A New Fault Diagnosis Method for Planetary Gearbox

Transcription

1 Internatonal ournal of Performablty Engneerng, Vol. 2, No. 4, uly 26, pp Totem Publsher, Inc., 4625 Stargazer Dr., Plano, Texas 7524, U.S.A A New Fault Dagnoss Method for Planetary Gearbox HAIPING LI *, IANMIN ZHAO, XINGHUI ZHANG and XIANGLONG NI Mechancal Engneerng College, Shjazhuang, Chna (Receved on May 2, 25; revsed on Nov. 9, Dec. 22, 25, and March 25, 26) Abstract Planetary gearbox s wdely used n many felds due to ts robustness and hgh power-weght rato, but mplementaton of fault dagnoss on t s challengng. Ths paper proposes a new fault dagnoss method for planetary gearbox based on emprcal mode decomposton (EMD) and adaptve mult-scale morphologcal gradent flter (AMMGF). The proposed method has two domnant strengths: t can be appled to non-lnear and nonstatonary sgnal, and t can acheve the goal of de-nosng. The framework of the proposed method s ntroduced frst. Expermental data acqured from a planetary gearbox test-rg s then utlzed to valdate effectveness of the proposed method. The method s demonstrated to have good performance on both extractng faults characterstc frequency and de-nosng. Keywords: planetary gearbox, fault dagnoss, emprcal mode decomposton, adaptve mult-scale morphologcal gradent flter.. Introducton Planetary gearboxes have been wdely and ncreasngly used n recent years as they can provde a larger transmsson rato n a more compact package. Ther functon s to transfer torque and power from one shaft to another. A falure of gearbox may cause shutdown of the entre tran and result n major economc losses []. Therefore, the fault dagnoss of the planetary gearboxes s crucal to prevent the mechancal system from malfuncton. To ths end, many technques have been used n planetary gearbox fault dagnoss. Such as support vector machne (SVM) [2], wavelet packet transformaton (WPT) [3] and hdden markov model (HMM) [4, 5]. Anyway, the ntellgent methods are often lmted n a settled condton and would not work on all cases. Some of these technques are nonadaptve and some works based on the assumpton that the process generatng sgnal s statonary and lnear. However, the structure of planetary gearbox s very complcate, the fault sgnal of planetary gearbox are usually non-statonary and non-lnear. Many dfferent feature frequences can be depcted n ts frequency spectrum and the ampltudes of rng gear and planet gears fault frequences are very low. In addton, nose nterference s very serous because of the harsh workng condton. Therefore, fault dagnoss method of planetary gearbox whch s adaptve and ft for ths knd of sgnal s needed urgently. Frequency spectrum analyss [6] s one of the most useful means and t s based on the ampltude changng of fault characterstc frequency. However, the functon of the tradtonal frequency spectrum analyss s lmted to planetary gearbox sgnal as there wll be many frequences n ts frequency spectrum. Emprcal mode decomposton (EMD) [7], as a new tme-frequency analyss technque, has been developed and wdely appled n fault dagnoss of machnery recently. EMD can decompose the complcate sgnal nto a set of complete, smple and almost orthogonal components named ntrnsc mode functon (IMF). The IMFs represent the natural oscllatory mode embedded n the sgnal and work as the bass functons, whch are determned by the sgnal tself, rather than pre- * Correspondng author s emal: hp_l929@63.com 389

2 39 H. L,. Zhao, X. Zhang, and X. N determned kernels. Thus, t s a data-drven and self-adaptve sgnal processng method that can be appled to non-lnear and non-statonary process perfectly. Addtonally, some researchers ntroduced mathematcal morphology (MM) [8] to fault dagnoss feld n recent years. Fault frequences of gears can be extracted more explctly by usng mathematcal morphologcal flters. Therefore, n ths study, a new fault dagnoss method for planetary gearbox s presented by usng EMD and MM. 2. Framework of Proposed Method EMD s a popular method and ts fundamental theory can be found n many documents. Thus, the theory of EMD wll be not ntroduced n detals here and only the specfc applcaton wll be llustrated n ths paper. The fundamental theory of MM can be seen n Ref. [9]. In general, dfferent results wll be obtaned when selectng dfferent structurng elements. Selectng a sutable structurng element s very mportant. Ths paper proposed the adaptve mult-scale morphologcal gradent flter (AMMGF), as follows: Assume that X s dspersed sgnal, T s morphologcal transform, and then the AMMGF can be summarzed as the set of{ T >, Z}. Where T s defned as: T X = T X () ( ) ( ) Smlarly, assume that f(n), F={,,2,, N-} and g(m), G={,,2,,M-} (N>>M) are nput sgnal and structurng element, respectvely. Then the mult-scale morphologcal dlaton and eroson flters can be defned as: f g n = f g n = f g n n = N (2) ( ) ( ) ( )( ) ( ),,,2,, ( f g) ( n) ( f g)( n) f g( n), n,,2,, N Θ = Θ = Θ = (3) Where g s the structurng element whch ts scale s. It can be obtaned through dlate g by - tmes, as follows. g = g g g (4) At the same tme, the algorthems also can be appled to the followed equatons. f + g n = f g g n, n=,,2,, N (5) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) fθ + g n = fθg Θ g n, n=,,2,, N (6) The mult-scale morphologcal openng, closng and two gradent flters can be obtaned accordng to the above equatons, as follows: f g n = f Θg g n n = N (7) ( ) ( ) ( ) ( ),,,2,, ( f g ) ( n) ( f g ) g ( n), n,,2,, N DE = Θ = (8) ( ) ( ) ( ) ( ),,,2,, MGF f n = f g n f Θ g n n = N (9) OC ( ) ( ) = ( ) ( ), =,,2,, MGF f n f g n f g n n N () Many mult-scale morphologcal transformed results would be gotten through the method descrbed above. Then how to merge them together s another problem. Ths paper utlzed weghtng and averagng method.

