the transition into the 6 Conclusions HSM range. 3) Increasing the feed per tooth value causes a linear This paper presents the results of experimental study of the increase in the values of all cutting force components, AZ31 magnesium alloy milling process. Two different tools regardless of the technological parameters or type of were used in experimental studies, a PCD and a TiAlN- cutting tool. coated tool. First, modal analysis was performed to obtain a 4) Regardless of the technological parameters or type of stability lobe diagram which was next verified for selected cutting tool, the highest values for the analysed param- points by means of statistics and the multiscale entropy eters were recorded in most cases for the component F , method. Additionally, a prediction was made of cutting force whereas the lowest were recorded for F . components and the amplitudes of components of cutting 5) Lower values of parameters for milling with variable force F and root mean square F for the TiAlN-coated feed per tooth were obtained when using a tool with amp rms tool. a TiAlN coating, something which was particularly A novel and rarely employed approach was used in the noticeable for the component F . Nevertheless, in the analysis of the experimentally obtained signals. The SLD case of changes in the cutting speed, the type of tool curves obtained using CutPro commercial software were used did not show an unambiguous impact on the results verified for selected processing parameters. This is because obtained. these curves were obtained based on the static parameters 6) An analysis of entropy indicated a lower level of dis- of the machine-holder-workpiece-tool (MHWT) system. order for cutting force component signals recorded at 1 3 1 Page 14 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 Fig. 12 Numerical results from network depending on the cutting speed v and feed per tooth f for a maximum cutting force component F , b c z x maximum cutting force component F , c amplitude of cutting force component F , d root mean square of cutting force component F y x x Table 4 Correlation R and F F F F x y x_amp x_rms sensitivity analysis of input parameters for the analysed Network MLP 2-2-1 MLP 2-6-1 MLP 2-9-1 RBF 2-9-1 networks Corelation R 0.9658 0.9986 0.9896 0.9952 Sensitivity analysis f /v 35.03/11.01 1392.78/269.03 2871.62/39.00 84.87/62.56 z c 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 15 of 19 1 Fig. 13 Comparison of experimental and numerical results a cutting force component F , b cutting force component F , c amplitude of cutting x y force component F , d Root mean square of cutting force component F x x the highest cutting speed of v = 1200 m/min and at the as well as for the amplitudes of components of cutting highest feed per tooth of f = 0.30 mm/tooth. force F and root mean square F . The R correlation z amp rms 7) During milling with variable cutting speeds, a lower coefficients were respectively F —0.9658, F —0.9986, x y level of disorder was observed for cutting force compo- F —0.9896, and F —0.9952; thus it can be x_amp x_rms nent signals recorded when milling using the PCD tool, stated that the trained networks are a reliable predictor while when milling with changes in the feed per tooth of utility values of cutting indicators. this lower level was observed for the TiAlN-coated tool. 10) The results of modelling and the simulations conducted 8) It is possible to predict the impact of technological may be used to create tools while establishing machining parameters (f and v ) on the values of cutting force conditions in industrial settings, as support for techni- z c components as well as on the value of the amplitudes of cians in the design of technological processes. Exces- cutting forces F and root mean square F . In most sively high cutting force values may have a negative amp rms cases, better results were obtained for the MLP neural impact on the deformation of machined elements. network than for RBF. 9) The modelling of neural networks may be an effective tool for predicting the components of total cutting force Author contributions Conceptualization: IZ, AW, MK; Methodology: IZ, AW, JK, MK; Formal analysis and investigation: IZ, AW, JK, MK; 1 3 1 Page 16 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 Writing—original draft preparation: IZ, AW, JK, MK; Writing—review (SANN)" version = "2.0"/ > < /Header > < Dat aDictionar y num- and editing: IZ, MK, RR; Funding acquisition: MK; Resources: IZ, berOfF ields = "3" > < Dat aF ield name = "Fy" op type = "con- MK; Supervision: IZ, MK. t i n u o u s " / > < D a t a F i e l d n a m e = " f z " o p t y p e = " c o n t i n u - ous"/ > < Dat aF ield name = "vc" op type = "continuous"/ > < / Dat aDictionar y > < N eur alN e tw or k modelN ame = "Dane Funding The project/research was financed in the framework of the dl_MLP 2–6-1" functionN ame = "r eg r ession" > < Mining - project Lublin University of Technology-Regional Excellence Initia- Sc hema > < MiningF ield name = "Fy" usag eType = "pr e - tive, funded by the Polish Ministry of Science and Higher Education dicted"/ > < MiningF ield name = "fz" lowValue = "0.050000" (contract no. 030/RID/2018/19). highValue = "0.300000"/ > < MiningF ield name = "v c" lowValue = "200.000000" highValue = "1200.000000"/ > < /Min- Data availability The raw/processed data required to reproduce these ingSchema > < N eur alIn puts numberOfIn puts = "2" > < Neu- findings cannot be shared at this time as the data also forms part of an r alIn put id = "0" > < Der iv edF ield > < N or mCon - ongoing study. tinuous f ield = "fz" shif t = "-2.00000000000000e-001" scale = "4.00000000000000e + 000" > < LinearN or m Code availability Sieć MLP 2-2-1 or ig = "5.00000000000000e-002" nor m = "0.000000"/ > < Linear- < ?xml version = “1.0” “encoding = "UTF-8"? > Nor m or ig = "3.00000000000000e-001" nor m = "1.000000"/ > < / < PMML version = "3.0" > < Header copyr ight = "Copyr ight Nor mContinuous > < /Der ivedField > < /NeuralInput > < Neural- 1984–2017 TIBCO Software Inc. All rights reserved." > < Appli- Input id = "1" > < Der ivedField > < Nor mContinuous f ield = "vc" cation name = "STATISTICA Automated Neural Networks shif t = "-2.00000000000000e-001" scale = "1.00000000000000e- (SANN)" version = "2.0"/ > < /Header > < Dat aDictionar y num- 003" > < LinearN or m or ig = "2.00000000000000e + 002" berOfF ields = "3" > < Dat aF ield name = "Fx" op type = "con- nor m = "0.000000"/ > < LinearNor m or ig = "1.20000000000000 t i n u o u s " / > < D a t a F i e l d n a m e = " f z " o p t y p e = " c o n t i n u - e + 003" nor m = "1.000000"/ > < /Nor mContinuous > < /Der ived- ous"/ > < Dat aF ield name = "vc" op type = "continuous"/ > < / Field > < /NeuralInput > < /NeuralInputs > < NeuralLayer num- Dat aDictionar y > < N eur alN e twor k modelN ame = "A1—k_ berOfN eur ons = "6" activationF unction = "t anh" > < N eur on MLP 2–2-1" functionN ame = "r eg r ession" > < Mining - id = "2" bias = "9.16077678635015e + 000" > < Con from = "0" Sc hema > < MiningF ield name = "Fx" usag eType = "pr e - weight = "6.01837602778105e-001"/ > < Con fr om = "1" wei dicted"/ > < MiningF ield name = "fz" lowValue = "0.050000" ght = "5.82694078133876e + 000"/ > < /N eur on > < N eur on highValue = "0.300000"/ > < MiningF ield name = "v c" id = "3" bias = "-1.01907749095250e + 000" > < Con from = "0" lowValue = "200.000000" highValue = "1200.000000"/ > < /Min- weight = "-4.95428801320388e-001"/ > < Con from = "1" weight = ingSchema > < N eur alIn puts numberOfIn puts = "2" > < Neu- "4.83869212777818e + 000"/ > < /Neuron > < Neuron id = "4" bia r alIn put id = "0" > < Der iv edF ield > < N or mCon - s = "6.32992536199350e + 000" > < Con from = "0" weight = "2.3 tinuous f ield = "fz" shif t = "-2.00000000000000e-001" 5693811320159e + 001"/ > < Con from = "1" weight = "-5.19456 scale = "4.00000000000000e + 000" > < LinearN or m 918989006e + 001"/ > < /Neuron > < Neuron id = "5" bias = "-5.2 or ig = "5.00000000000000e-002" nor m = "0.000000"/ > < Linear- 2706775808340e + 000" > < Con from = "0" weight = "7.6277619 Nor m or ig = "3.00000000000000e-001" nor