RELATIONAL ANALYSIS ON WEAR DIFFERENCE OF CUTTER FLANK FACE UNDER VIBRATION IN HIGH-SPEED MILLING

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1 RELATIONAL ANALYSIS ON WEAR DIFFERENCE OF CUTTER FLANK FACE UNDER VIBRATION IN HIGH-SPEED MILLING Mighui ZHANG 1, Bi JIANG 1, Mili ZHENG 1, ad Guisheg YAO 2 1 Harbi Uiversity of Sciece ad Techology, Natioal & Local Uited Egieerig Laboratory of High Efficiecy Cuttig ad Tools, Harbi , Heilogjiag, Chia mh_zhag610@hotmail.com; basuke720@163.com; fx0zmh@163. com; 2 Xi a Aerospace Precisio Electromechaical Istitute (No.16 Istitute), Xi a , Shaxi, Chia @qq.com ABSTRACT: This paper aims to aalyse the wear differece of cutter flake face uder vibratio i high-speed miig. The cuttig trajectory of the cutter tip ad the tooth posture are obtaied, seekig to idetify the vibratio-iduced dyamic relatioship betwee the frictio pairs of tooth flak face. The, the frictio pair is modelled based o the vibratio sigals of cutter teeth captured by a high-speed camera, ad the time-varyig behaviour sequeces are obtaied. The aalysis reveals that the frictio cotact positios of two cutters chaged dyamically. Thus, the differeces i the time-varyig behaviour of dyamic frictio are quatitatively characterized by the discrete degree ad correlatio aalysis. The above models ad methods are verified by the iitial phase results of the wear experimet. This study puts forward a effective way to capture the exact time-varyig features ad predict the cutter wear, layig the basis for efficiecy ehacemet ad life extesio of the cutter. KEYWORDS: high-speed millig cutter, wear differece, vibratio, relatioal aalysis 1 INTRODUCTION Durig millig operatios, the whole millig machie is subject to a strog impact. The millig cutter vibrates uder the cuttig ad the cetrifugal forces ad deviates from the origial positio uder the periodic impact, leadig to costat chages of the trasiet cuttig state. I this case, dyamic features are observed o the frictio pair betwee the tooth ad the workpiece (Zhag et al., 2017). The time-varyig behaviour of flak face frictio chages with the vibratio of the millig cutter, leadig to the differeces i the flak face frictio process of each tooth (Wu et al., 2015; Tamás et al., 2016). The vibratio-iduced dyamic chages of flak face frictio i millig cutter should be evaluated uder the cuttig load. The millig cutter is boud to suffer from wear due to log-time frictio (Asari et al., 2016). Curretly, the cutter wear is usually measured by the average or maximum wear width of flak surface (Mihalache & Nagit, 2016). By this method, wear feature curves ca be draw through millig cutter wear experimets, revealig the variatio of flak face wear width with the cuttig stroke. The tool wear stadards limit the service life of the cutter (Zhag et al., 2016; Liu et al., 2001). Tambe et al. studied the frictio velocity of the higher pair cotact, cosiderig the microcosmic aspect (Tambe et al. 2005). Xie et al. suggested moitorig cutter wear olie by vibratio sigals (Xie et al., 2013; Xie et al., 2016). Based o vibratio sigal processig, feature aalysis ad diagosis algorithms, Wag et al. put forward a method that ispects dimesio error ad auto-compesates tool wear olie for turig operatio (Wag et al., 2016). Liu et al. examied how the flak face wear of the tool is affected by the vibratio features of the toolholder system i high-speed millig (Liu et al., 2008). To sum up, these studies oly reflect the average tool wear of differet cuttig paths, but fail to disclose the dyamic features of frictio wear. I this paper, the vibratio-iduced tooth cuttig behaviour is evaluated to simulate the dyamic frictio pair of the tooth flak face, ad to aalyse the variatio i frictio pair vectors of the flak face. The simulatio model ca calculate the positio ad velocity of frictio cotact poits. Based o the model, the time-varyig behaviour sequeces of flak face frictio uder the vibratio are obtaied. The, the differeces i the timevaryig behaviour of dyamic frictio are quatitatively characterized by the discrete degree ad correlatio aalysis. The above models ad methods are verified by the iitial phase results of the wear experimet. 