Strojniški vestnik - Journal of Mechanical Engineering 54(2008)12, 883-891 Paper received: 25.07.2008
UPC 534:519.61/.64:621.63 Paper accepted: 25.09.2009
Characterization of the Vibrations and Structural Noise
of a Suction Unit's Cover
Ju rij Ž u m e r 1, A n d re j B ič e k 2, M ih a B o lte ž a r 1’*
1 F a c u lty f o r M e c h a n ic a l E n g in e e rin g , U n iv e rs ity o f L ju b lja n a , S lo v e n ia 2 D o m e l d .d ., Ž e le z n ik i, S lo v e n ia
In this paper we report on a study o f the vibrations o f a suction unit's cover and the relation with the generated structural noise. The existing cover o f the suction unit was designed, taking into account only the geometrical requirements. Two different methods were used fo r characterization o f the vibration and structural noise o f the cover: numerical modal analysis made with the F E M (Finite Element Method) and experimental modal analysis made during the operation o f the suction unit. The results o f the experimental modal analysis o f the cover ’s vibrations visually confirm ed the results o f a numerical modal analysis up to the F ' B P F (Blade Passing Frequency) and characterized the main exciting sources with the prevailing aerodynamic excitation. The vibration modal analysis tries to fin d a relation with the cover’s structural noise using an experimental local noise modal analysis. A different method o f measurement o f local structural noise is introduced.
© 2008 Jo u rn a l o f M e c h a n ic a l E n g in e e rin g . A ll rig h ts rese rv e d .
Keywords: suction unit, suction unit’s cover, vibrations, structural noise, numerical modal analysis
0 IN T R O D U C T IO N
N o w a d a y s , e v e ry h o u s e h o ld d e v ic e te n d s to be u s e r frie n d ly a n d is d e s ig n e d n o t to h a v e a n eg a tiv e e ffe c t o n h u m a n h e a lth . F lo w ev er, th e v ib ratio n s a n d n o is e c a u s e d b y ro ta tio n a l m ach in es a re p a rtic u la rly p ro b le m a tic in th is respect. T h e su c tio n u n its p ro d u c e d b y D o m e l Ltd., Ž e le z n ik i, S lo v e n ia , h a v e a v a rie ty o f vib ratio n so u rce s th a t te n d to p ro d u c e n o ise . In this p a p e r w e fo c u s o n th e c o v e r o f a su c tio n u n it that w a s o n ly d e s ig n e d in te rm s o f its fittin g to g eth er w ith th e o th e r p a rts o f th e u n it. C o n seq u en tly , th e c o v e r ’s g e o m e try is m a tc h e d to the sh ap e o f su c tio n u n i t ’s h o u s in g a n d b lo w e r. A s a re s u lt th e re a re n o tic e a b le v ib ra tio n s o f th e co v er d u rin g th e su c tio n u n it’s o p e ra tio n , a n d becau se th e c o v e r is th e o u te rm o s t p a r t o f th e u n it w e can also e x p e c t a n in c re a s e d le v e l o f n o is e g en e rate d b y th e c o v e r ’s v ib ra tio n s , g e n e ra lly referred to as th e stru c tu ra l n o ise .
A n y a n a ly tic a l a n a ly s is o f th e c o v e r ’s vib ratio n s is c o m p lic a te d b y th e c o m p le x structure o f th e c o v e r a n d th e a n a ly tic a lly u n k n o w n so u rc e s o f th e v ib ra tio n s . In g e n e ra l, there is n o t a lo t o f p u b lic ly a v a ila b le a n a ly tic a l research o n th e stru c tu ra l n o is e a s s o c ia te d w ith su ctio n u n its. A n e x p e rim e n ta l-b a s e d a p p ro a c h w as m ad e to c h a ra c te riz e th e n o is e o f a s u c tio n
u n it, a n d it w a s fo u n d th a t a e ro d y n a m ic so u rc e s p re v a il [1], d e s p ite e v id e n c e th a t th e stru c tu ra l n o is e is m a in ly c a u s e d b y th e e le c tro m o to r [2]. T h e n o is e c a u s e d b y th e v ib ra tio n o f th e c o v e r is p ro b a b ly re la te d to th e aero d y n am ic co n d itio n s [3], T h e firs t p a rt o f th is p a p e r p re s e n ts tw o d iffe re n t ste p s in th e a n a ly sis o f th e p ro b le m : a n u m e ric a l a n d e x p e rim e n ta l a n a ly s is o f th e v ib ra tio n s o f the su c tio n u n it’s c o v e r to c h a ra c te riz e th e m a in so u rc e s o f th e v ib ra tio n s , fo llo w in g th e b a sic m e th o d ste p s as in [4]; an d , fo r c o m p a ris o n , an e v a lu a tio n o f th e e x p e rim e n ta l m o d e s w ith th e n u m e ric a l re su lts.
