OnVibrationJointTime-FrequencyInvestigationsofCNCMilling ...used a small CNC 3D milling machine working on wood samples (as experimental work pieces). During the experi-ments, it was

Research ArticleOnVibration JointTime-Frequency Investigations ofCNCMillingMachines for Tool Trajectory Task Conformity Estimation

Silviu Nastac

Research Centre for Mechanics of Machines and Technological Equipments, Engineering and Agronomy Faculty in Braila,“Dunarea de Jos” University of Galati, Calea Calarasilor 29, Braila 810017, Romania

Correspondence should be addressed to Silviu Nastac; [email protected]

Received 2 July 2018; Revised 14 August 2018; Accepted 6 September 2018; Published 10 October 2018

Academic Editor: Matteo Aureli

Copyright © 2018 SilviuNastac.'is is an open access article distributed under the Creative CommonsAttribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

'is study deals with estimation of milling shape accuracy and trajectory conformity for small CNC 3D milling machines, based onvibration monitoring during the regular working cycles. 'e author made a large number of experimental tests, acquiring the ac-celeration signals, both on the milling tool-holder and on the bed frame. In order to evaluate the appropriate spectral characteristics ofdifferentmachine parts and their weights on equipment dynamics, it was analyzed both the complete and the partial working cycle (suchas forward tool motion, with or without effective milling, with or without tool driving, exclusively the milling cutter transitory/stabilizedregime) for different basic milling shapes. 'e acceleration signals were jointly time-frequency investigated in order to evaluate specificspectral indicators related to the real motion characteristic of milling tool. It was used short time fast Fourier transform (STFFT) andHough transform (HT) algorithms, along with stochastic evaluation of signal parameters, within time and frequency domains. 'eresults reveal an accurate correlation between the specific transitory dynamics of the machine and the imposed milling shape. Mainimplications of the results within this analysis involve the noninvasive and facile investigation for milling errors of the CNC machine,conformity of tool head trajectory, identification of potential failure source, or damaged machine part.

1. Introduction

Nowadays, CNC milling machine, stands for computer nu-merical control, denotes a milling machine commonly usedin manufacturing process for industrial fields. CNC machineperforms the operations of drilling and turning and hasvarious types of cutting tools used to cut wood, metal, or othermaterials. Each process of the CNCmilling machine has to beconsidered a set of complex dynamic interactions between themachine tool mechanical structure and the workpiece cutting[1, 2]. Izelu et al. [3] showed that the vibrations generatedduring CNC operations have multispectral composition and,in addition, depend directly by the manufacturing process,being a decisive factor in high-speed limiting of the processingvelocity. Choudhury et al. [4] developed a system for onlinevibration control on a lathe, through correlation betweencutting parameters. Dimla [5] described a tool-wear moni-toring procedure in a metal turning operation, intended tocorrelate vibration signals with the tool wear. Particular at-tention was paid to the manner that the sensor signals

acquired from the cutting process have been harnessed andused into the development of tool condition monitoringsystems. Some researchers focus their study on character-ization of the dynamic properties of a machine tool, duringmachining within the chosen revolution speed range. 'enatural frequency of each mode shape was estimatedthrough the linear modal analysis approach, using finiteelement method or experimental/operational modal anal-ysis, by the help of modal impact hammer testing specificprocedures [6, 7]. Patoommakesorna et al. [8] proposeda new algorithm (named Hough line transform) fora straight line matching, by integration of vision-basedimage processing. Using the same method, Robles et al.[9] obtained the effective localisation of cutting edges withinthe milling-head edge profile. Wu et al. [10] identified dy-namic characteristics and developed fault diagnosis methodof a CNC machine, by using a spectrum analysis procedureof the milling-tool vibration signals. In addition, Zaghbanyand Songmene [11] investigated the operational modalanalysis (OMA) for dynamic modal parameter estimations,

