Prediction of Surface Roughness Based on Cutting Parameters and Machining Vibration in End Milling Using Regression Method and Artiﬁcial Neural Network

applied sciences

Article Prediction of Surface Roughness Based on Cutting Parameters and Machining Vibration in End Milling Using Regression Method and Artiﬁcial Neural Network

Yung-Chih Lin 1,2, Kung-Da Wu 1, Wei-Cheng Shih 1, Pao-Kai Hsu 1 and Jui-Pin Hung 1,*

1 Graduate Institute of Precision Manufacturing, National Chin-Yi University of Technology, Taichung 41170, Taiwan; [email protected] (Y.-C.L.); ﬃ[email protected] (K.-D.W.); [email protected] (W.-C.S.); [email protected] (P.-K.H.) 2 Intelligent Machinery Technology Center, Industrial Technology Research Institute, Taichung 40852, Taiwan * Correspondence: [email protected]; Tel.: +88-6423-924-505 (ext. 7181); Fax: +88-6423-925-714

Received: 14 May 2020; Accepted: 3 June 2020; Published: 5 June 2020

Abstract: This study presents surface roughness modeling for machined parts based on cutting parameters (spindle speed, cutting depth, and feed rate) and machining vibration in the end milling process. Prediction models were developed using multiple regression analysis and an artificial neural network (ANN) modeling approach. To reduce the effect of chatter, machining tests were conducted under varying cutting parameters as defined in the stable regions of the milling tool. The surface roughness and machining vibration level are modeled with nonlinear quadratic forms based on the cutting parameters and their interactions through multiple regression analysis methods, respectively. Analysis of variance was employed to determine the significance of cutting parameters on surface roughness. The results show that the combined effects of spindle speed and cutting depth significantly influence surface roughness. The comparison between the prediction performance of the multiple regression and neural network-based models reveal that the ANN models achieve higher prediction accuracy for all training data with R = 0.96 and root mean square error (RMSE) = 3.0% compared with regression models with R = 0.82 and RMSE = 7.57%. Independent machining tests were conducted to validate the predictive models; the results conclude that the ANN model based on cutting parameters with machining vibration has a higher average prediction accuracy (93.14%) than those of models with three cutting parameters. Finally, the feasibility of the predictive model as the base to develop an online surface roughness recognition system has been successfully demonstrated based on contour surface milling test. This study reveals that the predictive models derived on the cutting conditions with consideration of machining stability can ensure the prediction accuracy for application in milling process.

Keywords: artiﬁcial neural network; cutting parameters; machining vibration; regression analysis; surface roughness

1. Introduction High-speed, high-precision machining with a high material removal rate has been an important goal in the manufacturing industry because of the high-efficiency and high-quality requirements. Further, machined parts with a high surface finish are in high demand under considerations of assemblage precision, fatigue strength, and tribological properties of the mechanical product. To achieve high productivity and high precision, machining is implemented with a higher level of cutting parameters. However, surface quality and dimensional accuracy are affected by several factors such as machining

Appl. Sci. 2020, 10, 3941; doi:10.3390/app10113941 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 3941 2 of 22 conditions, tool geometry and vibrations, cutting parameters, and machining dynamics [1]. In particular, surface finish deteriorates because of the machining vibration caused by inappropriate machining conditions and process parameters [2–7]. Bhogal et al. [2] suggested that cutting speed is a major factor affecting tool vibration, which thereby affects surface finish. Amin et al. [3] showed the effect of chatter amplitude on surface roughness under various cutting conditions with different tool holders via machining experiments. Arizmendi et al. [5] demonstrated that the surface topography of the machined part is influenced by cutting tool vibrations. Further, David et al. [6] demonstrated that workpiece topomorphy is affected by the vibration caused by a poor runout of the cutter. They found that an increased cutting force with an increasing cutting depth and feed rate leads to higher vibration, and it accordingly increases surface roughness. Zahoor [7] reported that surface roughness was affected by the vibration amplitude of the machine tool and the axial cutting depth. The vibration levels are closely related to the cutting parameters and they increase with an increase in the cutting speed and feed rate [8–10]. To ensure machining performance with better surface quality, the selection of optimum process parameters is crucial in metal machining. To achieve this goal, a majority of studies has employed experimental and modeling approaches to determine strategies to obtain the best final surface quality and dimensional accuracy [11–15]. The effect of cutting parameters on surface roughness can be effectively examined via the statistical data analysis of data collected from machining experiments under specifically designed process parameters. Subsequently, the optimization of the machining process with a better surface quality and less vibration can be obtained based on prediction models established by various approaches such as analytical modeling, statistical regression based on response surface methodology, and artificial intelligence-based models [16]. Response surface methodology is a statistical technique used to establish relationships between continuous dependent variables with independent variables in terms of mathematical models using multiple regression analysis. Prediction models derived from experimental data can help clarify the influences and contributions of cutting parameters on surface roughness or tool vibration; these models can further be applied to optimize cutting parameters [2,4,14,17–21]. Routara et al. [17] identified that all three cutting parameters (spindle speed, cutting depth, and feed rate) and their interactions have significant effects on surface roughness. Further, the surface response model shows significant dependence on the combination of the tool and workpiece material. Yang et al. [14] proposed an optimization process for machining conditions to ensure a desirable surface roughness based on surface response methodology. With an optimized solution, the material removal rate can be improved significantly without sacrificing surface roughness. Hayajneh et al. [22] and Joshua et al. [18], respectively, reported that feed rate has a significant effect on the surface roughness of machined alumina material compared with spindle speed and cutting depth. However, the effect of the interaction between cutting parameters has no definite tendency based on the machining conditions used in the tests. Hessainia et al. [23] conducted an investigation on the interactive effects of cutting parameters and tool vibration on surface roughness. Their results indicated that feed rate was the dominant factor affecting surface roughness, and vibrations in the radial and main cutting force directions had a low effect on surface roughness. Further, to obtain a desirable surface finish, optimum cutting parameters with less machining vibration were obtained using a predictive regression model. Ramesh et al. [24] and Premnath et al. [25] showed that the interaction of cutting speed and feed rate had a greater influence on surface roughness compared to other interactions. As mentioned previously, tool vibration and chatter affect the surface quality of the machined product and the machining performance directly. Therefore, monitoring and controlling machining vibration has been considered an effective approach to enhance the surface precision and dimension accuracy of a machined product [26–28]. Bhogal et al. [2] employed mathematical models to predict the surface finish, tool vibration, and tool wear with different combinations of cutting parameters. With these models, the optimum feed rate, cutting depth, and cutting speed were obtained to reduce tool vibrations and enhance surface finish. Shelar and Shaikh [20] proposed a multiobjective optimization Appl. Sci. 2020, 10, 3941 3 of 22 algorithm to minimize vibration amplitude and surface roughness. The objective functions and the second-order response surface models for surface roughness and vibration amplitude were created by performing regression analysis on experimentally collected data. Surface roughness modeling has been comprehensively investigated using artificial neural network (ANN) analysis incorporated with optimization algorithms [11,25–27,29,30]. For example, Asilturk et al. [11] employed artificial neural networks and multiple regression approaches to model the surface roughness of AISI 1040 steel in turning. Three training algorithms—back-propagation training, scaled conjugate gradient (SCG), and Levenberg–Marquardt (LM)—were used in ANN modeling; the SCG algorithm was proven to achieve the best prediction accuracy. Tsai et al. [29] proposed statistical regression and ANN models to predict the surface roughness on aluminum 6061 after end milling based on three cutting parameters (spindle speed, feed rate, and cutting depth) and machining vibration. The experimental results show that the ANN surface recognition model has a higher accuracy rate compared with the regression model. In addition, a two hidden-layer ANN model shows a slightly higher accuracy (99.27%) than that of the one hidden-layer model (95.87%); however, it has low efficiency in the training model. A similar study was reported by Oktem [31], who developed a feedforward neural network integrated with a genetic algorithm to optimize machining conditions for obtaining the best surface finish of a plastic injection mold. The model was finally validated with prediction errors of 5.34% in comparison with the measurement of the machined surface roughness. Nalbant et al. [32] explored the influence of the cutting parameters and interactions between them on surface roughness; further, they established a surface roughness model based on ANN analysis, in which the SCG training algorithm with nine neurons demonstrates the best fitness and prediction accuracy in ANN modeling. Zain et al. [33] presented an ANN model to predict surface roughness in end milling. In ANN modeling, the number of layers and neurons in the hidden layers are factors that determine the prediction accuracy. Based on the prediction model, the best combination of cutting conditions for achieving the best surface roughness value can be obtained at a high speed with a low feed rate and radial rake angle. The vibration induced in a machining process can be modeled as a function of cutting parameters via ANN analysis. As presented in the study by Zagórski et al. [34], individual vibration components (ax, ay, and az) were well predicted based on the ANN model for a specified cutting depth, feed rate, and cutting speed in the milling process for the AZ91D alloy. Further, the prediction accuracy based on a multilayered perception model was better than that of the radial basis function. The accurate modeling of vibration components allows optimizing the cutting conditions to enhance machining stability. Abouelatta et al. [35] considered the influence of machining vibration on surface quality when establishing the surface prediction model, wherein the input variables include cutting parameters, tooling condition, and tool vibration were assessed in the turning process. Such models have higher prediction accuracies compared to those of models determined by only cutting parameters. To include the effects of cutting forces and tool vibrations in a surface roughness prediction model, Chen et al. [36] proposed a nested ANN composed of two networks: An enclosed network that uses the cutting parameters to predict the cutting force and tool vibration, and an output network that takes all outputs of the first network and the cutting parameters as inputs to predict surface roughness. According to the analysis results, the nested-ANN model using three cutting parameters as inputs shows superior prediction accuracy than any other regression and ANN models that use the cutting parameter and tool vibration as inputs. These investigations clearly illustrate the significant influences of the machining state such as the cutting forces and tool vibrations on the machined surface roughness; these effects can be adequately introduced in the roughness prediction models by acquiring sensory data from machining or through an estimation algorithm with cutting parameters as inputs. From previous studies, it is clear that factors affecting machined surface quality are multifaceted, including cutting parameters, tooling conditions, workpiece material, and machining state. The effect of each factor and the interactions between them on surface quality and machining vibration are found to be inconsistent because of the scope of machining conditions defined in different researches [20–23]. Appl. Sci. 2020, 10, 3941 4 of 22

Further, various factors used as input variables in the modeling of surface roughness enable the model demonstrating different prediction accuracies; this limits the application in practical machining. The results obtained may work well in the design space of experiments; however, there are constraints in the ranges of the cutting parameters, which limit the application of the specific models in the machining process with different cutting conditions for the desired precision or productivity [37]. This study was aimed to model the surface roughness of the machined part based on cutting parameters with the effect of machining vibration. As the occurrence of chatter is a common factor affecting productivity and surface quality, selecting an optimum chatter-free cutting parameter is prerequisite to ensure machining performance [38]. Considering the effect of chatter on the machining process, the cutting parameters from rough to finish machining were selected within the stable regions defined by the machining stability lobes of the milling tool. Then, machining vibration and surface roughness of the machined parts were collected from milling experiments conducted on the aluminum alloy under various cutting conditions. Multivariable linear regression analysis was employed to establish the mathematical models for predicting the surface roughness and machining vibration. In addition, the surface roughness was modeled as a function of cutting parameters and machining vibration using a multilayer perception neural network with a back-propagation algorithm. The prediction capabilities of the models derived from different approaches were compared based on the measurements and predictions in the training data group and the validation of physical milling machining.

