Shell Stiffness for Diffe ent Modes

Transcription

1 Engneerng Mem N 28 February SUGGESTONS FOR THE DEFORMABLE SUBREFLECTOR Sebastan vn Herner Observatns wth the present expermental versn (Engneerng Dv nternal Reprt 09 July 978) have shwn that a defrmable subreflectr can ndeed crrect the gravtatnal astgmatc defrmatn f the mal reflectr t a gd degree At 20 elevatn suth and east the effcency at A = 345 cm was already ncreased by mre than a factr f tw n spte f the lmted defrmatn range f the present versn and enlargng ths range wuld be desrable Hwever the ther three pssble mdes f defrmatn dd nt gve sgnfcant changes f effcency but we d nt knw at present whether r nt the reflectr shell actually dd defrm by suffcent amunts n these ther mdes The present MEMO treats three tems Frst we suggest measurng the shell stffness fr all fur pssble mdes f defrmatn Secnd we defne a desrable range fr the astgmatc defrmatn Thrd regardng sme planned new feed lcatns n the Cassegran twer we calculate the effcency as a functn f feed lcatn suggestng rather narrw lmts fr the latter Hw much f all these suggestns s actually feasble wll then depend n the avalable mney manpwer and tme Shell Stffness fr Dffe ent Mdes Fgure defnes and descrbes the fur mdes f defrmatn whch are pssble wth fur actuatrs t s mmedately clear than an pen segment f a curved shell s much sfter aganst an astgmatc defrmatn than aganst any ther knd Frm the fur mdes f Fgure the shell wll be stffest

2 aganst Mde 2 but ths als seems t be the least mprtant ne Regardng the strng EW defrmatns bserved n Reprt 09 (Fg 2-5) t culd well be that Mde 4 s mprtant enugh fr applcatn and maybe als Mde 3 fr sme smaller nn-astgmatc NS defrmatn t thus seems wrthwhle t nvestgate these pssbltes The prper prcedure seems frst t measure the stffness n terms f klgram f frce as appled t the shell at the actuatng pnts dvded by the resultng ampltude f the rm defrmatn n mllmeter Ths shuld be dne fr each f the fur mdes separately Secnd we must defne a desred range fr these ampltudes The astgmatc mde wll be treated n the fllwng sectn Fr the ther three mdes we need enugh defrmatn t measure a sgnfcant change f the effcency fr the better r wrse; and thnk the desred range shuld be at least 3 mm say fr the rm ampltude whch wuld gve abut mm rms ver the whle surface wth 5 db taper Thrd we need sme estmate r guess f hw much frce the shell surface can take wthut breakng r beng pulled apart Ths lmtng frce dvded by the stffness f a mde gves a safety range fr the rm ampltude f ths mde Furth f ths safety range s much smaller than the desred range fr sme mde then ths mde cannt be used Ffth fr each f the remanng usable mdes we fnd the needed frce (desred r safety whchever s smaller) and the next questn s whether r nt we fnd mtrs whch delver these frces wth the requred accuracy (< 02 mm say) fr a reasnable prce Prevus measurements f the subreflectr shape have been dne alng 24 rad wth 6 pnts per radus (ttal f 45 pnts) f pssble regardng manpwer t wuld be gd t d t nw the same way sx tmes: frst wth the undefrmed surface then nce fr each f the fur mdes usng just the

3 maxmum frce (r maxmum travel whchever cmes frst) f ur present mtrs and fnally an undefrmed case agan n addtn t the value fr the stffness ne wuld lke t btan f pssble a cmplete cntur map fr each defrmatn mde Furthermre n each mde a small number f pnts shuld be measured wth varus dfferent frces as a check fr lnearty and acluracy As a measure f the frce appled t the actuatng pnts t seems best t use the vltage suppled t the mtrs Ths wuld need a calbratn frst n kg/vlt Desred Astgmatc Range We wrte the astgmatc defrmatn as A r 2 cs(20) () where r = at the rm Q = 0 nrth and where the rm ampltude A depends nly n elevatn 3 as A(3) = -A + ( - sn f3) B (2) The tw cnstants have been measured n 977 wth an elngated feed hrn as A = 72 mm and B = 870 mm Wth these values A(3) has been pltted n Fgure 2 tgether wth the ar mass M(3) = lsn Hw clse t hrzn shuld we be able t crrect the astgmatsm? Because f the steep ncrease f the ar mass bservatns at shrt wavelengths wll seldm g belw 5 elevatn (but ccasnally dwn t 0 0 fr spectrum lnes f suthern surces) As explaned n Fgure 2 we suggest t specfy 0 = 5 but t add a safety margn f S = 3 mm yeldng a desred range f -30 mm < A < +60 mm