m = "1.000000"/ > < / 7170835e + 000"/ > < Con from = "1" weight = "3.685784851887 Nor mContinuous > < /Der ivedField > < /NeuralInput > < Neural- 40e + 001"/ > < /Neuron > < Neuron id = "6" bias = "2.421072240 Input id = "1" > < Der ivedField > < Nor mContinuous f ield = "vc" 87247e + 001" > < Con from = "0" weight = "2.72924735009545e shif t = "-2.00000000000000e-001" scale = "1.00000000000000e- + 001"/ > < Con from = "1" weight = "-3.31596231243579e + 001 003" > < LinearN or m or ig = "2.00000000000000e + 002" "/ > < /Neuron > < Neuron id = "7" bias = "-2.98010600504767e- nor m = "0.000000"/ > < LinearNor m or ig = "1.20000000000000 001" > < Con fr om = "0" w eight = "-6.14657209571972e- e + 003" nor m = "1.000000"/ > < /Nor mContinuous > < /Der ived- 002"/ > < Con from = "1" weight = "1.01557638112404e-002"/ > < / Field > < /NeuralInput > < /NeuralInputs > < NeuralLayer number- Neuron > < /NeuralLayer > < NeuralLayer numberOfNeurons = "1" OfNeurons = "2" activationFunction = "t anh" > < Neuron id = "2" activationFunction = "identity" > < Neuron id = "8" bias = "6.8759 bias = "-1.18589924841596e + 000" > < Con from = "0" weight = 3873105184e + 000" > < Con from = "2" weight = "-5.962291148 "-3.11229883898561e + 000"/ > < Con from = "1" weight = "9.990 52509e + 000"/ > < Con from = "3" weight = "-5.1166562107657 02570918014e + 000"/ > < /Neuron > < Neuron id = "3" bias = "4. 4e + 000"/ > < Con from = "4" weight = "-3.17158638187285e + 0 86682950265097e + 000" > < Con from = "0" weight = "-5.420052 00"/ > < Con from = "5" weight = "1.52596438545984e + 000"/ > 87404041e + 000"/ > < Con from = "1" weight = "-1.12476163604 < Con from = "6" weight = "-5.42228562354627e + 000"/ > < Con 482e + 001"/ > < /Neuron > < /NeuralLayer > < NeuralLayer num- from = "7" weight = "-1.65370312406208e + 001"/ > < /Neuron > < / berOfNeurons = "1" activationFunction = "sine" > < Neuron id = "4" NeuralLayer > < NeuralOutputs numberOfOutputs = "1" > < Neu- bias = "4.14031536478860e-001" > < Con from = "2" weight = "-1.251 ralOutput outputNeuron = "8" > < Der ivedField optype = "continu- 64661820436e + 001"/ > < Con from = "3" weight = "-1.267551283688 ous" > < NormContinuous field = "Fy" shift = "-2.04592901878914e- 54e + 001"/ > < /Neuron > < /NeuralLayer > < NeuralOutputs number- 001" scale = "2.08768267223382e-003" > < LinearNorm orig = "9.80 OfOutputs = "1" > < NeuralOutput outputNeuron = "4" > < Derived- 000000000000e + 001" norm = "0.00000000000000e + 000"/ > < Lin- Field op type = "continuous" > < Nor mContinuous f ield = "Fx" earNor m or ig = "5.77000000000000e + 002" nor m = "1.0000000 shif t = "-2.82051282051282e-001" scale = "1.06837606837607e- 0000000e + 000"/ > < /Nor mContinuous > < /Der ivedField > < / 003" > < LinearN or m or ig = "2.64000000000000e + 002" NeuralOutput > < /NeuralOutputs > < /NeuralNetwork > < /PMML > nor m = "0.00000000000000e + 000"/ > < LinearNor m or ig = "1. Sieć MLP 2-9-1 20000000000000e + 003" nor m = "1.00000000000000e + 000"/ < ?xml version = "1.0" encoding = "UTF-8"? > > < /Nor mContinuous > < /Der ivedField > < /NeuralOutput > < / < PMML version = "3.0" > < Header copyr ight = "Copyr ight NeuralOutputs > < /NeuralNetwork > < /PMML > 1984–2017 TIBCO Software Inc. All rights reserved." > < Appli- Sieć MLP 2-6-1 cation name = "STATISTICA Automated Neural Networks < ?xml version = "1.0" encoding = "UTF-8"? > (S ANN)" v ersion = " 2.0"/ > < /Header > < Dat aD iction - < PMML version = "3.0" > < Header copyr ight = "Copyr ight ar y numberOfF ields = "3" > < Dat aF ield name = "Fx_am p" 1984–2017 TIBCO Software Inc. All rights reserved." > < Appli- optype = "continuous"/ > < Dat aField name = "fz" optype = "con- cation name = "STATISTICA Automated Neural Networks tinuous"/ > < DataField name = "vc" optype = "continuous"/ > < / 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 17 of 19 1 Dat aDictionar y > < N eur alN e tw or k modelN ame = "Ar k u_ < PMML version = "3.0" > < Header copyr ight = "Copyr ight MLP 2–9-1" functionN ame = "r eg r ession" > < Mining - 1984–2017 TIBCO Software Inc. All rights reserved." > < Appli- Schema > < MiningField name = "Fx_am p" usageType = "pr e- cation name = "STATISTICA Automated Neural Networks dicted"/ > < MiningF ield name = "fz" lowValue = "0.050000" (SANN)" version = "2.0"/ > < /Header > < Dat aDictionar y num- highValue = "0.300000"/ > < MiningF ield name = "v c" berOfFields = "3" > < DataField name = "Fr ms_x" optype = "con- lowValue = "200.000000" highValue = "1000.000000"/ > < /Min- t i n u o u s " / > < D a t a F i e l d n a m e = " f z " o p t y p e = " c o n t i n u - ingSchema > < N eur alIn puts numberOfIn puts = "2" > < Neu- ous"/ > < Dat aF ield name = "vc" op type = "continuous"/ > < / r alIn put id = "0" > < Der iv edF ield > < N or mCon - Dat aDictionar y > < N eur alN e twor k modelN ame = "A1—k_ tinuous f ield = "fz" shif t = "-2.00000000000000e-001" RBF 2–9-1" functionN ame = "r eg r ession" > < Mining - scale = "4.00000000000000e + 000" > < LinearN or m Schema > < MiningF ield name = "F r ms_x" usageType = "pr e- 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weight = "5.00000000000000e-001"/ > < /Neur on > < Neur on from = "7" weight = "1.07684841114401e + 001"/ > < Con from = "8" id = "10" widt h = "6.00000000000000e-001" > < Con from = "0" weight = "-2.64076240956808e + 001"/ > < Con from = "9" weight w eight = "1.00000000000000e + 000"/ > < Con fr om = "1" = "-2.98683784829308e + 001"/ > < Con from = "10" weight = "3. weight = "6.00000000000000e-001"/ > < /Neuron > < /Neur al- 37435868452225e + 000"/ > < /Neuron > < /NeuralLayer > < Neu- Layer > < NeuralLayer numberOfNeurons = "1" activationFunc- r alOutputs numberOfOutputs = "1" > < Neur alOutput output- tion = "identity" > < Neuron id = "11" bias = "-3.26915420082916e- Neuron = "11" > < Der ivedField optype = "continuous" > < Nor- 001" > < Con from = "2" weight = "2.20601468486232e-001"/ > < Con mContinuous field = "Fx_amp" shift = "-2.02290076335878e-001" from = "3" weight = "9.40700728115262e-001"/ > < Con from = "4" scale = "6.36132315521629e-004" > < LinearNor m or ig = "3.1800 w eight = "-5.21245667594871e-001"/ > < Con fr om = "5" 0000000000e + 002" nor m = "0.00000000000000e + 000"/ > < Lin- w eight = "1.31646831970374e-001"/ > < Con fr om = "6" earNor m or ig = "1.89000000000000e + 003" nor m = "1.0000000 w eight = "-9.39266928160472e-001"/ > < Con fr om = "7" 0000000e + 000"/ > < /Nor mContinuous > < /Der ivedField > < / w eight = "1.12820217709549e + 000"/ > < Con fr om = "8" NeuralOutput > < /NeuralOutputs > < /NeuralNetwork > < /PMML > w eight = "-5.17628419352205e-001"/ > < Con fr om = "9" Sieć RBF 2-9-1 weight = "7.08016955495058e-002"/ > < Con from = "10" wei < ?xml version = "1.0" encoding = "UTF-8"? > ght = "1.28932490272739e + 000"/ > < /N eur on > < /N eur al - Layer > < NeuralOutputs numberOfOutputs = "1" > < NeuralOutput 1 3 1 Page 18 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 outputNeuron = "11" > < DerivedField optype = "continuous" > < Nor- 9. Oczoś KE, Kawalec A. Kształtowanie stopów lekkich. Wyd. Nau- mContinuous field = "Fr ms_x" shift = "-2.08791208791209e-001" kowe PWN; Warsaw; 2012. scale = "1.83150183150183e-003" > < LinearNor m or ig = "1.1400 10. Zagórski I, Kulisz M. The influence of technological parameters 0000000000e + 002" nor m = "0.00000000000000e + 000"/ > < Lin- on cutting force components in milling of magnesium alloys earNor m or ig = "6.60000000000000e + 002" nor m = "1.0000000 with PCD tools and prediction with artificial neural networks. 0000000e + 000"/ > < /Nor mContinuous > < /Der ivedField > < / In: Gapiński B, Szostak M, Ivanov V, editors. Advances in manu- NeuralOutput > < /NeuralOutputs > < /NeuralNetwork > < /PMML > facturing II. Cham: Springer; 2019. (MANUFACTURING 2019. Lecture Notes in Mechanical Engineering). 11. Shi K, Zhang D, Ren J, Yao Ch, Huang X. Effect of cutting param- Declarations eters on machinability characteristics in milling of magnesium alloy with carbide tool. Adv Mech Eng. 2016;8(1):1–9. https:// Conflict of interest The author declares that he has no conflict of inter - doi. org/ 10. 