HindawiShock and VibrationVolume 2018, Article ID 7375057, 9 pageshttps://doi.org/10.1155/2018/7375057

during machining operations. Bisu et al. [12] proposeda method for vibration analysis, in order to monitor themilling process quality online. �e vibration envelopeanalysis was proposed to detect the cutting capacity of thetool, with application into the optimization of cutting pa-rameters. Within her study [13], Debeleac proposed ananalysis based onmultibody model approach for mechanicalsystems with complex con�guration and used an advancedcomputational method to investigate nonlinear dynamics ofsuch systems. Gelman [14] proposed new higher orderspectral technique, especially the cross covariance of com-plex spectral components, in order to monitor the damagelevel of structures and machineries.

Taking into account the large-scale utilization of CNCmilling machines, the previously in-brief presentation of theactual studies, regarding dynamical aspects within exploitationof such machineries, reveals the high importance of develop-ment of new methods, which combine operational and com-putational investigations, in order to optimize technologicalcapabilities of these milling equipment. In addition, the ana-lyzed references dignify the opportunity and the particularcontribution of advanced signal processing methods for theanalysis and the characterization of CNC machine dynamics.Hereby, the signi�cance of this study arises both from theoperational noninvasive dynamic testing procedure (withoutany involvement on regular con�guration of technologicalcycle) and from the proposed computational technique, basedon a suitable combination between the joint time-frequencyanalysis and theHTalgorithm for graphical shape identi�cation.Obviously, the conformity of the tool trajectory task denotes the�nal desideratum of all studies, apart from its particular ob-jective, which �nally increases the milling process quality.

2. Experimental Setup andInvestigation Methods

�e images in Figure 1 present a general view of the ex-perimental setup (a) and a detailed view of the e�ective

milling area (b). On the picture in Figure 1(a) weremarked the positions of the two acceleration sensors, withthe motion-monitoring axis. In addition, on the image inFigure 1(b) were depicted both the two basic shapes thatwere analyzed during the milling process and the forwardmotions of the tool head. As it can seen in Figure 1, it wasused a small CNC 3D milling machine working on woodsamples (as experimental work pieces). During the experi-ments, it was supposed two di�erent shapes as follows:a squared 150×150mm shape and, respectively, a circularshape with 40mm radius. Both tasks were positioned in thesame area of the wood sample, thus the run of the millinghead, from the rest position, to the start position of thecurrent task, approximately involves the same motions.Within the same hypothesis, the forward motions were setup onto the same direction.

Acceleration signals were acquired using a triaxial ac-celerometer, mounted on the milling tool-holder anda simple accelerometer mounted on the bed frame, near themilling area (Figure 1(a)). Acquisition setup also involvesthe hardware NI USB-9233 quad inputs DAQ board anda software application developed within NI-LabVIEW.Subsequent data postprocessing and analyzing were per-formed with some applications developed within theMATLAB software.

�e experiments scheduler supposes four cases, appliedfor each milling shape, as follows: (i) milling-head runningon the programmed shape trajectory without tool driving,(ii) idem �rst case, but with tool driving at regular speed andno interaction between milling cutter and workpiece, and(iii) the e�ective milling of the programmed shape. In ad-dition, it was considered a supplementary case of no motionof the milling equipment (along X, Y, or Z axes), just onlydriving the milling cutting tool (from start, through stabi-lized speed regime, to stop).

�e �rst category of investigation methods containsfrequency domain analyses, as follows: (a) the spectralcomposition of signals, with detection of signi�cant

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Circular shape,R 40 mm

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Figure 1: �e general view of the experimental setup (a) with indication of measurement points and vibration monitoring directions and,respectively, a detailed view of the milling area (b) containing examples of milling shapes.