F a r m o re c o m p lic a te d th a n th e a n a ly tic a lly d e fin e d v ib ra tio n s o f th e c o v e r is th e a n a ly tic a l c o m p u ta tio n o f th e stru c tu ra l n o is e g e n e ra te d b y th e v ib ra tio n s o f th e co v e r. T h e so u n d -p re s s u re le v e l (S P L ) is th e su m o f th e d iffe re n t s o u n d so u rc e s w ith a m a jo r o r m in o r effec t. O u r a im in th e se c o n d p a r t o f th is p a p e r w a s to c o m p a re th e m o d e s o f th e c o v e r ’s v ib ra tio n s a n d th e s o u n d flu c tu a tio n s d ire c tly a b o v e th e c o v e r ’s s u rfa c e to fin d a c o n n e c tio n b e tw e e n th e m o d e s o f th e v ib ra tio n a n d th e m o d e s o f th e stru c tu ra l so u n d . T o o b ta in th e m o d e s o f th e so u n d flu c tu a tio n s w e in tro d u c e a m e th o d o f m e a s u rin g th e flu c tu a tio n s o c c u rrin g d ire c tly a b o v e th e su rfa c e o f th e co v e r.
B e c a u s e o f th e c o m p le x ity o f th e s tru c tu ra l n o is e a t th e c o v e r ’s s u rfa c e , in th is p a p e r w e h a v e
trie d to in tro d u c e a sim p le w a y to u n d e rs ta n d th e v ib ra tio n s a n d th e g e n e ra te d n o is e u n d e r a rb itra ry o p e ra tin g co n d itio n s.
A s w e m e n tio n e d a b o v e , w e u s e d tw o ste p s to c h a ra c te ris e th e v ib ra tio n o f th e co v er. F irs tly , a n u m e ric a l m o d a l a n a ly sis w a s m a d e w ith th e F E M w h e re w e u s e d so m e sim ila r ste p s as in [5] a n d [6]; a n d se c o n d ly , a n e x p e rim e n ta l m o d a l a n a ly sis w a s m a d e d u rin g th e o p e ra tio n o f th e s u c tio n u n it. T h e s e p ro c e d u re s are in d e p e n d e n t, b u t th e re su lts are im p o rta n t fo r c o m p a rin g a n d e v a lu a tin g th e m o d e s.
1 F E M M O D A L A N A L Y S IS O F T H E S U C T IO N U N IT
T h e a im o f th e F E M m o d a l a n a ly sis w a s to fin d th e m o d e s in th e fre q u e n c y ra n g e o f th e p r e v a ilin g e x c ita tio n . W e e x p e c te d th a t d u rin g o p e ra tio n th e c o v e r ’s m o d e s w o u ld fo llo w th e c o v e r ’s o w n m o d a l sh a p es. H o w e v e r, i f th is w e re tru e w e c o u ld o n ly p re d ic t th e b e h a v io u r w ith a n u m e ric a l a n a ly sis. In fa c t all th e c o v e r ’s v ib ra tio n s are e x c ite d b y d iffe re n t m e c h a n is m s d u rin g th e u n it’s o p e ra tio n , w h ic h w e w ill d e s c rib e in S e c tio n 2. In a n u m e ric a l sim u la tio n w e c a n n o t c o n s id e r th e d e ta ile d e x c ita tio n m e c h a n is m s o f th e v ib ra tio n s b e c a u s e w e d o n o t k n o w th e ir m a g n itu d e a n d th e p h a s e a n g le b e tw e e n th e m . W e c a n o n ly p re d ic t th e p la c e s w h e re th e e x c ite d v ib ra tio n s are tra n s m itte d to th e co v e r.
T o m a k e th e n u m e ric a l a n a ly sis as a c c u ra te as p o s s ib le w e in c lu d e d all th e u n i t ’s
. 8S6E-03 2.778 5.552 $.327 IL.lOt
1. i t S 4.1(4 (.939 9.71S 12.49
SE463
F ig . 1. M ode at freq u en cy/ = 2284 H z
sta tic p a rts: th e h o u s in g , th e e le c tric - m o to r ’s sta to r, th e v a n e d d iffu s e r a n d th e co v e r. By
in c lu d in g a ll th e s e p a rts w e e x te n d e d th e tim e o f th e c o m p u ta tio n , b u t w e e n s u re d a b e tte r d e p e n d e n c y o f th e c o v e r o n th e o th e r elem e n ts [7]. W e a c h ie v e d th is w ith th e c o rre c t c o n tac t c o n d itio n s b e tw e e n th e p a rts, b e c a u s e th is can a lso c o n trib u te v e ry im p o rta n tly to o b ta in in g the c o rre c t re s u lts [8]. I n c lu d in g all th e p a rts also m a k e s it e a s ie r to d e fin e th e b o u n d a ry co n d itio n s. W ith r e s p e c t to th is th e s u c tio n u n it w a s fre e-free s u p p o rte d in o rd e r to b e c o m p a tib le w ith the e x p e rim e n ta l a n a ly sis.
