Production Test of Rotary Compressors Using Wavelet Analysis

Transcription

1 Purdue Uiversity Purdue e-pubs Iteratioal Compressor Egieerig Coferee Shool of Mehaial Egieerig 2006 Produtio Test of Rotary Compressors Usig Wavelet Aalysis Haishui Ji Shaghai Hitahi Eletrial Appliatio Co. Hogqiag Xiao Shaghai Hitahi Eletrial Appliatio Co. Haoyog Fa Shaghai Hitahi Eletrial Appliatio Co. Follow this ad additioal works at: Ji, Haishui; Xiao, Hogqiag; ad Fa, Haoyog, "Produtio Test of Rotary Compressors Usig Wavelet Aalysis" (2006). Iteratioal Compressor Egieerig Coferee. Paper This doumet has bee made available through Purdue e-pubs, a servie of the Purdue Uiversity Libraries. Please otat epubs@purdue.edu for additioal iformatio. Complete proeedigs may be aquired i prit ad o CD-ROM diretly from the Ray W. Herrik Laboratories at Herrik/Evets/orderlit.html

2 Produtio Test of Rotary Compressors with Wavelet Aalysis Ji Haishui Xiao Hogqiag Fa Haoyog R&D Ceter Shaghai Hitahi Eletrial Appliatio Co., Ltd 1051, Yuqiao Road, Pudog Jiqiao, Shaghai, P.R.Chia Tel: *5346, Fax: , Postode: C016, Page 1 ABSTRACT Detetio of eletro-mageti soud is a importat step i ompressor produtio proess. First the paper itrodues the mehais of eletro-mageti soud ad the oept of wavelet aalysis method. The the eergy of vibratio sigals i differet frequey bad of wavelet was alulated. After that we map the eergy i differet frequey bads to two differet ompressors: oe with ollisio betwee stator ad rotor, the other without suh ollisio. By this way the ompressor with ollisio a be deteted. Fially several tests were doe to prove the effetivity of this method. 1. INTRODUCTION Today i lie test of ompressors there is a step alled mageti soud test. That is for ma to liste to the soud aused by ollisio betwee rotor ad stator. This is a subetive test performed uder diffiult irumstaes, iflueed by bakgroud oise, varyig oetratio level, ad varyig mood of the test perso et, all leadig to varyig results. Compressor s eletro-mageti soud is aused by ollisio betwee rotor ad stator whe motor starts up. Its mai part is trasiet eergy whih lasts very short ad is omposed of wide frequey, ad it is oliear. Traditioal Fourier Frequey Trasform method is ot suitable for aalyzig trasiet sigal beause its frequey ompoet is ofte submerged by oises. Wavelet aalysis is a time-frequey method, it a ath trasiet sigal. So as a ew mathemati tool it has bee widely used i the detetio, separatio ad quatitative measuremet of trasiet sigal. Wavelet method has reliable mathematial theory ad mature algorithm ad has bee suessfully used i may ases. So i this paper we use wavelet method to detet eletro-mageti soud of rotary ompressor by establishig the relatioship betwee vibratio s wavelet haraters ad eletro-mageti soud. 2. STATIC WAVELET ANALYSIS METHOD 2.1 Disrete wavelet trasform ad stati wavelet trasform(swt) The wavelet trasform of ay futio f ( t) L2 ( R) is defied as W f ( a, b) f ( t) ψ a, b( t) = dt = where ψ (x) is wavelet futio, a is sale fator, b is shiftig fator. 1 t b f ( t ) ψ ( ) dt ( 1) a a Whe a is otiuous variable, (1) is alled otiuous wavelet trasform. Whe a = 2, b = k2, (1) is alled disrete trasform. May wavelet is orthogoal ad the trasform w( a, b) is o-redudat Iteratioal Compressor Egieerig Coferee at Purdue, July 17-20, 2006