2 FLANK FACE FRICTION PAIR A global coordiate system O-xyz is established with the origi O beig the itersectio poit of the two sides ad the upper surface of the workpiece, the x-axis alog the feed directio, y-axis alog the 121

2 cross feed directio, ad z-axis alog the axial Cosiderig the deviatio of the millig cutter, the directio of the machie tool spidle. Figure 1 cutter tip trajectory uder vibratio ca be shows the global coordiate system O-xyz ad the calculated by: local coordiate system of millig cutter O d -abc. x0 R cos si( t pi ) zi si v f t R x y0 Rsi si si( t pi) Rcos cos( t pi) zi siccos sae R y (1) z R cos si si( t ) Rsi cos( t ) z cos cos h a z 0 Figure 1. Millig cutter motio uder vibratio where R is the cutter radius; ω is the agular velocity; φ is the iitial phase agle; θ pi is the agle betwee the ith tooth ad the first tooth cuttig ito the workpiece; Δz i is the axial istallatio error of ith tooth; v f is the feed velocity; a e is the cuttig width; a p is the cuttig depth; s is the umber of tool path itervals; Δx, Δy ad Δz are the x-axis, y-axis si r ir where λ is, κ ir ad γ i0 are the icliatio agle, eterig agle ad rake agle of ith tooth, respectively. pi pi i w p ad z-axis compoets of the vibratio-iduced cutter displacemet, respectively. Figure 2 presets the referece poit J c at a distace of a p /2 from the cutter tip o the cuttig edge. The referece poit ca be obtaied by: a si p is aij c 2siir ap cos is ap bij c 2si ir 2 ap cij c (2) The theoretical cotact positio betwee the trasitio surface ad the flak face is set to poit J. The, the frictio cotact poit of flak face uder vibratio i the coordiate system O d -abc ca be obtaied by: 2 2 ( a, b, c a ) R ta cos, a cos a a R ta cos, p is p is p r p ij ij ij i0 i0 2si 2 2siir v v w v 2 2 f c w x z (3) v 2 ( vc cos w vy ) (4) ( v v si v ) ( v ) Figure 2. Referece poit of cutter fictio pair Figure 3 decomposes the cuttig speed uder vibratio i the global coordiate system. As show i the figure, the relative speed amog the frictio pairs varies with the positio of tooth frictio. Accordig to the velocity compoet of the frictio cotact poit o the millig plae uder vibratio, the velocity of frictio cotact poit relative to the workpiece ca be obtaied by the equatio below: 122 Figure 3. Decompositio of cuttig speed uder vibratio 3 RECOGNITION AND SOLUTION OF TRANSIENT CUTTING BEHAVIOUR OF TOOTH Figure 4 shows the five-axis CNC machiig cetre (Mikro UCP710). I the platform, the cutter diameter is 63mm, the cuttig edge agle is 45, the relief agle is 20, the rake agle is 0, ad cutter

3 teeth are umbered clockwise. The parameters of two cutter structures are listed i Table 1. Durig the experimet, the cuttig speed is 700m/mi, the millig depth is 0.5mm, the feed per tooth is 0.15mm, the cuttig width is 56mm, the cuttig legth is 0.5m ad the workpiece material is 45# steel. Tool Cutter A Cutter B Table 1. Structure parameters of millig cutter Distributios of cutter teeth (º) Istallatio error of the tooth (mm) The feature parameters of kurtoses ad waveform factors are extracted to aalyse the variatio i the time-domai waveform of the millig cutter vibratio. The, the cuttig period is determied based o the critical poit i the timedomai waveform (Cosma, 2015). Figure 6 displays