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Article Root Cause Identification of Machining Error Based on Statistical Process Control and Fault Diagnosis of Machine Tools

Hongrui Cao *, Denghui Li and Yiting Yue

Key Laboratory of Education Ministry for Modern Design and Rotor-Bearing System, Xi’an Jiaotong University, Xi’an 710049, China; [email protected] (D.L.); [email protected] (Y.Y.) * Correspondence: [email protected]; Tel.: +86-29-8266-3689

Received: 3 April 2017; Accepted: 4 September 2017; Published: 6 September 2017

Abstract: The essence of the machining process is the interaction that occurs between machine tools and a workpiece under certain conditions of cutting parameters. Root cause identification (RCI) is critical to the quality control and productivity improvement of machining processes. The geometric error caused by fixture faults can be identified in most RCI methods; however, the influence of machine tool degradation on workpiece quality is usually neglected. In this paper, a novel root cause identification scheme of machining error based on statistical process control and fault diagnosis of machine tools is proposed. With the pattern recognition of control charts, quality fluctuations can be detected in a timely manner. Once the machining error occurs, the fault diagnosis of machine tools are carried out. The relationship between machine tool condition and workpiece quality is established and the root cause identification of the machining error can be achieved. A case study of the machining of a complex welded box-type workpiece is presented to illustrate the feasibility of the proposed scheme. It is found that the coaxiality error of the two holes in two sides of the box’s wall is caused by the wear of the worm gear in the rotary work table of the machine tool.

Keywords: root cause identification; machining error; statistical process control; fault diagnosis

1. Introduction In order to maintain competition, manufacturing enterprises have to cope with growing demands for increasing product quality, greater product variability, and less cost. Quality control is a lasting topic in manufacturing engineering. In the past, quality in terms of geometric variation has been studied extensively. Many researchers have focused on modeling and controlling variation sources such as static deformation, kinematic error, thermal error, tool wear and vibration induced error. Statistical process control (SPC) is widely used in manufacturing processes for process monitoring and anomaly detection. SPC can sound the alarm for process anomalies; however, it cannot identify the root causes of the alarm. Thus, root cause identification (RCI) is critical to the quality control and productivity improvement of manufacturing processes. The RCI methods in manufacturing processes can be divided into artificial intelligence (AI)-based methods and model-based methods. Artificial neural networks (ANNs) have been applied to improve data analysis and quality control in manufacturing processes [1]. It is well known that detecting the change point is an essential step in root cause identification, so some researchers have used ANNs to identify the change point at which the mean vector shifted [2,3]. Although ANN-based methods are efficient ways to detect the changes in the process mean vector, the root causes leading to these changes cannot be identified. In order to identify the root cause of process variations, process monitoring and diagnosis approaches based on Bayesian network [4], modified Bayesian classification [5], and dynamic Bayesian network [6] have been proposed. As for model-based methods, state space models are widely

Machines 2017, 5, 20; doi:10.3390/machines5030020 www.mdpi.com/journal/machines Machines 2017, 5, 20 2 of 11 used, especially in multi-station manufacturing processes. A number of methodologies based on state space models have been presented for the diagnosis of fixture failures and dimension error in multistage manufacturing processes [7–9]. The state space models in the multistage manufacturing processes can characterize the propagation of fixture fault variation along the production stream. However, due to the presence of various uncertain factors in the manufacturing process, it is not enough to describe workpiece quality only in the geometrical dimensionality, and the causes of machining error are various and not limited to the fixture fault. Fault diagnosis is an effective method for root cause identification. With the increase of service time, the performance of the machine tool degrades, such as spindle-bearing damage or the wear of guide and transmission components. The performance degradation of machine tools results in machining error and low-precision parts. To date, the condition monitoring of machining processes and machine tools has been studied widely to detect tool wear/breakage [10–15], spindle bearing damage [16–18], and chatter onset [19–21] effectively. However, there is still a gap between the fault diagnosis of machine tools and the root cause identification of machining error. On one hand, researchers in the field of machine condition monitoring (MCM) focused on running the state identification of machine tools and cutting processes; however, the influence of the machine tool state on the workpiece quality was usually neglected. On the other hand, investigations into root cause identification of machining errors were primarily conducted by varying the source transmission in a multistage manufacturing process. Through this method, the geometric errors caused by fixture faults can be identified, but other error sources induced by machine tool degradation are not considered. In order to bridge the gap between the fault diagnosis of machine tools and the root cause identification of machining error, a novel scheme based on statistical process control and fault diagnosis of machine tools is proposed for the root cause identification of machining error. With the pattern recognition of control charts, the quality fluctuations can be detected in a timely fashion. Once the machining error occurs, the condition monitoring and fault diagnosis of machine tools are carried out to identify the root cause. An application case is used to demonstrate the feasibility of the proposed scheme.