2. Experiment Approaches In this study, the mathematical model for predicting the surface roughness of a milled workpiece was established based on an experimentally data driven approach that employs regression analysis and an ANN model. The training data required for prediction models were collected from machining tests. To conduct a comprehensive study, the cutting parameters, cutting depth, and spindle speed were selected within the range of spindle speed and cutting depth between low speed, rough machining to high speed, and ﬁnish machining. In particular, to ensure machining in a stable state with a higher removal rate, the cutting depth and spindle speed within the stable region were selected based on the machining stability of the cutter [38]. The stability lobes were calculated based on the frequency response function assessed from the impact test.

2.1. Assessment of Machining Stability of Milling Cutter

2.1.1. Impact Vibration Test of Cutter Figure1 shows the experimental conﬁguration for assessing the frequency response function of the milling cutter, in which a 10 mm 4-tooth carbide cutter with a BT tool holder was installed in the spindle. In the test, the spindle head was located at an appropriate height from the working table. An accelerometer was mounted on the tool end to assess the vibration response excited by an impact hammer hit on the opposite side of the cutter, as shown in Figure1. Appl. Sci. 2020, 10, 3941 5 of 22

Appl. Sci. 2020, 10, 3941 5 of 22

Appl.Appl. Sci. 2020, 10,, 39413941 5 of 22

(a) (b)

Figure 1. Experimental configurations of vibration test of milling spindle with and without tool holder/cutter. (a) Measurement at tool tip. (b) Measurement at spindle nose. (a) (b)

2.1.2. FrequencyFigure 1. ExperimentalResponse Function configurations and(a) Machiningof vibration testStability of milling(b ) spindle with and without tool holder/cutter. (a) Measurement at tool tip. (b) Measurement at spindle nose. FigureFigure 2 shows 1.1. Experimental the frequency configurations configurations response of of vibration functions test of of millingthe tool spindle end withmeasured and without in the tool x direction. The2.1.2. milling Frequencyholderholder/cutter. cutter/cutter. showsResponse ((a)) MeasurementMeasurement the Function maximum atat tooltooland tip.tip. complianceMachining (b) Measurement Stability of 1.82 at spindle μm/N nose. at a frequency of 5332 Hz. Based on this2.1.2. Figuredominant Frequency 2 shows mode, Response the frequencymachining Function response and stability Machining functions lobes Stability ofwere the toolcalculated end measured according in the to x thedirection. analytical approachThe milling proposed cutter showsby Altintas the maximum [39]. Tocompliance calculate of 1.82machining μm/N at stability,a frequency the of 5332cutting Hz. Basedresistance Figure2 2 shows shows thethe frequencyfrequency responseresponse functionsfunctions ofof thethe tooltool endend measuredmeasured inin thethe xx direction.direction. coefficientson this dominantfor the milling mode, material machining Al6061 stability with lobes a carbide were calculatedcutter were according identified to asthe K tanalytical = 796 N/mm 2 TheThe millingmilling cuttercutter showsshows the the maximum maximum compliance compliance of of 1.82 1.82µ mμ/m/NN at at a frequencya frequency of 5332of 5332 Hz. Hz. Based Based on andapproach Kthisonr = this0.21 dominant dominantproposed[39]. mode,Figure mode,by machining 3Altintas illustratesmachining stability [39]. thestability To lobes stability calculate werelobes calculatedlobes weremachining diagramcalculated according stability, of according the to the cutter,the analytical tocutting thewhich analytical approach resistance suggests the 2 machiningcoefficientsproposedapproach conditions byforproposed Altintas the milling with [by39 ]. Altintas ormaterial To without calculate [39]. Al6061 machining chatterTo withcalculate in a stability, carbidete rmsmachining of thecutter the cutting wereaxialstability, resistance identifiedcutting the coecuttingdepth asffi Kcientst =asresistance 796 fora N/mmfunction the of r 2 spindleandmillingcoefficients Kspeed.= 0.21 material forAs[39]. theshown Al6061Figure milling with3in materialillustrates the a carbide lobes Al6061 the cutter diagram, stability with were a carbide identifiedlobes the diagram limitedcutter as K weret =ofcutting796 theidentified N cutter,/mm depth asandwhich Kist K = r 796~2.0 =suggests0.21 N/mm mm, [39 ].2the which Figure3 illustrates the stability lobes diagram of the cutter, which suggests the machining conditions indicatesmachiningand Kthatr = 0.21 conditionsstable [39]. machining Figure with 3 orillustrates without the chatterchatter stability in ca telobesnrms be diagramofobtained the axial of whenthe cutting cutter, the depth cuttingwhich as suggests adepth function thebelow of the criticalspindlewithmachining value or speed. without is adopted.conditions As chatter shown with in terms in or thewithout of thelobes axial chatter diagram, cutting in te depth rmsthe of aslimited athe function axial cutting cutting of spindle depth depth speed. is as~2.0 a As function mm, shown which inof indicatesthespindle lobes thatspeed. diagram, stable As the machiningshown limited in cutting thewithout lobes depth chatterdiagram, is ~2.0 ca mm, nthe be which limitedobtained indicates cutting when that depththe stable cutting is machining ~2.0 depth mm, withoutbelow which the criticalchatterindicates value can that beis obtainedadopted.stable machining when the without cutting depthchatter below can be the obtained critical valuewhen isthe adopted. cutting depth below the critical value is adopted.

(a) FRF—Dynamic compliance (b) FRF—Real part (a) FRF—Dynamic compliance (b) FRF—Real part Figure 2. Frequency(a) FRF—Dynamic response compliancefunction (FRF) of the milling cutter.(b) FRF—Real(a) FRF—Dynamic part compliance. (b) FigureFigure 2. 2.FrequencyFrequency response response function function (FRF) (FRF) of of the the milling milling cutter. cutter. (a ()a FRF—Dynamic) FRF—Dynamic compliance. compliance. (b) Figure 2. Frequency response function (FRF)FRF—Real of the milling part. cutter. (a) FRF—Dynamic compliance. (b) (b) FRF—Real part. FRF—Real part. FRF—Real part.

FigureFigure 3. 3. StabilityStability lobes diagramdiagram in in the the X X direction. direction. Figure 3. Stability lobes diagram in the X direction.

Appl. Sci. 2020, 10, 3941 6 of 22

2.2. Machining Tests Experiments were conducted on the Feeler U600 (Fair Friend Ent. Co., Ltd, Taipei City, Taiwan) milling machineAppl. Sci. 2020 with, 10, 3941 a 4-tooth tungsten carbide end mill cutter. The workpiece material6 of 22 is an aluminum alloy (Al6061) with a size of 150 mm × 150 mm × 80 mm. Machining operations were performed2.2. by Machining full immersion Tests of slot milling, as shown in Figure 4. Each slot was milled in the X-direction underExperiments specific were cutting conducted parameters on the Feeler at different U600 (Fair levels. Friend Ent.Considering Co., Ltd, Taipei the effect City, Taiwan) of chatter on the machiningmilling process, machine with the a cutting 4-tooth tungsten parameters carbide from end mill rough cutter. to The finish workpiece machining material were is an aluminum selected within the stablealloy regions (Al6061) that with were a size defined of 150 mm by the150 machining mm 80 mm. stability Machining lobes operations of the were milling performed tool. byThe axial × × full immersion of slot milling, as shown in Figure4. Each slot was milled in the X-direction under cutting depth (ap) was defined in the range of 0.1 and 2.0 mm with an increment of 0.1 mm. The specific cutting parameters at different levels. Considering the effect of chatter on the machining spindle speed (n) was set to 3000–8000 rpm, increased in increments of 1000 rpm, respectively. The process, the cutting parameters from rough to finish machining were selected within the stable regions linear feed rate (f) was set at 600 to 2400 mm/min with increments of 100, which was determined by that were defined by the machining stability lobes of the milling tool. The axial cutting depth (ap) spindle speedwas defined (n) and in the feed range per of tooth 0.1 and of 2.0 the mm cutter with an based increment on the of 0.1 formula: mm. The spindlef (mm/min) speed (=n )n was (rpm) × fz (mm/tooth)set to× 3000–8000z (number rpm, of increasedtooth). Herein, in increments feed of per 1000 tooth rpm, respectively.of the cutter The was linear specified feed rate (atf ) wastwo levels, 0.05 and set0.075 at 600 mm/tooth, to 2400 mm respectively./min with increments For a given of 100, whichspindle was speed, determined the linear by spindle feed speed rate (inn) andmachining feed per tooth of the cutter based on the formula: f (mm/min) = n (rpm) fz (mm/tooth) z (number was set at lower and higher rate, respectively. During milling operations,× a triaxial× vibration sensor of tooth). Herein, feed per tooth of the cutter was specified at two levels, 0.05 and 0.075 mm/tooth, was mountedrespectively. on the For spindle a given spindle housing speed, to themeasure linear feed the rate acceleration in machining signals was set atof lower the andvibration higher in the orthogonalrate, directions respectively. (X, During Y, and milling Z) operations,simultaneous a triaxially. vibrationFor each sensor slot wasmachining, mounted onthe the average spindle value taken fromhousing the time to measure domain the acceleration root mean signals square of the (R vibrationMS) values in the of orthogonal the accelerations directions (X, were Y, and calculated Z) and usedsimultaneously. to compare Forthe each vibration slot machining, extent theof averagemilling value under taken different from thetime cutting domain parameters. root mean After square (RMS) values of the accelerations were calculated and used to compare the vibration extent machining tests, the surface roughness (Ra) was measured using white light interferometer (Optical of milling under different cutting parameters. After machining tests, the surface roughness (Ra) was Surface Profiler,measured Zygo, using whiteNewView™ light interferometer 8000 Series (Optical (Zyzo Surface Corporation, Profiler, Zygo, Middlefield, NewView ™CT8000 USA). Series For each machined(Zyzo slot, Corporation, roughness Middlefield, values were CT USA). measured For each at machined five equally slot, roughness spacedvalues points were along measured the feeding direction,at and five equallythen, the spaced average points of along these the values feeding direction,was recorded and then, for the subsequent average of these analysis. values There was are a total of 240recorded machining for subsequent conditions analysis. defined There are by a totalthe different of 240 machining levels conditions of cutting defined parameters, by the diff erentincluding 6 spindle speeds,levels of 2 cutting feed rates, parameters, and 20 including cutting 6 spindledepths. speeds, 2 feed rates, and 20 cutting depths.

