Purdue University

Purdue e-Pubs International Compressor Engineering Conference

School of Mechanical Engineering

1980

Analytical Model of an Oil-Free Screw Compressor J. Brablik

Follow this and additional works at: http://docs.lib.purdue.edu/icec Brablik, J., "Analytical Model of an Oil-Free Screw Compressor" (1980). International Compressor Engineering Conference. Paper 418. http://docs.lib.purdue.edu/icec/418

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FRE E SCR EW COM PRE SSO R ANA LYT ICAL MOD EL OF AN OIL-

Jose f Brab lik,

Com press or Divi sion

CKD Prah a , Prag ue ,

Czec hoslo vakia

ABS TRA CT fican t The use of analy tical mode lling is a signi rese arch in costs ntal rime expe way in redu cing of of an oiland deve lopm ent. An analy tical mode l used to and ribed desc is sor pres com free screw ressi on comp d, spee ion rotat study the effec ts of rnal pres • loss es and diffe renc e of built -in and exte influ enThe ess. proc on ressi comp on sure ratio g upon ce of gas pulsa tion in the disch arge pipin sor is pres the work ing proc ess of the screw com inclu ded. INTR ODU CTIO N art analy With the deve lopm ent of the comp uter in an ever tical mode ls are asse rting them selve s rime nts expe y costl them By ure. meas incre asing posing Amo t. exten in certa a to can be repla ced lling tive displ acem ent com pres sors the mode on retechn ique has been most high ly deve loped.stan cipro catin g com pres sors. Thei r pres ent on and dard perm its the cour se of the comp ressi sivel y the motio n of the valv es to be comp rehen piected conn the of t effec the treat ed and also calcu laping to be inclu ded, Depe nden ces thus tion of ted are usua lly the basi s for optim aliza . ment the plann ed equip mode lling The good expe rienc es gaine d from the incen the were sors pres com ting roca recip of l of an tive for the crea tion of a simi lar modeept of the oil-f ree screw com pres sor. The conc comanaly tical mode l corre spon ds to screwpress or pres sors whic h the CKD Prah a, Com , has been manu factu rlng alrea dy Divi sion ce of for a numb er of year s (Fig .l) in the licen r acSVE NSK A ROT OR MAS KINE R A. B. Thei each tive parts are two roto rs enga ging with hroothe r the mutu al rotat ion of whic h is sync ther nized by a set of gear s. The roto rs, toge d paire four form , shell sor pres com with the The cham bers whic h are the work ing spac es. arge cycle of sucti on, comp ressi on and disch with take s its cour se, with these cham bers, a revo a phas e displ acem ent of one quar ter of onic comlutio n and caus es that the fourt h harm ency , frequ ber cham as also to rred pone nt, refe and trum spec noise the mani fests itsel f in both way. t fican signi a in tion vibra the

by the Disc ount ing the poss ibili ty that vibra tion act of cont by ed caus be may ency cham ber frequ quic the roto rs - such a case woul d lead very caus e able prob most the down break a to kly pipin g. of vibra tion is pulsa tion in the disch arge leve l its sors pres com n Simi larly as· with pisto g and will depe nd· on the dime nsion s of the pipinthe by ted aifec edly mark be , over will, more the dispres sure in the cham ber at the mom ent well char ge port is open ed. Thes e facts are ed maprov y ntall rime expe been have and n know ny time s. ver, very Expe rime ntal rese arch beco mes, howe um optim an find to rs avou ende one costl y when gia for s ition cond 1ting oper1 desig n or optim um e this ven case . A suita ble mean s to ratio naliz ever, it is work is the mode lling techn ique . How be procan l mode tical analy an only rare ly that ence s duce d whic h take s all subs tanti al influ ces can into acco unt. Only some of the depe nden h the be studi ed, depe ndin g on the purp ose whic whic h aifec t mode l is inten ded to serv e, all othe rs ler measmal a in on rvati obse r unde ess proc the ed. gard sure being disre comp re-The prop osed analy tical mode l of a screwthe worrving obse of aim the with built sor was nctio n king proc ess of the comp ressi on in conju arge piwith the dyna mic proc esse s in the dischof the sucr ping . The relat ively unifo rm beha viou its smal l also thus and sor pres com tion of a screw on pisucti the in gas the of effec t on the dyna mics phen omen a ping were the reas on why the dyna mic d. in the sucti on pipin g were not cons idere pres sor Fig. 2 show s the diag ram of a screw coma noise with a disch arge pipin g whic h lead s into the indil damp er. The diag ram repr esen ts a mode desc rily vidu al part s of whic h will be analy tical bed below . COM PRE SSIO N SPA CE paire d The comp ressi on spac e cons ists of four disp laally mutu is h whic of 1 actio6 cham bers the e of ced in phas e by 90 . A chan ge of the volum by mean s one paire d cham ber can be expr esse d al work ing of the mode l show n in Fig. 3. The actu equa l voan by ced repla is spac e of the cham ber whic h a lume in the shap e of an obliq ue prism in ing work the of e volum The ng. movi parti tion is

356

space determine d in th1s way changes from Ot.t to oc. It and its change is protted against angle ol , also in Fig. 3. With screw compress ors the compress ion process is affected by untightne sses to such an extent that, for purposes of the calculatio n of the compression, it cannot be disregard ed. The calculation is made by steps and one calculatin g step correspon ds to time interval Lit in which the main rotor turns through angle L1 0(. Thus

td;;: ~01.

The volume quantity of gas which escapes from the chamber to the suction space in time interval L1 f is determine d by the relation I

t1 Uj

= ( 'ls ~s) at· A-M

where

A=

~of

2 :, R

r at-(] rt·lt-e'sp;s )~

The resultant pressure in the chamber in the course of the compress ion will be, after the main motor has turned through angle t1 ex and after time Lit

p.

_ p. ( t

t+f .-

Vi= f(cx.,j and Ll Vi

where

o