2. The Root Cause Identification Method Based on Statistical Process Control and Fault Diagnosis

The essence of the machining process is the interaction process that occurs between the machine tool and the workpiece under certain cutting parameters. The input is the cutting parameters, such as cutting speed, feed speed, and depth of cut, while the output is the surface roughness, part dimension, and so on. The dynamic characteristics of the machine tool determine the machining accuracy. With the increase of service time, the performance of machine tools' main components degrades. Bearing damage and other faults in the transmission system may occur, which will eventually cause the reduction of machining accuracy. With the pattern recognition of control charts, quality fluctuations can be detected in a timely fashion. Meanwhile, the machine tool condition is monitored in real time with condition monitoring systems. The root cause identification of machining error can be achieved at the machine tool level by mapping the relationship between the machine tool state and the workpiece quality. Figure1 shows the scheme of root cause identification based on the statistical process control and fault diagnosis of machine tools. The information of machine tool condition and workpiece quality is the foundation of the root cause identification of machining error. In order to obtain the full operational information of machine tools, a sensor network is used to collect the condition information via monitoring systems. Due to the nonlinearity of machine tools in machining processes, the measured signals are usually non-stationary with noise. Advanced signal processing techniques are needed to extract features from the measured data. Through control charts and process capability analysis, the current fluctuations of quality can be monitored. If there are abnormal patterns, then abnormal process pattern recognition Machines 2017,, 5,, 2020 3 of 11 featuresMachinesfeatures2017 fromfrom, 5, 20 thethe measuredmeasured data.data. ThroughThrough controcontroll chartscharts andand processprocess capabilitycapability analysis,analysis,3 ofthethe 11 current fluctuations of quality can be monitored. IfIf therethere areare abnormalabnormal patterns,patterns, thenthen abnormalabnormal process pattern recognition will be carried out, and the fault diagnosis of machine tools will be processwill be carriedpattern out, recognition and the faultwill diagnosisbe carried of out, machine and the tools fault will diagnosis be conducted of machine to provide tools proofs will forbe conducted to provide proofs for root cause identification. conductedroot cause identification.to provide proofs for root cause identification.

Figure 1. TheThe schemescheme ofof root root cause cause identification identificationidentification base basedbased on the statisticalstatistical process control and fault diagnosis of machine tools.

