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(1)

Tabellen voor tandwielen : berekening van de geometrische

afmetingen van tandwieloverbrengingen met een gering

aantal tanden

Citation for published version (APA):

Cuypers, M. H., Kymmell, G. R. W., & Verduin, M. (1968). Tabellen voor tandwielen : berekening van de

geometrische afmetingen van tandwieloverbrengingen met een gering aantal tanden. Technische Hogeschool

Eindhoven.

Document status and date:

Gepubliceerd: 01/01/1968

Document Version:

Uitgevers PDF, ook bekend als Version of Record

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(2)

I

I

Berekening van de geometrische afmetingen van tandwieloverbrengingen

met een gering aantal tanden

Afdeling Werktuigbouwkunde

Sectie Kleine werktuigen

(3)

....

~- '

• i.

VoorwOord

OYerzicht

Resuml der gebruikte

fozanlea

Tabelt gebzuikte symbolen in de

foxma.lea

met

bijbehorende Algol-notatie

.l:tglll~:nke!Îp:rograma

Tabellen

· Bl.s.a

---·

. '•,·n,

n

ID:

VII

XI

'XIII

~: .

. 001.002

003+221

. I ·'."-. ·>·

(4)

De toepassing van tudwielen Mt kleine tandaantallen 'bi3 P'Ot& ove:rbreDg'Verhoudingen

~,.,.,JIIIifüTOordelen."

De

beekening

Van

de afmetingen

van

deze tandwielen

s:t:~n

echter

nop.l.

pooçliceerd

en

dit

werkt

rellilend op

a.

toepaasina enan.

In

dit boek is flèn reeks tabellen opgenomen voor een beperkt aantal overb:rengingen met veraclrllleDle

t&lld-·- .. , •' . -· .

hoekan en verschillende

kopho~etaotor&n

van het· theoretisch heuplprotiel en geldend voor taa.claantallen'·"

van

het rondsel

van

1

tot

1

o.

De wer.k:tekeniag gesevens voor de

~wielen

kwmen aan ie

hand

van de tabellen gemakkelijk bepaald worden.

Het. :rekeJJProg:r.'IUilm&, cJ.a.t

aan

deze tabellen ten gmndsl.ag

li~'.

ia vitgevoerd op

cle

Eleotroloc:toa-CODlpUter_

ELX-8

van

de atdeliDg willltumle der 'feolm:f.aohe Hogesehoool Ein4hoTen.

Ei.Ddhoven,

Mi

1968,

ir.

I.R.

CuJpers ·'· '

ir.

a..:s..w.

~11

x.

Veft.tdn.

";·

,.t ...

(5)

Overzicht

; De tabellen en formules zijn opgesteld voor de normaalmodulus m • 1 mm.

"

/

·.

n

De

factoren:

~~

:x:

1

,

À

en rk

1

van het :n:>ndsel

.

en

~,

•v en rkl van het wiel

behoeven dus slechts met de gewenste moduul vennÉmigvuldigd te worden om de juiste afmetingen te verkrijgen.

'

• :In

IEJi'16g9~;is

·de: ·khphoogtefactor

~

van het theoretisch heugelprofiel gelijk

aan

1.

Illar in de fijnmechanische techniek reeds andere waamen toegepast worden zijn de tabellen opgesteld voor

~

- 1.

blz.

ooo; .

tjm

0072

~

• 1,1

blz. 007; t/m 0742

~--

1,2

blz. 014; t/m 0212.

De drukhoek is

voor

alle gevallen&

«· -

2tf.

• Om

een voldoende doorgangsquotient

(= profielingrijpquotient

+

overlappingsquotient) te verkrijgen, worden

scmdne tanden toegepast.

De tandhoeken vs.rilren

van

10° tot 40° opklimmend met 5°, n.l.:.

0 . 0

p - ••...

o.