1177/ 16878 14016 628392. est. 12. Sivam SPSS, Bhat MDJ, Natarajan S, Chauhan N. Analysis of residual stresses, thermal stresses, cutting forces and other output Open Access This article is licensed under a Creative Commons Attri- responses of face milling operation on ZE41 Magnesium alloy. Int bution 4.0 International License, which permits use, sharing, adapta- J Mod Manuf Technol. 2018;10(1):92–101. tion, distribution and reproduction in any medium or format, as long 13. Fu ZT, Yang WY, Wang XL, Leopold J. Analytical Modelling as you give appropriate credit to the original author(s) and the source, of Milling Forces for Helical End Milling Based on a Predic- provide a link to the Creative Commons licence, and indicate if changes tive Machining Theory. 15th CIRP Conference on Modelling of were made. The images or other third party material in this article are Machining Operations 2015;31:258-263. included in the article's Creative Commons licence, unless indicated 14. Salguero J, Batista M, Calamaz M, Girot F, Marcos M. Cutting otherwise in a credit line to the material. If material is not included in forces parametric model for the dry high speed contour milling the article's Creative Commons licence and your intended use is not of aerospace aluminium alloys. Procedia Eng. 2013;63:735–42. permitted by statutory regulation or exceeds the permitted use, you will https:// doi. org/ 10. 1016/j. proeng. 2013. 08. 215. need to obtain permission directly from the copyright holder. To view a 15. Kecik K, Borowiec M, Rusinek R. Verification of the stability copy of this licence, visit http://cr eativ ecommons. or g/licen ses/ b y/4.0/ . lobes of Inconel 718 milling by recurrence plot applications and composite multiscale entropy analysis. 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Analysis and prediction of the impact of technological parameters on cutting force components in rough milling of AZ31 magnesium alloy

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Abstract

This paper presents the results of experimental study of the AZ31 magnesium alloy milling process. Dry milling was carried out under high-speed machining conditions. First, a stability lobe diagram was determined using CutPro software. Next, experimental studies were carried out to verify the stability lobe diagram. The tests were carried out for different feed per tooth and cutting speed values using two types of tools. During the experimental investigations, cutting forces in three direc- tions were recorded. The obtained time series were subjected to general analysis and analysis using composite multiscale entropy. Modelling and prediction were performed using Statistica Neural Network software, in which two types of neural networks were applied: multi-layered perceptron and radial basis function. It was observed that milling with high cutting speed values allows for component values of cutting force to be lowered as a result of the transition into the high-speed machining conditions range. In most cases, the highest values for the analysed parameters were recorded for the component F , whereas the lowest were recorded for F . Additionally, the paper shows that a prediction (with the use of artificial neural x y networks) of the components of cutting force can be made, both for the amplitudes of components of cutting force F and amp for root mean square F . rms Keywords High-speed dry milling · Cutting forces · Magnesium alloys · Entropy · Neural networks 1 Introduction which occur in the cutting process. A change in the cutting force components during the milling process may affect the The machining allowance can be removed by means of deformation of a workpiece. [1]. In addition, changes in the machining methods using high cutting speeds (HSM cutting force may affect phenomena such as adhesion and –High Speed Machining, HPC–High Performance Cut- accretion, leading to an additional decrease in surface qual- ting, HSC–High Speed Cutting), which allows for shorter ity, shape and dimensional accuracy. There are also stud- machine time, increased volumetric efficiency and reduced ies investigating power demand in the milling of different manufacturing costs. Parts for the machine-building and materials, including magnesium alloys. Compared to other aircraft industries are usually machined by milling. The so- metals [2], the milling of magnesium alloys can be done called “utility” indicators of machinability include forces (F) in an effective way due to the possibility of applying high values of the technological parameters of the milling process [3], both during the square shoulder milling and roughing plunge milling process [4]. For instance, unlike in the case * M. Kulisz m.kulisz@pollub.pl of Al-Si alloys, the cutting force generated in the milling of magnesium alloys is lower by approx. 50%. Given the low Department of Organisation of Enterprise, Management cutting resistance [5] and temperature [6] in this process, the Faculty, Lublin University of Technology, Lublin, Poland thermal and mechanical loads on the tools are low, too [7]. Department of Production Engineering, Mechanical Cutting speed has a significant impact on the efficiency Engineering Faculty, Lublin University of Technology, of milling processes. Given the ranges of cutting speed Lublin, Poland 3 v , milling processes are often divided into those per- Department of Applied Mechanics, Mechanical Engineering formed applying “conventional” parameters and those Faculty, Lublin University of Technology, Lublin, Poland Vol.:(0123456789) 1 3 1 Page 2 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 performed at higher values of v (characteristic of HSM). an increase in resistance, and as a consequence also an The moment of “transition” into a range of the parameters increase in temperature generated in the cutting zone. which are typical of HSM can be defined in the following In the study [12] an analysis was performed of, among way: ∂F/∂v < 0 (HSM) and ∂F/∂v > 0 (conventional mill- others, cutting forces that were obtained during the dry face c c ing) [8]. The distinction between conventional milling and milling operation of ZE41 magnesium alloy. The variable HSM is generally made when an increase in the cutting input parameters in the process were: spindle speed, feed speed v leads to a decrease in the cutting force. HSM is per tooth, depth of cut, and tool diameter. Based on studies defined as a highly efficient cutting method ensuring high conducted, it was observed that the cutting forces gradually surface quality (Ra—arithmetical mean roughness of the increased with an increase in input parameters. These cut- profile parameter is often lower than 1 µm). The use of ting forces are more closely linked with spindle speed than HSM helps eliminate finishing which is usually done by feed per tooth. The authors also concluded that both constant grinding. For instance, the use of HSM enables the short- depth of cut and tool diameter are proportionally related to ening of milling time (by as much as four times) with- the cutting forces at increasing spindle speeds and feed per out decreasing surface quality and shape accuracy. The tooth, respectively. These forces should be kept under con- desired shape accuracy can be attained thanks to, among trol as they can impact the cutting tool. When the cutting others, a decrease in the cutting forces in high-speed mill- force is excessive, this also has a negative effect on the qual- ing. Among the high-speed machining methods, one can ity of a machined surface. With an increasing feed rate, the distinguish two highly efficient methods: high perfor- vibration in the machine-holder-workpiece-tool (MHWT) mance cutting (HPC), used for pre-treatment or forming, system increases, too. This is caused by the impact of exces- and high-speed cutting (HSC), which is used for finishing. sive cutting force [13]. One recent definition of HSC has introduced the concept Based on the above, it can be seen that the values of the of so-called limit cutting speed v which marks the range cutting force and of its components are influenced by