T h e re s u lts o f th e n u m e ric a l a n a ly sis are s h o w n in F ig. 1 fo r th e m o d e a t a n eigen fre q u e n c y o f / = 2 2 8 4 H z , a n d in F ig . 2 fo r the m o d e a t a n e ig e n fre q u e n c y o f / = 6 5 3 3 H z. T h ese m o d e s are in te re s tin g , b e c a u s e th e y a re the n e a r e s t m o d e s to th e fre q u e n c ie s w h e re the e x c ita tio n s o f th e c o v e r o c c u r, w h ic h w ill be e x p la in e d la te r in S e c tio n 2 .2 .1 . F u rth e rm o re , w e w ill c o m p a re th e n u m e ric a l m o d e s w ith the e x p e rim e n ta l m o d e s n e a r th e s e fre q u e n c ie s.
2 E X P E R IM E N T A L M O D A L A N A L Y S IS O F T H E C O V E R ’S V IB R A T IO N S A N D T H E
L O C A L N O IS E
T h e e x p e rim e n ta l m o d a l a n a ly s is o f th e c o v e r’s
v ib ra tio n s a n d th e lo c a l n o is e h a d tw o m a in goals:
firstly, to fin d th e so u rces o f th e v ib ratio n excitation
a n d th e m o d e s at th e ex citatio n frequencies
in o rd e r to v a lid a te th e n u m e ric a l re s u lts a n d seco n d ly , to o b ta in m o d e s o f th e p re s s u re flu ctu atio n s d ire c tly a b o v e th e c o v e r ’s su rfa c e in o rd er to c o m p a re th e m w ith th e v ib r a tio n ’s m o d e s
2 1 Method for Measuring the Vibrations and
the Local Noise
T h e m e a s u re m e n ts o f th e v ib ra tio n s an d
the local n o is e w e re m a d e in D o m e l’s la b o ra to ry
for v ib ra tio n s a n d a c o u s tic s in an a n e c h o ic
ch am b er u s in g th e sa m e o p e ra tin g c o n d itio n s fo r
m e a su re m e n ts o f th e v ib ra tio n s a n d th e lo c al
noise. T h e p e rfo rm a n c e o f th e su c tio n u n its w ith a
van ed d iffu s e r d e p e n d s o n th e c h a ra c te ris tic s o f
the e le c tric -m o to r, th e b lo w e r, th e v a n e d d iffu s e r
and th e b a c k -flo w c h a n n e ls, a n d th e w o rk in g
c o n d itio n s, lik e th e v o lta g e su p p ly , th e o rific e ,
etc. T h e re is th e b e s t e ffic ie n c y fo r th e su c tio n
u nit at th e d e s ig n p o in t o f o p e ra tio n , w h ile at o ff-
desig n o p e ra tio n e ffic ie n c y is re d u c e d .
O u r e x p e rim e n ts w e re ru n a t a v o lta g e su p p ly o f 2 2 0 V w ith o u t u s in g th e a d d itio n a l orifice to m a k e in le t c ro s s -s e c tio n s m a lle r, so th ese m e a s u re m e n ts d iffe r fro m th e u s u a l on e. T he ro ta tio n a l sp e e d f R u n d e r th e d e s c rib e d c o n d itio n s w a s 4 3 2 0 0 m in"1. W e m u s t b e a w a re that th is is n o t th e d e s ig n p o in t o f o p e ra tio n , b u t w e as su m e d th e a rb itra ry o p e ra tin g c o n d itio n s. T his m e an s th a t w e are in te re s te d o n ly in the sou rce o f th e v ib ra tio n s a n d th e ir in flu e n c e o n th e stru ctu ra l n o is e ; w e a re n o t in te re s te d in th e ir m a g n itu d e u n d e r d iffe re n t o p e ra tin g c o n d itio n s.
W e u s e d th e fo llo w in g e q u ip m e n t to m e a s u re th e v ib ra tio n s: a la s e r v ib ro m e te r (P o ly te c C L V 7 0 0 ), a la s e r a m p lifie r (P o ly te c C L V 1000), an a c c e le ro m e te r (B & K 4 5 1 7 -0 0 2 ), a sig n a l a n a ly z e r (B & K P U L S E T y p e 3 5 6 0 -C ) an d a s o ftw a re e n v iro n m e n t (B & K L a b s h o p 9.0).
F ig . 3 p re se n ts th e e n v iro n m e n t in w h ic h th e v ib ra tio n s w e re m e a su re d . T h e su c tio n u n it lies o n a m a s s iv e m e ta l b lo c k w ith fo a m to s im u la te th e fre e s u p p o rt; th is is a lso im p o rta n t d u rin g th e n u m e ric a l an a ly sis in th e p re v io u s se c tio n . I f w e w a n t to m a k e an e x p e rim e n ta l m o d a l a n a ly sis o f th e v ib ra tio n s a n d la te r c o m p a re it w ith th e s o u n d a n a ly sis w e m u s t g et th e rig h t re la tio n s b e tw e e n th e m a g n itu d e an d the p h a s e a n g le s f o r th e d iffe re n t m e a s u re m e n t p o in ts. W e ca n do th is b y in tro d u c in g a f re q u e n c y -re s p o n s e fu n c tio n (F R F ). H o w e v e r, w e m u s t firs t c h o o s e a re fe re n c e p o in t o n th e u p p e r su rfa c e o f th e co v e r. W e ca n th e n c a lc u la te th e F R F b e tw e e n th e m e a s u re d p o in t a n d the re fe re n c e p o in t [9], A n a c c e le ro m e te r w a s u s e d to m e a s u re th e a c c e le ra tio n o f th e re fe re n c e p o in t, a n d a la s e r w a s u s e d to m e a s u re th e v e lo c ity o f th e m e a s u re d p o in t. W ith th e d iffe re n tia tio n o f the la s e r ’s v e lo c ity s ig n a l to g e t th e a c c e le ra tio n o f th e m e a s u re d p o in t, w e c o u ld fin a lly c a lc u la te F R F u sin g L a b sh o p so ftw are.