3 A New Fault Dagnoss Method for Planetary Gearbox 39 Assume that the set of all scales of structurng elements s I { I,I,,I } obatned fltered results are fg ( n ), j 2,,, n 2,,,,N be merged usng weghtng and averagng method as follows: Where wj = I j I j, j =,2,,. j =, the 2 = =. Then the results can j j () ( ) = ( ) fg n w fg n Theoretcally, the above AMMGF can both keep the specfc characterstc of pulse sgnal and weaken the nterference of nose sgnal. However, due to the specalty of planetary gearbox, the practcal applcaton result may be unsatsfactory. Therefore, ths paper proposed the fault dagnoss method for planetary gearbox based on EMD and AMMGF. The steps can be descrbed as follows.. Performng EMD on the raw sgnal and gettng k IMFs. 2. Processng every IMF usng AMMGF and obtanng a lot of processed results wth dfferent scales of structurng elements. 3. Mergng the processed result of each IMF usng weghtng and averagng method, as Eq () descrbed, gettng AMMGF results of k IMFs. 4. Calculatng the mean value of the k results as the fnal sgnal. 5. Analyzng the frequency spectrum of the fnal sgnal and evaluatng the health condton of planetary gearbox. fg(n) IMF fg2(n) fg( n) = wj fgj( n) fg(n) Raw sgnal EMD IMF2 fg2(n) fg22(n) fg2( n) = w2j fg2j( n) K k K k = ( ) ( ) fg n = fg n fg2(n) Frequency spectrum analyss fgk(n) IMFk fgk2(n) fgk(n) fgk ( n) = w fg ( n) kj kj Fault dagnoss results 3. Case Study Fgure : Flowchart of the method proposed n ths paper A mechancal test bed s used n ths research to valdate the effectveness of the method proposed n ths paper, as shown n Fgure 2 (). The expermental setup can be seen n Ref. [9]. Ths s a ntroduced falure experment and wear falure s seeded on one tooth of sun gear, planet gear and rng gear, respectvely. The falures are as Fgure 2 (2) shows. The samplng frequency of ths expermental system s 2K Hz, and 24 ponts of data are recorded for every sgnal. The nput shaft, shaft, was drven by the motor at three knds of rotary speed, 4, 8 and 2 rpm. To each speed, four dfferent knds of loads are mplemented. They are,.4,.8 and.2 Nm, respectvely.

4 392 H. L,. Zhao, X. Zhang, and X. N () (2) Fgure 2: () Expermental system; (2) Seeded falure: Sun, Planet, (c) Rng gear Accordng to confguraton parameters of the planetary gearbox, relevant fault characterstc frequences can be calculated, as seen n Table I. Table I. Fault characterstc frequences (Hz) of every gear Rotary speed (rpm) Meshng frequency Fault frequency of sun gear Fault frequency of planet gear Fault frequency of rng gear Frstly, the sun gear fault sgnal whch acqured from the workng condton of 2 rpm and.2 Nm was analyzed to valdate the effectveness of the method proposed n ths paper. The fault characterstc frequency of the sun gear n ths condton s Hz. The vbraton sgnal acqured by Accelerometer 3 was utlzed n ths example. Fgure 3 shows the waveform n tme doman and frequency spectrum of the sun gear fault sgnal. It can be seen that the ampltudes of the dsturbed sgnal s even hgh that the health condton of the sun gear cannot be assessed Tme/s Dsturbed sgnal Fgure 3: Sun gear fault sgnal: Waveform n tme doman; Frequency spectrum Fgure 4 shows the envelope waveform of the sun gear fault sgnal and s the frequency spectrum. It can be seen from the fgure that the, 2 and 3 tmes of sun gear fault characterstc frequency are very obvous. However, the nose nterference s also very serous Tme/s Hz Hz Hz Fgure 4: Envelope waveform of sun gear fault sgnal; Frequency spectrum Fgure 5 shows the result of EMD and AMMGF whch the method proposed n ths paper. Where the black bold lne and blue thn lne n are the results of morphologcal flter and the waveform n tme doman of orgnal sgnal, respectvely. It can be seen