many c-gr of high-speed milling [9]. factors associated with the machining process, including but Both when the milling process is performed by tools with not limited to the materials from which tool is made and the so-called “classical end mill geometry,” as well as when a material being machined, the tool geometry, and the machin- wave-shaped cutting edge is used, the cutting force compo- ing parameters. Of these, however, the most significant is the nents and their amplitudes are more affected by changing selection of appropriate machining parameters, as has been the feed per tooth f rather than by variations in the cut- demonstrated by researchers in work such as [14], while ting speed v . In the milling of AZ91HP alloy, the cutting others claim that the use of high cutting speeds, feed rates, force components are the highest when the tool with a PCD and cutting depths allows for an increase in machining effi- (polycrystalline diamond) end mill is used. The type of tool ciency. The relationships between the factors listed above are coating (e.g. TiB and TiAlCN) has a significant effect on frequently nonlinear in nature. An additional drawback may the cutting force, too. This can be particularly observed in be the process instability resulting from the translational the case of carbide end mills. The cutting force components motion of the end mill [15]. Moreover, during machining, (F —component of the cutting force in the x-axis direction, at specific combinations of cutting depth and spindle speed, F —component of the cutting force in the y-axis direction) the regenerative effect may arise. Under chatter conditions, in the milling process for EN AW-6082 alloy are the lowest the vibration developed is sometimes so strong that the when a TiB -coated tool is used. With a change in the value amplitude of the vibration between the tool and workpiece is of v , one can observe a characteristic point of “transition” larger than the chip thickness, so that the chip becomes dis- into an HSC machining range (at v = 450 ÷ 600  m/min) sected, and the machined surface is spoiled by chatter marks. c-gr [10]. This phenomenon is the so-called machining instability [16]. Additionally, the effects of tool wear on cutting perfor - The manufacturing industry requires quality machined sur- mance were investigated for milling of magnesium alloy faces, and so violent chatter or machining instability must within the cutting speed range of 1600–2000 m/min under therefore be avoided. dry conditions in studies by [11]. These mechanisms were A stability chart is commonly used to indicate stable dominantly categorized into adhesion wear, abrasion, and (chatter-free) cutting as a function of spindle speed and diffusion under dry conditions. Extensive flaking was the depth of cut [17]. It has long been recognized that sub- significant failure mode at the cutting speed of 1600 m/min, stantial gains in productivity can be achieved by exploit- while serious flank wear and gross fracture were mainly ing the lobed nature of the stability chart, particularly at responsible for failures at the cutting speeds of 1800 and high speeds. The stability lobe diagram (SLD) is used in 2000 m/min. An increase in power consumption may also the processing of various types of materials, those com- result in an increase in cutting force components and cause monly considered as difficult to process (titanium alloys, steel, nickel alloys), lightweight alloys (aluminium alloys, 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 3 of 19 1 magensium alloys), as well as various composite materials entropy method (MSE), defined as a measure of the degree [18]. In this paper, the authors additionally conducted statis- of disorder or uncertainty of a given signal, allowing for an tical, recurrence, and composite multiscale entropy analyses. assessment of the complexity of time series. This is based The authors performed a classic trial involving changing the on a granulation procedure conducted by averaging original spindle speed and observed the appearance of chatter vibra- points on the time series [30]. Unfortunately, with a large tions and signatures of intermittency. scale factor τ, the results may be skewed by an error which Thus, due to the complexity of the milling processes and can be eliminated by applying the concept of composite mul- their nonlinear nature as well as due to phenomena occur- tiscale entropy (CMSE) [31]. ring in the cutting zone, attempts are being more and more The aim of this paper is to analyse the impact of changes commonly made to model the machining processes using in technological parameters on the cutting force values in the mathematical analytical methods [4], semi-analytical tech- case of milling an AZ31 magnesium alloy with two differ - niques namely the Chebyshev collocation method and tem- ent tools. This alloy is relatively rarely analysed in milling poral finite element analysis (TFEA) [19] or using Artificial processing, to a much lesser extent than the AZ91D mag- Intelligence (AI) systems [20]. Apart from Danis et al. [4], nesium alloy. Carrying out investigations for two types of mathematical modelling was also employed by Fu et  al. cutting tools can reveal some differences in the course of [13], and Weremczuk et al. [21]. When the nature of a pro- milling process. analysis made use of courses of cutting cess is too complex to be described in mathematical terms forces obtained experimentally, based on which a statistical using equations, modelling is often performed using Neural analysis was conducted. The study also made use of compos- Network Toolbox [22] or Statistica software package [20]. ite multiscale entropy (CMSE) as a measure of disorder in Artificial neural networks are most often employed for this the time series of the cutting force signal. It is believed that purpose, which is confirmed in the works by Kilickap et al. it can be an extension of the analyses conducted on the basis [23] or Kazemi et al. [24] of commonly used indicators and provide additional infor- The main aim of the modelling of cutting processes is mation on the course of the cutting process. Additionally, the prediction of the course of the technological processes the use of neural networks was proposed to develop predic- which are of a nonlinear nature. This may serve to create tive models for the component values of total cutting force, systems supporting decision-making processes in a business, and the values of the amplitudes of cutting forces F and amp for example when selecting technological machining param- root mean square F for the TiAlN-coated tool. The input rms eters. For the modelling and simulation of cutting force com- parameters for modelling were the technological parameters ponents, neural networks can be used, such as RBF (Radial of the process (cutting speed and feed per tooth). An analysis Basis Function) and MLP (Multi-Layered Perceptron). of the literature shows that no such modelling has been so The authors of one study [25] presented a model for the far conducted. prediction of components of cutting force for an AZ91HP alloy with two inputs, namely the machining parameters (cutting speed and feed per tooth). Other materials which 2 Experimental set‑up have been studied by other researchers using simulations of cutting force components include aluminium alloy (input The main aim of the study was to investigate the effect of parameters: spindle speed, feed per tool, radial depth and parameters such as cutting speed v and feed per tooth f on c z axial depth) [26], 7050 aluminium alloy (input parameters: the dynamics of a system during milling. The experimental spindle speed, feed per tooth, milling width) [27], Inconel investigations were conducted on AZ31 magnesium alloy 718 (input parameters: tool wear, feed per tooth, cutting specimens cut on an AVIA VMC 800HS machining cen- depth, cutting width, cutting speed) [28], and also AZ31 tre. Chemical composition and mechanical properties of the magnesium alloys with a PCD tool (cutting speed range machined magnesium alloy are shown in the Table 1. and feed per tooth as input