A n o th e r im p o rta n t ste p is th e se le c tio n o f th e m e a s u re d p o in ts. T h e re s o lv a b ility o f the c o v e r ’s m o d e s d e p e n d s o n th e fre q u e n c y ran g e . F ro m th e F E M m o d a l a n a ly s is w e ca n se e th a t th e m o d e in F ig . 1 h as a sim p le sh a p e, b u t as th e e ig e n fre q u e n c y in c re a se s th e m o d e is n o lo n g e r s im p le (se e F ig. 2).
R e g a rd in g th e n u m e ric a l re su lts in S e c tio n 1, w e c o n fig u re d th e c o a rs e m e s h (F ig . 5 a n d 6) w ith 5 m e a su re d p o in ts in ea c h rad ia l d ire c tio n (4 w e re lo c a te d in a x ia l d ire c tio n a n d 1 in ra d ia l d ire c tio n o f th e su c tio n u n it), w ith an e q u id ista n t p a rtitio n o f 12 p arts in a c irc u la r d ire c tio n aro u n d th e c o v e r’s c irc u m fe re n c e .
W ith th is k in d o f m e s h w e c a n c o v e r th e
m o d a l lin es o n ly at firs t fe w e ig e n fre q u e n c ie s.
T o sa tis fy th e m o d e s at h ig h e r e ig e n fre q u e n c ie s w e h a d to c o n fig u re a d e n s e r m e s h (F ig . 5 a n d 7)
w ith 10 p o in ts in th e e a c h ra d ia l d ire c tio n (7 w ere
lo c a te d in a x ia l d ire c tio n a n d 3 in ra d ia l d irec tio n
o f th e su c tio n u n it) a n d 6 p a rts in th e circ u lar
d ire c tio n , w ith a n e q u id is ta n t a n g le 02 = 10°
w ith in th e ra n g e <£>=130-180° fro m th e startin g a n g le (se e F ig . 5).
reference
arbitrary point with mark 1.3
W ith a d e n s e r m e s h w e w e re a b le to
i m p r o v e th e re s o lu tio n o f th e m o d e s.
F o r th e n o ise m e a s u re m e n t o n a lo cal are a
w e u se d tw o c o n d e n s e r m ic ro p h o n e s w ith an am p lifier (E M K A Y M D 4 5 3 0 A S Z -1 w ith c o n s ta n t se n sitiv ity to 10 k H z ), a sig n a l a n a ly z e r a n d th e
L abshop so ftw are.
F ig. 4 p re s e n ts a n o is e m e a s u re m e n t o f th e e n v iro n m en t d ire c tly a b o v e th e c o v e r ’s su rfa c e in the d istan c e o f 2-3 m m . T h e sm a ll siz e o f th e m ic ro p h o n es (<54.5x3 m m ) m e a n s th a t th e y ca n be p o sitio n e d a b o v e th e sa m e p o in ts th a t w e d efin ed d u rin g th e v ib ra tio n m e a s u re m e n t; th is is the rea so n fo r u s in g o u r id e a a b o u t c o m p a rin g th e v ib ratio n a n d th e s o u n d m o d es.
H o w e v e r, in th e n e a r s o u n d fie ld th e m e asu rem en t c o u ld b e u n c e rta in [10]. T h e n o ise directly a b o v e th e c o v e r ’s su rfa c e ca n b e a co m b in atio n o f d iffe re n t so u rc e s. In g e n e ra l, h ow ever, w e c a n su p p o se th a t it is a c o m b in a tio n o f the n o ise tra n s m itte d th ro u g h th e c o v e r ’s thin w all an d th e n o is e g e n e ra te d b y th e th in w a ll’s v ibrations. T h e re s p o n s e o f th e lin e a r d y n a m ic m odel is e x p e c te d to h a v e th e sa m e fre q u e n c ie s as the ex c ita tio n . W e e x p e c t th e sa m e to h a p p e n w ith th e s o u n d fie ld n e a r th e c o v e r ’s su rfa c e o n a sm all area, w h ic h th e m e a s u re d p o in t c e rta in ly is. D espite th e fa c t th a t w e a re in a n e a r so u n d field w e can e x p e c t p re s s u re flu c tu a tio n s . T o m in im iz e , in p a rtic u la r, th e e ffe c t fro m a n e a rb y p o in t w e isolate all a ro u n d th e m ic ro p h o n e , w h ic h is situ ated a fe w m illim e tre s a b o v e th e c o v e r ’s surface, w ith h ig h ly a b s o rb e n t fo a m (th e ty p e used in a n e c h o ic c h a m b e rs ) in o rd e r to o b ta in th e p rev a ilin g p re s s u re flu c tu a tio n in th e n o rm a l d irec tio n (se e F ig u re 4 ). W e u s e tw o is o la te d m ic ro p h o n es a t th e sa m e tim e: o n e f o r th e referen ce p o in t, w h ic h is th e sa m e as a t the vib ratio n m e a s u re m e n ts ; a n d o n e fo r th e m easu red p o in t.