3 C016, Page 2 By applyig low-pass ad high-pass filter, sigal will be deomposed ito low frequey approximatio ad high fre quey details. The deompositio proess a be iterated, with suessive approximatios beig deomposed i tur, so that oe sigal is broke dow ito may lower resolutio ompoets. This is alled the wavelet deompositi o tree. The SWT method a be desribed as follows. At eah level, whe the high-pass ad low-pass filters are applied to the data, the two ew sequees have the same legth as the origial sequees. To do this, the origial data is ot deimated. However, the filters at eah level are modified by paddig them out with zeros. Supposig a futio f (x) is proeted at eah step o the subset. This proetio is defied by the salar produt of f (x with the salig futio φ (x) whih is dilated ad traslated, k ), k =< f ( x), φ ( x), k ) > (2) φ ( x) = 2 φ(2 x ) (3), k k Where φ (x) is the salig futio, whih is a low-pass filter. is also alled a disrete approximatio at the resolutio 2. If ψ (x) is the wavelet futio, the wavelet oeffiiets are obtaied by k,k w, k =< f ( x),2 ψ (2 x k) > (4) w, is alled the disrete detail sigal at the resolutio 2. As the salig futio φ (x) has the followig property: 1 x φ( ) = h( ) φ( x ) 2 2 1, k + a be obtaied by diret omputatio from k The salar produts < + 1, k = h( 2k),, 1 x ψ ( ) = g( x) φ( x ) (5) 2 2 f ( x),2 ( + 1) ψ (2 ( + 1) x k) > are omputed with w + 1, k = g( 2k), (6) Equatios (5) ad (6) are the multi resolutio algorithm of the traditioal DWT. I this trasform, a dow samplig algorithm is used to perform the trasformatio. That is, oe poit out of two is kept durig trasformatio. Therefore, the whole legth of the futio f (x) will redue by half after the trasformatio. This proess otiues util the legth of the futio beomes oe. However, for statioary or redudat trasform, istead of dow samplig, a up samplig proedure is arried out before performig filter ovolutio at eah sale. The distae betwee samples ireasig by a fator of two from sale to ext. + 1, k is obtaied by + 1, k = h l ), k + 2 l l ad the disrete wavelet oeffiiets w + 1, k = g l), + 2 l ( (7) ( (8) k l Iteratioal Compressor Egieerig Coferee at Purdue, July 17-20, 2006

4 C016, Page 3 The reduday of this trasform failitates the idetifiatio of saliet features i a sigal, so it a be used to idetify the soud of ollisio betwee rotor ad stator. 2.2 Multi Bad Detail Eergy Aalysis Method Just like frequey i Fourier Trasform, the disrete detail oeffiiets represet the eergy of sigal i the orrespodig sales. So this paper the multi-bad detail eergy method is used to lassify sigal, espeially sigals otaiig trasiet ompoets. A disrete sigal with legth of 2048 is used to illustrate the above method. The 4th Daubehies Wavelets db4 is hose as wavelet futio to deompose sigal.for 2 11 = 2048, the sigal a be deomposed to 10 levels ad obtai the wavelet oeffiiets at 10 resolutio 2, the oeffiiets are ombied as matrix w with row 10 ad olum every row represet the eergy of sigal at sale 2, 2 ad 2.the smaller the sale, the higher the frequey, ad steeper the sigal. The detail eergy Idex at differet resolutio is defied as follow: Idex 1 2 w(, k) N k ) = 10log( ) 9 A ref ( 2 Where represet deomposed level, = 1,2,..., 10 k is sequee umber of wavelet oeffiiet, k = 1,2,..., 2048 N is legth of disrete sigal, A is referee aeleratio, 0.01 m / s ref ( ) 2.3 Detetio of Eletro-Mageti Soud by Detail Eergy Idex Beause there is strog bakgroud oise i workshop it is hard to detet the ollisio betwee rotor ad stator by aalyzig the soud. Alteratively we measure aeleratio of shell. Beause the stress wave traslate to shell from stator diretly, so this method is more reasoable Whe motor starts up the mai oil is eletrified ad seod oil is ot eletrified, the rotor dose ot rotate. A lateral mageti fore is imposed o rotor. The fore pull the rotor, make the rak urve, ad ause the rotor ad stator to ollide, simultaeously a sharp soud is produed alled eletro-mageti soud. Experiees show that three fators ifluee mageti soud: (1)the positio of rakshaft, (2)voltage of stator ad (3)gap betwee rotor ad stator. By ombiig the three fators we get 12 operatig modes. At eah of the 12 modes we measure aeleratio o the shell show i Fig 2, here we use #3. At same time we liste to the soud by ad wath the lateral movig proess of rotor by eye to udge whether there is ollisio happeed. The aeleratio measurig use B&K PULSE system, the samplig frequey is 64K Hz. Usig formula (9), for every test mode we a get a detail eergy Idex to represet detail eergy at 10 differet deomposig levels. By superimpose the 12 Idex we a get Fig 4. The absissa represets bad sequee, the vertial ordiate represets eergy idex. It is show from figure 3 that urve 6, 8, 9 are quite differet from the rest 9 urves, i bad 1~6 the idex of 6,8,9 is higher tha the rest 6 urve,it meas that the 3 urves have high eergy i high frequey. This orrespods to the fats that ollisio betwee rotor ad stator produes high-frequey aeleratio sigal o shell. This result math the fat i Table 1. The above experimet proved that wavelet-eergy-bad method a detet eletromageti soud effetively. Iteratioal Compressor Egieerig Coferee at Purdue, July 17-20, 2006