parameters) [10]. The models The tools used in the study were 16 mm end mills (z = 2), developed allow for the testing of different configurations one carbide TiAlN-coated (Fenes) and the other with a PCD of input parameters (machining parameters) without having end mill (Guhring). On the basis of the conducted literature to simultaneously conduct experimental tests. The results of review, it was observed that these tools enable achieving our experiments show that the measured results and simu- favourable machining effects during the milling of magne - lated results correspond well with each other. Modelling sium alloys. These tools are frequently employed in mill- and simulation can also be used to predict the influence of ing of various lightweight alloys, a carbide TiAlN-coated technological parameters on other indicators, e.g. the surface tool is relatively cheap and yields good machining effects, quality [29] achieved by machining processes. whereas a PCD tool enables to achieve high quality of the Additionally, it is becoming increasingly common in surface, comparable to grinding Ra ≤ 0.16 µm (elimination the analysis of dynamic processes to use the multiscale of additional machining processes). A constant radial depth 1 3 1 Page 4 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 Table 1 Chemical composition and mechanical properties of AZ31 magnesium alloy [32] Chemical composition Al Mn Zn Cu Others Mg 2.5–3.5 0.1–0.2 0.7–1.3 0.05 0.04 Rest Mechanical properties R (MPa) R (MPa) E (GPa) A (%) HB ρ (g/cm ) m p0.2 5 250–290 150–220 ~ 45 12–21 46–73 1.78 of cut a = 14 mm, axial depth of cut a = 6  mm, and the lobe diagram (SLD). The modal hammer is used to excite the e p following technological parameter ranges were applied: tool and then the resulting vibrations are measured by the v = 200–1200 m/min and f = 0.05–0.30 mm/tooth, as shown low mass accelerometer mounted at the tool tip. Next, the c z in Table 2. The technological parameter ranges v and f were modal parameters in the form of frequency response func- c z selected on the basis of the previous studies on magnesium tion (FRF) are implemented to CutPro9 software, which alloys, which can be found in other available publications calculates and plots SLD for three different values of feed as well as on the basis of the previous own studies and lit- per tooth f (Fig. 2). In the second step of the experiment, a erature review. In addition, v was obtained via studies and verification of unstable lobes is performed for series of spin- analyses of HSM; however, it is limited by the technological dle speeds and the depths of cut presented as black points capacity of the machining device (maximum spindle speed in the SLD. Experimental verification of stability lobes is of 24,000 rpm). frequently employed during the experimental studies of the Figure 1 shows a plan of the experiments and a schematic machining processes. The parameters, based on which the diagram of the experimental set-up. The experimental set- CutPro software determines the stability curves, are static. up is composed of two subsystems: a modal analysis system However, these parameters may change during processing and a dynamometer system. The former is used to meas- and thus change the location of stability lobes. ure tool-holder stiffness and damping coefficient (modal SLD was prepared only for a carbide TiAlN-coated tool. parameters). It consists of the modal hammer PCB 086C03, In the case of PCD tool, creation of SLD would be risky, accelerometer PCB 352B10, data acquisition card (DAQ) because a relatively brittle part of the tool made of poly- NI9234 and CutPro software. The latter is used to measure crystalline diamond should be struck with a modal hammer, the cutting force components (F , F and F ) by means of a which could result in its damage. x y z Kistler 9257B piezoelectric dynamometer connected to a The location of SLD curves affects the rigidity and vibra - Kistler 5017B signal conditioner and a SCADAS Mobile tion damping of the system. Diameter and free length of the LMS analyser. Both experimental rigs are integrated in the tool were the same in both cases; thus, the system rigidity computer system. Measurements are conducted in two steps. did not change. The influence of blade shape and the type In the first, the impact test is done to get data for the stability of coating affect the MHWT system rigidity to a minimal Table 2 Technological Cutting tool Cutting speed Feed per tooth Axial depth of cut a (mm) Radial depth of cut a (mm) p e parameters with which the v (m/min) f (mm/tooth) c z milling process was carried out PCD, TiAlN 200 0.15 6 14 800 0.05 0.10 0.15 0.20 0.25 0.30 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 5 of 19 1 Fig. 1 Design of the: a experiment and b schematic diagram of the experimental set-up c schematics of the artificial neural network with the analysed process parameters degree. Thus, it can be concluded and assumed with high the highest positive value of the signal. The F amplitude amp degree of probability that the SLD curves are similar for is the highest deviation from equilibrium. Higher values F amp both tools (or even identical). than F result from the signal asymmetry (shifted towards max The cutting forces generated on the workpiece during the bottom). In the presented case, F is approximately max the machining were measured by a dynamometer mounted equal to 400 N, while F is about 900 N. amp on the milling machine underneath the workpiece. The cor- An additional aim of this study was to verify whether it is responding force signals from the dynamometer were first possible to predict the impact of technological parameters (f transmitted to the charge amplifier, next to the analyser and, and v ) on the maximum values of the components of total finally, to the computer system. The sampling rate of data cutting force and on the values of the amplitudes of cut- recorded during the test was set to 1 kHz. ting forces F and the root mean square F when rough amp rms A typical, experimentally obtained time series is pre- milling an AZ31 magnesium alloy using a carbide TiAlN- sented in Fig. 3. In the paper, the maximum value F is coated tool. Thus, a simulation of selected components of max 1 3 1 Page 6 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 for training the network were the machining parameters v = 200–1200  m/min and f = 0.05–0.30  mm/tooth, while c z the output neuron for modelling a given networks was the cutting force component/amplitude of component F /root mean square of the component F . Therefore, modelling was performed for 4 different networks. Two types of network were used for modelling, an MLP (multi-layered Perceptron) network and an RBF (Radial Basis Function) network. The set of training and verification data was divided in a propor - tion of 75% (training set) to 25% (verification set). The test data set was omitted due to the small number of input data for training the network [21]. With the MLP network, linear, logistic, exponential, tanh and sinus activation functions were applied, while with the RBF network, Gaussian (hidden neurons) and linear (output neurons) functions were applied. The networks were mod- elled with a single layer of hidden neurons within a range of 2–9. The number of epochs fluctuated from 150 to 500. For each model, 100 networks were constructed and the best of these was selected based on training and verification qual- ity as well as on errors in these sets. Errors were calculated Fig. 2 Stability lobe diagram for milling processes using a carbide using the least squares method. TiAlN-coated (Fenes) tool 3 Experimental test results In the following study, the statistical analysis waveform forces were produced by experimental investigations. The bar charts show the results of the forces in three directions for two different tools (a PCD and a TiAlN-coated tool). The tests were carried out for six parameters, and are shown in the stability lobe diagram as points from 1 to 6 (Fig. 2). 