0

10

15°

20°

25°

'500

35°

40°

p • •••••••

zadialen

0

0,1745;

0,26179

0,34906

0,436;;

o,52;6o

0,61086

o,69e1;.

I I I

(6)

• Het tandental' 'Vàn het zondsel varieert van:

.

.

iit •

1 t/m 10 opklimmend met 1 tand.

Het tandental ván het

wiel

varieert vans

•a •

6

t/m.

34

opklimmend met 1 tand

ea -

36

t/m.

6o

"

"

2 tanden

•a - 72 t/m. 120

"

n

12 tanden

i

3

150 t/m 270 "

"

30

taiuten.

Voor •a als heugel is gerekend met

z

1

· •

1.000.000

t~en.

I •

• De BJ.'Ootte van de pro.fielverschuivings.faotoren x

1

en x

2

zi~n

de theo:retische minimale waa.l.'den zodanig,

dat net geen ondersnijding optreedt bij .fabricage met een steekheugel, zie punt

3

blz.

:vz:r

en

pun:~

8 blz. VIII.

Daar

het tandental van het rondsel klein is wordt in practisch alle gevallen een positieve

pro.fielverschui-v.l.ngs.faotor gevonden. Alleen

voor~ • 1 en voor grote tandhoeken

p

0

35

en 40c en tandaantallen z

1

9

en

10 vind.t men een negatieve pro.fielverschuivings.factor x • Het is raadzaam voor deze vier gevallen de rond-

.

.

.

1

sel&tm.etingen;· de asa.fstand en de inschuiffaotor opnieuw te

berekene~

voor een pro.fielverschuivings.factor

x -

1

o.

. :

De

ld.nimale

p1'().fi~lverschuivings.faotor

xa is vooral voor de

~1;ere

tandaantallen za negatief.

Daar

wielen met negatieve profielverschuiving buiten beschouwing blijven is in dat geval bij de berekening

de profielverscbuivingstactor x • 0 gesteld.

.

2

..

(7)

• Een

negatieve waarde voor de lmpverkdlrtingsfactor

(A.<())

betekent, dat de tanden spits zouden worden

buiten de cirkel met straal:

z

+h.

+

rkt •

2cosp

-x

x1.

'

0

De

st:raal

van de kopcilkel

van

het rondsel wordt dan de RIC1-waarde uit de tabel venn:indèrt met de u-waarde

behorende

bij

het tandental

z

2

waarmee het rondsel

samenwerkt, zie fig.1.

\ <

0

· A.

ia negatief

u-fig.

1.

In

dit

geval

worden de tanden niet spits.

Bij

een

positie'!e waarde van

A.

(A.~~)

kunnen

de tanden wel, spits worden binnen de

cirkel~met

-st:raata·

1kt ' •

2

cos

z

p

0

+ \:

+

x1 •

Er kiDmen

zich

m. twee gevallen voordoen&

À>O

(8)

a.

De kopvertandi:ngsfaetor ).. is kleiner

dan

de ··

inscbuiffaotor u

1<u

I

tig.

2.

l

rk

1

" •

werkelijke waarde voor de

kopcirkel-atraal vóor

~

=

~.

1ia

n -

m-wa.a:rae uit tabel

~(u

-: )..) •

De

tanden worden niet spits •

u

--~

... · ..

.'"'.''b•:~~De

kopvertandingsfaotor

k'·,i~t:~glfoter··.daii.~:de

inschuiffaotor u

A>u

In dit geval is de kopcirkelstraal van het rondsel

gelijk aan de RK1-wà&:rde uit de tabellen.

u

tig.

3.

I

·De ·tanden worden spits.

·I

• In

de

RX2-waarde is de u-waarde reeds verwerkt, zodat de kopcirlèelstraal van het wiel direkt ontleend

kan

worden aan

de tabel waarde. - .::

• De a;ymbolen

in

de tabellen zijn dezelfde als d:ie voor het Algol-progr&lJ1Ila gebruiktJ met behulp van de

(9)

Resum' der

~ebruikte

formules

1. Bepaling drukhoek op de steekcirkel gemeten in het vlak

!

op de ashartlijna

tan

u

tan «a •

cos~

ft

o

.• o

.