FigureFigure 4. Machining 4. Machining test test and workpiece. workpiece.

2.3. Machined Surface Morphology and Vibration Spectrum 2.3. Machined Surface Morphology and Vibration Spectrum Figure5 shows the morphologies of machined surfaces and the vibration spectrum of the milling Figurespindle 5 shows under speciﬁcthe morphologies machining conditions, of machined which indicates surfaces that and the cuttingthe vibration depth with spectrum a greater of the milling spindlevibration under level has specific a rougher machining surface. For example,conditions for a, which cutting depthindicates of 0.7 mmthat at the a speed cutting of 3000 depth rpm, with a greater vibrationRa was measured level has as 0.494a rougherµm, while surface. it caused For a ex vibrationample, level for a of cutting 0.035 (g). depth When of the 0.7 cutting mm depthat a speed of was set at 0.6 mm, Ra = 0.580 µm was generated under a spindle speed of 6000 rpm with a vibration 3000 rpm, Ra was measured as 0.494 μm, while it caused a vibration level of 0.035 (g). When the level of 0.05 (g). When the cutting depth was set at 1.3 mm, Ra = 0.704 µm was generated with the cutting depthhigher was level set of vibration at 0.6 mm, of 0.83 R (g).a = 0.580 μm was generated under a spindle speed of 6000 rpm with a vibration level of 0.05 (g). When the cutting depth was set at 1.3 mm, Ra = 0.704 μm was generated with the higher level of vibration of 0.83 (g). Appl. Sci. 2020, 10, 3941 7 of 22 Appl. Sci. 2020, 10, 3941 7 of 22

Figure 5. MorphologiesMorphologies of the machined surfaces under different diﬀerent cutting parameters.

3. Data Analysis Approach In machining practice,practice, surfacesurface roughness roughness and and tool tool vibration vibration are are desired desired objects objects to to be be monitored monitored in thein the machining machining operation, operation, whereas whereas the cuttingthe cutting parameters parameters are independentare independent variables variables that havethat have been verifiedbeen verified to show to show different different influences influences on the on monitoring the monitoring target. target. Therefore, Therefor thee, establishmentthe establishment of the of predictionthe prediction models models of surface of surface roughness roughness or tool vibration or tool canvibration help optimize can help the optimize cutting parameters the cutting to achieveparameters a desired to achieve surface a desired quality surface with low quality tool vibration.with low tool vibration. 3.1. Multivariable Regression Analysis 3.1. Multivariable Regression Analysis Multiple regression analysis is used to determine the dependency of surface roughness on selected Multiple regression analysis is used to determine the dependency of surface roughness on machining parameters and vibrations in the machining. Besides the main influences of these variables, selected machining parameters and vibrations in the machining. Besides the main influences of the effects of their interactions were included in the analysis. these variables, the effects of their interactions were included in the analysis. In the response surface methodology, all independent variables are correlated to the response as In the response surface methodology, all independent variables are correlated to the response as y == φ(x x x )+ +ε y φ (x11,, x2,2...... ,...... xnn) ε (1)(1) where yyis is the the desired desired model model of surface of surface roughness, roughness,φ is the ϕ response is the response surface function surface to function be determined to be bydetermined the independent by the independent variables xi ,variables and ε is x thei, and statistical ε is the errorstatistical of the error measurements. of the measurements. The response The surfaceresponse function surface canfunction also be can defined also asbea defined linear combination as a linear ofcombination several independent of several variables independent with theirvariables interactions with their and interactions one dependent and variable.one dependent An explicit variable. mathematical An explicit quadratic mathematical form is givenquadratic by form is given by XN XN X X y = b + N b x + N b x2 + b b x x +ε (2) y = b0 + b ix i + b iixi2 + b ib jxi xj +εi 0 i=1 i i i=1 ii i i j i j i j i (2) i=1 iij=1 where b , b , and b , are coefficients of the linear, quadratic, and interaction terms, respectively; x and where bii, biiii, and bijij, are coefficients of the linear, quadratic, and interaction terms, respectively;i xi x are input variables; and N is the number of the independent variables. andj xj are input variables; and N is the number of the independent variables. In this study, the relationship between R is correlated to the cutting parameters such as cutting In this study, the relationship between Raa is correlated to the cutting parameters such as cutting depth (a ), spindle speed (n), and feed rate (f ) using a nonlinear quadratic model and power law depth (ap), spindle speed (n), and feed rate (f) using a nonlinear quadratic model and power law model, respectively.

Ra =R β=0 β+ β+1βa a++ββ2nn++ββ3 ff++β4 ⋅a ⋅n ++ββ5⋅nn⋅f +f β+ β⋅6a a⋅ f +fβ+⋅βa7 ⋅af ⋅nf n (3)(3) a 0 1p p 2 3 4 · pp · 5 · · 6 p· p · 7 p· p · · = β ⋅ ββ1 1 ⋅ ββ22⋅ β33 RRa = β aap n f (4)(4) a 00· p · · In thethe aboveabove equation, equation, the the inﬂuences influences of individualof individual parameters parameters and and the interactionsthe interactions between between them onthem the on surface the surface quality quality are considered. are considered. The multiple The multiple linear regression linear regression analysis is analysis performed is performed to determine to thedetermine values ofthe the values coeﬃ ofcients the coefficients with the least with squares the least method. squares method.

Appl. Sci. 2020, 10, 3941 8 of 22 Appl. Sci. 2020, 10, 3941 8 of 22

3.2.3.2. Artificial Artiﬁcial Neural Neural Network Network Model Model TheThe artificial artiﬁcial neural neural network network (ANN) (ANN) approach approach has has the the capability capability to to learn learn from from an experimental datasetdataset to establishestablish aa highhigh nonlinear nonlinear correlation correlation between between surface surface roughness roughness and and input input parameters parameters [33]. [33].Because Because a wide a rangewide ofrange cutting of cutting parameters parameters were adopted were inadopted machining in machining tests, the response tests, the surface response plot surfaceof the roughness plot of the against roughness the cutting against parameters the cutting are pa expectedrameters toare show expected highly to nonlinear show highly characteristics. nonlinear characteristics.This study, therefore, This employedstudy, therefore, an ANN employ techniqueed toan model ANN and technique predict the to roughness model and of thepredict machined the roughnesssurface based of the on cuttingmachined parameters. surface based A simple on cutting multilayered parameters. architecture A simple of amultilayered typical ANN architecture is shown in ofFigure a typical6. ANN is shown in Figure 6.

Figure 6. Multilayered architecture of a typical artificial neural network. Figure 6. Multilayered architecture of a typical artificial neural network. The network has three layers, namely, input, hidden, and output. The input and output layers are definedThe asnetwork nodes orhas neurons, three layers, and the namely, hidden input, layer hidden, provides and the output relationship. The input between and output the input layers and areoutput defined layers as usingnodes di orfferent neurons, numbers and ofthe neurons. hidden la Theyer processing provides the neurons relationship in the hidden between layer the deliver input andthe processedoutput layers data using from different the neurons numbers in the inputof neurons. layers The to neurons processing in the neurons output in layer. the hidden For example, layer deliverthe input the data processed to the neurons data from in thethe hiddenneurons layer in the can input be characterized layers to neurons by the in general the output form: layer. For example, the input data to the neurons in the hidden layer can be characterized by the general form: n Xn xhidden,j == Wijui++ θj (5) Wijui θ j (5) xhidden, j i=1 i=1 where Wij is the weight coefficient between the input neurons and hidden neurons, ui is the value where Wij is the weight coefficient between the input neurons and hidden neurons, ui is the value of of the input, and θj denotes the biases of the hidden neurons. The effectiveness of neural networks the input, and θj denotes the biases of the hidden neurons. The effectiveness of neural networks modelsmodels is is dependent dependent on on various various characteristics characteristics such such as as network network architecture, architecture, activation activation functions, functions, andand training algorithms. In In this this study, study, the the MLP MLP network network was was trained trained with with the the application application of of the the Broyden–Fletcher–Goldfarb–ShannoBroyden–Fletcher–Goldfarb–Shanno (BFGS) (BFGS) method method,, conjugate conjugate gradient, gradient, and and the the steepest steepest descent trainingtraining algorithm.algorithm. To To realize realize the bestthe network,best network, the activation the activation functions—linear, functions—linear, exponential, exponential, hyperbolic, hyperbolic,logistic, and logistic, sin—were and changed sin—were in the changed hidden and in outputthe hidden layers, and wherein output the hyperboliclayers, wherein function the is hyperbolicgiven by function is given by e2x 1 f (x) = (6) 2x2x −− = ee +11 f(x) 2x (6) In addition, the linear function was used as thee output+ 1 layer activation function. In ANN modeling analysis,In addition, the input the neurons linear are function the cutting was depth, used spindle as the speed, output feed layer rate, activation and vibration function. level; theIn outputANN modelingis the surface analysis, roughness. the input A trial-and-error neurons are schemethe cutting has beendepth, used spindle to determine speed, feed the appropriaterate, and vibration number level;of hidden the output neurons. is Further,the surface the roughness. error function A trial-and-error was used to determine scheme errorshas been between used actualto determine values andthe appropriatecalculated values number during of hidden learning, neurons. testing, Further, and validation, the error which function is defined was used as to determine errors between actual values and calculated values during learning, testing, and validation, which is defined as Appl. Sci. 2020, 10, 3941 9 of 22

XN Errors = (y t )2, (7) i − i i=1 where N is the number of dataset in ANN modeling.