T h e su c tio n u n it w a s s u p p o rte d in the an ech o ic c h a m b e r in th e sa m e p o s itio n as d u rin g the v ib ra tio n m e a s u re m e n t, a n d d u rin g b o th m e asu rem en ts w e d id n o t c h a n g e a n y p a ra m e te r o f th e u n it’s o p e ra tio n to e n s u re th e sa m e co n d itio n s fo r e v e ry m e a s u re m e n t p o in t. T h e signal d u rin g th e n o is e m e a s u re m e n t w a s pro cessed in th e sa m e w a y as fo r th e v ib ra tio n m easu rem en t. T h e g o a l w a s to c a lc u la te th e F R F b etw een e v e ry m e a s u re d a n d r e fe re n c e p o in t.
F in a lly , w e u s e d n u m e ro u s F R F s o f th e v ib ra tio n a n d th e s o u n d -p re s s u re field fo r p re s e n tin g m o d e s, u s in g th e LM S so ftw are.
2.2 Results of the Experimental Modal
Analysis
2.2.1 Characterization o f the Vibration
W e ca n d e te rm in e th e m a in so u rc e s o f v ib ra tio n s fro m an a m p litu d e a u to -sp e c tru m . W e w ill sh o w th e re p re s e n ta tiv e v ib ra tio n a m p litu d e a u to -s p e c tru m (F ig . 8) on th e c o v e r su rfa c e w ith th e a rb itra ry c h o s e n p o in t 1.3 (m a rk e d in Fig. 5). T h e s p e c tru m c le a rly sh o w s th e d isc re te so u rce s o f th e v ib ra tio n s a t c h a ra c te ris tic fre q u e n c ie s. T h e p o s itio n o f th e d is c re te fre q u e n c ie s in th e sp e c tru m d e p e n d s o n th e o p e ra tin g c o n d itio n s d e s c rib e d a n d e x p la in e d in th e firs t p a ra g ra p h o f S u b se c tio n 2.1. O n th e b a s is o f th is w e are in te re s te d in w h e re a n d w h y th e s e so u rc e s ap p ear.
T h e first in te re s tin g fre q u e n c y ra n g e e x te n d s u p to I k H z , w h e re th e ro ta tio n a l fre q u e n c y f R o f th e e x is tin g su c tio n u n its ca n b e fo u n d . A d is tin c t fre q u e n c y ca n b e fo u n d e x a c tly a t th e ro ta tio n a l fre q u e n c y f R. T h e fo rc e d v ib ra tio n s are c a u s e d b y th e u n b a la n c e d ro to r, an d th e y are tra n s m itte d firs tly to th e c o v e r o v e r th e h o u s in g a n d th e v a n e d d iffu s e r th ro u g h th e b e a rin g s, an d se c o n d ly a t th e b lo w e r ’s in le t ed g e a t th e c o n ta c t w ith th e c o v e r ’s w a sh e r. T h e m a g n itu d e o f the e x c ita tio n a lso d e p e n d s on th e q u a lity a n d th e w e a rin g o u t o f th e b e a rin g s, th e c o n ta c ts , etc. T h e fo rc e d e x c ita tio n a t th e ro ta tio n a l fre q u e n c y ca n b e d e s c rib e d as a m e c h a n ic a l e x c ita tio n .
O th e r d is c re te fre q u e n c ie s o f in te re s t are in ra n g e a b o v e 1 k H z. W e c a n se e in th e a m p litu d e a u to -s p e c tru m in F ig . 8 th a t w e h a v e th re e sig n ific a n t p e a k s , e q u id is ta n t w ith r e s p e c t to th e ro ta tio n a l fre q u e n c y f R u p to 2 0 k H z. T h is is a c o n s e q u e n c e o f th e b la d e p a s s in g fre q u e n c y (B P F ) e ffe c t th a t h a p p e n s w h e n th e ro to r b la d e p a s s e s th e d iffu s e r v a n e [3]. A p a s s re s u lts in air- p re s s u re flu c tu a tio n s . T h e d isc re te fre q u e n c ie s f c a n b e c a lc u la te d as:
f t = n - z - f R n = 1,2,... (1)
b la d es. T h e B P F e ffe c t is a n a e ro d y n a m ic e x c ita tio n o f th e c o v e r ’s v ib ra tio n . T h e p re s s u re flu c tu a tio n s are tra n s m itte d d ire c tly to th e th in w a ll o f th e co v e r, a n d th e s e a re th e p re v a ilin g ex c ita tio n s.
W e c a n also d e s c rib e tw o e x c ita tio n m e c h a n ism s th a t a re s im ila r to th e B P F e ffe c t fo r a d e te rm in a tio n o f th e d isc re te fre q u e n c ie s.