0

tan·

.

:« •

:.o

tan

20 •

2. Bepaling tandhoek op l:asiscil'kel:

tanp:b • tan:

p •

eos-:

111 •:

a..

--O

a

~· Bepaling van de minimale profielverséhuivingsfactór

van

het· rondsel zodanig dat geen ondersn:ljding

op-treedt b,ij fabricage met een steekheugels

· z s i n

2

• ·

·

t •

""a

~

• 1;c -

2.cos

A •

.

"'o

4.

Bepaling van de kopverkortingsfactor

À

van het rondsel· tengevolge

van oversnijding:

zmn

rk •

2

oosp

+

~

mn

+

z~1mn

.

0

~:n

cosua.

re • 2 oosp •coa«

8

.

0

~"

tig.

'

VII

(10)

5.

Bepaling

'V8.n

de kopcirkel

'V8.n

het roiulself er zijn 2 mogelijkheden:

iDdien

A.'>

01

L.::5.snil14ien~A. <

01

kOJoir.kelstraal roD4selt

kopcirkelstraal rondsel:

··

.· · • •n . ·

. ·

·.

. ·

.

·

•1mn ·

.

. rkt • 2. oos(3

0

+

~

•n

+

x1mn- 1a.n

rk . • 2 oos(3

0

+

~

mn

+ :r:,mii

7•

Bepaling van het virtuele Îand.4pnaanta1 van het. rondsela

·.. ,

• - .

t

Tl

4)0&

2

f3t,.

008(30

. . ' . . . .

. e.

Bepaling

van

de miniuale profielversoluivingsfactor

van

het wiel zodanig dat geen ondersnijding optreedt

bi3 fabricage met een 1teekheugel1

.

.

. •a•aiD

«a

· ·

~

~

-

2 oos(3

0

.

.

.

l:Ddien

·Za

c 0: is, wordt verder

aa~om.en

:r:

2

Ot tandwielen met negatievE! profielverschuiving worden

1:r.:t5.

1Diten besohourine platen.

·

9.

Jepaling

van

de bedr:L3fsc1ruk:boek in het transversale vlak bij spelingsvr:l.je ingrijpinga:· ._,

·.·.~

indien x

2

c

Oa

%1 •

2tan«

0

.

evcz .•

+w«

(11)

10 ..

Bepaling van de basiscirkel van het wiela:

z2•mu•coscr:a

rba •

2

cos

~

0

11.

Bepaling van de hartafstand bij spelingavrije ingrijpinga

, rb1

+

rb2

"

• cos

a;

&V

12. Bepaling

van

de asverschuivit1gsfactora

z1+

z2

. 7 •

av -

2

cos~

mn•

.

0

.

1,. Bepaling van de insclmiffactort

indien

:z

2

>

0

u .

%1

+

~

- 7

14. Bepaling

van

de kopcirkelstraal

van

het wiela

•amn

r.

+

lt.

+

:z

-

u.m •

·fl::

'>•

k2

2oos~

0

'"'"k:~:~

2mu .

n

..

indien

~"C

0

u .

%1 -

7•

Dt

(12)

c • (e

1

+

e

2 )

cosf3

0

·

..coe«&Jna

Bierbij is&

e1 •

1

rk1 2 ... rb12'- rb1.tan

uav

en

,I

2

2'

e2 • ., rk2 - rb2 ·- rb

2

tan «av•

16.

Bepaling van het minimale overl.appingsquotilnt&

17.

Bepaling van de minimale tandbreedte van het wiel&

b

>

sinf3 .mn•

•••

0

18.

Bepaling van het virtuele tandaantal van het wiela

z2

z

~

-

2

.

