UNBALANCED MACHINE FAULT DETECTION USING INSTANTANEOUS FREQUENCY

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1 158 UNBALANCED MACHINE FAULT DETECTION USING INSTANTANEOUS FREQUENCY Dhay Arifiato ad Adi Rahmadiasyah Departmet of Egieerig Physics, Faculty of Idustrial Techology Sepuluh Nopember Istitute of Techology Campus ITS Sukolilo Surabaya dhay@ep.its.ac.id Abstract This paper presets a ovel techique to aalyze acoustical sigal emitted from rotatig machiery by usig istataeous frequecy (IF). IF is defied as the derivative of phase with respect to time from the aalytic sigal to track a timevaryig parameter. This techique essetially is derived from the spectrum of short-time Fourier trasform (STFT) ad the remapped that spectrum to derivatio of widow used i STFT aalysis. As a result, the time ad frequecy ca be located simultaeously with better represetatio tha spectrogram. I this work, we focused o the ubalaced rotatig machie due to ueve mass at the ceter of rotatio. The soud patter of the vibratio machie simulator was recorded i Pusdiklat Migas Cepu with kow ubalaced mass to simulate damage coditios. The more mass was added to the rotor, the louder soud of ubalaced would be ad this also implied the higher value of the amplitudes of the fudametal frequecy. For ubalaced coditio with 7.8gr of mass, the domiat fudametal frequecy at 600 rpm, was at Hz (15.41 db SPL). Keywords : rotatig machiery, istataeous frequecy, fudametal frequecy, soud patter 1. INTRODUCTION Rotatig machiery is commoly foud i daily life from home appliaces (e.g., bleder) to large-scale idustry (e.g., electric turbie). Essetially, this type of machiery is drive by electrical iput ad trasformed ito mechaical eergy (rotatio). The rotatio ad its iteractio betwee movig parts durig cyclic motio cause vibratio ad emit audible soud. Due to mechaical imperfectio such as wear-time, frictio, the each rotatig machiery has a uique soud characteristic. This research focuses o aalyzig the emitted vibratio soud of its particular frequecy, i which, the damage of oe particular part of the rotatig machie will emit a specific frequecy. Recetly, LPA method was used i previous research [3]. This techique is based o the assumptio that the slow chages of sigal spectrum i a short rage of widow (< 30 msec). However, the vibratio of rotatig machie is cosiderably lower tha huma laryx. Therefore, the probability of frequecy estimatio error is larger due to the differece from of the ma s soud spectrum ad machie i a short rage of widow. Istataeous frequecy, which is defied as the derivative of phase with respect of time, is a ovel tool to estimate time-varyig parameter with high accuracy. This work also exteds previous ivestigatio by usig a simulator of a real plat [1]. The results were obtaied by determiig the value of fudametal frequecy of ormal machie ad compared it with the other damage part. We used vibratio machie simulator i Pusdiklat Migas Cepu after kowig the kid of machie fault for validatio.. MODEL, ANALYSIS, DESIGN, AND IMPLEMENTATION Rotatig machiery is used to trasform the electrical eergy ito mechaical eergy i form of rotatio. I this research we focused o the damaged typically foud o a rotatig machiery called ubalace. This class of damage is caused by a ueve mass at rotor (the cetre of rotatio)..1 Short Time Fourier Trasform (STFT) STFT is the Fourier Trasform covoluted with a widow fuctio. Fourier Trasformatio from the sigal x(t) chaged ito discrete from is expressed as, L 0 X (e ) = x(m)ω( m)e m (1) m= 0 The eq. (1) has two differet iterpretatios : usig the is costat, X (e ) is same as discrete Fourier Trasformatio which multiplied by the widow fuctio, expressed as,