3.3. Determination of the Effectiveness of Prediction Models The effectiveness of the regression models and selected neural networks were evaluated based on root mean square error (RMSE), determination coefficient (R), and mean absolute percentage error (MAPE). These values are determined by

  1/2 XN  1  2 RMSE =   t y  (8)  N  | i − i|  i=1

 N   P ( )2   ti yi  2  i=1 −  R = 1   (9)  N  −  P 2   (y i  1 PN ((ti yi)/ti) 100) i=1 − × MAPE = (10) N where t is the target value, y is the predicted value, and N is the number of samples in analysis.

4. Results and Discussions

4.1. Surface Roughness under Different Cutting Parameters Figure7 illustrates surface roughness with varying spindle speeds and cutting depths under specific feed of 0.05 and 0.075 mm/tooth, respectively, in which the spindle speed ranges from 3000 to 8000 rpm and cutting depth ranges from 0.1 to 2.0 mm. The response surface graphs indicate that surface roughness is affected to different extents by the combined effect of spindle speed and cutting depth, and by changing the feed rate. Overall, the roughness scatters from 0.5 µm under a lower cutting depth and spindle speed to a higher value of 0.9 µm under a high spindle speed and larger cutting depth. Further, it is noted that cutting depth has an apparent positive influence on surface roughness: increasing the cutting depth increases the roughness of the machined surface. The influence trend is more significant with a correlation coefficient (r 0.8–0.9) at feed of 0.075 mm/tooth as compared with feed of 0.05 mm/tooth (r 0.5–0.8). There is no significant relationship between the surface roughness and spindle speed defined in the range from 3000 to 8000 rpm for machining under lower feed per tooth. However, at a higher feed per tooth, the roughness increases with an increase in spindle speed when the cutting depth is greater than 1.0 mm, and the roughness decreases with an increase in spindle speed when machined with a lower depth (<1.0 mm). At a lower feed rate, the roughness increases at a spindle speed from 4000 to 7000 rpm, and then, the roughness decreases at speeds below 4000 rpm or those higher than 8000 rpm. Figure8 illustrates the variation of surface roughness under di fferent feed rates and cutting depths. The linear feed rate is expressed in units of mm/min and ranges from 600 to 2400 mm/min, which corresponds to a corresponding spindle speed from 3000 to 8000 rpm and feed of 0.05 and 0.075 mm/tooth. As shown in Figure8, the surface roughness generated in machining is a ffected by a change in the combination of the feed rate and cutting depth. Within the entire range of testing data, there is no significant correlation between the surface roughness and the feed rate. However, when machining conditions are confined within the testing conditions (Z > 1.0 mm, F = 1800–2000 mm/min, and S = 6000–8000 rpm), machining vibration apparently increases with an increase in the feed rate, Appl. Sci. 2020, 10, 3941 9 of 22

N = − 2 Errors (yi ti ) , (7) i=1

where N is the number of dataset in ANN modeling.

3.3. Determination of the Effectiveness of Prediction Models The effectiveness of the regression models and selected neural networks were evaluated based on root mean square error (RMSE), determination coefficient (R), and mean absolute percentage error (MAPE). These values are determined by

1/ 2 N  1   RMSE =   |t − y |2  (8)  N  i i    i=1 

 N   (t − y )2    i i  R 2 = 1− i=1  N  (9)  2   (yi )   1 

N ((t − y )/t )× 100)  i i i (10) MAPE = i=1 N

where t is the target value, y is the predicted value, and N is the number of samples in analysis.

4. Results and Discussions

4.1. Surface Roughness under Different Cutting Parameters Figure 7 illustrates surface roughness with varying spindle speeds and cutting depths under specific feed of 0.05 and 0.075 mm/tooth, respectively, in which the spindle speed ranges from 3000 to 8000 rpm and cutting depth ranges from 0.1 to 2.0 mm. The response surface graphs indicate that surface roughness is affected to different extents by the combined effect of spindle speed and cutting depth, and by changing the feed rate. Overall, the roughness scatters from 0.5 μm under a lower cutting depth and spindle speed to a higher value of 0.9 μm under a high spindle speed and larger cutting depth. Further, it is noted that cutting depth has an apparent positive influence on surface roughness: increasing the cutting depth increases the roughness of the machined surface.

Appl.Appl.The Sci. Sci.influence 20202020, ,1010, ,3941trend 3941 is more significant with a correlation coefficient (r ≅ 0.8–0.9) at feed of1010 0.075 of of 22 22 mm/tooth as compared with feed of 0.05 mm/tooth (r ≅ 0.5–0.8). There is no significant relationship between the surface roughness and spindle speed defined in the range from 3000 to 8000 rpm for spindlemachining speed, under and lower cutting feed depth, per tooth. which However, shows a at significant a higher feed negative per tooth, influence the roughness on surface increases equality withwith aan correlation increase in coe spindlefficient speed (r > 0.8).when In the particular, cutting depth it is observed is greater that than surface 1.0 mm, roughness and the roughness scatters in lowerdecreases ranges with when an increase machining in spindle is performed speed usingwhen various machined cutting with depths a lower at depth some critical(< 1.0 mm). feed ratesAt a suchlower as feed 900, rate, 1200, the and roughness 1500 mm/ min,increases corresponding at a spindle to spindle speed speedsfrom 4000 of 3000, to 7000 4000, rpm, and and 5000 then, rpm andthe theroughness feed of 0.075decreases mm/ attooth. speeds below 4000 rpm or those higher than 8000 rpm.

Figure 7. Variation of surface roughness with varying spindle speed and cutting depth at lower and higher feed rate, respectively.

Figure 8 illustrates the variation of surface roughness under different feed rates and cutting depths. The linear feed rate is expressed in units of mm/min and ranges from 600 to 2400 mm/min, whichAppl. Sci. corresponds 2020, 10, 3941 to a corresponding spindle speed from 3000 to 8000 rpm and feed of 0.0510 and of 22 0.075 mm/tooth. As shown in Figure 8, the surface roughness generated in machining is affected by a change in the combination of the feed rate and cutting depth. Within the entire range of testing data, there is no significant correlation between the surface roughness and the feed rate. However, when machining conditions are confined within the testing conditions (Z > 1.0 mm, F = 1800–2000 mm/min, and S = 6000–8000 rpm), machining vibration apparently increases with an increase in the feed rate, spindle speed, and cutting depth, which shows a significant negative influence on surface equality with a correlation coefficient (r > 0.8). In particular, it is observed that surface roughness scatters in lower ranges when machining is performed using various cutting depths at some critical feed rates such as 900, 1200, and 1500 mm/min, corresponding to spindle speeds of 3000, 4000, and FigureFigure 7.7. VariationVariation ofof surfacesurface roughnessroughness withwith varyingvarying spindlespindle speedspeed andand cuttingcutting depthdepth atat lowerlower andand 5000 rpm and the feed of 0.075 mm/tooth. higherhigher feedfeed rate,rate, respectively.respectively.

mm/min, and S = 6000–8000 rpm), machining vibration apparently increases with an increase in the Figure 8. Variation of surface roughness under diﬀerent feed rates and speciﬁc cutting depths. feed rate, spindle speed, and cutting depth, which shows a significant negative influence on surface

4.2.equality Spindle with Vibration a correlation under Di coefficientfferent Cutting (r > Parameters0.8). In particular, it is observed that surface roughness scatters in lower ranges when machining is performed using various cutting depths at some critical FigureFigure9 illustrates 8. Variation the of surface variation roughness of machining under different vibration feed with rates varying and specific cutting cutting parameters depths. under feed rates such as 900, 1200, and 1500 mm/min, corresponding to spindle speeds of 3000, 4000, and constant feed of 0.05 and 0.075 mm/tooth. The response surface graphs clearly indicate that the 5000 rpm and the feed of 0.075 mm/tooth. 4.2.vibration Spindle level Vibration induced under in Different machining Cutting is clearly Parameters affected by the combined effect spindle speed and cuttingFigure depth. 9 illustrates Roughly the speaking, variation vibration of machining amplitude vibration increases with with varying an increase cutting in parameters the spindle under speed constantand cutting feed depth, of 0.05 as foundand 0.075 in Figure mm/tooth.9. It is noted The response that machining surface with graphs di fferent clearly cutting indicate depths that and the at vibrationa constant level feed induced 0.075 mm in/tooth, machining vibration is clearly apparently affected increases by the with combined an increase effect in spindle the spindle speed speed and cuttingfrom 3000 depth. to 8000 Roughly rpm, with speaking, a correlation vibration coe ffiamplitudecient (r = 0.92–0.96).increases with For machiningan increase at in a constant the spindle feed speed0.05 mm and/tooth, cutting the depth, correlation as found between in Figure roughness 9. It andis noted spindle that speed machining is not significant with different (r = 0.3–0.66) cutting depthsdepending and at on a theconstant cutting feed depth. 0.075 In mm/tooth, particular, vibration when the apparently cutting depth increases is greater with an than increase 1.6 mm, in the the spindlevibration speed level from increases 3000 withto 8000 an increasingrpm, with speeda correlation and reaches coefficient the maximum (r = 0.92–0.96). value atFor a spindlemachining speed at of 6000 rpm; it then decreases with an increasing speed. a constant feed 0.05 mm/tooth, the correlation between roughness and spindle speed is not significant (r = 0.3–0.66) depending on the cutting depth. In particular, when the cutting depth is greater than 1.6 mm, the vibration level increases with an increasing speed and reaches the maximum value at a spindle speed of 6000 rpm; it then decreases with an increasing speed. Figure 8. Variation of surface roughness under different feed rates and specific cutting depths.