(13)

'

Cf:ebruikte symbolen in de formules met de bijbehorende Algol-notatie

Benami;D6.

Aa.nduidi;D6

Kophoogtefactor

TandbOek op steekcirkel

Drukhoek op de steekcirkel in

t1'6118Vers&le

vlak

Profielverschuivi;D6Sfactoren

Drukhoek

aan

de scherpe top van de

tand in het transversale vlak

!Dpverkórtingsfa~or

l'opcirkelstraal rondsel

"

"

w:iel

Basiscirkelstraal rondsel

"

"

wiel

Asafstand bij spelingavrije ingrijping

•·

-lïc

Po

:cos Po

sin p

0

2.cos

p

-

.0

a: a

sin

a:a

cos a:a

,

~a:a

~

~

CZS

ev

a:a

cos a:.

1

:"la

rk2

rb1

rb2

•v

Algolcode

hk

bo

ccosbo

sàinbo

twice

aa

sàina

as

l.J.iaÏil1aa

*11

à:22

rb11

rb22

(14)

Benaming

Aanduiding

...A.;tgolcode

Bedrijfsdrukhoek bij spelingavrije

•av

a.

.~~&V'. ë ,#

..

1ngrijping

ev «av

eva.v

cos cr._.y

oosaav

·ain «av

aiDaav

tan

•av

tanaav

Ingrijpweg voor en na de pool

.,

e11

..

••

e22

InBr.tjpquotilnt

c

epa

OVerlappinpq,uotilnt

'

.

,_

phi

Tandhoela op de basiscirkel

~

àb·

cos~

ccoabb

Virtueel tandenaantal

-.,.,

SY11

.V2

·lrt'22

Asversohuivingsfaotor

7

7

Inschuiffaotor

u

u

Tand.aantal

•t

...

...~

(15)

Voorbeelden bij het gebruik der tabellen

Voorbeeld 1 :

---Gegeven: kophoogtefactor van het theoretisch heugelprofiel:

~

=

1

,o.

toegepaste tandhoek:

~

0

=

20°

=

0,34906 radialen.

tandaantallen: rondsel: z • 8

t

wiel:

z

2

=

33.

te gebruiken moduuls mn • 1, 5.

Gev:ra.agd: afmetingen der tandwielen.

Antwoord: te gebruiken tabellen blz. 0030.

:rondsel&.

•:lminima.l~ prof'ielverl:rchui~ngsfà.ct0r:~xf

'""'""-: >t9;44470

...

~c'lcópverkortingsfactor

À=

-o,13254J

À

is negatief dus de tanden worden niet spits

,.. de inschuiffactor voor z

~:r

8 en z

=

33 is: u ",. 0,02579.

.

1

2

.

.

De werkelijke kopcirkeldiameter van het rondsel wordt nu:

dk

1

=2.mn (n:1 -u) =2.1;5 (5,70141 -0,02579)

=1.7.,.0268~"mm•>·

!'!.!!!= •

minimale profielverschuivingsfactor x

2

=

-1 ,29060; tandviidlsn

:met lT"-;::g.:Jitrinve

]Irófie~ver

... ·

schuiving worden buiten beschouwing gelaten, dus verder rekenen met x "' 0 ·

2

• kopcirkeldiameter:

~

=

2.mn.rk2

=

2.1 ,5.18,5331

=

55

11

.59,930c.mm •

XIII

• Het profielingrijpquotiënt e is groter dan één; dus wordt er geen minimale tandbreedte vereist.

a.safsta.nd bij spelingavrije ingrijping is:

(16)

---~---· Gesavant kophoÓgtefacto.r van het theoretisch heugelprofiéla

~

• 1,0

. . 0

·

toegepaste tandhoekt

~

0

20 • 0

1

34906

~alen

·

t&ndaantallen: z •

4

. .

1

.

• • 9·

2 ..