T h e firs t e x c ita tio n h a s an a e ro d y n a m ic o rig in w h e n th e a ir flo w e x its th e d iffu s e r th ro u g h b a c k -flo w c h a n n e ls in th e sp a c e o f th e ro ta te d ro to r. T h e e x c ite d v ib ra tio n d e p e n d s o n th e n u m b e r o f v a n e s o f th e b a c k -flo w c h a n n e ls, w h ic h in o u r c a se is 12. A lso u s in g E q. (1 ), w e ca n e x p la in th e 12th h a rm o n ic p e a k a t 8 6 4 0 H z.
T h e se c o n d e x c ita tio n h a s its s o u rc e in th e c o n ta c t b e tw e e n th e e le c tric -m o to r’s b ru s h e s an d th e c o lle c to r ’s la m ellas. T h is ty p ic a l m e c h a n ic a l ex c ita tio n , d e s c rib e d in [1 1 ], is tra n s m itte d to th e c o v e r o v e r th e v a n e d d iffu se r. U s in g E q . (1) an d c o n s id e rin g th e c o lle c to r ’s 22 la m e lla s w e g e t th e 2 2 nd h a rm o n ic p e a k at 1 5840 H z. B o th th e se e x c ita tio n e ffe c ts h a v e a sig n ific a n t firs t h a rm o n ic , w h ile th e h ig h e r h a rm o n ic s a re n o t
s ig n ific a n t o r are a b o v e 2 0 k H z.
C o n s id e rin g th e d e fin e d v ib ra tio n so u rc e s o n th e c o v e r ’s su rfa c e w e ca n fo c u s o n th e a e ro d y n a m ic e x c ita tio n , e s p e c ia lly th e B P F
e ffe c t, w h ic h ra d ia te s a p re s s u re flu c tu a tio n d ire c tly o n to th e c o v e r ’s in n e r su rfa c e . T he m a g n itu d e s o f th e a e ro d y n a m ic so u rc e s d e p e n d o n th e v ic in ity o f th e d e s ig n p o in t o f o p era tio n . B e c a u s e th e e x p e rim e n t w a s ru n a t o ff-d e sig n p o in t o f o p e ra tio n , th e B P F e ffe c t e x c ita tio n w as m o re e m p h a tic .
2.2.2 Comparison and Findings o f the F E M and Experimental Modes o f the Cover ’s Vibrations
T h e fin a l ste p in th e v ib r a tio n ’s signal p ro c e s s in g w a s to d e fin e th e F R F s b e tw e e n the m e a s u re d p o in ts a n d th e re fe re n c e p o in t to o btain th e e x p e rim e n ta l m o d e s at th e ch a ra c te ristic fre q u e n c ie s d e s c rib e d in S e c tio n 2 .2 .1 so as to c o m p a re th e m w ith th o s e th a t w e re n u m e ric a lly d e fin e d in S e c tio n 1. W h e n w e m a k e co m p ariso n , w e h a v e to a s su m e , th a t th e ex p e rim en tal v ib ra tio n m o d e a t th e s e le c te d fre q u e n c y w ill fo llo w to th e n u m e ric a l v ib ra tio n m o d e a t the fre q u e n c y , w h ic h is th e n e a r e s t to th e selected fre q u e n c y .
W e re s e a rc h e d th e fre q u e n c y ra n g e up to 10 k H z. T h e re a s o n s f o r th is a c tio n are , in p a rtic u la r, th e u n re lia b ility o f m e a su re m e n ts
Ah
cn
frequency [Hz]
above 10 k H z a n d a lo t o f d is tin c tiv e o r in d istin c tiv e m o d e s c lo se to ea c h o th e r at h ig h e r freq u en cies. W e sh o u ld , in fa c t, m e a s u re a v e ry dense m e sh o n th e c o v e r ’s e n tire s u rfa c e , b u t th is is a v e ry tim e -c o n s u m in g ta sk , a n d w h y it is better to m a k e a c o m p a ris o n at th e firs t few ex c ita tio n fre q u e n c ie s. ___
T h e firs t c o m p a ris o n o f th e m o d e s w a s m ade at th e ro ta tio n a l fre q u e n c y / « = 7 2 0 H z. T h e e x p e rim en tal m o d e is p r e s e n te d in F ig . 9. W e ca n co m p are th is w ith th e n e a r e s t n u m e ric a l m o d e , w hich is su rp ris in g ly a t fre q u e n c y 2 2 8 4 H z, p rese n ted in F ig . 1. T h e re s u lt is v isu a l acco rd an ce.
T h e m o d e s b e c o m e m o re c o m p le x w ith fre q u en c ies h ig h e r th a n th e ro ta tio n a l fre q u e n c y f O n e p a rt o f th e e x p e rim e n ta l m o d e is rep re se n te d in F ig . 10 f o r th e B P F ( a t 6 4 8 0 H z). Its o rie n ta tio n ca n b e se e n fro m F ig s. 5 a n d 7. T h e e x p e rim en tal m o d e in F ig . 10 s h o u ld b e c o m p a re d w ith th e n u m e ric a l m o d e a t th e n e a re s t fre q u e n c y 6533 H z, s h o w n in F ig . 2. T h e re is a c c o rd a n c e in the m o d e , e s p e c ia lly o n th e c o v e r ’s u p p e r su rfa c e , w here w e ca n fin d o n e p e a k a n d o n e tr o u g h in th e radial d ire c tio n o n 1/6 o f th e c o v e r ’s circ u m feren c e.