3.1 Influence of cutting speed First, the impact of the cutting speed v was investigated. Figure 4a shows the change in the maximum cutting forces F in relation to the cutting speed. In the case of both tools, max the highest values of maximum forces F were observed max in the x direction (feed direction), the smallest in the z direc- tion. Similar relations are visible when analysing the ampli- tudes of cutting forces F (Fig. 4b). In the case of cutting amp speed v = 800 m/min, a significant difference in the value of the cutting force amplitudes F was observed for both amp Fig. 3 Time series for PCD tool (f = 0.05 mm/tooth) tools in the feed direction. The highest values of standard deviations F (Fig. 5b) and root mean square F (Fig. 5a) std rms cutting force (F and F ) and amplitude of the component were observed at the cutting speed of v = 600 m/min. x y c F as well as the root mean square for the component F was From the experimental tests carried out for the AZ31 x x conducted. The component F was selected because it has alloy, it can be concluded that with the increase of the the greatest impact on the total cutting force. cutting speed v to 600 m/min, all the components of the To conduct the simulation, the Statistica 13 Neural Net- cutting forces increase (most components in the feed direc- works software package was used, and input data comprised tion). At the same time, above v = 800 m/min a significant the results of experimental studies. The input neurons reduction in cutting forces was observed for both tools. 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 7 of 19 1 Fig. 4 The effect of change in cutting speed v on the value of cutting forces for f = 0.15 mm/tooth a maximum F and b amplitude F in the c z max amp milling of AZ31 magnesium alloys using different tools Fig. 5 The effect of change in cutting speed v on the value of cutting forces for f = 0.15 mm/tooth a root mean square F and b standard devia- c z rms tion F in the milling of AZ31 magnesium alloys using different tools std This is due to the characteristic transition to HSM machin- the TiAlN-coated tool. In the case of effective value F rms ing for higher cutting speeds. Significantly, lower maxi- and standard deviation F , the highest values were again std mum cutting forces F were observed when cutting using obtained for the component F . The lowest values of indi- max x the PCD tool. However, when analysing the amplitude of cators when milling at low cutting speeds were noted for cutting forces F , smaller values were obtained using amp 1 3 1 Page 8 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 component F , though after achieving a cutting speed of be concluded that the waveforms obtained during cutting v = 800 m/min the lowest values were seen for F . with the PCD tool show greater variability. This is evi- c y The dramatic increases in values which are repeated denced by the much higher F (Fig. 6b), F (Fig. 7a) amp rms in the case of all analysed indicators, particularly visible and F (Fig. 7b) values for the F component in the case std x for the cutting speed range of v = 400–800  m/min, can be of the PCD tool. associated with the course of stability curves. Rotational The use of a carbide tool with a TiAlN coating provides speeds equivalent to cutting speeds of v = 400  m/min and greater stability of the milling process at a wide range of v = 800 m/min were determined based on stability curves feed per tooth. As in the case of changes in cutting speed, to be speeds which generated instability during the machin- the highest values of the analysed indicators were noted for ing process. Despite the fact that the machining process was component F , while the lowest were noted for F . x z conducted with all remaining values of technological param- eters within the unstable machining zones of the stability curves, clear increases in these values were not observed. This may be associated with the feed per tooth value of 4 Multiscale entropy analysis f = 0.15 mm/tooth which the sample millings were con- ducted at, as the stability curves were generated for feed per In further analysis of the cutting forces, the composite tooth of f = 0.05 mm/tooth and f = 0.30 mm/tooth. multiscale entropy (CMSE) method was used [31]. In this z z method, τ is the scale factor. The original time series is 3.2 Influence of feed per tooth divided into non-overlapping windows of length τ and the data points inside each window are averaged. In the next step, the influence of the feed per tooth f was i=j+k−1 1 N investigated. The change of the feed per tooth was car- () y = x ,1 ≤ j ≤ ,1 ≤ k ≤ , (1) k,j ried out in the range f = 0.05–0.30 mm/tooth in six steps. i=(j−1)+k Together with the increase of the feed per tooth, all compo- where N—length of data series, x—time series. nents of the cutting forces increase; this is visible for the F At each scale factor τ, the composite multiscale entropy component (feed direction) for both tools (Fig. 6 and Fig. 7). calculation is based on the averaged time series {y} and In the case of cutting with the TiAlN-coated tool, higher reads as values of maximum forces F for the F component were max x observed. However, observing the other indicators, it can Fig. 6 The effect of change in feed per tooth f on the value of cutting forces for v = 800  m/min a maximum F and b amplitude F in the z c max amp milling of AZ31 magnesium alloys using different tools 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 9 of 19 1 Fig. 7 The effect of change in feed per tooth f on the value of cutting forces for v = 800 m/min a root mean square F and b standard deviation z c rms F in the milling of AZ31 magnesium alloys using different tools std Fig. 8 The composite multiscale entropy analysis for measured cutting force components a F and b F signals for two different values of the x y cutting speed and f = 0.15 mm/tooth where m = 2 is the pattern length and r is the similarity crite- () CMSE(x, , m, r) = SampEn(y , m, r), (2) rion, which is usually equal to 10% of the standard deviation k=1 of the original time series {x} used. 1 3 1 Page 10 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 Fig. 9 The maps of composite multiscale entropy against cutting speed and scale factor τ at f = 0.15 mm/tooth for the TiAlN-coated tool a F , b z x F and for PCD tool c F , d F y x y Next, the method of composite multiscale entropy was impacted the change in the level of entropy when using the used to analyse the experimental cutting forces. Figure 8 TiAlN-coated tool. Similar behaviour was observed for the shows the composite multiscale entropy for two values entropy levels of component F (Fig. 8b). of cutting speed (v = 200  m/min and v = 1200  m/min— The change in multiscale entropy of the component sig- c c points 1 and 6 on Fig.  2) and two different tools. In the nals F and F dependent on the change in cutting speed is x y case of component F , a considerable increase in entropy also presented in the form of maps for the TiAlN-coated was observed for milling using the PCD tool at a speed of tool (Fig. 9a, b) and the PCD tool (Fig. 9c, d). The high- v = 200  m/min (Fig. 8a). Change in speed only slightly est levels of entropy when milling with the TiAlN-coated 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 11 of 19 1 Fig. 10 The composite multiscale entropy analysis for measured cutting force components a F and b F signals for two different values of feed x y per tooth and v = 800 m/min tool occurred for cutting speed of v = 800  m/min, which increases, then gradually decreases, particularly in the coincide with dramatic rises in the values of cutting force case of the PCD tool. The character of changes in entropy components and which may be the result of machining in is maintained for both tools throughout the full range of the unstable SLD area. In the case of component F , the changes in feed per tooth. A decrease in the level of entropy level of entropy increases for successive values of the scale of both cutting force components can only be seen when factor τ, and this effect subsides along with an increase milling with the TiAlN-coated tool at the highest feed per in cutting speed. The level of entropy for component