· . te gebruiken aoduula

~

• 1 ,5.

GeYzaagdt &f•tingen der tandWielen

.Antwoordt te gèbruiken tabellen blz. 002fi.

. '

'

.

zondsela • miDimale plOfielverscbuivingsfactor xt •

+0

1

72235

• kopverkortingsf&ctor

A

•·+0

1

21398 (dus

A>

0)

• inschuif'factor u bij z

1

4

en

z

2

·•

9 is u • 0

1

25584, dus

A<

u.

' De werkelijke kopcirkeldiameter

Wll

het rondsel wordt

mu

~ • 2.mn

{rk1 ...

(u-

A)} •

2.1,5 {3,63672 - (0,25584 - 0,21398)} •1.0,.7.845a

mm.

· De

tanden worden niet spits.

!!!!t

~m!n:tibaltt::piófielveriJ"?huivinetsfàctor ~

•"'t0;31592

• kopoi:dceldiam.eter Va.n

liet

wiel:

·

. •

.

~

2.~.1'k

- 2.1,5.5,9082

•1.7.,.7~1~

.. .,.'!'

Bet p:mfielingr.(jpquotilnt

E •

0,8352J dus

&

·<

1,

• minimale

overlappings~otilnt

' • 0,16480

• de

miniale

breedte van wiel en rondsel is nut

b .

- m

!e11

1 5

o.

16480

lf ,,

1415 • 2,.27.05()-•

.mm.

ldn

n si!l. 200

'

0

1

342020

asatstand bij spelingavrije ingrijping is:

(17)

Joorbeeld 3

Gegeven: kophoogtefactor van het

t~oretisch

heugelprofiel

~

• 1

,o

toegepaste tandhoek

.

~

0

• 20° •

o,

349o6 radialen

tandaantallena z • 4

.

1

.2 -

33 •..

te ge bruiken moduul

lb. •

1 , 5.

Gevraagde afmetingen der tandwielen

Antwoorde te gebruiken tabellen blz. 0026.

,

rondsel: • minimale profielversehui vingafactor x, •

o,

72235

• kopverkortingsfactor A • 0,21398 (dus A >0)

• inschuiffactor voor z, • 4 en z

2

.· •

33 is u • 0,06657 '· . dus A > u •

. De werkelijke

lmpcirkeldiamet~r

van het rondsel wordt nua

;"'.#,?~

De

tanden worden spits.

!!.!!•

minimale profielversclmivingsfactor x

2

-1,29060

verder aan te houden: x

2

0

de kopcirkeldiameter van het wielwordt nu:

4q •

2,mn.rk2 • 2.1,5.18,4923 • 55,4769 ·

·Het profielingrijpquotiint c • 0;92317, dus

E

<

1.

· mini•le overlappingsquotiiint ., • 0,07683

minimale breedte van wiel en rondsel moet 110rdem

b ·

• m ·

!eft

1, 5 0,07683 · 3,14159 •1.

Q5856'•JDJD.e

ldn

n sin 200

O, 342020

r

asatstand bij spelingsvPlje ingrijpinga

r

(18)

~

coument 05261523,M. Verduin,Tandwielberekening;

reaJ. hk, bo, eosbo, sin.bo, twice,

aa,

sina, cosa,

tana,

xl,

x2,

evas,. aso, as, cosaa,

lambda,

rkl, rk2, rbl, rb2, av,

-e'VB&v, aav, aavo, cosaav, ail'lBav, ta.naav, el, e2, epa,

pbi,

bb, coabb, zv1, zv2,

:r,

u;

inte§!!: zl ,

z2;