4 amw The subreflectr culd then be used fr a feed at the desgn lcatn and at a secnd lcatn rtated abut the vertex by 80 0 t s better hwever t prvde tw mre lcatns at 90 0 and whch needs equal range fr bth sgns The desred astgmatc range then s -60 mm < A < +60 mm (3) Ths s the desred range fr the rm ampltude The frced defrmatn at the actuated pnts s less because they are further n but the travel range f the mtrs must be larger because the backup frame has sme flexblty As cmpared t ur present range -044 mm < A < +8 mm we have the fllwng desred mprvement factrs fr the astgmatc mde (the ther mdes may need mre frce): frce factr = 60/8 = 33 range factr = (604-60)/(84-044) 533 Feed Lcatn and Effcency The desgn lcatn f the feed s (f) = 225 * nrth f west fr ur present subreflectr see Fgure 3 f sme ther angle (f) s chsen the subreflectr must be rtated by 4 = ()-4) abut the telescpe axs ts stff dagnal and ts actuatrs then are set ff frm ther prper place by 4 whch degrades the astgmatc crrectn Ths degradatn has been calculated and the fllwng gves nly the results wthut dervatns f A s the astgmatc rm ampltude f the man reflectr and cp s the feed angle n Fgure 3 then the best defrmatn ampltude fr the subreflectr a s nt any mre equal t A but smaller and a least-squares treatment gves a = A cs 2(4)-4) 0 ) (6)

5 Usng ths best ampltude the remanng resdual averaged ver the whle surface and wth 5 db taper s Az = ms ) 0329 A sn 2(4-4)0) (7) a (Azastgm We add quadratcally the rms surface errr Az wthut gravtatnal defrmatn and btan the ttal surface errr The aperture effcency then s (wth n fr A c) = /A 2 + A a (8) T = n -(47rAz/A) 2 e (9) Fgure 3 was calculated wth A = 400 mm fr = 20 elevatn assumng Az = 20 mm and n = 60% We see that the fur maxma are mre narrw than the rather deep and wde mnma The maxmum effcency n ths calculated example s n max = 7%; f we d nt want t lse much say n > 57 then the feed lcatn must be n the range () = (f) Acp wth = 84 * fr f3 = 20 * elevatn Acp 7 =l5 (0) = 6 = 0

6 t ; ; 4 _4 r " - -- r t - -"" " - ---f : L _f _ 4 r C - -! _ - ; t f - t t!! Subreflectr fur mdes f defrmatn Mde N a defrmatns b c d descrptn / 3 y 4 4- astgmatsm Az cs(2q) next erder Az c 0 cs(4) + " 0 0 vertval shft f half-beam / hrzntal shft f half-beam

7 t ; * : --:4 " --- lt " "! c - t0 - _ :2 -- : T ll t r _ -_ kk r t TT; : " :: : r s s ss s ss s s s s ` 4r *; 7 l --s :t _ : : : : : : : ; r : : 40 : : Y: : /? : - f : ; :: ::!-:: et et3r 7: -- : -477-: :-----:-:-t - : ":::: t:::::: = desgn lcatn f feed center n Cassegran twer 0 equally gd pnts = R 4/ Ch = T04 M Aperture effcency as a functn f the feed lcatn angle y; wth and wthut (-- --*-- ) subreflectr defrmatn c Calculated fr elevatn p = 20 and wth 6 db llumnatn taper f the rm defrmatn f the subreflectr can be made equally large fr bth sgns 60 4 A 4: +60 MM then there are fur equally gd lcatns