2 08 Ubalaced Machie Fault Detectio usig Istataeous Frequecy- Dhay Arifiato 159 π 1 θ X (e ) = θ π X(e )* W(e )e d () π I this iterpretatio X ( e ) is Fourier Trasform from x(m)ω(-m), meas that, * < m <. It X ( e ) = X ( e ) X ( e ) (3) eq. (3) ca be expressed ito real ad imagiary part, X ( e ) = a ( ω) + jb ( ω). Usig certai value of ω, STFT ca be viewed as a bak of badpass filters with i is filter idex of ith-filter, i X (e ) = e i x i () (4) ad the impulse respose of sigle filter is expressed i h( ) = w( ) e with : 1. w( ) 0 for 0 L 1. Badwidth from h() is ω 0, 0, ω < ω where, 0 W ( e ) = 0, other ad ω 0 is the ceter frequecy of filter h() []. There are two kids of spectrogram, arrowbad ad widebad. Narrowbad is produced by wide widow, so it will produce the good resolutio at frequecy ad decreasig resolutio i time dimesio. O the other had, the widebad spectrogram, the usig of short widow will produce good resolutio i time dimesio while decreasig resolutio i frequecy dimesio.. Widowig Practically sigal is just moitored at certai period of time. Thus, the sigal spectrum must be approached usig some fiite data. If there is a sigal x 0 (t) with T 0 duratio, where T 0 T ad T = 1/Fs, so the ability to differ the frequecy will be restricted at F = 1/Fs. It some sample L is the result from Fs samplig, if the value of duratio x 0 (t) is loger tha T 0, so widow ω() with L duratio eed to be used, expressed as : ˆ = ω (5) x( ) x( ) ( ).3 Istataeous Frequecy The istataeous frequecy (IF) is a frequecy that is fuctio of time associated with the sigal which describes the frequecy value i istat time. The istataeous frequecy amplitude spectrum (IFAS) provides better the harmoic structure represetatio of speech sigal tha the STFT amplitude spectrum. As ca be see i Fig. 1, the IF techique ca elimiate Heiseberg s ucertaity which is the exact locatio of frequecy ca be determiate at its exact locatio i time simultaeously (represeted by spikes). IFAS is obtaied by rearragig the sigal x(t) covolved with widow fuctio w(t), τ X ( ω, t) = w' ( τ t) e x( τ ) dτ (6) t w (t) fuctio is the derivatio of widow w(t) with respect to time. Figure 1. Defiitio of istataeous frequecy amplitude spectrum [].4 Research Desig The experimetal uit of this research is vibratio machie simulator foud i the vibratio machie simulator room at Pusdiklat Migas Cepu. The machie specificatio is: Dimesio : legth = 89 cm, width = 0 cm, height = 31 cm Motor type is sigle phase AC electric Miimum rotatioal speed is 964 rpm ad maximum is 309 rpm at ormal coditio. We set the damaged as follows, 1. Ubalace coditio without mass. Ubalace coditio with.4 gr of mass 3. Ubalace coditio with 4.8 gr of mass The damaged level of ubalace ca be determied ca be determied by observig the value of amplitude at frequecy 1x rpm (machie rotatio) of vibratio spectra at each damaged coditio. Thus, the higher value of amplitude, the higher level of damaged due to the ubalace mass. The schematic of addig ubalaced mass was coducted, show i Figure. We set three differet variatios of rotatioal speed, 1160, 1840 ad 600 rpm. I order to kow the level damaged of each

160 4 th Iteratioal Coferece Iformatio & Commuicatio Techology ad System ubalace coditio coducted ubalace phase measuremet (for ubalace coditio without mass oly) ad the vibratio level (vibratio

3 160 4 th Iteratioal Coferece Iformatio & Commuicatio Techology ad System ubalace coditio coducted ubalace phase measuremet (for ubalace coditio without mass oly) ad the vibratio level (vibratio spectrum) usig VIBXPERT tool i Pusdiklat Migas Cepu. The level damaged at vertical misaligmet coditio was measured by usig ROTALIGN as baselie. Figure. Machiery scheme ad locatio of mass The soud pressure level measuremet was coducted usig the stadard of Oil Compaies Materials Associatio (OCMA) method for small source. Measuremet was take at 30 cm far from machie usig SLM (Rio Type NL-31) coected with computer. The steps are : Figure 3. Measuremet surface ad locatio of measuremet poit [5] I1 I I 3 0 D = + + (7) Do = commo dimesio, I 1 = legth (cm), I = width (cm), I 3 = high (cm) ad, r = Do (8) Usig equatio (7) ad (8), the value of Do was obtaied 55,147 cm, ad the, r = 110,194 cm. 1 The locatio of measuremet poits (show i Fig. 3) is determied by calculatig b ad h, where b is distace betwee poit ad source = 0.9r ad h is poit high = 0.4r. Result of the calculatio is b = 99.6 cm ad h =44.1 cm. Soud pressure level measured at each poit with average value, 0,1L1 0,1L 0,1L L = AV 10log (10) where L av is average SPL, L 1 L is SPL each poit (db), ad is amout of measuremet poit. The maximum frequecy of soud sigal was observed first to determie sample frequecy to fulfill the Nyquist criterio. The soud sigal machie rage is Hz ad weakeig amplitude occurs at frequecy over 5500 Hz. The samplig frequecy was set to 1105 Hz to avoid possible aliasig. The first step is STFT calculatio by dividig the sigal x(t) ito segmets usig shifted half of the legth of the widow alog samples. The spectrogram of the sigal shows the value of frequecy for each measuremet (ordiate) ad time axis i secod (abscissa). The shape ad width of the aalysis widow are importat features. It is ecessary to use the widow whose value of side lobe roll off is high to prevet loss due to frequecy leak. We chose Haig widow. Usig the fact that the istataeous phase agle of the iput sequece is the (uwrapped) agle of the aalytic sigal, the istataeous frequecy is the rate of chage of the istataeous phase agle with respect to time. First, the derivatio will depart from widowed Fourier trasform poit of view to estimate the istataeous frequecy. By meas of the otatio of istataeous frequecy amplitude spectrum, the the harmoic structure of sigal ca be revealed to determie the fudametal frequecy. First we calculated the STFT spectrum of the sigal x(t), the remapped the spectrum ito its respective IF bad. This bad was derivatio of widow fuctio with respect to time. I other words, the coefficiets i the movig widow method are calculated from the movig widow trasform (eq. ). The time-frequecy represetatio is costructed from the squared magitude of these coefficiets. The IF was computed for each STFT bi from partial derivatives of the phase spectrum as expressed by eq. (6). The upper ad lower boud of the IF value iside each frequecy bi were the frequecy cut-off of the badpass filters. If the IF value is outside the filter, the it will be excluded from further calculatio.