3. Application Application The proposedproposed RCI RCI scheme scheme is openis open in concept, in concept, and canandand thus cancanuse thusthus different useuse differentdifferent fault diagnosis faultfault diagnosisdiagnosis methods methodsaccording according to various to cases. various In thiscases. paper, In this the paper, scheme thethe is schemescheme applied isis to appliedapplied the machining toto thethe machiningmachining process of processprocess a complex ofof awelded complex box-type welded workpiece, box-type workpiece, as shown inas Figureshown2 .in The Figure box’s 2. overallThe box’s dimensions overall dimensions are large, withare large, thin withwalls. thin The walls. overall The rigidity overall of the rigidity part is of low, the and part many is low,low, areas andand need manymany to be areasareas processed. needneed Intoto addition,bebe processed.processed. welding InIn addition,stress and welding compression stress deformation and compression occur easily. deformati In theon machining occur easily. process In ofthe several machining previous process batches, of severalthe coaxiality previous (Φ0.01 batches, mm) the of two coaxiality holes (hole (Φ0.01 A andmm) hole of two B, Φ holes200H8) (hole in theA and two hole sides B, of Φ the200H8) box’s in wall the twoweretwo sidessides unable ofof tothethe meet box’sbox’s requirements. wallwall werewere unableunable The method toto meetmeet in requirements.requirements. this paper is used TheThe formethodmethod the root inin this causethis paperpaper identification isis usedused forfor of thethe root coaxialityroot causecause error. identificationidentification of the coaxiality error.

Figure 2. TheThe welded welded box-type workpiece.

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3.1. Control Charts and Process Capability Analysis The machining process of hole A and hole B is outlined as follows. Firstly, hole A was milled with the size of Φ200H8. Next, the rotary work table was rotated by 180◦, and then hole B was milled with the size of Φ200H8. The detailed process steps are shown in Table1.

Table 1. The key process stages in the machining process.

Sequence Process Steps Quality Requirements 1 Mill a hole with the size of Φ198H10 Unilateral allowance is 1 mm 2 Rotate the work table with 180◦ and mill a hole with the size of Φ198H10 Coaxiality ≤ Φ0.03 mm 3 Annealing and release internal stress 4 Mill a hole with the size of Φ200H8 Cylindricity ≤ 0.01 mm 5 Rotate the work table with 180◦ and mill a hole with the size of Φ200H8 Coaxiality ≤ Φ0.01 mm

Process capability analysis to ensure the coaxiality of hole A and hole B (Φ0.01 mm) was employed as follows. The quality information and the coaxiality of hole A and hole B were measured in the 24 groups. As shown in Table2, the maximum of measurement value ( Ma) is equal to 20 µm, and the minimum (Mi) is equal to 5 µm.

(1) These 24 data are divided into six groups (i.e., K = 6) and there are four data in each group, then calculate the distance of each group:

M − M 20 − 5 h = a i = = 3 (1) K − 1 6 − 1

(2) Calculate the upper and lower boundary value of each group and determine the occurrence frequency and frequency density, as shown in Table3. The distance between every two adjacent groups is h = 3.

(3) Calculate the process capability index Cp and standard deviation σ. The mean of the measured coaxiality is:

1 n x = ∑ xi = 12.54 µm (2) n i=1

The standard deviation of the measured coaxiality is:

s n 1 2 σ = ∑(xi − x) = 4.69 µm (3) n i=1

The maximum of the measured coaxiality is:

T = 20 µm (4)

The process capability index is:

T − T C = U L = (20 − 5)/(6 × 4.69) = 0.53 (5) p 6σ

Since Cp < 0.67, the process capability is insufficient. Machines 2017, 5, 20 5 of 11

Machines 2017, 5, 20 5 of 11 (4) Draw the control distribution chart using frequency density as the ordinate and the distance of groups as the abscissa,Table 2. as The shown measurement in Figure of3. the coaxiality of hole A and hole B. Sequence of Workpiece Coaxiality/μm Sequence of Workpiece Coaxiality/μm Table 2. The measurement of the coaxiality of hole A and hole B. 1 5 13 13 Sequence of Workpiece2 Coaxiality/15µm Sequence of Workpiece14 Coaxiality/12 µm 3 16 15 13 1 5 13 13 24 1517 1416 129 35 167 1517 1310 46 175 1618 911 57 720 1719 108 6 5 18 11 78 2019 1920 8 6 89 1918 2021 613 910 1820 2122 139 1011 2011 2223 917 11 11 23 17 12 9 24 18 12 9 24 18