4.2. Spindle Vibration under Different Cutting Parameters Figure 9 illustrates the variation of machining vibration with varying cutting parameters under constant feed of 0.05 and 0.075 mm/tooth. The response surface graphs clearly indicate that the vibration level induced in machining is clearly affected by the combined effect spindle speed and cutting depth. Roughly speaking, vibration amplitude increases with an increase in the spindle speed and cutting depth, as found in Figure 9. It is noted that machining with different cutting depths and at a constant feed 0.075 mm/tooth, vibration apparently increases with an increase in the spindle speed from 3000 to 8000 rpm, with a correlation coefficient (r = 0.92–0.96). For machining at a constant feed 0.05 mm/tooth, the correlation between roughness and spindle speed is not significant (r = 0.3–0.66) depending on the cutting depth. In particular, when the cutting depth is greater than 1.6 mm, the vibration level increases with an increasing speed and reaches the maximum value at a spindle speed of 6000 rpm; it then decreases with an increasing speed. Appl. Sci. 2020, 10, 3941 11 of 22

Appl. Sci. 2020, 10, 3941 11 of 22 Appl. Sci. 2020, 10, 3941 11 of 22

Figure 9. Variation of vibration levels with varying spindle speed and cutting depth at lower and higher feed rate, respectively. FigureFigure 9.9. Variation ofof vibrationvibration levelslevels withwith varyingvarying spindlespindle speedspeed andand cuttingcutting depthdepth atat lowerlower andand Figurehigherhigher 10 feedfeed illustrates rate,rate, respectively.respectively. the variat ion of the vibration level generated under different feed rates and cutting depths, in which the feed rates range from 600 to 2400 mm/min, corresponding to the spindleFigureFigure speed 10 10from illustrates illustrates 3000 to the the8000 variation variat rpmion and of of the feedthe vibration vibrationof 0.05 level and level generated0.075 generated mm/tooth. under under di Theff erentdifferent extent feed offeed rates the rates andeffect of cuttingfeedand cuttingrate depths, on depths,the in vibration which in which the varies feed the rates feedwith range ratesa cutting fromrange depth 600 from to in 2400600 machining. to mm 2400/min, mm/min, correspondingWithin correspondingthe entire to the testing spindle to the data, therespeedspindle is fromno speed significant 3000 from to 8000 3000 correlation rpm to 8000 and feedrpm between ofand 0.05 feed andthe of 0.075 vibration0.05 mmand/ tooth. 0.075level mm/tooth. Theand extent the ofThefeed the extent rate. effect ofHowever, of the feed effect rate as observedonof feed the vibration ratein Figure on the varies vibration10, withat a avarieslower cutting withcutting depth a cutting indepth machining. depth (Z < in 0.8 machining. Within mm), the machining entireWithin testing the vibration entire data, testing there is slightly isdata, no increasessignificantthere is with no correlation increasingsignificant between thecorrelation feed the rate, vibration between with levela correlationthe and vibration the feed coefficient level rate. However,and (r =the 0.6–0.7). feed as observed rate. In addition, However, in Figure within 10as, at a lower cutting depth (Z < 0.8 mm), machining vibration is slightly increases with increasing the feed theobserved testing conditions in Figure (Z10, > at 1.0 a mm,lower F =cutting 1800–2000 depth mm/min, (Z < 0.8 andmm), S =machining 6000–8000 vibration rpm), the is machining slightly rate, with a correlation coefficient (r = 0.6–0.7). In addition, within the testing conditions (Z > 1.0 mm, vibrationincreases apparently with increasing increases the feedwith rate, an increasewith a correlation in the feed coefficient rate, spindle (r = 0.6–0.7). speed, In and addition, cutting within depth, F = 1800–2000 mm/min, and S = 6000–8000 rpm), the machining vibration apparently increases with an whichthe testingshows conditionsa significant (Z influence> 1.0 mm, onF = vibration1800–2000 (r mm/min, > 0.8), and and therefore S = 6000–8000 a negative rpm), influencethe machining on the increasevibration in apparently the feed rate, increases spindle with speed, an increase and cutting in the depth, feed whichrate, spindle shows speed, a significant and cutting influence depth, on surface equality, as shown in Figure 10. vibrationwhich shows (r > 0.8),a significant and therefore influence a negative on vibration influence (r > on 0.8), the and surface therefore equality, a negative as shown influence in Figure on 10 the. surface equality, as shown in Figure 10.

FigureFigure 10. 10. VariationVariation of of vibration vibration level level under under different different feedfeed ratesrates and and specific specific cutting cutting depths. depths. Figure 10. Variation of vibration level under different feed rates and specific cutting depths. TheThe effect effect of of machining machining vibration vibration on on surface surface ro roughnessughness cancan bebe observedobserved from from Figure Figure 11 11,, which which showsshows thatThe that effectthey they areof are machining moderately moderately vibration correlated: correlated: on surface r r == 0.580.58 roughness and and 0.71 can for be feedfeed observed ofof 0.050.05 from and and Figure 0.075 0.075 mm 11,mm/tooth, /whichtooth, respectively. Evidently, the vibration level induced in machining affects the roughness of the machined respectively.shows that Evidently,they are moderately the vibration correlated: level rinduced = 0.58 and in 0.71machining for feed affectsof 0.05 theand roughness0.075 mm/tooth, of the surface to a different extent, which depends on the interactive effects of cutting parameters. As illustrated machinedrespectively. surface Evidently, to a differentthe vibration extent, level which induced depends in machining on the affectsinteractive the roughnesseffects of ofcutting the in Figure9, machining vibrations are relatively lower ( < 0.02 g) under a specific combination of feed rate parameters.machined Assurface illustrated to a indifferent Figure extent,9, machining which vibrationsdepends onare therelatively interactive lower effects (< 0.02 of g) cutting under a and spindle speed, such as 1200 mm/min and 4000 rpm and 1500 mm/min and 5000 rpm, respectively. specificparameters. combination As illustrated of feed inrate Figure and 9,spindle machining speed, vibrations such as are1200 relatively mm/min lower and 4000(< 0.02 rpm g) underand 1500 a Consequently, finer surfaces with less roughness are obtained. However, if the feed rate and spindle mm/minspecific and combination 5000 rpm, of respectively. feed rate and Consequently, spindle speed, finer such surfaces as 1200 mm/minwith less and roughness 4000 rpm are and obtained. 1500 speedmm/min are and 1000 5000 mm rpm,/min respectively. and 5000 rpm Consequently, or 1600 mm /finermin andsurfaces 8000 with rpm, less higher roughness level vibrations are obtained. are However, if the feed rate and spindle speed are 1000 mm/min and 5000 rpm or 1600 mm/min and generatedHowever, (if> 0.03the feed g) to rate deteriorate and spindle surface speed precision are 1000 with mm/min high roughness. and 5000 Therefore,rpm or 1600 the mm/min appropriate and 8000 rpm, higher level vibrations are generated (>0.03 g) to deteriorate surface precision with high 8000 rpm, higher level vibrations are generated (>0.03 g) to deteriorate surface precision with high Appl. Sci. 2020, 10, 3941 12 of 22 Appl. Sci. 2020, 10, 3941 12 of 22 roughness.selection of Therefore, the cutting the parameters appropriate can lessenselection the of vibration the cutting in the parameters machining ca operationn lessen the to obtainvibration better in thesurface machining quality. operation to obtain better surface quality.

FigureFigure 11. 11. CorrelationCorrelation between between surface surface roughness roughness and and machining vibration level. 4.3. Regression Models 4.3. Regression Models 4.3.1. Surface Roughness Model Based on Cutting Parameters 4.3.1. Surface Roughness Model Based on Cutting Parameters The surface roughness (Ra) was determined by the individual cutting parameter, depth of cutting (ap, mm),The feedsurface rate roughness (f, mm/min), (R anda) was spindle determined speed (n ,by rpm) the in additionindividual to interactivecutting parameter, parameters, depth such of as cuttingcutting depth(ap, mm), and spindlefeed rate speed. (f, mm/min), Based on the and regression spindle coespeedﬃcients (n, listedrpm) inin Tableaddition1, the to mathematical interactive parameters,model is given such by as cutting depth and spindle2212 speed. Based on the regression coefficients listed in Table 1, the mathematical model is given by 5 5 4 Ra = 0.2235 + 9.33 10− n + 0.2963 ap 3.6 10− n ap 2.6 10− ap f R = 0.2235 + ×9.33×10×-5 × n + 0.2963× × a −－ 3.6 ×10-5 ×× n× a× - 2.6− ×10×-4 × a × f × (11) a 8 n f + p 8 a np f p 3.48 10− 4.74 10− p (11) × −-8 × × × ×-8 × × × × - 3.48 10 × n × f + 4.74 10 × a p × n × f Table 1. Regression parameters for surface roughness prediction model.

Parameters Coefficients Standard Deviations p-Value Table 1. Regression parameters for1 surface roughness prediction2 model. 6 Intercept 2.235 10− 4.935 10− 9.459 10− × 5 × 5 × 9 Spindle speed (n) 9.330 10− 1.530 10− 4.754 10− × 1 Standard× 2 × 7 CuttingParameters depth (ap) 2.964 Coefficients10− 5.391 10− 1.010p-Value10− × 5 Deviations× × 3 Depth speed (ap n) 3.600 10 1.350 10 7.991 10 − × -1 ×− -2 × −-6 × Intercept× − ×2.235 4 10 4.935× 510 9.459× 10 11 Depth feed (ap f ) 2.600 10− 3.830 10− 8.078 10− Spindle× speed× (n) − ×9.330 8× 10-5 1.530× × 910-5 4.754× × 10-910 Feed speed (f n) 3.400 10− 5.130 10− 3.956 10− ×Cutting depth× (ap) − ×2.9648 × 10-1 5.391× × 910-2 1.010× × 10-711 Depth speed feed (ap n f ) 4.740 10− 6.650 10− 1.312 10− × Depth× × speed (×ap ×× n) ×−3.600 × 10-5 1.350× × 10- 7.991× × 10-3 Depth × feed (ap × f) −2.600 × 10-4 3.830 × 10-5 8.078 × 10-11 In Table2Feed, the × R-square speed (f × and n) adjusted R-square−3.400 are× 10 around-8 0.67,5.130 implying × 10-9 that the3.956 predicted × 10-10 values are closeDepth to the × speed measurements, × feed (ap × asn ×shown f) in Figure4.740 × 12 10.-8 Further, the6.650p-value × 10-9 of each input1.312 × variable 10-11 and their interactions against surface roughness are far less than 0.05, indicating all machining parameters haveIn apparent Table 2, influencesthe R-square on and the roughnessadjusted R-square of the machined are around surface. 0.67, implying The average that percentagethe predicted of valuesprediction are accuracyclose to forthe allmeasurements, testing data is ~90.3%as shown with in anFigure RMSE 12. of 7.57%,Further, indicating the p-value that of the each roughness input variableprediction and model their is wellinteractions fitted with against the cutting surface parameters roughness defined are far in wideless than ranges. 0.05, indicating all machining parameters have apparent influences on the roughness of the machined surface. The average percentageTable of prediction 2. Comparisons accuracy of statistical for all parameterstesting data of predictionis ~90.3% models.with an RMSE of 7.57%, indicating thatPrediction the roughness Model prediction model R is well R Square fitted with Adjusted the cutting R Square parameters RMSE defined MAPE in wide ranges. (a) Polynomial roughness model (Ra) 0.82665 0.68336 0.67521 7.57% 9.97% (a) Power-law roughness model (Ra) 0.747994 0.559496 0.55389 8.75% 11.8% (a) Polynomial Machining vibration ( Vb) 0.89478 0.80063 0.79549 0.47% 13.9% (b) Polynomial roughness model (Ra) 0.82676 0.68353 0.67398 7.57% 9.95% (b) Power-law roughness model (Ra) 0.749639 0.56204 0.554858 8.76% 11.8% (a) Based on cutting parameters (spindle speed, cutting depth, and feed rate). (b) Based on cutting parameters and machining vibration. RMSE: Root mean square error; MAPE: Mean absolute percentage error. Appl. Sci. 2020, 10, 3941 13 of 22

Table 2. Comparisons of statistical parameters of prediction models.