the time-domai waveforms extracted from the experimet i the x-directio ad y-directio. Figure 4. Five-axis CNC machiig cetre Durig the millig process, the vibratio time domai sigals icluded cuttig load sigals of multiple teeth ad the existig radomess o each tooth that cut ito the workpiece durig the iitial phase. Meawhile, there is a vague correspodece betwee the cuttig behaviour of each tooth ad the time domai vibratio sigals. Therefore, the cutter vibratio is tested by a dyamic sigal test system (DHDAS5922), which has a samplig frequecy of 20kHz, aalysis frequecy of 7.81kHz; the cuttig vibratio sigal is sesed by a 356A02 ICP threeaxis accelerometer, whose sesitivity is 10mV/g, rage is ±500g, ad resolutio is g. The millig process is tracked by a high-speed camera (Mega Speed), ad the real-time vibratio sigal is determied for each tooth (Figure 5). Figure 5. Real-time vibratio sigal of each tooth Figure 6. Cuttig period of each tooth I Figure 6, T 0 is the time the cutter eters the workpiece; T 1 is the time value of oe spidle period; t 1,, t i (i=1,, Z) are cuttig time of each tooth i oe spidle period; t 1,, t i are the time iterval of two adjacet teeth. The relatioship amog these variables ca be expressed as: 60 T1 T0 t1 L ti ( i 1, K, Z ) (5) 30 pi ti ( i 1,2, K, Z) (6) Accordig to the recogitio method of trasiet cuttig vibratio sigals, the last cuttig-out image of each tooth is extracted from the high-speed camera to idetify the correspodig vibratio sigal waveforms ad the cuttig-out time of each tooth. I this way, the author obtaied the vibratio iformatio of each tooth. The results of the vibratio experimet reveal the icosistecy of cutters of differet tooth spacig i vibratio ad cuttig period, ad the differece i amplitude of the cutter teeth at the same cuttig positio. These fidigs evidece the differece o the cutter flak face wear uder vibratio. Moreover, the high-speed ad short-taper shak Hohl Shaft Kegel (HSK) tool system is itroduced to the experimet. The cutter is featured by high positioig accuracy, great stiffess, small size ad light weight. Because of the sufficiet rigidity of the machie tool spidle, the tool shak selected to coect the cutter ad form a rigid coectio with the spidle. The resultig processig system, a flexible oe i ature, vibrated uder the cuttig force. The vibratio results of spidle sesor test poits are directly related to the millig cutter vibratio. The vibratio acceleratio equatios i the x, y ad z directios ca be expressed as 123

4 ax( t) Axi si( x it xi ) axisi bxit cxi i0 i1 ay ( t) Ayi si( yit yi ) ayisi byit cyi i0 i1 az ( t) Azi si( zit zi ) azisi bzit czi i0 i1 (7) where A xi, A yi ad A zi are the maximum amplitudes i the three directios, respectively; φ xi, φ yi ad φ zi are the vibratio phase agles i the three directios, respectively; ω xi, ω yi ad ω zi are the vibratio agular velocities i the three directios, respectively. I the Chapter 2, the spidle period of the millig cutter lasts 6.64ms. For the equal-pitch cutter A, the cuttig time of the curret tooth is 4.24ms whe the ext tooth cut i; for the uequalpitch cutter B, the cuttig times of the teeth are 4.322ms, 4.285ms, 4.191ms ad 4.144ms, respectively, i the clockwise directio. The features of the cutter time-domai sigal obeyed the sie wave distributio. The vibratio acceleratio data fittig is show i Figure 7. 