Table 3. The distribution of occurrence frequency. Table 3. The distribution of occurrence frequency. Group Number Group Limit/μm Central Value/μm Frequency Frequency/% Frequency Density/μm−1 Group Number1 Group3.5~6.5 Limit/ µm Central Value/ 5 µm Frequency 3 Frequency/%12.5 Frequency Density/ 4.2 µm−1 12 3.5~6.56.5~9.5 5 8 3 5 12.520.8 4.2 7 23 6.5~9.59.5~12.5 8 11 5 4 20.816.6 7 5.5 34 9.5~12.512.5~15.5 11 14 4 4 16.616.6 5.5 5.5 45 12.5~15.515.5~18.5 14 17 4 5 16.620.8 5.5 7 56 15.5~18.518.5~21.5 17 20 5 3 20.812.5 7 4.2 6 18.5~21.5 20 3 12.5 4.2

From the distribution chart (Figure 3), it can be seen that the dispersion range is wide and not centered,From theand distribution the actual distribution chart (Figure chart3), it is can the bebimodal seen that curve the with dispersion a superposition range is wide of two and normal not centered,distribution and curves. the actual Therefore, distribution random chart error is the may bimodal be mixed curve with with the a constant superposition systematic of two error, normal such distributionas the rotation curves. error Therefore, of the rotary random work error table, may the be clamping mixed with deformation the constant of the systematic workpiece, error, and such the asdeviation the rotation from error the cylindrical of the rotary form work of holes table, caused the clamping by the thermal deformation deformation of the workpiece, of tools. and the deviation from the cylindrical form of holes caused by the thermal deformation of tools.

Figure 3. The distribution chart. Figure 3. The distribution chart.

3.2. Analysis of Root Cause In an actual machining process, the root cause identification of machining error is a comprehensive problem, and the key is to identify the main error affecting the machining accuracy under specific conditions.

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3.2. Analysis of Root Cause In an actual machining process, the root cause identification of machining error is a comprehensive problem, and the key is to identify the main error affecting the machining accuracy under specificMachines 2017 conditions., 5, x FOR PEER REVIEW 3 of 10 According to the analysis of the process capability and distribution chart, it can be derived 149 that theAccording main factors to the affectinganalysis of the process coaxiality capability error areand thedistribution deformation chart, caused it can bybe derived clamping that force, the 150 themain accumulated factors affec errorting fromcoaxiality previous error procedures, are deformation and cutting caused conditions. by clamping force, the accumulated 151 errorIn from terms previous of the deformation procedure and caused cutting by clampingconditions force,. the dial indicator was applied to support 152 the plateIn terms and toof observethe deformation that the readingcaused by on clamping the dial indicator force, the is dial within indicator 0.01 mm. was However,applied to after support the 153 actualthe plate processing, and to observe the error that still the existed, reading so on the th deformatione dial indicator caused is within by clamping 0.01 mm. force However, can be excluded. after the 154 Asactual for the processing, accumulation the error of process still existerror,ed the, so accuracy the deformation in the last step caused was by strictly clamping controlled force andcan the be 155 heatexcluded treatment. As for was the usedaccumulation to eliminate of process the generated error, the stress. precision For in the the influence last step was of cutting strictly conditions, controlled 156 accordingand the heat to the treatment working was experience, used to eliminate a decrease the in generated cutting depth stress and. For an the appropriate influence increase of cutting in 157 cuttingcondition speeds, according are very useful to the to work controling experience, the workpiece a decrease deformation; in cutting however, depth after and several an appropriate attempts, 158 theincrease coaxiality in cutting error still speed could are not very be usefuleliminated. to control the workpiece deformation, but after several 159 attempts,Finally, the we coaxiality considered error that still the cannot main causebe eliminated. of this coaxiality error was from the machine tool itself, 160 and theFinally, preliminary we considered judgement that was the that main the cause error of was th causedis coaxiality by the error performance was from degradation the machine of tool the 161 rotaryitself, and work the table. preliminary judgement was that the error was caused by the performance degradation 162 of the rotary work table. 3.3. Condition Monitoring and Fault Diagnosis of the Rotary Work Table 163 3.3 Condition monitoring and fault diagnosis of the rotary work table The drive system of the rotary work table is shown in Figure4, which contains two levels of 164 transmission.The drive The system transmission of the rotary ratio work of the table belt is drive shown and in worm Figure gear 4, which are 2.5 contains and 72, two respectively. levels of 165 Thetransmission. worm gear The drives transmission the rotary ratio work of the table. belt Thedrive number and worm of threads gear are of 2.5 the and worm 72, respectively. Z1 = 1, and The the 1 166 numberworm gear of teeth drives of the rotary worm gearwork Z table.2 = 72. T Thehe number accuracy of ofthreads the rotary of the work worm, table Z mainly=1 and dependsthe number on 167 theof teeth accuracy of the of worm the worm gear, gears. Z2=72. The Accuracy main parameters of the rotary are work as follows: table mainly depends on the accuracy 168 of worm gears. The main parameters are as follows: (1) The rotating frequency of the worm wheel: about 0.18 Hz 169 (1) The rotating frequency of worm wheel : about 0.18Hz (2) The rotating frequency of the worm: 13.2 Hz