T h e F E M a n a ly s is w a s sa tis fa c to ry an d u seful, e s p e c ia lly in th e lo w e r fre q u e n c y ra n g e a t the first fe w e ig e n fre q u e n c ie s fo r d e te rm in in g th e v ib ratio n m o d e s, b e c a u s e th e y are su ffic ie n tly distinct. W e ca n , h o w e v e r, e n c o u n te r p ro b le m s even w h e n w e a re a ro u n d B P F , w h ic h s h o u ld b e as low as p o ss ib le . A s m e n tio n e d in S e c tio n 1, w e can n o t c o n s id e r th e e x c ita tio n m e c h a n is m s in th e FEM an a ly sis. In th e h ig h e r fre q u e n c y ra n g e th e e x p e rim en tal m o d e s a re s u p p o s e d to fo llo w to th e shapes o f th e n e a r e s t n u m e ric a l m o d e s. It is h a rd to d e te rm in e e x p e rim e n ta l m o d e c o n s id e rin g nu m ero u s n u m e ric a l m o d e s. O n th e b a s is o f th is p resu m p tio n w e c a n a p p ly th e F E M a n a ly s is in the v isu a l p re d ic tio n s o f n e w p r o d u c ts .
2.2.3 Analysis and Findings o f the Experimental Modes o f the C over’s Vibrations and the Noise at the Cover ’s Surface
W ith th e d e s c rib e d m e a s u re m e n t p ro ced u re in S u b s e c tio n 2.1 w e g e t th e S P L sp ectru m a n d th e F R F s f o r th e s o u n d -p re s s u re field at th e c o v e r ’s su rfa ce .
A S P L s p e c tru m fo r th e a rb itra ry p o in t 1.3 is p re s e n te d in F ig . 8. It is o b v io u s th a t th e S P L s p e c tru m h a s d is c re te to n e s at th e sa m e fre q u e n c ie s as th e v ib ra tio n s p e c tru m . T h is is lo g ic a l b e c a u s e th e o rig in s o f th e n o is e a n d th e c o v e r ’s v ib ra tio n a re r e la te d to ea c h o th e r. F ro m th e S P L sp e c tru m w e ca n see th a t th e a irb o rn e s o u n d p re v a ils. T h e m o s t im p o rta n t p a rt o f th e to ta l S P L is c o n trib u te d e s p e c ia lly b y th e B P F , a t 6 4 8 4 H z. W e c a n n o t also ig n o re th e c o n trib u tio n o f th e 12th h a rm o n ic o f th e ro ta tio n a l fre q u e n c y f R, b e c a u s e o f th e a ir o u tle t fro m th e b a c k -flo w c h a n n els. T h e c o n trib u tio n o f th e m e c h a n ic a l n o ise is v is ib le m o stly at th e ro ta tio n a l fre q u e n c y f R. F ro m th e S P L s p e c tru m w e c a n n o t d e te rm in e th e sh a re o f th e s tru c tu ra l n o is e , ev e n i f th e re is so m e re la tio n to th e c o v e r ’s s tru c tu ra l n o ise.
T h e n e x t ste p is th e c o m p a ris o n b e tw e e n th e c o v e r ’s e x p e rim e n ta l v ib ra tio n m o d e s a n d th e s o u n d -p re s s u re m o d e s at th e c o v e r ’s su rfa ce . M o d e s at F ig . 9 a n d 10 w e re d e fin e d w ith c a lc u la tio n o f F R F o f all m e a s u re d p o in ts. T h e re s e a rc h is lim ite d to th e lo w e r fre q u e n c y ra n g e , u p to 10 k H z.
F ig . 9 p re s e n ts a c o m p a ris o n o f th e m o d e s a ro u n d th e ro ta tio n a l fre q u e n c y f R=7 2 0 H z. W e c a n se e th a t th e re is n o a c c o rd a n c e b e tw e e n th e se m o d e s. T h e s o u n d -p re s s u re m o d e h a s n o e x p re s s iv e sh a p e, d e s p ite th e firs t c h a ra c te ris tic fre q u e n c y . W e h a v e tw o e x p la n a tio n s for: firstly , th e re is n o s u ffic ie n tly h ig h m a g n itu d e o f v ib ra tio n a t th is fre q u e n c y ; s e c o n d ly , th e m e c h a n ic a l e x c ita tio n o f th e so u n d p re s s u re by ro to r a t ro ta tio n a l fre q u e n c y f R=7 2 0 H z, tra n s fe rre d to th e c o v e r th ro u g h th e h o u sin g , v a n e d d iffu s e r a n d p a r tia lly b lo w e r, h a p p e n s u n d e r c ritic a l fre q u e n c y , i f w e s u p p o s e th e o ry a b o u t so u n d p re s s u re flu c tu a tio n at in fin ite p la te c a u s e d b y m e c h a n ic a l e x c ita tio n o f th is p la te [10]. C ritic a l fre q u e n c y d e p e n d s o n so u n d v e lo c ity in air, b e n d in g w a v e v e lo c ity in p la te a n d o n p la te ’s th ic k n e s s.
