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)i!rations of an *mpe%%er

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+a"&grond and Moti'ation

•  his app%i"ation stdies sma%%amp%itde free and for"ed 'i!rations

of an impe%%er.•  he app%i"ation sho$ ho$ to ma&e

se of the dynami" "y"%i" symmetry

"onditions $hen ana%y-ingrotationa%%y periodi" str"tres.

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ro!%em /e#nition

•  he impe%%er is madeof a%minm, and it isspposed to !e

monted on a shaft•  he monting

!ondary is mode%ed'ia a #xed "onstraint

• A%% possi!%e ee"ts ofthe shaft rotation areneg%e"ted

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ro!%em /e#nition, symmetry

•  he impe%%er haseight identi"a%!%ades

•  he geometry "an!e di'ided into eightidenti"a% parts, ea"h

represented !y ase"tor $ith an ang%eof π(

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ro!%em /e#nition, ana%yses

• igenfreqen"y and 3reqen"y ana%yses areperformed on a nit se"tor geometry $ith Cy"%i"symmetry "onditions app%ied on the periodi"ity

!ondaries• Cy"%i" symmetry is an option a'ai%a!%e $ithin the

eriodi" Conditions featre nder So%id Me"hani"sphysi"s interfa"e in COMSOL M%tiphysi"s

•

*n order to "ompare the res%ts and performan"e,the same type of stdies a%so performed on the$ho%e geometry.

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4es%ts, eigenfreqen"y

• *n order to se the Cy"%i" symmetry "onditionsnder an igenfreqen"y stdy, yo need toperform a parametri" s$eep $ith respe"t to the

a-imtha% mode nm!er from -ero to N(2 $hereN is the tota% nm!er of se"tors.

•  he eigenfreqen"y 'a%es and eigenmodes"ompted on a nit se"tor of the impe%%er are in

perfe"t agreement $ith those "ompted on the$ho%e geometry.

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4es%ts, freqen"y domain he #gres !e%o$ sho$ the tota% disp%a"ement at ex"itation freqen"yof 200 -.

 he %eft one sho$s the res%t "ompted on the f%% geometry. *n theright #gre, the res%ts "ompted on the nit se"tor are 'isa%i-ed o'er

the $ho%e geometry 'ia a se"tor data set.

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Con"%sions

•  he res%ts o!tained sing a nit se"tor are in'ery good agreement $ith that "ompted onthe f%% geometry of the impe%%er. +oth the

"omptationa% time and memory reqirementsare signi#"ant%y red"ed $hen sing a nitse"tor geometry.

• Cy"%i" symmetry "onditions a%%o$ to e6"ient%y

perform !oth eigenfreqen"y and freqen"yresponse ana%yses !y sing a nit se"torgeometry for a rotationa%%y periodi" str"tre.