08 Ubalaced Machie Fault Detectio usig Istataeous Frequecy- Dhay Arifiato 161 3.

rpm) preseted below : figure is at 1160 rpm, 1840 rpm for middle ad at the lower pael is at 600 rpm, respectively. As it ca be see i Fig.

Average SPL of each coditio Average SPL (db) Speed (RPM) Without mass,4 gr 4,8 gr 7,8 Gr Nrml Miss Miss vert 1160 69,3 69 69,4 69,4 68, 75,5 1840 73,4 7,9 73,3 73,3 71,9 77,3 600 76,8 78,9 81,7 81,7

4 08 Ubalaced Machie Fault Detectio usig Istataeous Frequecy- Dhay Arifiato RESULTS For SPL (soud pressure level, i db) measuremets, the samples are the value of L eq for 10 secods for each poit ad damaged coditio for three variatio of rotatioal speed (1160, 1840, ad 600 rpm) preseted below : figure is at 1160 rpm, 1840 rpm for middle ad at the lower pael is at 600 rpm, respectively. As it ca be see i Fig. 5, for lower speed, the spectrum of the motor ubalaced was udetected. As the speed icreased, the up-ad-dow spectrum of ubalaced appeared obviously. Table 1. Average SPL of each coditio Average SPL (db) Speed (RPM) Without mass,4 gr 4,8 gr 7,8 Gr Nrml Miss Miss vert , ,4 69,4 68, 75, ,4 7,9 73,3 73,3 71,9 77, ,8 78,9 81,7 81,7 73,9 8,7 The SPL sample measuremet is used to fid out machie SPL distributio at which poit will be used for recordig the ext machie soud sigal. As the ubalaced mass grew, the soud itesity emitted was also louder. We preset oly oe figure of the spectrogram. Figure 4 shows a arrowbad spectrogram of the ubalaced with 4.8 gram additioal mass to the rotor at 600 rpm. As it ca be see, the spectrogram idicates the spectrum of the sigal below 500 Hz. However, it fails to locate precisely the characteristic frequecy of the motor due to smeared frequecy ad poor temporal resolutio. Figure 4. Spectrogram of ubalace with 4.8 gr of mass at 600 rpm I first coditio, the motor was set i ubalace without additioal mass for baselie coditio. Fudametal frequecy was observed at about Hz at 1160 rpm ad at about Hz at 600 rpm. I the ext step,.4, 4.8, ad 7.8 gram of ubalaced mass was added to the machie for each coditio. Figure 5, 6 ad 7 show the patter of frequecy locatio of the.4, 4.8, ad 7.8 gram of ubalaced mass with three differet rotatio speeds. The rotatio speed at upper pael of each Figure 5. Soud patter of ubalace with.4 gram of mass at 1160rpm(upper pael), 1840 rpm (middle) ad 600 rpm.

16 4 th Iteratioal Coferece Iformatio & Commuicatio Techology ad System It was apparet that the domiat frequecy was below 100 Hz. The spectrum was also oscillatig with respect to time.

5, with the same amout of ubalaced mass ad the rotatio speed was icreased to the highest allowable speed of the motor, the amplitude of lower spectrum became higher tha the middle pael.