4 WEAR DIFFERENCE ANALYSIS OF CUTTER FLANK FACE 4.1 Time-varyig behaviour sequece of flak face frictio uder vibratio Durig the millig experimet, the vibratio sigal of the last cuttig tooth i each millig cutter was extracted by vibratio sigal recogitio ad the processig. The extracted sigal was substituted ito the model of dyamic frictio pair. Based o the positio ad velocity of frictio cotact poit, the frictio behaviour i the last millig period was solved ad recorded i Figures 8~11 (Deshmukh et al., 2016). Figure 8. Solutio results of frictio cotact positio of cutter A Figure 7. Vibratio acceleratio data fittig curves of cutters The vibratio displacemet equatio is obtaied by double itegratio: t t S ( t) a ( t) (8) x 00 x After fittig the vibratio acceleratio data of the cutter teeth i all directios, the vibratio velocity equatio ad the vibratio displacemet equatio of each tooth are processed through the itegratio, makig it possible to obtai the trasiet cuttig behaviour of each tooth i the iitial wear phase. The, the solvig models of cotact poit positio ad relative frictio pair velocity are established to describe the differeces of cutter teeth uder vibratio. Figure 9. Solutio results of frictio cotact positio of cutter B As show i Figures 8~11, i the vibratio-free state, the variatios i the positio ad velocity of frictio cotact poit i the flak face formed sie waveforms. Accordig to the frictio cotact state of the flak face with differet pitches uder vibratio, the positio of frictio cotact poit ad the frictio velocity of flak face are differet from the iitial phase; the cuttig agle chaged icosistetly with the trasiet cuttig positio agle i the cuttig process. Uder vibratio, the frictio pairs of the millig cutter deviated from the theoretical positio, ad the degree of vibratio is 124

5 reflected by the ideal speed at differet time ad the deviatio degree. Figure 10. Solutio results of frictio velocity of cutter A Figure 11. Solutio results of frictio velocity of cutter B 4.2 Relatioal aalysis o wear differece of flak face The discrete coefficiet V is adopted to compare the discrete degree of the positio ad velocity of the frictio cotact poit (Yu et al., 2011). The coefficiet ca be expressed as: V 1 N N i1 ( x x) i 2 100% (9) x The value of the discrete coefficiet is egatively correlated with the positio of the frictio cotact poit. I other words, the smaller the discrete coefficiet, the more cocetrated the positios of frictio cotact poit. For equal-pitch L v JAI) 125 cutter A, the discrete degrees of the positio of the frictio cotact poit are, i clockwise order, 21.61%, 14.13%, 14.73% ad 24.96% from tooth I to tooth IV, ad the correspodig discrete degrees of the velocity of the frictio cotact poit are 6.08%, 5.43%, 6.18% ad 6.30%. For uequal-pitch cutter B, the discrete degrees of the positio of the frictio cotact poit are, i clockwise order 13.31%, 7.91%, 8.45% ad 13.22% tooth I to tooth IV, ad the correspodig discrete degrees of the velocity of the frictio cotact poit are 6.33%, 5.79%, 5.95% ad 6.65%. From the results of the discrete degrees, it is clear that the correspodig teeth of the two millig cutters differed i the wear degree of flak face. Comparatively speakig, tooth II of each of the two millig cutters is closer to the vibratio-free frictio state tha the other teeth. For the other teeth of cutter A, the variatio i the positio ad velocity of frictio cotact poit is raked as tooth III, tooth I ad tooth IV i descedig order; The rakig does ot apply to the variatio i the positio ad velocity of frictio cotact poit i the other teeth of cutter B. The compariso of discrete coefficiet values reveals the wear differece of each tooth ad the overall wear state distributio of cutter teeth uder vibratio. Nevertheless, the discrete coefficiet aalysis oly discloses the degree of deviatio from the average, failig to pipoit the exact differece of dyamithe discrete coefficiet aalysis method ca be geerally used to evaluate the differece of the cutter tooth wear state. However, the method ca oly obtai the degree of deviatio from the