170 (3)(2) TheThe rotating rotating frequency frequency of worm: of the 13.2Hz big pulley: 13.2 Hz 171 (4)(3) TheThe rotating rotating frequency frequency of the of thebig smallpulley: pulley: 13.2Hz 33 Hz 172 (5)(4) TheThe rotating rotating frequency frequency of small of the pulley: servo 33Hz motor: 33 Hz 173 (5) The rotating frequency of servo motor: 33Hz

worm wheel output wheel shaft i2=72 big belt pulley

worm i1=2.5 small belt pulley

motor

couple 174 r Figure 4. The drive system of the rotary work table. 175 Figure 4. The drive system of rotary work table.

176  Data acquisition 177 Vibration signals are easy to measure and widely used in condition monitoring systems. The three-dimensional 178 piezoelectric accelerometer LC0110 was utilized to detect vibration acceleration signals of rotary work table

179 during rotation (Figure 5). The sampling frequency was set as fs = 12.8 kHz.

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Data acquisition Vibration signals are easy to measure and widely used in condition monitoring systems. The three-dimensional piezoelectric accelerometer LC0110 was utilized to detect the vibration acceleration signals of the rotary work table during rotation (Figure5). The sampling frequency wasMachinesMachines set 2017 as2017f,s, 55=,, 2020 12.8 kHz. 77 ofof 1111

FigureFigure 5.5. TheThe sensorsensor installation.installation.

•• Signal processing and feature extraction SignalSignal processing processing and and feature feature extraction extraction The vibration signal and its frequency spectrum in the X direction of the rotary work table are TheThe vibrationvibration signalsignal andand itsits frequencyfrequency spectrumspectrum inin thethe XX directiondirection ofof thethe rotaryrotary workwork tabletable areare shown in Figure 6. There are three concentrated peaks at 858 Hz, 1524 Hz, and 1960 Hz. These shownshown inin FigureFigure6 .6. ThereThere areare three three concentrated concentrated peaks peaks at at 858 858 Hz, Hz, 1524 1524 Hz, Hz, and and 1960 1960 Hz. Hz. These These frequencies are much higher than the rotating frequencies of the pulley and motor, and may be the frequenciesfrequencies areare muchmuch higherhigher thanthan thethe rotatingrotating frequenciesfrequencies of the pulleypulley andand motor,motor, andand maymay bebe thethe resonant frequencies of the rotary work table’s structure. resonantresonant frequenciesfrequencies ofof thethe rotaryrotary workwork table’stable’s structure.structure.