!2::,

hk :• 1 steE 0.1 until 1.21

2:2,

!2::,

bo :• 0.17453 steE o.o872667 until 0.69814

2:2,

be§!n cosbo :• cos(bo); sinbo :• sin(bo)J twice .:• 2

x

eosbo; aa :• arctan(0.36397/eosbo);

sina :• sin(aa); cosa :• cos(aa);

tana :•

sinafcosa; bb :• arcta.n((sinbo

x

eosa)fcosbo)J

cosbb :• cos(bb)J

~~

zl :• 1 steE 1 until 10

~

begin

-

JEWPAGE; PRDf.l'J:.i!:.ll1't(

1::

hk

bo

zl~)

J

M.CRJ

ABSFI:ler(l, 1, hk); SPACE(4); ABSFDC.T(O,

5,

bo); SPACE(3)J ABSFIXT(2,

O,

zl)J M.CR; NLCR;

xl :• hk- (zl

x

sina

.+.

2)/twice; evas :• (1 .5708o

+

2

x

xl x o.36397)/z1

+

tana -

aa;

aso : • arctan( evas);

iter: as :• arctan(eva.s

+

aso);

g:

aba(as - aso)

~

5

-5

~

bei!:,n aso :• as;

~to._iter end;

cosas :• cos( as);

l.ambda. :•

(z1ftwice)

x

(1 - cosafcosas)

+

hk

+

x1;

!!

lambda :;

0

~

rk1 :• z1/tv1ce,

+

hk

+

x1 -

lamb.da

!!!.!,

rk1

:=

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+

hk

+

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J

zvl :• z1 /(

c~bb

,;. 2

x

eosbo)

J

rb1 :• (z1 X cosa)ftwice;

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lambda

rk1

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rb1

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as

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5,

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SPACE(~)J

FDC.T(2, 5, rk1 ); SPACE(2);

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(19)

002

end

end

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x

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+

z2)

+

tana -

aa

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aa;

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i

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if'

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>

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11

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begin aavo :• aav; goto ite end; cosaav :• cos(aav); ainaav :• sin(aav);

-

-tanaav :• sinaavfcosaav; rb2 :• (z2

x

cosa)ftwice;

av :• (rbl

+

rb2)fcosaav;

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x2

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+

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u :•

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+

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~J

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~

2 - rb1

~

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x

tanaav; e2 :• sqrt(rk2

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x

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x

cosa); zv2 :• z2f(cosbb

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x

cosbo);

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1

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(20)

2U468

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(21)