average; it caot accurately reveal the differece of dyamic chage betwee cutter teeth. I order to further explore the time-varyig behavior of tooth frictio uder vibratio, the referece characteristic sequece of the positio ad velocity of the No. II tooth of two cutters are take i the fial cuttig period, ad the correlatio degree of the positio ad speed betwee the No. II tooth ad the other cutter teeth are show i Tables 2 ad 3 (Zhog et al., 2009; Ameur et al., 2017). Table 2. Correlatio degree betwee tooth II ad the other teeth of cutter A Correlatio degree of the positio Correlatio degree of the velocity γ(l v JAII, γ(l v JAII, γ(l v JAII, γ(v v JAII, γ(v v JAII, γ(v v JAII, L v JAIII) L v JAIV) v v JAI) v v JAIII) v v JAIV) Table 3. Correlatio degree betwee the tooth II ad the other teeth of cutter B Correlatio degree of the positio Correlatio degree of the velocity γ(l v JBII, L v JBI) γ(l v JBII, L v JBIII) γ(l v JBII, L v JBIV) γ(v v JBII, v v JBI) γ(v v JBII, v v JBIII) γ(v v JBII, v v JBIV)

6 Based o the omial-the-best features i statistical theory, the cuttig performace ad the proximity to the ideal state deped o the closeess i positios ad speeds of the frictio cotact poits i the tooth flak face (Li et al., 2013; Jagadish et al., 2016). Hece, the icremet features of the time-varyig sequece of teeth frictio are obtaied from the absolute correlatio degree ε ij ad relative correlatio degree r ij. The absolute correlatio degree describes the variatio i the waveform betwee cutter teeth, ad the relative correlatio degree shows the chage rate of each frictio cotact poit. The two parameters ca be expressed as follows: 1 si sj ij (10) 1 s s s s i j i j r ij 1 s' i s' j (11) 1 s' s' s' s' i j i j 1 s L ( ) L ( ) (12) N 1 v0 v0 i JI ik JI in k2 2 After comparig the correlatio coefficiet of tooth II with that of the other teeth, the author discovered the icosistecy betwee the results of correlatio coefficiet ad the results discrete degrees. This is because the chageable directio of the frictio cotact poit uder the vibratio is eglected i the calculatio method for discrete degree. The results of absolute ad relative correlatio degrees are show i Tables 4~7. Table 4. Absolute correlatio degree of frictioal cotact poit positio of millig cutter A ε(l v JAI, ε(l v JAI, ε(l v JAI, ε(v v JAII, ε(v v JAII, ε(v v JAIII, L v JAIII) L v JAIV) v v JAIII) v v JAIV) v v JAIV) ε(v v JAI, ε(v v JAI, ε(v v JAI, ε(v v JAII, ε(v v JAII, ε(v v JAIII, v v JAIII) v v JAIV) v v JAIII) v v JAIV) v v JAIV) L v JAII) v v JAII) Table 5. Rrelative relatio degree of frictioal cotact poit positio of millig cutter A r(l v JAI, r(l v JAI, r(l v JAI, r(v v JAII, r(v v JAII, r(v v JAIII, L v JAIII) L v JAIV) v v JAIII) v v JAIV) v v JAIV) r(v v JAI, r(v v JAI, r(v v JAI, r(v v JAII, r(v v JAII, r(v v JAIII, v v JAIII) v v JAIV) v v JAIII) v v JAIV) v v JAIV) L v JAII) v v JAII) Table 6. Absolute correlatio degree of frictioal cotact poit positio of millig cutter B ε(l v JBI, ε(l v JBI, ε(l v JBI, ε(v v JBII, ε(v v JBII, ε(v v JBIII, L v JBIII) L v JBIV) v v JBIII) v v JBIV) v v JBIV) ε(v v JBI, ε(v v JBI, ε(v v JBI, ε(v v JBII, ε(v v JBII, ε(v v JBIII, v v JBIII) v v JBIV) v v JBIII) v v JBIV) v v JBIV) L v JBII) v v JBII) Table 7. Rrelative relatio degree of frictioal cotact poit positio of millig cutter B r(l v JBI, r(l v JBI, r(l v JBI, r(v v JBII, r(v v JBII, r(v v JBIII, L v JBIII) L v JBIV) v v JBIII) v v JBIV) v v JBIV) r(v v JBI, r(v v JBI, r(v v JBI, r(v v JBII, r(v v JBII, r(v v JBIII, v v JBIII) v v JBIV) v v JBIII) v v JBIV) v v JBIV) L v JBII) v v JBII) Similar to the flak face frictio state of the two high-speed millig cutters, the relative ad absolute correlatio degrees of the two cutters are differet i terms of the positio ad velocity of the frictio cotact poit. This meas the frictio time-varyig 126 behaviour of the flak face exhibited obvious differeces uder vibratio. The absolute ad relative correlatio degrees of the frictio cotact poit are raked as tooth II, tooth III, tooth I ad tooth IV i ascedig order i cutter A. The