5 16 4 th Iteratioal Coferece Iformatio & Commuicatio Techology ad System It was apparet that the domiat frequecy was below 100 Hz. The spectrum was also oscillatig with respect to time. I the lower pael of Fig. 5, with the same amout of ubalaced mass ad the rotatio speed was icreased to the highest allowable speed of the motor, the amplitude of lower spectrum became higher tha the middle pael. It is also obvious that the side-spectrum (about 450 Hz) appears. This implies that the more eergy was required to drive the motor with additioal ubalaced mass as the speed icreased. Fudametal frequecy was observed at about 4.7 Hz ad 49.9 Hz i 600 rpm. Whe more ubalaced mass was added to the rotor, the damaged spectrum appeared earlier i the 1840 rpm (see middle pael of Fig. 6). Its amplitude was also comparable to the case of.4 gram ubalaced mass with 600 rpm (lower pael of Fig. 5). However, the siusoid-like oscillatio of the spectrum became deser which idicated higher oscillatio frequecy. It is also easily observed the side spectrum at about 300 Hz, which is ot easily observed with spectrogram. The other sidefrequecy is appeared at about 450 Hz while the mai ad the first side frequecy at 300 Hz have higher amplitude (i.e., itesity). Figure 6. Soud patter of ubalace with 4.8 gram of mass at 1160rpm(upper pael), 1840 rpm (middle) ad 600 rpm. Figure 7. Soud patter of ubalace with 7.8 gram of mass at 1160rpm(upper pael), 1840 rpm (middle) ad 600 rpm.

6 08 Ubalaced Machie Fault Detectio usig Istataeous Frequecy- Dhay Arifiato 163 Fudametal frequecy appeared at about.47 Hz at 1840 rpm ad Hz at 600 rpm for 4.8 gram ubalaced mass case. I the third case, 7.8 gram ubalaced mass was added ad the results are show i Fig. 7. Both the domiat spectrum ad side-spectrum were observed at 1840 rpm speed. However, the domiat spectrum was shifted upward to higher frequecy. I the lower pael of Fig. 7, the domiat spectrum at 600 rpm shifted eve higher tha that of at 1840 rpm. Two side-spectrums appear clearly with siusoid patter at about 50 Hz ad 400 Hz. The frequecy of oscillatio patter at 400 Hz is the same as the domiat spectrum. This suggests that the additioal mass may have iduced a ew vibratig place at the rotor. Compared to the spectrogram, the gradual additio of the ubalaced mass, the patters were also observable which was blurred dark lie patter i rage Hz of frequecy, as if it was oly oe domiat spectrum. The oly obvious differece was, as the ubalaced mass icreased the domiat spectrum appeared darker. Usig IF-based timefrequecy represetatio, the cyclic movemet of the rotatig part of the machie ca be viewed clearly ad the exact umeric value of frequecy ca be obtaied precisely compared to that of the spectrogram. This techique shows a prospective practical usage i the idustry for maiteace ad early failure detectio. [] Arifiato, Dhay. Fudametal Frequecy Estimatio ad Voiced / Uvoiced Determiatio Usig Istataeous Frequecy. Doctoral Dissertatio, Departemet of Iformatio Processig Tokyo Istitute of Techology, Tokyo, 005. [3] Hasa, Fuad. 00. Study of Patter Recogitio i Rotatig Machie Fault Detectio usig Liear Predictio (i Idoesia), udergraduate thesis, Dept. Egieerig Physics ITS, Surabaya, 00. [4] Uited Natios Eviromet Programme, Eergy Efficiecy Guide for Idustry i Asia- Electrical Motor (i Idoesia) USA, 006. [5] Yag, S.J. ad A. J. Elliso Machiery Noise Measuremet. New York, USA : Claredo Press Oxford. 4. CONCLUDING REMARKS I this study, we applied istataeous frequecy based time-frequecy represetatio to show the spectrum cotet of gradual additioal ubalaced mass to a rotor of a motor. We also compared the results with the spectrogram. The ubalaced mass was added to the rotor.4, 4.8, ad 7.8 gram, as well as the rotatio speed was varied to 1600, 1840, ad 600 rpm, respectively. Usig istataeous frequecy techique, the domiat spectrum was clearly observed. As the rotatio speed was icreased ad more ubalaced mass was added, the spectrum amplitude was gettig higher. It was also clearly show the side-spectrum also appeared. This suggests that the ubalaced mass may have iduced additioal vibratio elsewhere i the machie simultaeously with the mai vibratio at the rotor. REFERENCES [1] Ada, Ahmad Rifqi Applicatio of Istataeous Frequecy Techique for Fault Detectio of Electrical Motor. (i Idoesia), udergraduate thesis, Dept. Egieerig Physics ITS, Surabaya, 006.

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