F ig . 9. Vibration mode (below) and sound-pressure mode (above) at the rotational frequency f g —715 Hz
fo u n d in a s ta te m e n t th a t is th e o p p o site o f th a t in
th e p re v io u s p a ra g ra p h : firs tly , th e m a g n itu d e o f
th e v ib ra tio n s at th e B P F c o u ld b e h ig h e n o u g h to
e x c ite th e s o u n d -p re s s u re flu c tu a tio n s ; an d ,
se c o n d ly , th e e x c ita tio n fre q u e n c y in th e c o v e r ’s
w a ll is a b o v e th e lim it fre q u e n c y , w h ic h e x c ite s
th e so u n d p re ssu re . W e c a n n o t also n e g le c t th e
fa c t th a t th e s o u n d -p re s s u re flu c tu a tio n a t th e
u p p e r su rfa c e o f th e c o v e r c o u ld b e a
c o n s e q u e n c e o f th e tra n s fe rre d s o u n d flu c tu a tio n s
th ro u g h th e c o v e r ’s w a ll [10].
T h e in c re a s e d in flu e n c e o f th e B P F e ffe c t
a t its firs t fre q u e n c y p r o v e d to b e th e m o st
im p o rta n t s o u rc e o f th e su c tio n u n it’s n o ise , w ith
a m a jo r c o n trib u tio n to th e c o v e r ’s v ib ra tio n s a n d
th e c o v e r ’s stru c tu ra l n o is e in th e fre q u e n c y ra n g e
u p to 10 k H z . In g e n e ra l, w e h a v e to c o m b in e it
w ith th e a e ro d y n a m ic o rig in o f th e s o u n d , w h o s e
sid e p ro d u c t is also th e stru c tu ra l s o u n d . W e
c a n n o t fin d a re la tio n b e tw e e n th e m e c h a n ic a lly
e x c ite d v ib ra tio n s a n d th e stru c tu ra l n o is e , o r th is
e ffe c t is u n tr a c e a b le u s in g th e d e s c rib e d
m e a s u re m e n t m e th o d .
F ig . 10. Vibration mode (below) and sound-pressure mode (above) at the B P F frequency
f= 6503 Hz, partial view
3 C O N C L U S IO N
T h is p a p e r a v o id s c o m p lic a te d and u n c e rta in a n a ly tic a l e x p re s s io n s fo r d e term in in g th e v ib ra tio n s e x c ite d in a su c tio n u n it’s cover. W ith a n e x p e rim e n ta l m o d a l a n a ly s is o f the c o v e r ’s v ib ra tio n s u n d e r fre e d e liv e ry o p eratin g c o n d itio n s w e fo u n d th e m a in so u rc e s o f v ib ra tio n s th a t h a v e a n a e ro d y n a m ic or m e c h a n ic a l o rig in , w h e re th e a e ro d y n a m ic BPF e ffe c t is th e p re v a ilin g e x c ita tio n . T h e B P F effect d e p e n d s o n th e o p e ra tin g c o n d itio n s a n d the g e o m e try o f th e sta tic a n d r o ta tin g p a rts o f the su c tio n u n it. T h e s m a lle s t e ffe c t is a t d e s ig n p o int o f o p e ra tio n . T h e d e s ig n o f th e s u c tio n unit s h o u ld te n d to r e d u c e th e B P F effec t.
A n e x a c t r e la tio n b e tw e e n th e c o v e r ’s v ib ratio n s a n d th e stru c tu ra l n o is e is h a rd to d iffe ren tia te d u rin g th e o p e ra tio n o f th e s u c tio n unit. W ith a c o m p a ris o n o f th e v ib r a tio n ’s m o d e s and th e so u n d -p re s s u re flu c tu a tio n ’s m o d e s a b o v e the c o v e r w e fo u n d a c c o rd a n c e b e tw e e n th e m odes at th e B P F (6 4 8 0 H z). T h e n u m e ric a l an d e x p e rim en tal re su lts a ro u n d th is fre q u e n c y a n d its m ode can h e lp u s p re p a re a n e w c o v e r sh a p e, a c co rd in g to th e m a in v ib ra tio n a n d th e n o ise ex citatio n s. T h e c o v e r w o u ld b e tte r r e s is t th e v ib ra tio n e x c ita tio n w ith an in c re a s e d b e n d in g stiffness. T h e p a ra m e tric a l c o v e r m o d e l is su g g ested fo r a la te r p a ra m e tric a l o p tim iz a tio n .
4 A C K N O W L E D G E M E N T S
T h e a u th o rs w o u ld lik e to th a n k th e D o m el d.d fo r h e lp a n d s u p p o rt w ith th e e x p e rim e n t.
5 R E F E R E N C E S
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