7 absolute ad relative correlatio degrees of the frictio cotact poit of each tooth i cutter B are lower tha those of the correspodig tooth i cutter A, due to the relatively cocetrated distributio of frictio cotact poits of the uequal-pitch cutter uder the same cuttig coditios. Furthermore, the flak face of cutter B had a slower frictio velocity tha that cutter A, idicatig that the uequal pitch ca reduce vibratio i the desig. Despite the suppressio of the uequal pitch uder vibratio, there is still the differece i the time-varyig behaviour of the vibratio ad frictio for the cutter teeth. The variatio i frictio velocity of the cotact poit i the flak face is a evidece of the vibratio effect. The frictio velocity varied with the shift i frictio cotact poit i the flak face. The discrete coefficiets of Teeth II ad III i cutter B are barely differet, ad the cotact poit speed of Tooth III is close to that of Tooth II. Furthermore, the flak face wear is a dyamic process with variable speed. The vibratio brigs chages to the positio ad the speed of the frictio cotact poit i the flak face. Sice the speed of frictio cotact poit surpassed the theoretical value, the frictio cotact poits shifted away from the theoretical positios, which itesified the flak face wear. 5 VERIFICATION OF WEAR DIFFERENCE OF FLANK FACE This chapter compares the calculated results with the damage test results, aimig to verify the frictio cotact state model of the two millig cutters. The wear features of cutters A ad B are measured by a microscope with a large depth of field (Figures 12 ad 13). Accordig to the test results of wear width, abrasive wear is observed o the flak faces of the two millig cutters alog the cuttig speed directio. The abrasive wear is attributable to the microcracks, surface oxidatio ad roughess o the surface before cuttig. It ca be see that the wear is wider o cutter A tha o cutter B. I each tooth of the two cutters, the wear width raged from 11.65μm to 5.05μm. Therefore, cutter B has a smaller rage of wear width. The above aalysis cofirmed that the two cutters differ i wear behaviours; the four teeth o both cutters are raked as tooth II, tooth III, tooth I ad tooth IV i ascedig order of wear volume. The differece i discrete degree coicides with the differece i the iitial phase positio ad speed of frictio cotact poit i the flak face obtaied by the model. Therefore, the solvig model ca reflect the exact time-varyig features, ad predict the 127 cutter wear, layig the basis for efficiecy ehacemet ad life extesio. (a) Cutter A (b) Cutter B Figure 12. Results of wear width of two cutters Figure 13. Measured wear width o flak faces 6 SUMMARY I this paper, the vibratio-iduced tooth cuttig behaviour is evaluated to simulate the dyamic frictio pair of the tooth flak face, ad to aalyse the variatio i frictio pair vectors of the flak face. The simulatio model ca calculate the positio ad velocity of frictio cotact poits. Based o the model, the author obtaied the timevaryig behaviour sequeces of flak face frictio ad vibratio, ad acquired the time-varyig behaviour sequeces of flak face frictio uder the vibratio. The, the differeces i the time-varyig behaviour of dyamic frictio are quatitatively characterized by the discrete degree ad correlatio aalysis. The above models ad methods are verified by the iitial phase results of the wear experimet.