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WaveletWavelet transformtransformtransform isis oneone ofof theththee mostmost popularpopular time-frequency-transformations,time-frequency-ttime-frequency-transformations,ransformations, andand cancan provideprovide usus withwith thethe frequencyfrequency ofof thethe signalssignals andand thethe timetime associatedassociatedassociated toto thosethose frequencies,frequencies, makingmaking itit veryvery convenientconvenient forfor itsits applicationapplication inin mechanicalmechanical signalsignalsignal analysis.analysis.analysis. ApplyingApplying waveletwavelet decompositiondecomposition ofof thethe originaloriginal signalsignal toto threethree levels,levels, thethe approximationapproximation signalsignal A3A3 andand threethree detaileddetailed signalssignals D1,D1, D2,D2, andand D3D3 areare obtainedobtained andand shownshown inin FigureFigure7 7.7.. Among AmongAmong them, them,them, A3 A3A3 belongs belongsbelongs to toto the thethe frequency frequencyfrequency band bandband 0~0.8 0~0.80~0.8 kHz, kHz,kHz, and andand thethe frequencyfrequency bandbandband widthswidthswidths ofofof D3-D1D3-D1D3-D1 areareare 0.8~1.60.8~1.60.8~1.6 kHz,kHz, 1.6~3.21.6~3.2 kHz, kHz, and and 3.2~6.4 3.2~6.4 kHz, kHz, respectively. respectively.

Machines 2017, 5, 20 8 of 11 MachinesMachines 20172017,, 55,, 2020 88 ofof 1111

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• IdentificationIdentification of of error error sources sources TheThe transmissiontransmission systemsystem isis relativelyrelatively simple.simple. The vibration of the motormotor isis greatlygreatly reducedreduced throughthrough thethe soft soft belt belt and and the the motor motor frequency frequency does does not appearnot appear in the in spectrum the spectrum of the of vibration the vibration signal. Thus,signal. the Thus, motor the is motor unlikely is unlikely to affect to the affect rotation the rotation accuracy accuracy of the output of the shaft.output shaft. InIn thethe waveletwavelet analysisanalysis resultresult ofof thethe vibrationvibration signal,signal, itit cancan bebe foundfound thatthat thethe mainmain frequencyfrequency componentscomponents of of its its envelope envelope demodulation demodulation spectrum spectr areum the are worm’s the worm’s rotation rotation frequency frequency and its harmonic and its frequencies.harmonic frequencies. The vibration The of vibration the worm of gearthe worm excites ge thear naturalexcites the frequency natural of frequency the work of table the andwork causes table theand amplitude causes the modulation amplitude phenomenon. modulation phenomenon. In fact, failure modesIn fact, of failure the worm modes gear of are the similar worm to gear those are of thesimilar gear to pair, those such of asthe wear, gear fatiguepair, such pitting, as wear, surface fatigue spalling pitting, of teeth,surface etc. spalling Because of theteeth, material etc. Because of the wormthe material gear teeth of the is usuallyworm gear softer teeth than is that usually of the soft wormer than and that because of the the worm relative and sliding because at the meshing relative is large,sliding abrasive at meshing wear is pronelarge, toabrasive occur, andwear the is failure prone always to occur, occurs and on the the failure worm always gear. The occurs wear on of thethe wormworm andgear. worm The wear gear leadsof the to worm the vibration and worm increase gear leads of the to rotary the vibration work table increase and a largerof the amplitude rotary work at thetable rotation and a frequency larger amplitude of the worm at the compared rotation to thefrequency normal condition.of the worm An impulsecompared is generatedto the normal once percondition. revolution An impulse when the is worm generated and wormonce per gear revolution enter into when the mesh the worm area. Combinedand worm withgear theenter signal into analysisthe mesh results, area. Combined the sever wearwith the of the signal worm analysis gear can results, be confirmed. the sever wear Due toof thethe wearworm of gear the can worm be gear,confirmed. the clearance Due to inthe the wear mesh of areathe worm results gear, in the the decreased clearance rotating in the mesh accuracy area ofresults the rotary in the work decreased table. Sincerotating other accuracy factors of (e.g., the clampingrotary wo force,rk table. the Since accumulated other factors error from(e.g., previousclamping procedures, force, the accumulated and cutting conditions)error from previous affecting coaxialityprocedures, error and are cutting excluded, condit theions) accuracy affecting degradation coaxiality of error the rotaryare excluded, work table the becomesaccuracy thedegradation primary reason of the forrotary the work machining table becomes error. the primary reason for the machining error.