Prediction Model R R Square Adjusted R Square RMSE MAPE (a) Polynomial roughness model (Ra) 0.82665 0.68336 0.67521 7.57% 9.97% (a) Power-law roughness model (Ra) 0.747994 0.559496 0.55389 8.75% 11.8% (a) Polynomial Machining vibration(Vb) 0.89478 0.80063 0.79549 0.47% 13.9% (b) Polynomial roughness model (Ra) 0.82676 0.68353 0.67398 7.57% 9.95% (b) Power-law roughness model (Ra) 0.749639 0.56204 0.554858 8.76% 11.8% (a)Based on cutting parameters (spindle speed, cutting depth, and feed rate). (b) Based on cutting parameters and machining vibration. Appl. Sci. 2020, 10, 3941RMSE: Root mean square error; MAPE: Mean absolute percentage error. 13 of 22

(a) (b)

FigureFigure 12. 12. ComparisonsComparisons of ofthe the predicte predictedd and and measured measured values: values: (a) surface (a) surface roughness roughness and and(b) machining(b) machining vibration. vibration.

4.3.2.4.3.2. Vibration Vibration Model Model Based Based on on Cutting Cutting Parameters Parameters UsingUsing the the regression regression coefficients coeﬃcients in Table 33,, thethe vibrationvibration levellevel inducedinduced inin thethe machiningmachining cancan bebe relatedrelated to to the the cutting cutting parameters in terms of the following form. = × 3 -3 + × -66 + × -3 3 + × -6 6 Vb =Vb 5.18 - 5.181010− + 4.29 4.29 10− × nn 2+.602.60 10 10×− a p a3.21p + 3.2110 ×10 a−p × nap n − × 6 × ×10 × × 10 × × × (12)(12) 6.3 × 10-−6 ap f 4.2× 10-10− n f × 2.6-10 10− ap n f − - 6.3 ×10 ×× a p ××f -−4.2 ×10 × n× × f -×2.6 −10 × × a p × n× f × ×

Table 3. Regression parameters of the vibration prediction model.

ParametersTable 3. Regression parameters Coefficients of the vibration Standard prediction Deviations model. p-Value 3 3 2 Intercept 5.180 10− 3.105 10− 9.655 10− − × 6 Standard× 7 × 5 SpindleParameters speed (n) 4.290Coefficients10− 9.650 10− p-Value1.350 10− × 3 Deviations× 3 × 1 Cutting depth (ap) 2.603 10− 3.392 10− 4.435 10− Intercept −5.180× × 106 -3 3.105 ×× 10-3 7 9.655 × 10×-2 4 Depth speed (ap n) 3.210 10− 8.520 10− 2.140 10− × × × × 6-6 ×× -7 6 × ×-5 3 DepthSpindlefeed speed (ap f()n) 6.3004.290 10 10− 9.6502.410 1010 − 1.3509.133 10 10 − × × − × × 10-3 ×× -3 10 × ×-1 1 FeedCuttingspeed depth (f n ()ap) 4.2002.603 10 −10 3.3923.230 1010− 4.4351.931 10 10 − × × × × − × × 10-6 ×× -7 10 × ×-4 1 Depth Depthspeed feedspeed (a p(ap n n) f ) 2.6003.210 10 10 8.5204.180 1010 2.1405.371 10 10 × × × × − × − × − × − Depth × feed (ap × f) −6.300 × 10-6 2.410 × 10-6 9.133 × 10-3 Feed × speed (f × n) −4.200 × 10-10 3.230 × 10-10 1.931 × 10-1 As listed in Table3, the p-value of spindle speed and its interaction with cutting depth are far Depth × speed × feed (ap × n × f) −2.600 × 10-10 4.180 × 10-10 5.371 × 10-1 less than 0.05, which demonstrates the significant influences on the vibration level of the machining systemAs inlisted the modelingin Table 3, of the machining p-value vibration.of spindle Figurespeed 8and shows its inte thatraction the predicted with cutting values depth are in are good far lessagreement than 0.05, with which the measured demonstrates values. the According significant to influences Table2, there on is the a significant vibration correlationlevel of the between machining the systempredicted in andthe measuredmodeling values,of machining with R-square vibration. and adjustedFigure 8 R-squareshows that of ~0.80. the predicted The average values percentage are in goodof prediction agreement accuracy with the for measured all testing values. data is aboutAccordin 86.1%g to with Table an 2, RMSE there ofis 4.7%.a significant This indicates correlation that betweenmachining the vibration predicted can and be appropriatelymeasured values, estimated with fromR-square the cutting and adjusted parameters R-square by using of this~0.80. model. The average percentage of prediction accuracy for all testing data is about 86.1% with an RMSE of 4.7%. 4.3.3. Surface Roughness Model Based on Cutting Parameters with Machining Vibration In this case, the machining vibration was incorporated with cutting parameters in regression analysis to derive the mathematical model for estimating surface roughness. Based on the regression coefficients in Table4, Ra is expressed as

5 5 4 Ra = 0.225 + 9.17 10− n + 0.295 ap 3.710− ap n 2.6 10− ap f ×8 × × 8− × × − × × × (13) 3.3 10 n f + 4.75 10 ap n f + 0.372 V − × − × × × − × × × × b Appl. Sci. 2020, 10, 3941 14 of 22

Table 4. Regression parameters of the nonlinear polynomial model.

Parameters Coeﬃcients Standard Deviations p-Value 1 2 6 Intercept 2.254 10− 4.974 10− 9.330 10− × 5 × 5 × 8 Spindle speed (n) 9.170 10− 1.600 10− 3.080 10− × 1 × 2 × 7 Cutting depth (ap) 2.954 10− 5.408 10− 1.210 10− × 5 × 5 × 3 Depth speed (ap n) 3.700 10− 1.400 10− 7.929 10− × × − × 4 × 5 × 10 Depth feed (ap f ) 2.600 10− 3.890 10− 2.190 10− × × − × 8 × 9 × 10 Feed speed (f n) 3.300 10− 5.160 10− 5.790 10− × × − × 8 × 9 × 11 Depth speed feed (ap n f ) 4.750 10− 6.670 10− 1.360 10− × × × × × 1 × × 1 Vibration (Vb) 3.721 10 1.043 7.217 10 × − × −

In this case, the determination coefficients (i.e., R-square and adjusted R-square) between the predicted values and measured values are around 0.67. It is found that the input variables associated with the cutting parameters have significant influence on surface roughness, with a small p-value < 0.05; however, the effect of machining vibration is insignificant. The average percentage of prediction accuracy for all testing data is ~90.05% with an RMSE of 7.57%, and this shows that the surface roughness can also be predicted with good accuracy based on the cutting parameters and the measured vibration level in machining. In addition, the surface roughness was also modeled by power law model, as follows.

(1) Surface roughness model based on cutting parameters

0.152955 0.636362 0.40132 Ra = 0.04552(a n f − (14) p × × (2) Surface roughness model based on cutting parameters with machining vibration

0.136115 0.543685 0.36599 0.0606 Ra = 0.09804(a n f − VB (15) p × × × In Table2, the R-square and adjusted R-square for the two power law models are ~0.55 and the average percentage of prediction accuracy is ~88% with an RMSE of 8.87%. Comparisons of the statistical parameters clearly indicate that polynomial models show better prediction performance in modeling the surface roughness than power law models.

4.4. Neural Network Analysis In the neural network analysis, data collected from machining tests were divided into three groups, in which 70% of datasets are randomly selected for neural network training, 15% for testing, and the remaining 15% for validation. The architecture of the network includes one input layer, one hidden layer, and one output layer. The ANN modeling was conducted using multi-layered perception (MLP) by Statistica Neural Networks software [40]. The prediction models of surface roughness were first created based on the cutting parameters that include spindle speed, feed rate, and axial depth of cutting as neurons in input layers. Then, the vibration level of machining was included in the input layer to show the effect of spindle vibration on the machined quality. The surface roughness and vibration amplitude can be the output neuron to be determined in the output layer. Other network parameters, such as learning rate, number of neurons in the hidden layer, iteration times, and error function, are obtained by trial and error. After many attempts, different ANN models are selected for comparison by observing the best ANN performance and the correlation coefficient. In this case, four models with better performance were selected, as listed in Table5. The ANN models are labeled with the number of neurons in each layer, and the number of neurons in the hidden layer is optimized. For example, model MLP 3-12-1 has 1, 3, and 12 and neurons in the output, input, and hidden layers, respectively. The models with four input neurons—MLP 4-15-1 and MLP 4-22-1—were optimized with 15 and 22 neurons in the hidden Appl. Sci. 2020, 10, 3941 15 of 22 layer, respectively. Further, Table5 shows the sensitivity level of constructed ANN input parameters. The larger the value, the less influence this parameter has on the output parameter; conversely, the smaller the value, the greater is the influence. It is found that in models MLP4-15-1 and MLP 4-22-1 with four input variables (three cutting parameters and machining vibration), the spindle speed has the largest sensitivity values among the parameters.

Table 5. Sensitivity level of the input variables of the selected neural network models.