20468

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Z2 X;2 AV AAV EPS PHI t;\12

u

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b •.63.591 +5.0448 +,71483 •.62631 •.37.569 +6,2592 +,52881 •4.1514 7 +,57289 •5.5410 +,68642 +,63.564 ... 36636 •7,3024 ... 479.51 •4.6476 8 •.51187 +6,0331 ... 66104 ... 64009 ... 35991 •8.3456 +,43383 •5.1398 9 .... 45086 +6,5219 ... 63811 +,6458/ +,35413 +9,3888 +,39181 •5.6285 10 +,38984 +7,0074 •.61716 +, 65112 +,34888 +111,4320 ... 35293 •6.1140 11 +,32883 +7,4902 +,59786 +,65595 +,34405 +11.4752 ... 31687 •6.5968 12 +,26781 +7,9703 +,57992 ... 66043 +,33957 +12.5184 +,28344 •7.0769 13 •.20680 +6.4481 +.56317 +,66463 +,33537 +13.5616 +.25236 +7,5547 14 +,14578 +8,9236 +,54741 +.668!'>9 +, 33141 +14.6048 +.22352 +8,0302 1~ +.08471 +9,3971 +,53252 +,67236 +,32764 +15.6480 +,19676 +8,5037 16 +. 0:?375 +9.8686. +,51837 +,67596 +,32404 +16,6912 +,17199 •a. 9752 17 -.03727 +10.3647 +,50949 +,67832 +,32168 +17.7344 +,15978 +9,4713 18 -.09828 +10.8772 +.50403 +,67964 +.32016 +18. ?776 +,15498 +9.9839 19 -.15930 +11, 3895 +,49897 +,68126 +,31874 +19.8208 +.1504( +10.4961 20 -.22031 +11,9014 +,49425 +,68258 +,31742 +20.8640 +,14629 +11.0080 21 -.28133 +12.4131 +,48986 +,68..'182 +,31618 •21.9072 +.14230 +11.51\li' 22 -.34234 +12.9246 +,48575 ... 68498 +,31502 +22,9504. +,13853 +12.0312 23 •.40336 +13.4358 +,48189 +,68607 +,31393 +23,9936 •.13502 +12.5424 24 •.46438 +13.9469 ... 47827 ... 68709 +,31291 +<:!5,0368 ... 13164 +13.0535 25 -.52539 +14.4577 +,47484 +.68806 +,31194 +26.0800 +.12849 +13.56"13 26 -.58641 +14,9685 +,47162 +,68896 +,31102 +27.1232 •·12544 +14.0751 27 -.64742 +15,4791 +,468!'>8 +,68985 •.J1015 +28.1665 +,12253 +14.58,7 28 -.7084"1 +15.9895 +,46569 •.6906-/ +,30933 +29.2097 +,11982 +15.0961 29 -.76945 +16.4999 +,46295 +,69146 +.30854 •30.2529 +,11717 +15.6065 30 -.83047 +17.0101 +,46034 +,69220 •.30780 •,H, 2961 +.11471 +16,1167 31 -.89149 •17.5202 •.45787 •.69291 •.30709 +32.3393 +,11228 •16.6268 32 -.95250 +18.0302 +,45551 +,69359 +,30641 +33.3825 +,11003 +17.1368 33 -1.01352 +18.5401 +,45325 +,69424 +,30576 +..S4.4257 +,10787 +17,6467 34 •1.07453 +19,0499 +,45111 •.69486 •.30514 •..'15,4689 +,1()513 •18,1565 36 -1.19656 +20.0693 +,44709 •.69603 ... ;so397 +37,5553 +,10176 +19.1759 38 -1.31859 +21.0883 +,44339 +,69710 +,30290 +39.6417 +,09811\ +20,1949 40 -1.44063 •22.1072 +,43999 +,69810 ... 30190 +41.7281 ... 09475 +21.2138 42 -1. 5626b +23.12!'>8 +.43684 +,69902 •.30098 +4..S.8145 +,09156 +22.2324 44 -1.68469 •24,1441 •.43392 +,69988 +,30012 +"15.9009 ... 08868 •23.2507 46 -1.80672 +25.1623 +,43121 ... 70068 ... 29932 +47.9873 +,08589 +24,2689 48 -1.9287? +26.1803 ... 42868 +,70143 +,29857 +50.0737 ... 06327 +25.2870 5G -2.0507!! +27.1981 +,42630 +,70213 +,29787 +!:>2.1601 +,08091 +26,3047 5' -2.17281 •2&.2159 +,42409 +,70~79 +. 29721 _+54.2465 +,07856 •27,3225 54 -2.29465 •29.233~ +,42200 ... 70342 +,29658 +56.3329 ... 07648 +28.3400 56 -2.41688 +30.2509 +,42004 +,70400 +,29600 +58,4193 +,01440 +29.3575 58 -2.53891 •31.?.682 +.41819 +,70456 +,29544 +60.5057 +,0'7253 +30.3748 60 -2.66094 •32.285? +,41644 +,70509 +,29491 +62.5921 +,07065 +31.3921 72 -3.39313 +38.387?. +:40769 +,70174 +,29226 +75.1105 +,061!:11 +37,"1938 84 -4.12531 +44,4866 +,40111 +,70976 +,29024 +87.6290 +,05467 +43.5932 96 -4.85750 +50.584/ +,39598 +,71135 +,28865 +100.1474 +,04912 +49.6913 108 -5.58969 •56.6816 +,39186 +, 71264 +.28736 +112 •. 6656 +.04416 •55.7882 12:) -6.32:1.88 +62. 77'78 +,38848 +,71..S70 +,28630 •125.1842 +.04116 +61.8844 150 -8.15235 +78.0159 +,38220 +,71:>70 ... 28430 •1!:>6.4803 +.03448 +77.1225 181] -9.9828?. +93.?.517 +,37785 +,71/09 •.28291 •1iH. 7763 +.03006 +92 ,'3!:183 21U -11.81329 +108.4863 +. 37467 +,71812 +.28188 +219.0724 +,0;,>6!!4 +107,5929 :.!4() -13.64376 +123.7202 +,37223 +,711:!91 •.28109 +250.3684 +;024;)7 •122.8268 270 -15.4742:~ •138,9535 +,37032 •• 71954 •.28046 •21:11. 664, ... 02238 +13tl.0601 1000001) •61014.64853 •507702.6727 +.35395 ... 72500 ... 27500 +1043201. 8'H7 +12.26478 +507701. 7793