4. Conclusions 4. Conclusions In this work, a novel root cause identification scheme to identify machining error based on the In this work, a novel root cause identification scheme to identify machining error based on the combination of the statistical process control and fault diagnosis of machine tools was proposed. combination of the statistical process control and fault diagnosis of machine tools was proposed. The SPC was used to detect fluctuations of the workpiece quality, while the fault diagnosis of machine The SPC was used to detect fluctuations of the workpiece quality, while the fault diagnosis of tools was employed to identify failure parts that affect machining accuracy. The relationship between machine tools was employed to identify failure parts that affect machining accuracy. The the machine tool condition and the workpiece quality was established to achieve deep root cause relationship between the machine tool condition and the workpiece quality was established to identification of the process error. The scheme was verified with the machining of a welded box-type achieve deep root cause identification of the process error. The scheme was verified with the workpiecemachining asof a welded case study. box-type The resultsworkpiece showed as a case that study. the surface The results wear ofshowed the worm that gearthe surface resulted wear in theof the decreased worm gear precision resulted of in the the rotary decreased work precis table andion of subsequently the rotary work the coaxialitytable and subsequently error of the two the holescoaxiality in two error sides of ofthe the two box’s holes wall. in Intwo future sides work, of the the box’s online wall. vibration In future measurements work, the online and coaxialityvibration measurementmeasurements during and coaxiality machining measurement will be carried during out in ordermachining to elucidate will thebe relationshipcarried out betweenin order the to coaxialityelucidate the and relationship vibration. between the coaxiality and vibration.

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Acknowledgments: This work was supported by National Natural Science Foundation of China (No. 51575423 and 51421004), and the Fundamental Research Funds for the Central University. Author Contributions: H.C. conceived the original idea of root cause identification, finished the experimental validation, and analyzed the data. D.L. and Y.Y. wrote and edited the paper. Conflicts of Interest: The authors declare no conflict of interests.