8 The research shows that there are differeces i the time-varyig behaviour ad icremet features of flak face frictio uder vibratio; the uequal pitch cutter ca effectively reduce the differece of frictio for each tooth by distributig the vibratio eergy; the two tooth pitches resulted i differet degrees of wear o the flak face. The degree of wear for each tooth coicides with the simulated ad test results of the time-varyig behaviour of flak face frictio. The models ad methods i the research ca be utilized to study the evolutio process of the flak face wear differece. 7 ACKNOWLEDGEMENTS This study was supported by the Natioal Natural Sciece Foudatio of Chia uder the Grat No REFERENCES Ameur M.F., Habak M., Keae M., Aouici H., Cheikh M. (2017). Machiability aalysis of dry drillig of carbo/epoxy composites: cases of exit delamiatio ad cylidricity error. Iteratioal Joural of Advaced Maufacturig Techology, 88(9-12), pp Asari M.M., Chakrabarti A., Iqbal M.A. (2016). Effects of impactor ad other geometric parameters o impact behavior of FRP lamiated composite plate, Modellig, Measuremet ad Cotrol A, 89(1), pp Cosma M. (2015). Ifluece of tool orietatio i five-axes machiig process, Academic Joural of Maufacturig Egieerig, 13:(1), pp Deshmukh S.V., Patil S.G. (2016). Mathematical relatioship betwee depedet ad idepedet parameters of operators workig o rock drill machie by dimesioal aalysis, Advaces i Modellig ad Aalysis A, 53(2), pp Jagadish, Ray A. (2016). Optimizatio of process parameters of gree electrical discharge machiig usig pricipal compoet aalysis (PCA). Iteratioal Joural of Advaced Maufacturig Techology, 87(5-8), pp Li S.P., Zhag E.J. (2013). Static ad dyamic robust desig based o grey relatioal aalysis. Joural of Mechaical Egieerig, 49(5), pp Liu A.M., She H., Kruth J.P. (2008). Mechaism of the tool flak wear iflueced by the vibratio characteristics of the toolholder system i high speed millig. Joural of Mechaical Egieerig, 44(4), pp Liu Z.Q., Ai X. (2001). Ivestigatio of wear lifespa of cuttig tools i high-speed machiig, Tool Egieerig, 35(2), pp Mihalache M. A., Nagit G. (2016). A theoretical algorithm for fea aalysis ad c maufacturig, Academic Joural of Maufacturig Egieerig, 14(4), pp Tamás P., Illés B. (2016). Process improvemet treds for maufacturig systems i idustry 4.0, Academic Joural of Maufacturig Egieerig, 14(4), pp Tambe N.S., Bhusha, B. (2005). Frictio model for the velocity depedece of aoscale frictio, Naotechology, 16(10), Wag S.M., Che Y.S., Lee C.Y., Yeh C.C., Wag C.C. (2016). Methods of i-process omachie auto-ispectio of dimesioal error ad auto-compesatio of tool wear for precisio turig, Applied Scieces, 6(4), pp Wu S., Liu X.L., Sog S.G., Qu D. (2015). Ifluece of millig cutter wear o millig stability ad surface locatio error. Joural of Vibratio, Measuremet & Diagosis, 35(4), pp Xie H.Z., Huag M. (2013). Research of umerical cotrol machie tools wear moitorig method based o vibratio testig, Istrumet Techique ad Sesor, 2, pp Xie N., Ma F., Dua M.L., Li A.P. (2016). Tool wear coditio moitorig based o pricipal compoet aalysis ad C-support vector machie, Joural of Togji Uiversity (Natural Sciece), 44(3), pp Yu K.Z., Shi D.M., Zou H. (2011). The radom coefficiet discrete-valued time series model, Statistical Research, 28(4), pp Zhag C.L., Zhag S., Ya X.F., Zhag Q. (2016). Effects of iteral coolig chael structures o cuttig forces ad tool life i side millig of H13 steel uder cryogeic miimum quatity lubricatio coditio, Iteratioal Joural of Advaced Maufacturig Techology, 83:(5-8), pp Zhag Y.T., Zhag W.M., Guo J., Guo J.Y., Guo R. (2017). Aalysis o the effects of the shapes of flexible fluid-filled cotaiers o their impact respose, Iteratioal Joural of Heat ad Techology, 35(1), pp Zhog X.F., Liu S.F. (2009). Grey relatio grade for the aalysis of robust desigs with dyamic characteristics. Systems Egieerig-Theory & Practice, 29(9), pp