F tooth of f = 0.30 mm/tooth. y z is characterized by considerably greater variability. This effect occurs regardless of the type of cutting tool used. Figure  10 shows the composite multiscale entropy 5 Simulation results for two values of feed per tooth (f = 0.05  mm/tooth and f = 0.30 mm/tooth) and two different tools. In the case of Based on the results of the modelling process conducted feed direction (Fig. 10a), it was observed that for the feed for selected maximum cutting force components (F and f = 0.30 mm/tooth, the value of entropy is reduced. Sig- F ), amplitude of component F , and root mean square z y x nificantly lower values are observed when cutting with the for component F for each model a network with the best x, TiAlN coating tool. Similar results were observed in the y indicators was selected, for which the quality of training direction (Fig.  10b), but the value of entropy was higher and verification was the highest, and for which the errors than the x direction. Moreover, the difference in the obtained in training and verification were the lowest. The character - values (Frms/Fstd and entropy) confirms that the applica- istics of these networks are described in Table 3. The best tion of an additional index, i.e. composite multiscale entropy results were obtained for component F for the network enables observing the process from a different point of view. MLP 2-2-1 with two neurons obtained in 315 iterations, A map of changes in multiscale entropy of component while for component F the best results were obtained for signals F and F for the TiAlN-coated tool (Fig. 11a, b) and a network with six neurons (MLP 2-6-1) obtained in 438 x y PCD tool (Fig. 11c, d), also presented in relation to changes iterations. In the case of modelling of the amplitude of in feed per tooth. cutting force component F , the best network was obtained In the case of component F , the course of entropy dis- in 356 iterations, having 9 neurons in the hidden layer plays considerable variability, while for component F the (MLP 2-9-1). For these three models, the best models were level of entropy in the initial range of the scale coefficient obtained for the MLP network, while only in the case of 1 3 1 Page 12 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 Fig. 11 Maps of composite multiscale entropy against of feed per tooth and scale factor τ at v = 800 m/min for TiAlN-coated tool a F , b F and c x y for PCD tool c F , d F x y root mean square of cutting force component F were bet- component F , Fig. 12c for the amplitude of cutting force x y ter parameters obtained for the RBF 2-9-1 network. component F , and Fig. 12d) for the root mean square of The numerical results for the modelled parameters cutting force component F . These are the results of a sim- are presented below. Figure 12a) presents results for the ulation obtained after entering the assumed input param- cutting force component F , Fig.  12b) for cutting force eters v , f for each of the generated networks. x c z 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 13 of 19 1 Table 3 Characteristics of Network Network Quality Quality Error Error Activation Activation selected networks: cutting No Name (Training, %) (Validation, %) (Training) (Validation) (Hidden) (Output) force components (F and F ), x y amplitude of component F , and x Cutting force component F root mean square for component  1 MLP 2-2-1 97.35 99.98 1934.4 4222.3 Tanh Sinus Cutting force component F  2 MLP 2-6-1 99.95 99.74 10.1 467.8 Tanh Linear Amplitude of cutting force component F (F ) x x_amp  3 MLP 2-9-1 99.12 99.99 1956.5 2365.9 Logistic Linear Root mean square of cutting force component F (F ) x x_rms  4 RBF 2-9-1 99.73 99.95 74.2 263.8 Gaussian Linear Table 4 presents the R correlation coefficients and sen- During processing, these parameters may change as a result sitivity analysis of input parameters (f and v ) of the ana- of the occurrence of dynamic phenomena, which affects the z c lysed networks. It can be seen that neural networks are an location of stability lobes. Then, the cutting force signals appropriate tool to predict assumed values, and that both were subjected to a thorough analysis. Apart from the clas- input parameters have a significant impact on these values. sic and commonly employed approach, a dynamic analy- Moreover, the charts presented in Fig. 13 show this correla- sis was performed using multiscale entropy and numerical tion (between experimental results and those obtained in the simulations using artificial neural networks. The obtained simulation). The charts present a correlation for networks results confirm the appropriateness of the proposed research which are presented in a visual form in Fig. 12. approach. The analysis using dynamic indices enables to Based on the charts presented above, it can be stated that analyse both the limit values of measured forces and the sig- the networks obtained show satisfactory predictive capacity. nal complexity, which significantly contributes to the quality All obtained correlation coefficients are higher than 0.95. of the performed studies. Thus, it can be stated that neural networks may be an effec- Based on the studies conducted, it can be stated that: tive tool for the simulation of, for example, cutting force components and their amplitudes or their root mean square. 1) Increasing the cutting speed at low ranges of values Neural networks may be effectively used for the numerical causes an increase in cutting force in all directions. modelling of machining processes. 2) Performance of the machining process with high cut- ting speed values allows for component values of cutting force to be lowered as a result of the transition into the 6 Conclusions HSM range. 3) Increasing the feed per tooth value causes a linear This paper presents the results of experimental study of the increase in the values of all cutting force components, AZ31 magnesium alloy milling process. Two different tools regardless of the technological parameters or type of were used in experimental studies, a PCD and a TiAlN- cutting tool. coated tool. First, modal analysis was performed to obtain a 4) Regardless of the technological parameters or type of stability lobe diagram which was next verified for selected cutting tool, the highest values for the analysed param- points by means of statistics and the multiscale entropy eters were recorded in most cases for the component F , method. Additionally, a prediction was made of cutting force whereas the lowest were recorded for F . components and the amplitudes of components of cutting 5) Lower values of parameters for milling with variable force F and root mean square F for the TiAlN-coated feed per tooth were obtained when using a tool with amp rms tool. a TiAlN coating, something which was particularly A novel and rarely employed approach was used in the noticeable for the component F . Nevertheless, in the analysis of the experimentally obtained signals. The SLD case of changes in the cutting speed, the type of tool curves obtained using CutPro commercial software were used did not show an unambiguous impact on the results verified for selected processing parameters. This is because obtained. these curves were obtained based on the static parameters 6) An analysis of entropy indicated a lower level of dis- of the machine-holder-workpiece-tool (MHWT) system. order for cutting force component signals recorded at 1 3 1 Page 14 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 Fig. 12 Numerical results from network depending on the cutting speed v and feed per tooth f for a maximum cutting force component F , b c z x maximum cutting force component F , c amplitude of cutting force component F , d root mean square of cutting force component F y x x Table 4 Correlation R and F F F F x y x_amp x_rms sensitivity analysis of input parameters for the analysed Network MLP 2-2-1 MLP 2-6-1 MLP 2-9-1 RBF 2-9-1 networks Corelation R 0.9658 0.9986 0.9896 0.9952 Sensitivity analysis f /v 35.03/11.01 1392.78/269.03 2871.62/39.00 84.87/62.56 z c 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 