2 Shock and Vibration

magnitude peaks; (b) the transfer function between the bedframe and the milling head, with evaluation of magnitudepeaks and angle sharply changes; and (c) the coherencebetween the bed frame and the tool accelerations, withidenti�cation of the essential frequency range for subsequentanalyses. �e next step on evaluating the dynamic charac-teristics and their changes was supposed to be a joint time-frequency analysis, based on the signals spectrograms, usingSTFFT, followed by peaks identi�cation procedure and theirtimed tendency, during the e�ective working cycle. �eanalysis of the tendencies within the peaks diagram wasperformed using a qualitative procedure, based on com-parison between the both milling shapes and two particularmethods, which provide qualitative and quantitative mea-sures of vibration spectrum evolution in time. First methodsupposed the standard deviation of previous identi�edpeaks, both on frequency and on time variables. Secondmethod uses the HT algorithm [15] in order to estimate thespeci�c parameters (distance rho and angle theta from originto a straight line) of the linear evolutions in peaks diagram.

3. Results and Discussions

Firstly, it has to be mentioned that the results within thispaper involved only the cases of full milling process ofa squared shape (named Case I) and a circular shape (namedCase II). Additionally, it was presented the test case con-sisting only by the tool driving (rotational motion of themilling cutter), without any other equipment parts motionsand milling tool interactions with the material. Actually, thislast case of analysis (named third case as follows) exclusivelypresents the speci�c dynamics of the milling cutter drivingsystem (without technological charging due to the millingprocess).

Taking into account the two stages in accelerationsanalysis, previously presented, the next paragraph containsthe �rst step of investigations, which involves just thefrequency-domain analysis methods. �us, the diagrams inFigure 2 present the timed evolutions of the milling head andbed frame accelerations, during the whole cycle of each task

(tool driving start, mobile ensemble displacement from therest position to the start milling point, tool head verticalpositioning, e�ective milling, tool head withdrawal, andmobile ensemble parking). Spectral composition of acquiredaccelerations, in terms of normalized magnitude, is depictedin Figure 3. �e signi�cance of each graph was mentioned inthe diagram title.

Supposing dynamic in�uences on the bed frame due tothe milling process, the diagrams in Figure 4 present thetransfer functions (in terms of normalized magnitude andangle) between the base and the tool-holder vibration ac-celerations. In the same manner, the diagrams in Figure 5depict the evolution of coherence in respect with frequencydomain. As a diminishing of vibration in�uences in respectto the decrease in frequency was observed, the author ini-tially assumed the 5 kHz high limit within the spectral di-agrams. Tracking the coherence evolutions (Figure 5), it wasreconsidered the frequency high limit at 2 kHz (for thesecond stage analyses). Diagrams in Figures 2–5 compara-tively present the �rst and the second cases, respectively, ofexperimental tests. Regarding the third case of analysis, theaccelerations diagrams, according to the timed evolutions,spectral composition, and transfer and coherence functions,are grouped in Figure 6.

�e second step of investigations takes into accountthe joint time-frequency analysis of the vibration ac-celeration acquired during the experiments. It wasadopted the STFFT algorithm in order to evaluate thecontinuous changes in magnitude spectrum of signals. Aspecial procedure for �nding peaks rising abovea threshold (50% of maximummagnitude in spectrogramon the whole) was used, and the results were depictedinto a peaks diagram. For the three cases within thisstudy, the spectrograms and related-to peaks diagramsare, respectively, depicted in Figures 7–9. At this point, ithas to be mentioned that the joint time-frequencyanalysis results, in this paper, were exclusively consid-ered for the acceleration signal acquired on the bed frameof the CNC machine, the justi�cation of this aspect beingexplained in the discussions section.

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Figure 2: Timed evolutions of acquired acceleration for the case of squared shape (a) and circular shape (b).

Shock and Vibration 3

Following the main purpose of the research, to identifythe spectral di�erences between the linear and circularmilling shape, the peaks diagrams were adequately croppedaccording to the time domain of e�ective milling process.Taking into account that the analysis will be mainly performedin respect with the frequency domain, the di�erences betweenthe three times ranges do not imply any e�ect into the results.A qualitative analysis of the peaks constancy during theworking process was made through the evaluation of time-frequency standard deviation for each cropped peaks diagram.�e results obtained for proposed experimental cases are,respectively, presented in Figures 10(a), 11(a), and 12(a).