References

1. Du, S.C.; Lv, J.; Xi, L.F. A robust approach for root causes identification in machining processes using hybrid learning algorithm and engineering knowledge. J. Intell. Manuf. 2012, 23, 1833–1847. [CrossRef] 2. Atashgar, K.; Noorossana, R. An integrating approach to root cause analysis of a bivariate mean vector with a linear trend disturbance. Int. J. Adv. Manuf. Technol. 2011, 52, 407–420. [CrossRef] 3. Guh, R.-S. On-line identification and quantification of mean shifts in bivariate processes using a neural network-based approach. Qual. Reliab. Eng. Int. 2007, 23, 367–385. [CrossRef] 4. Dey, S.; Stori, J.A. A bayesian network approach to root cause diagnosis of process variations. Int. J. Mach. Tools Manuf. 2005, 45, 75–91. [CrossRef] 5. Liu, J.L.; Chen, D.S. Fault detection and identification using modified bayesian classification on pca subspace. Ind. Eng. Chem. Res. 2009, 48, 3059–3077. [CrossRef] 6. Yu, J.; Rashid, M.M. A novel dynamic bayesian network-based networked process monitoring approach for fault detection, propagation identification, and root cause diagnosis. Aiche J. 2013, 59, 2348–2365. [CrossRef] 7. Ding, Y.; Shi, J.J.; Ceglarek, D. Diagnosability analysis of multi-station manufacturing processes. J. Dyn. Syst. Meas. Control-Trans. Asme 2002, 124, 1–13. [CrossRef] 8. Djurdjanovic, D.; Ni, J. Dimensional errors of fixtures, locating and measurement datum features in the stream of variation modeling in machining. J. Manuf. Sci. Eng. 2003, 125, 716–730. [CrossRef] 9. Zhang, F.P.; Lu, J.P.; Tang, S.Y.; Sun, H.F.; Jiao, L. Locating error considering dimensional errors modeling for multistation manufacturing system. Chin. J. Mech. Eng. 2010, 23, 765–773. [CrossRef] 10. Grasso, M.; Colosimo, B.M.; Moroni, G. The Use of Adaptive pca-Based Condition Monitoring Methods in Machining Processes; American Society Mechanical Engineers: New York, NY, USA, 2012; pp. 133–140. 11. Liu, H.Q.; Lian, L.N.; Li, B.; Mao, X.Y.; Yuan, S.B.; Peng, F.Y. An approach based on singular spectrum analysis and the mahalanobis distance for tool breakage detection. Proc. Inst. Mech. Eng. Part C-J. Eng. Mech. Eng. Sci. 2014, 228, 3505–3516. [CrossRef] 12. Ritou, M.; Garnier, S.; Furet, B.; Hascoet, J.Y. Angular approach combined to mechanical model for tool breakage detection by eddy current sensors. Mech. Syst. Signal Proc. 2014, 44, 211–220. [CrossRef] 13. Azmi, A.I. Monitoring of tool wear using measured machining forces and neuro-fuzzy modelling approaches during machining of gfrp composites. Adv. Eng. Softw. 2015, 82, 53–64. [CrossRef] 14. Nouni, M.; Fussell, B.K.; Ziniti, B.L.; Linder, E. Real-time tool wear monitoring in milling using a cutting condition independent method. Int. J. Mach. Tools Manuf. 2015, 89, 1–13. 15. Cao, H.; Chen, X.; Zi, Y.; Ding, F.; Huaxin, C.; Jiyong, T.; Zhengjia, H. End milling tool breakage detection using lifting scheme and mahalanobis distance. Int. J. Mach. Tools Manuf. 2008, 48, 141–151. [CrossRef] 16. Chen, X.; Li, B.; Cao, H.; He, Z. The condition monitoring and performance evaluating of digital manufacturing process. In Proceedings of the First International Conference Intelligent Robotics and Applications, Wuhan, China, 15–17 October 2008; pp. 593–603. 17. Cao, H.R.; Li, B.; He, Z.J. Study on modeling of digital machining process and its condition monitoring & diagnosis method. In Precision Engineering and Non-Traditional Machining; Wang, J.H., Zhang, C.F., Jin, X., Zou, J.L., Eds.; Trans Tech Publications Ltd.: Stafa-Zurich, Switzerland, 2012; Volume 411, pp. 622–625. 18. Law, L.-S.; Kim, J.H.; Liew, W.Y.H.; Lee, S.-K. An approach based on wavelet packet decomposition and hilbert–huang transform (wpd–hht) for spindle bearings condition monitoring. Mech. Syst. Signal Proc. 2012, 33, 197–211. [CrossRef] 19. Cao, H.; Zhou, K.; Chen, X. Chatter identification in end milling process based on eemd and nonlinear dimensionless indicators. Int. J. Mach. Tools Manuf. 2015, 92, 52–59. [CrossRef] Machines 2017, 5, 20 11 of 11

20. Cao, H.; Lei, Y.; He, Z. Chatter identification in end milling process using wavelet packets and hilbert–huang transform. Int. J. Mach. Tools Manuf. 2013, 69, 11–19. [CrossRef] 21. Cao, H.; Zhang, X.; Chen, X. The concept and progress of intelligent spindles: A review. Int. J. Mach. Tools Manuf. 2017, 112, 21–52. [CrossRef]

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