15 of 19 1 Fig. 13 Comparison of experimental and numerical results a cutting force component F , b cutting force component F , c amplitude of cutting x y force component F , d Root mean square of cutting force component F x x the highest cutting speed of v = 1200 m/min and at the as well as for the amplitudes of components of cutting highest feed per tooth of f = 0.30 mm/tooth. force F and root mean square F . The R correlation z amp rms 7) During milling with variable cutting speeds, a lower coefficients were respectively F —0.9658, F —0.9986, x y level of disorder was observed for cutting force compo- F —0.9896, and F —0.9952; thus it can be x_amp x_rms nent signals recorded when milling using the PCD tool, stated that the trained networks are a reliable predictor while when milling with changes in the feed per tooth of utility values of cutting indicators. this lower level was observed for the TiAlN-coated tool. 10) The results of modelling and the simulations conducted 8) It is possible to predict the impact of technological may be used to create tools while establishing machining parameters (f and v ) on the values of cutting force conditions in industrial settings, as support for techni- z c components as well as on the value of the amplitudes of cians in the design of technological processes. Exces- cutting forces F and root mean square F . In most sively high cutting force values may have a negative amp rms cases, better results were obtained for the MLP neural impact on the deformation of machined elements. network than for RBF. 9) The modelling of neural networks may be an effective tool for predicting the components of total cutting force Author contributions Conceptualization: IZ, AW, MK; Methodology: IZ, AW, JK, MK; Formal analysis and investigation: IZ, AW, JK, MK; 1 3 1 Page 16 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 Writing—original draft preparation: IZ, AW, JK, MK; Writing—review (SANN)" version = "2.0"/ > < /Header > < Dat aDictionar y num- and editing: IZ, MK, RR; Funding acquisition: MK; Resources: IZ, berOfF ields = "3" > < Dat aF ield name = "Fy" op type = "con- MK; Supervision: IZ, MK. t i n u o u s " / > < D a t a F i e l d n a m e = " f z " o p t y p e = " c o n t i n u - ous"/ > < Dat aF ield name = "vc" op type = "continuous"/ > < / Dat aDictionar y > < N eur alN e tw or k modelN ame = "Dane Funding The project/research was financed in the framework of the dl_MLP 2–6-1" functionN ame = "r eg r ession" > < Mining - project Lublin University of Technology-Regional Excellence Initia- Sc hema > < MiningF ield name = "Fy" usag eType = "pr e - tive, funded by the Polish Ministry of Science and Higher Education dicted"/ > < MiningF ield name = "fz" lowValue = "0.050000" (contract no. 030/RID/2018/19). highValue = "0.300000"/ > < MiningF ield name = "v c" lowValue = "200.000000" highValue = "1200.000000"/ > < /Min- Data availability The raw/processed data required to reproduce these ingSchema > < N eur alIn puts numberOfIn puts = "2" > < Neu- findings cannot be shared at this time as the data also forms part of an r alIn put id = "0" > < Der iv edF ield > < N or mCon - ongoing study. tinuous f ield = "fz" shif t = "-2.00000000000000e-001" scale = "4.00000000000000e + 000" > < LinearN or m Code availability Sieć MLP 2-2-1 or ig = "5.00000000000000e-002" nor m = "0.000000"/ > < Linear- < ?xml version = “1.0” “encoding = "UTF-8"? > Nor m or ig = "3.00000000000000e-001" nor m = "1.000000"/ > < / < PMML version = "3.0" > < Header copyr ight = "Copyr ight Nor mContinuous > < /Der ivedField > < /NeuralInput > < Neural- 1984–2017 TIBCO Software Inc. All rights reserved." > < Appli- Input id = "1" > < Der ivedField > < Nor mContinuous f ield = "vc" cation name = "STATISTICA Automated Neural Networks shif t = "-2.00000000000000e-001" scale = "1.00000000000000e- (SANN)" version = "2.0"/ > < /Header > < Dat aDictionar y num- 003" > < LinearN or m or ig = "2.00000000000000e + 002" berOfF ields = "3" > < Dat aF ield name = "Fx" op type = "con- nor m = "0.000000"/ > < LinearNor m or ig = "1.20000000000000 t i n u o u s " / > < D a t a F i e l d n a m e = " f z " o p t y p e = " c o n t i n u - e + 003" nor m = "1.000000"/ > < /Nor mContinuous > < /Der ived- ous"/ > < Dat aF ield name = "vc" op type = "continuous"/ > < / Field > < /NeuralInput > < /NeuralInputs > < NeuralLayer num- Dat aDictionar y > < N eur alN e twor k modelN ame = "A1—k_ berOfN eur ons = "6" activationF unction = "t anh" > < N eur on MLP 2–2-1" functionN ame = "r eg r ession" > < Mining - id = "2" bias = "9.16077678635015e + 000" > < Con from = "0" Sc hema > < MiningF ield name = "Fx" usag eType = "pr e - 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Sieć MLP 2-9-1 20000000000000e + 003" nor m = "1.00000000000000e + 000"/ < ?xml version = "1.0" encoding = "UTF-8"? > > < /Nor mContinuous > < /Der ivedField > < /NeuralOutput > < / < PMML version = "3.0" > < Header copyr ight = "Copyr ight NeuralOutputs > < /NeuralNetwork > < /PMML > 1984–2017 TIBCO Software Inc. All rights reserved." > < Appli- Sieć MLP 2-6-1 cation name = "STATISTICA Automated Neural Networks < ?xml version = "1.0" encoding = "UTF-8"? > (S ANN)" v ersion = " 2.0"/ > < /Header > < Dat aD iction - < PMML version = "3.0" > < Header copyr ight = "Copyr ight ar y numberOfF ields = "3" > < Dat aF ield name = "Fx_am p" 1984–2017 TIBCO Software Inc. All rights reserved." > < Appli- optype = "continuous"/ > < Dat aField name = "fz" optype = "con- cation name = "STATISTICA Automated Neural Networks tinuous"/ > < DataField name = "vc" optype = "continuous"/ > < / 1 3 Archives of Civil and Mechanical Engineering (2022) 22:1 Page 17 of 19 1 Dat aDictionar y > < N eur alN e tw or k modelN ame = "Ar k u_ < PMML version = "3.0" > < Header copyr ight = "Copyr ight MLP 2–9-1" functionN ame = "r eg r ession" > < Mining - 1984–2017 TIBCO Software Inc. 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eight = "-5.21245667594871e-001"/ > < Con fr om = "5" 0000000000e + 002" nor m = "0.00000000000000e + 000"/ > < Lin- w eight = "1.31646831970374e-001"/ > < Con fr om = "6" earNor m or ig = "1.89000000000000e + 003" nor m = "1.0000000 w eight = "-9.39266928160472e-001"/ > < Con fr om = "7" 0000000e + 000"/ > < /Nor mContinuous > < /Der ivedField > < / w eight = "1.12820217709549e + 000"/ > < Con fr om = "8" NeuralOutput > < /NeuralOutputs > < /NeuralNetwork > < /PMML > w eight = "-5.17628419352205e-001"/ > < Con fr om = "9" Sieć RBF 2-9-1 weight = "7.08016955495058e-002"/ > < Con from = "10" wei < ?xml version = "1.0" encoding = "UTF-8"? > ght = "1.28932490272739e + 000"/ > < /N eur on > < /N eur al - Layer > < NeuralOutputs numberOfOutputs = "1" > < NeuralOutput 1 3 1 Page 18 of 19 Archives of Civil and Mechanical Engineering (2022) 22:1 outputNeuron = "11" > < DerivedField optype = "continuous" > < Nor- 9. Oczoś KE, Kawalec A. Kształtowanie stopów lekkich. Wyd. Nau- mContinuous field = "Fr ms_x" shift = "-2.08791208791209e-001" kowe PWN; Warsaw; 2012. scale = "1.83150183150183e-003" > < LinearNor m or ig = "1.1400 10. Zagórski I, Kulisz M. The influence of technological parameters 0000000000e + 002" nor m = "0.00000000000000e + 000"/ > < Lin- on cutting force components in milling of magnesium alloys earNor m or ig = "6.60000000000000e + 002" nor m = "1.0000000 with PCD tools and prediction with artificial neural networks. 0000000e + 000"/ > < /Nor mContinuous > < /Der ivedField > < / In: Gapiński B, Szostak M, Ivanov V, editors. Advances in manu- NeuralOutput > < /NeuralOutputs > < /NeuralNetwork > < /PMML > facturing II. Cham: Springer; 2019. (MANUFACTURING 2019. Lecture Notes in Mechanical Engineering). 11. Shi K, Zhang D, Ren J, Yao Ch, Huang X. Effect of cutting param- Declarations eters on machinability characteristics in milling of magnesium alloy with carbide tool. 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Journal

Archives of Civil and Mechanical Engineering – Springer Journals

Published: Oct 21, 2021

Keywords: High-speed dry milling; Cutting forces; Magnesium alloys; Entropy; Neural networks

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