Sensitivity Levels ANN Model Spindle Speed Feed Rate Cutting Depth Vibration Level MLP 3-12-1 29.22 12.73 12.13 - MLP 3-13-1 28.02 24.40 11.97 - MLP 4-15-1 71.22 16.71 12.58 31.16 MLP 4-22-1 61.68 27.94 15.20 8.67

The statistical values for the ANN model, correlation coefficient (R), RMSE, and MAPE are used as the basis for determining the performance of the neural network, as summarized in Table6. The value of R represents the agreement extent between the predicted values and measured values. The values of R for the models MLP 3-12-1 and MLP 3-13-1 within the training, validation, and testing data are in the range 0.9285–0.9693. For neural models with an additional variable (machining vibration), higher values of R are found in the range of 0.9611 to 0.9785. Figure 13 shows the comparison of measured and predicted data of the surface roughness for all data, which indicate that high agreements of the prediction results with a correlation coefficient are achieved by neural network models. For the ANN models MLP 3-12-1 and MLP 3-13-1, which were derived from cutting parameters only, the average percentage prediction accuracy of all datasets is approximately 94.9% and 95.4%, respectively. Both models have RMSE values of 4.0%. Although for models MLP 4-15-1 and MLP 4-22-1—which were modeled considering the effect of machining vibration—the average percentage prediction accuracy of all datasets is approximately 96.2% and 96.1%, respectively, and the RMSE values is ~3.0%. The comparison of the performance of four models indicates that surface roughness can be well predicted based on the proposed ANN models. Further comparisons of the RMSE and MAPE values listed in Table6 indicate that the prediction accuracy can be increased if the spindle vibration in machining was also fed in the prediction models (MLP 4-15-1 and MLP 4-22-1), which have less RMSE values compared with the models based on only the three cutting parameters. It is observed that among the presented neural network models, the model (MLP 4-15-1) with four variables in the input layer and 15 neurons in the hidden layer shows better performance in the predictions of the surface roughness for all testing data as compared with other models. Further, in comparison with the regression models, the neural network modeling based on cutting parameters with machining vibration shows better accuracy in predicting machined surface quality.

Table 6. Statistical values of neural network models.

Training Dataset Validation Dataset Testing Dataset Dataset R RMSE MAPE R RMSE MAPE R RMSE MAPE ANN Model ANN models based on cutting parameters (three input variables) MLP 3-12-1 0.968 3.31% 4.25% 0.929 5.82% 7.90% 0.932 4.77% 6.86% MLP 3-13-1 0.969 3.24% 4.21% 0.958 4.31% 5.93% 0.947 4.14% 5.91% ANN models based on cutting parameters and vibration level (four input variables) MLP 4-15-1 0.978 2.72% 3.53% 0.973 4.02% 4.92% 0.976 2.87% 3.96% MLP 4-22-1 0.975 2.70% 3.56% 0.961 4.13% 5.06% 0.976 3.02% 4.35% R: Correlation coeﬃcients; RMSE: Root mean square error; MAPE: Mean absolute percentage error. Appl. Sci. 2020, 10, 3941 15 of 22

layer. Other network parameters, such as learning rate, number of neurons in the hidden layer, iteration times, and error function, are obtained by trial and error. After many attempts, different ANN models are selected for comparison by observing the best ANN performance and the correlation coefficient. In this case, four models with better performance were selected, as listed in Table 5. The ANN models are labeled with the number of neurons in each layer, and the number of neurons in the hidden layer is optimized. For example, model MLP 3-12-1 has 1, 3, and 12 and neurons in the output, input, and hidden layers, respectively. The models with four input neurons—MLP 4-15-1 and MLP 4-22-1—were optimized with 15 and 22 neurons in the hidden layer, respectively. Further, Table 5 shows the sensitivity level of constructed ANN input parameters. The larger the value, the less influence this parameter has on the output parameter; conversely, the smaller the value, the greater is the influence. It is found that in models MLP4-15-1 and MLP 4-22-1 with four input variables (three cutting parameters and machining vibration), the spindle speed has the largest sensitivity values among the parameters.

Table 5. Sensitivity level of the input variables of the selected neural network models.

The statistical values for the ANN model, correlation coefficient (R), RMSE, and MAPE are used as the basis for determining the performance of the neural network, as summarized in Table 6. The value of R represents the agreement extent between the predicted values and measured values. The values of R for the models MLP 3-12-1 and MLP 3-13-1 within the training, validation, and testing data are in the range 0.9285–0.9693. For neural models with an additional variable (machining vibration), higher values of R are found in the range of 0.9611 to 0.9785. Figure 13 shows the comparison of measured and predicted data of the surface roughness for all data, which indicate that high agreements of the prediction results with a correlation coefficient are achieved by neural network models.

Table 6. Statistical values of neural network models.

Training Dataset Validation Dataset Testing Dataset Dataset R RMSE MAPE R RMSE MAPE R RMSE MAPE ANN Model ANN models based on cutting parameters (three input variables) MLP 3-12-1 0.968 3.31% 4.25% 0.929 5.82% 7.90% 0.932 4.77% 6.86% MLP 3-13-1 0.969 3.24% 4.21% 0.958 4.31% 5.93% 0.947 4.14% 5.91% ANN models based on cutting parameters and vibration level (four input variables) MLP 4-15-1 0.978 2.72% 3.53% 0.973 4.02% 4.92% 0.976 2.87% 3.96% Appl.MLP Sci. 4-22-12020, 10 , 3941 0.975 2.70% 3.56% 0.961 4.13% 5.06% 0.976 3.02% 164.35% of 22 R: Correlation coefficients; RMSE: Root mean square error; MAPE: Mean absolute percentage error.

Appl. Sci. 2020, 10, 3941 16 of 22

Figure 13. Comparison of the target and output values of the surface roughness for all data. Figure 13. Comparison of the target and output values of the surface roughness for all data. 4.5. Validation of the Models For the ANN models MLP 3-12-1 and MLP 3-13-1, which were derived from cutting parameters only,Previous the average models percentage with better prediction performances accuracy were of selected all datasets for further is approximately validation with 94.9% comparisons and 95.4%, ofrespectively. the measurements Both models and prediction have RMSE of thevalues surface of 4.0%. roughness Although through for independentmodels MLP machining4-15-1 and tests.MLP The4-22-1—which machining testswere weremodeled conducted considering with thethe sameeffect toolingof machining conditions vibration—the on the milling average machine percentage used inprediction the previous accuracy tests. of The all detailsdatasets of is the approximately cutting parameters, 96.2% and measured 96.1%, surfacerespectively, roughness, and the and RMSE the Appl. Sci.predictedvalues 2020, 10 is, 3941~3.0%. values The are listedcomparison in Table of7 .the The performance vibration levels of four assessed models in indicates the machining that surface and the roughness surface19 of 22 morphologiescan be well predicted of the workpieces based on arethe illustratedproposed inAN FigureN models. 14. Further comparisons of the RMSE and MAPE values listed in Table 6 indicate that the prediction accuracy can be increased if the spindle vibration in machining was also fed in the prediction models (MLP 4-15-1 and MLP 4-22-1), which have less RMSE values compared with the models based on only the three cutting parameters. It is observed that among the presented neural network models, the model (MLP 4-15-1) with four variables in the input layer and 15 neurons in the hidden layer shows better performance in the predictions of the surface roughness for all testing data as compared with other models. Further, in comparison with the regression models, the neural network modeling based on cutting parameters with machining vibration shows better accuracy in predicting machined surface quality.

4.5. Validation of the Models

Previous models with better performances were selected for further validation with comparisons of the measurements and prediction of the surface roughness through independent machiningFigure Figuretests. 14. 14.The MorphologiesMorphologies machining of oftests the the machined machinedwere conducted surfac surfaceses underwith variousvariousthe same cutting cu ttingtooling parameters. parameters. conditions on the milling machine used in the previous tests. The details of the cutting parameters, measured surface Theroughness, statistical and values the ofpredicted multiple values regression are listed models in (#1Table and 7. #3) The and vibration the ANN levels models assessed (MLP in3-13-1 the and MLP 4-15-1)machining are presented and the surface in Table morphologies 8 for performance of the workpieces comparison; are illustratedthey are evaluated in Figure based14. on correlation coefficients, RMSE, and MAPE between the measured and predicted roughness values. As listed in Table 8, the ANN models show better prediction ability and accuracy than the regression models. In particular, the ANN model MLP 4-15-1 predicts the surface roughness with more than 93% accuracy and the least values of RMSE (4.89%) and MAPE (6.86%). This validation clearly indicates that the machining vibration plays a crucial role in affecting the surface quality of the workpiece in the milling operation. The inclusion of the machining vibration as the input variable in the modeling of the surface roughness indeed enhances the prediction performance. As a whole, the ANN model demonstrates superior performance in the prediction of the surface roughness of machined parts when compared with conventional models.

Table 8. Comparisons of the statistical values of the prediction models.

Model Type R RMSE MAPE (a) Regression model #1 0.8157 6.91% 9.73% (b) Regression model #3 0.8172 6.85% 9.63% (a) ANN MLP 3-13-1 0.8766 5.78% 7.77% (b) ANN MLP 4-15-1 0.9065 4.89% 6.86% (a) Based on cutting parameters (spindle speed, cutting depth and feed rate). (b) Based on cutting parameters and machining vibration

4.6. Contour Surface Milling Test To illustrate the effectiveness of the presented model in predicting surface roughness in machining process, another milling test was conducted for part contour surface, as shown in Figure 15. The machining the part contour was carried out using 4-tooth end mill with diameter of 10 mm under the following cutting parameters; cutting depth 1.0 mm, spindle speed 6000 rpm, and feed rate 1800 mm/min. The vibrations of spindle tool along the milling path were assessed using the accelerometer mounted on the spindle housing. Surface roughness at specific points was measured, respectively, as listed in Table 9. It is found that the surface roughness at different point scatters from 0.526 to 0.584 μm, with mean value and deviation (0.5528 ± 0.0249), and the vibration level induced in machining also changes with the feeding of cutter with mean value and deviation (0.024467 ± 0.002817). Experimental results indicate that vibration of spindle tool is one of the factors contributing the variation of the surface roughness at different points although machined under the same cutting conditions. The surface roughness at the selected points can also be predicted by ANN model, in which the vibration level along with cutting parameters are fed in prediction model. The average prediction accuracy of the surface roughness by ANN model MLP 4-15-1 is ~96% compared with the measured values. The validation tests clearly verify the superior performance of the ANN models in predicting the surface roughness in end milling Appl. Sci. 2020, 10, 3941 17 of 22

Table 7. Details of the cutting parameters, measured surface roughness, and predicted values for model validation.