As it was mentioned in the previous section, a quanti-tative analysis of peaks diagrams was performed based onHT algorithm [15, 16]. �e classical Hough technique forcurve detection is applicable if little is known about thelocation of a boundary, but its shape can be described asa parametric curve (e.g., straight line or conic). Its main

advantages relate to that it is relatively una�ected by gaps incurves and by noise. In this study, the HT is used to extractlinear features from speci�c datasets using the concept ofparameter space. Brie�y, the HT provides pertinent in-formation regarding the lines and their length within a di-agram, based on evaluation of a pair of distance and angleparameters, from an initially �xed point to each identi�edline.�e basic output of this analysis results in a 3D diagram,wherein the sharp peaks indicate a straight line in originaldiagram (identi�ed by a pair of distance and angle valuesinto a parameter space diagram). In addition, the HTanalysis was augmented with a supplementary procedure ofestimation of the angle distribution, for the angular values inHT diagram corresponding to the sharp peaks (overleapinga suiting threshold). According to these aspects, the com-puted HT of the cropped peaks diagrams and the polarrepresentation of the relevant angles distribution were, re-spectively, depicted in Figures 10(b), 11(b), and 12(b). �e

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Figure 3: Spectral composition of acquired acceleration (normalized magnitudes) for the case of squared shape (a) and circular shape (b).

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Figure 4: Transfer functions between the bed frame and milling head (normalized magnitudes on left side column and angles in radians onthe right side column) for the case of squared shape (a) and circular shape (b).

4 Shock and Vibration

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Figure 5: Coherence functions between the bed frame and milling head for the case of squared shape (a) and circular shape (b).

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Figure 6: Timed evolution of accelerations (a), with normalized magnitudes of their spectrum (b), transfer functions (c), and coherences (d)between the bed frame and milling head, for the third case.

Shock and Vibration 5

threshold of the peaks in HT, for histogram computation,was set at 10% of the maximum peak.

Individual and comparative analyses of the results withinthis study indicate a few relevant aspects as follows onto nextparagraphs.

First, the magnitudes of the spectral composition (Fig-ure 3) dignify an intensi�ed spectrum corresponding to thesecond case (circular shape), independent of measuringpoint and direction. Taking into account the third casespectral diagrams (Figure 6(b)) results that the bed framevibration can reveal more accurately the particularities intoacceleration spectrum. Viewing the transfer functions(Figure 4), the same densi�cation of the peaks within themagnitude diagrams can be observed. In addition, the anglechanges became more sharply for the circular milling case.

As it was previously mentioned, the coherences betweenthe bed frame and the milling head vibrations (see Figure 5)indicate that a frequency range of (0–2000)Hz provides

relevant information regarding the machine dynamics, atleast for the e�ective milling process analysis.

From the spectral diagrams in Figure 3, it is di¥cult toidentify the peaks related to the particular working cycleparts. Proceeding to analyze the spectrograms inFigures 7–9, the spectral characterization of each workingstage becomes evident. Going further to the peaks dia-grams, respectively, in the same �gures, missing of thespectral noise facilitates and improves the qualitativeanalysis of frequencies changes, according to the particularcase and particular stage of tasks. �us, it can be observedthat �uctuations of spectral components, for square mill-ing, are reduced, especially at low frequencies, and provideshort sharply peaks during the changes of the milling re-gime (that indicates the moment of the changes in millingdirection). In the same time, the spectrogram of the circularmilling case presents a large �uctuation of frequenciesduring the e�ective milling process.

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Figure 7: �e spectrogram (a) with suitable peaks diagram (b) of the bed frame acceleration, for the �rst case of squared shape.