5 A New Fault Dagnoss Method for Planetary Gearbox 393 from the fgure that the de-nosng effect s satsfactory compared wth Fgure 4. More mportant s that the ampltudes of the extracted sun gear fault characterstc frequences are much hgher than before Tme/s Hz Hz Hz Fgure 5: Sun gear fault sgnal: Result of EMD and AMMGF; Frequency spectrum Fgures 6 and 7 are results of EMD and AMMGF that are appled to planet and rng gears, respectvely. In order to consder all workng condtons, the data acqured from 4 rpm and.4 Nm condton s utlzed when analyzng planet gear sgnal. When analyzng rng gear sgnal, the data acqured from 8 rpm and.8 Nm condton s used. Fault characterstc frequences of the planet gear and rng gear n the two condtons are.243 and 3.27 Hz, respectvely.it can be seen from Fgures 6 and 7 that the proposed method can extract the fault characterstc frequences of the planet and rng gear obvously even though the frequences are very low. In addton, effects of de-nosng of the proposed method s also satsfactory compared wth the orgnal frequency spectrum as Fgures 8 and 9 shows Tme/s Hz 2.243Hz 3.243Hz Fgure 6: Planet gear fault sgnal: Result of EMD and AMMGF; Frequency spectrum Tme/s Hz Hz Fgure 7: Rng gear fault sgnal: Result of EMD and AMMGF; Frequency spectrum Tme/s.5.243Hz Hz Fgure 8: Envelope waveform of planet gear fault sgnal; Frequency spectrum

6 394 H. L,. Zhao, X. Zhang, and X. N Hz Hz Tme/s Fgure 9: Envelope waveform of rng gear fault sgnal; Frequency spectrum Therefore, the proposed method s more suted to planetary gearbox fault dagnoss than the other morphologcal gradent flters utlzed n Ref. [9]. There are three reasons:. The ampltudes of every extracted gear fault characterstc frequences are much hgher than before. 2. The proposed method can extract the fault characterstc frequences of the planet and rng gear obvously even though the frequences are very low. 3. The effect of de-nosng of the proposed method s also satsfactory. 4. Conclusons In ths paper, a new planetary gearbox fault dagnoss method based on EMD and AMMGF s proposed. Effectveness of the proposed method s valdated through experments. It s found that combnaton of EMD and AMMGF s sutable for the planetary gearbox fault dagnoss. References [] Feng, Z.P. and M. Zuo. Vbraton sgnal models for fault dagnoss of planetary gearboxes. ournal of Sound and Vbraton 22; 33: [2] Khawaja, T.S., G. Georgoulas and G. Vachtsevanos. An effcent novelty detector for onlne fault dagnoss based on least square support vector. IEEE Autotestcon Conference 28; September 8-: [3] Hadad, K., M. Pourahmad and H. Maragh. Fault dagnoss and classfcaton based on wavelet transform and neural network. Progress n Nuclear Energy 2; 53: [4] Ln, C. and V. Maks. A comparson of hdden markov and sem-markov modelng for a deteroraton system subject to vbraton montorng. Internatonal ournal of Performablty Engneerng 25; : [5] L, Z.N., Z. Wu, Y. He and F. Chu. Hdden markov model-based fault dagnostcs method n speed-up and speed-down process for rotatng machnery. Mechancal Systems and Sgnal Processng 25; 9: [6] Huang, N.E., Z. Shen and S. Long. The emprcal mode decomposton and the hlbert spectrum for nonlnear and non-statonary tme seres analyss. Proceedngs of the Royal Socety of London Seres 998; 454: [7] Wang, X., C. Lu, F. B, X. B and K. Shao. Fault dagnoss of desel engne based on adaptve wavelet packets and EEMD-fractal dmenson. Mechancal Systems and Sgnal Processng 23; 4: [8] Morenlla, A.., R. Carmona and. Romero. Mathematcal morphology for desgn and manufacturng. Mathematcal and Computer Modelng 2; 54: [9] L, H.P.,. Zhao and X. Zhang. Planetary gearbox fault dagnoss usng morphologcal gradent flters. Vbroengneerng PROCEDIA 24; 4: Hapng L s currently a PhD student n Mechancal Engneerng College, Shjazhuang, Chna. anmn Zhao s currently a professor at Mechancal Engneerng College, Shjazhuang, Chna. Xnghu Zhang receved the PhD degree from Mechancal Engneerng College, Chna n 25. Xanglong N s currently a PhD student n Mechancal Engneerng College, Shjazhuang, Chna.