Input Variables Predictions of Surface Roughness Multiple Regression Model Artiﬁcial Neural Network Model Measured Spindle Cutting Feed Rate Vibration Roughness Model #1 Model #3 MLP 3-13-1 MLP 4-15-1 Speed (rpm) Depth (mm) µ (mm/min) Levels ( m) Predicted Predicted Predicted Predicted Error (%) Error (%) Error (%) Error (%) Value (µm) Value (µm) Value (µm) Value (µm) 3000 0.70 900 0.013 0.529 0.469 11.26 0.470 11.09 0.483 8.78 0.488 7.80 3000 0.80 900 0.014 0.526 0.478 9.22 0.479 9.02 0.488 7.24 0.490 6.83 4000 1.00 1200 0.017 0.513 0.502 2.24 0.502 2.21 0.493 3.86 0.489 4.69 4000 1.30 1200 0.019 0.565 0.521 7.76 0.521 7.73 0.527 6.66 0.496 12.25 6000 0.60 1800 0.024 0.58 0.494 14.84 0.495 14.62 0.539 7.05 0.603 3.89 6000 1.30 1200 0.038 0.704 0.681 3.27% 0.683 3.04 0.762 8.20 0.749 6.38 8000 0.90 1600 0.033 0.67 0.717 6.98 0.715 6.75 0.717 6.99 0.740 10.50 8000 1.30 1600 0.039 0.689 0.795 15.35 0.793 15.14 0.822 19.29 0.762 10.53 6500 1.00 1300 0.035 0.581 0.669 15.09 0.670 15.27 0.606 4.32 0.587 1.03 7500 1.35 2250 0.030 0.781 0.677 13.28 0.677 13.31 0.710 9.11 0.712 8.87 7500 1.45 2250 0.032 0.775 0.701 9.56 0.701 9.53 0.731 5.66 0.739 4.63 7500 1.55 2250 0.033 0.787 0.725 7.93 0.725 7.90 0.740 6.01 0.748 4.99 Average 9.73 Average 9.63 Average 7.78 Average 6.86 Appl. Sci. 2020, 10, 3941 18 of 22

The statistical values of multiple regression models (#1 and #3) and the ANN models (MLP 3-13-1 and MLP 4-15-1) are presented in Table8 for performance comparison; they are evaluated based on correlation coeﬃcients, RMSE, and MAPE between the measured and predicted roughness values. As listed in Table8, the ANN models show better prediction ability and accuracy than the regression models. In particular, the ANN model MLP 4-15-1 predicts the surface roughness with more than 93% accuracy and the least values of RMSE (4.89%) and MAPE (6.86%). This validation clearly indicates that the machining vibration plays a crucial role in aﬀecting the surface quality of the workpiece in the milling operation. The inclusion of the machining vibration as the input variable in the modeling of the surface roughness indeed enhances the prediction performance. As a whole, the ANN model demonstrates superior performance in the prediction of the surface roughness of machined parts when compared with conventional models.

Table 8. Comparisons of the statistical values of the prediction models.

4.6. Contour Surface Milling Test To illustrate the effectiveness of the presented model in predicting surface roughness in machining process, another milling test was conducted for part contour surface, as shown in Figure 15. The machining the part contour was carried out using 4-tooth end mill with diameter of 10 mm under the following cutting parameters; cutting depth 1.0 mm, spindle speed 6000 rpm, and feed rate 1800 mm/min. The vibrations of spindle tool along the milling path were assessed using the accelerometer mounted on the spindle housing. Surface roughness at specific points was measured, respectively, as listed in Table9. It is found that the surface roughness at di fferent point scatters from 0.526 to 0.584 µm, with mean value and deviation (0.5528 0.0249), and the vibration level induced in ± machining also changes with the feeding of cutter with mean value and deviation (0.024467 0.002817). ± Experimental results indicate that vibration of spindle tool is one of the factors contributing the variation of the surface roughness at different points although machined under the same cutting conditions. The surface roughness at the selected points can also be predicted by ANN model, in which the vibration level along with cutting parameters are fed in prediction model. The average prediction accuracy of the surface roughness by ANN model MLP 4-15-1 is ~96% compared with the measured values. The validation tests clearly verify the superior performance of the ANN models in predicting the surface roughness in end milling operation. This can further be used as the prototype to develop on-line surface roughness recognition system in future work, as shown in Figure 16. Machining vibration assessed from accelerometer can be displayed in different ways such as the time domain with vibration level in RMS or frequency domain with vibration level as function of frequency. Besides, mathematical models derived from regression analysis or ANN model can be implemented in system for predicting the surface roughness in process. Appl. Sci. 2020, 10, 3941 20 of 22 operation. This can further be used as the prototype to develop on-line surface roughness recognition system in future work, as shown in Figure 16. Machining vibration assessed from accelerometer can be displayed in different ways such as the time domain with vibration level in RMS or frequency domain withAppl. Sci.vibration 2020, 10, 3941level as function of frequency. Besides, mathematical models derived from regression20 of 22 analysis or ANN model can be implemented in system for predicting the surface roughness in process. operation. This can further be used as the prototype to develop on-line surface roughness recognition system in future work, as shown in Figure 16. Machining vibration assessed from accelerometer can be displayed in different ways such as the time domain with vibration level in RMS or frequency domain with vibration level as function of frequency. Besides, mathematical models derived from regression analysisAppl. or Sci. ANN2020, 10 model, 3941 can be implemented in system for predicting the surface roughness in process.19 of 22

Figure 15. Contour surface milling sample for verification of predictive model.

FigureTable 15.9. PredictionsContour surface of surface milling roughness sample for in veriﬁcation end milling of process predictive by model.ANN.

SpindleTable 9.CuttingPredictions of surface roughness in end millingMeasured process by ANN. Figure 15. Contour surfaceFeed milling Rate sampleMachining for verification of predictivePredicted model. Points Speed SpindleDepth Cutting Machining RoughnessMeasured Predicted μ Error (mm/min)Feed RateVibration (g) Value ( m) Points(rpm) Speed(mm) Depth Vibration Roughness(μm) Value Error Table 9. Predictions of surface(mm roughness/min) in end milling process by ANN. 1 6000 (rpm) 1.0 (mm) 1800 0.0239(g) 0.524(µm) (µm) 0.540 3.00% 1Spindle 6000Cutting 1.0 1800 0.0239Measured 0.524 0.540 3.00% 2 6000 1.0 Feed1800 Rate Machining0.0256 0.563 Predicted 0.550 2.25% Points 2Speed 6000Depth 1.0 1800 0.0256Roughness 0.563 0.550 2.25%Error 3 6000 1.0 (mm/min)1800 Vibration0.0234 (g) 0.547 Value 0.535(μm) 2.27% 3(rpm) 6000(mm) 1.0 1800 0.0234(μm) 0.547 0.535 2.27% 4 46000 60001.0 1.01800 18000.0280 0.0280 0.586 0.545 0.545 7.02% 7.02% 51 560006000 60001.0 1.018001800 18000.02390.0261 0.0261 0.524 0.571 0.551 0.540 0.551 3.47%3.00%3.47% 62 660006000 60001.0 1.018001800 18000.02560.0198 0.0198 0.563 0.526 0.485 0.550 0.485 7.88%2.25%7.88% 3 6000 1.0 1800 0.0234 0.547 0.535 2.27% AverageAverage 0.02446 0.02446 0.553 0.5340.534 4.31% 4.31% 4 6000 1.0 1800 0.0280 0.586 0.545 7.02% 5 6000 1.0 1800 0.0261 0.571 0.551 3.47% 6 6000 1.0 1800 0.0198 0.526 0.485 7.88% Average 0.02446 0.553 0.534 4.31%

FigureFigure 16. 16. MonitoringMonitoring system system for for machining machining vibration andand predictionprediction of of surface surface roughness. roughness.

5. Conclusions 5. Conclusions ThisFigure study 16. presents Monitoring the predictionsystem for machining models for vibration estimating and theprediction surface of roughness surface roughness. of machined parts This study presents the prediction models for estimating the surface roughness of machined parts under various cutting conditions from low-speed to high-speed stable machining. The prediction under various cutting conditions from low-speed to high-speed stable machining. The prediction modes 5. Conclusionsmodes were developed using multiple regression analysis and an ANN modeling approach. According were developed using multiple regression analysis and an ANN modeling approach. According to the toThis the study analyzed presents results, the the prediction following models conclusions for es weretimating drawn. the surface roughness of machined parts analyzed results, the following conclusions were drawn. under various cutting conditions from low-speed to high-speed stable machining. The prediction modes 1. The response surface graphs indicate that the surface roughness and machining vibration level are were developed using multiple regression analysis and an ANN modeling approach. According to the affected to different extents by the combined effect of the spindle speed and cutting depth. Overall, analyzed results, the following conclusions were drawn. roughness scatters at lower values under a lower cutting depth and spindle speed. Further, vibration amplitude increases with an increase in spindle speed and cutting depth; in particular, vibration apparently increases with an increase in the spindle speed from 3000 to 8000 rpm, with a correlation coefficient (R = 0.92–0.96). Overall within the whole testing conditions, the influence of feed rate on machining vibration and roughness cannot be clearly demonstrated. However, current results reveal that for machining with given cutting depth, the lower level of cutting speed and lower feed rate generated lower roughness than the higher speed and fast feed rate. Such interaction effect of spindle speed and feed rate on machining vibration is more significant than on surface roughness. Appl. Sci. 2020, 10, 3941 20 of 22

2. Both the surface roughness and machining vibration can be modeled with nonlinear quadratic forms based on cutting parameters and their interactions via multiple regression analysis. 3. In the ANN modeling of surface roughness, predictive models (MLP 3-12-1 and MLP 3-13-1) based on three cutting parameters—spindle speed, cutting depth, and feed rate—have high correlation coefficients (R 0.9285 to 0.9693) between the predicted and measured values within training, validation, and testing data. The average percentage prediction accuracy of all datasets is about 94.5%. For neural models (MLP 4-15-1 and MLP 4-22-1) with additional variables (machining vibration), a higher correlation coefficient (R) is found in the range of 0.9611 to 0.9785. The average percentage prediction accuracy of all datasets is about 96.2%. 4. In the final validation of the predictive models through another machining test, the ANN models were found to demonstrate more accurate predictions of surface roughness. Based on the RMSE and MAPE values, the neural model MLP 4-15-1 with four input variables (three cutting parameters and machining vibration) shows a higher average prediction accuracy of 93.14% than that of the model MLP 3-13-1 with three cutting parameters. This result clearly verifies that the prediction accuracy can be increased if the spindle vibration in machining was also fed in the prediction algorithm.

The predictive model can be the base to develop an on-line surface roughness recognition system, in which cutting parameters and spindle tool vibration assessed in machining can be fed into system to estimate the surface roughness in process. Besides, these models can be eﬀectively used to optimize the cutting conditions for rough or ﬁnish machining with better surface quality and low machining vibration.

Author Contributions: Y.-C.L. contributed to the experiments with data analysis, interpretation, and manuscript preparation. K.-D.W. and W.-C.S. conducted the experimental measurements and data analysis. P.-K.H. helped with experiments and data collection. J.-P.H. organized the research work and revised the paper. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: We gratefully acknowledge the support for this work provided by Intelligent Machinery Technology Center, Industrial Technology Research Institute, Taiwan. Conﬂicts of Interest: The authors declare no conﬂicts of interest.

References

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