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Figure 8: �e spectrogram (a) with suitable peaks diagram (b) of the bed frame acceleration, for the second case of circular shape.

6 Shock and Vibration

�e comparative analysis of diagrams in Figures 10(a)and 11(a) reveals two types of qualitative indicators, relatedto the investigations that involve the time-frequency stan-dard deviation (StD) estimators, as follows. Firstly, thespeci�c width of the peaks within StD, in respect withfrequency scale (red graphs in diagrams), grows up ac-cordingly to the presence of circular shapes into monitoredprocess. Secondly, the StD in respect with time scale (bluegraphs in diagrams) provides a relative stable evolution, withless values, for the same case of process. Scattered aspect ofthe peak diagram, for the circular milling shape, comparative

with the �rst case, leads to the previously digni�ed changesin StD evolutions.

�e analysis of the HTdiagrams (Figures 10(b) and 11(b)),together with the associate polar histograms, underlines theprevious observations and provides both qualitative andquantitative tool for characterization of milling shape and of itsconformity with the initial task. Even if the distribution of theangular parameter of HT, for both cases, presents two lobes(near the 0° and 180°), on the second case, it can be observedthat the polar distribution supplies a relative largespreading of relevant values, with approximate interval

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Figure 9: �e spectrogram (a) with suitable peaks diagram (b) of the bed frame acceleration, for the third case.

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Figure 10: Time-frequency standard deviations (a) and HTdiagram with relevant theta’s polar histogram (b) of the peaks diagram (croppedwithin e�ective milling time range) of bed frame acceleration, for the �rst case of squared shape.

Shock and Vibration 7

width between 30° and 20° respectively, comparative with10° and 5°, for the �rst case. Correspondent peaks can beobserved on the HT diagrams.

�e results of the third case were provided in order tocorrelate the information regarding the exclusive tool dynamicsonto the �rst two cases, assuming that a pertinent identi�cation

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Figure 12: Time-frequency standard deviations (a) and HTdiagram with relevant theta’s polar histogram (b) of the peaks diagram (croppedwithin e�ective milling time range) of bed frame acceleration, for the third case.

8 Shock and Vibration

and analysis of milling shape conformity with initial task mustinvolve a rejection of tool dynamics influences.

Adequate thresholds for peaks evaluation, both inspectrogram, and in HT diagram, are able to provide lesserror in tool trajectory estimation according to the initialimposed task.

4. Conclusions

'is study consists of an experimental approach for solvingthe technical problems dealing with evaluation or esti-mation of the CNC machinery tool-task conformity, basedon vibration measurements, and using stochastic aug-mented available joint time-frequency techniques. 'econformity of tool trajectory, for various workpiece shapesexecution, need to be identified and quantified, because thematerial-tool interactions have major influence over thequality of the final product (due to transitory dynamiceffects that affect tool trajectory precision), finally, affectingquality and productivity of the CNC machine.

Experimental tests within this study were exclusivelyperformed using wood workpiece samples. 'eoreticallyspeaking, the proposed analysis procedure is able to supplymilling process characterization for various workpiecematerials, such as metal, composites, plastics, etc. In thissense, practical implementation must take into account thespecific tool-material interaction aspects, depending onmaterial type, thus it is necessary to perform estimativestudies for each particular case.

'e results within this study show that the proposedcomputational postprocessing technique acts as a powerfulanalyzing tool, yielding a significant enhancement in thedetection capability of milling shape accuracy and final tra-jectory conformity, just taking into account the vibrationmeasurements within an operational noninvasive procedure.

'is paper reports preliminary results, focused on qual-itative detection performances, which appear to be verypromising. 'e improvement in parameters estimation,intended for quantitative conformity characterization, andenlarging the workpiece material domain, will be discussed ina forthcoming work.

Data Availability

'e data used to support the findings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

'e author declares that there are no conflicts of interest.

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