5 C016, Page 4 Tab.1 Collisio oditio betwee rotor ad stator No Result N N N N N Y N Y Y N N N Fig 1 Multiple-Level Deompositio Fig.2 Positio of Collisio ad Aelerators Fig.3 Detail Eergy Idex Iteratioal Compressor Egieerig Coferee at Purdue, July 17-20, 2006

6 C016, Page 5 3. SOUND SOURCES IDENTIFICATION Eve though the above method is effetive to detet whether eletromageti soud exists, there is a risk: vibratio wave a propagate to aelerator 3 from other plaes ad the aeleratio a be very high at aelerator 3, that will led to misudge. I rotary ompressors the mehaial ollisio a also happe i pump, for example ollisio betwee rakshaft ad mai bearig, or betwee pisto ad blade. The stress wave produed by both ollisios a propagate to shell through weldig part. To simulate huma ears, we use 4 aelerators to reeive aeleratig sigal simultaeously, #1 ad #2 are loated at weldig positio,#3 ad #4 are at middle positio of stator, #1 ad #3 are for ormal aeleratio, #2 ad #4 are for vertial shear aeleratio. The soud soures a be idetified by omparig delay times of stress wave to differet aelerators. The delay times of two time sequees X() ad Y() a be obtaied by alulatig their orrelatio futio Where γ XY ( m) E{ X * ( ) Y ( + m)} σ σ = (10) X Y σ X σ Y are variaes of X ad Y. m is samplig delay. γ XY is betwee 1 ad 1. the delay time orrespods to maximal absolute value of γ XY. Figure 4 shows results of two group of aelerators. Fig 4a represets results of ormal vibratio, the delay is 10 samplig poits. Fig 4b represets result of vertial vibratio., the delay is 3 samplig poits. They both show that the wave propagates from the high part to the low part of shell, that is from stator positio to weldig positio. The differet delay times a be explaied as follow: ormal vibratio represet flexural wave, vertial vibratio represet logitudial wave, ad the veloity of logitudial wave is larger tha that of flexural wave. 4. CONCLUSIONS Firstly the paper itrodues stati wavelet aalysis method ad the presets the method of idetifyig eletromageti soud resoures by wavelet aalysis. I order to loate soud soures,4 aeleratios are measured ad time delays are alulated by alulatig their orrelatio futio. By the two methods, the ollisio soud soures a be loated orretly. m REFERENCES 1 X. H. Wag, Robert S. H. Istepaia, Miroarray Image Ehaemet by Deoisig Usig Statioary Wavelet Trasform, IEEE TRANSACTIONS ON NANOBIOSCIENCE, VOL. 2, NO. 4, DECEMBER 2003 Iteratioal Compressor Egieerig Coferee at Purdue, July 17-20, 2006

7 C016, Page 6 (a) #1 ad #3 ormal aeleratio ad orrelatio (b) #2 ad #4 vertial shear aeleratio ad orrelatio Fig.4 Aeleratios ad Correlatios Iteratioal Compressor Egieerig Coferee at Purdue, July 17-20, 2006