(22)

MK BO l1

1.0 • 17453 3

x1 l-AMBDA RK1 ZV1 RB1 AA AS BB

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l2 Xt! AV AAV EPS PHI LV2

u

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(23)

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+,?!:)594 +.28739 +3,49940 +4,17281 +1.90492 +,35401 +,99518 + .16391

Z2 X2 AV AAV EPS PHI ZV2 u ><K2

6 +,6,3391 +6,U331 +,66104 +,79<!95 ··20705 +6.2!)92 +,43383 +4.2464 7 +,57289 +6,5219 +,63811 +.80652 •·19348 +7.3024 +,39161 +4,7351 8 +,51187 +7.0074 +.61716 +,811!62 +,18138 +8,3456 +,3?293 +5.2207 9 +.45086 +7,49()2 +,59786 +,829?6 +,17044 +9.3888 +.31687 +5,7034 10 +.38984 +7.9703 +,57992 +,83959 +,16041 +10.4320 +.28344 +6.1835 11 +,32883 +8.4481 +,56317 +,84888 + .15112 +11.4752 +.25236 +6,6613 12 +,26781 +8.9236 +,54741 +.85155 +,14245 +12.5184 •·22352 +7.1369 13 +,2068(! +9,3971 +,53252 +. 86572 +,13428 +13.5616 +,19676 +7,6103 14 +,14578 +9,8686 +,51837 +,87347 +,12653 +14.6048 +.17199 +8,0818 15 +,08477 +10.3381 +,50487 +,88081 +,11913 ~15.6480 +,14910 +8,5514 16 +,0237'::> +10.8059 +.49193 +.88798 +,11202 +16.6912 •·12802 +9,0191 17 •.0.3727 +11.2998 +,48422 +,89255 +,10745 +17.7344 • .uBü8 +9,5130 18 -.09828 +11.8110 +,47987 +,89543 +,10457 +18.7776 + .11461 +10,0242 19 -.15930 +12.3219 +.47581 +,89811 +.10189 •19.8208 .. ·11139 +10.5352 20 -.22031 +12.8327 ... 47202 +.90061 +,09939 +20.8640 +.10832 +11.045Q 21 -.28133 +13.3433 +,46847 +,90295 +,09705 +21.9072 +.1()542 +11.5566 22 -.34234 +13.8538 +.46513 +,90'::>15 +,09485 +<!2.9504 +,10272 +12.0670 23 -.40336 +14.3641 +,46200 +,90122 +.09278 •<!3.9936 +,10011 +12.5773 24 -.46438 +14.8742 +,46904 +,90\117 +,09083 •2::0.0368 +. 09770 +13,0874 25 -.52539 +15.3843 +,45625 +,91100 +,08900 +26.0800 +.09534 +13.5975 26 -.58641 +15.8942 +,45360 +. 91275 +,08725 +27.1232 +,09316 +14.1074 27 -.64742 +16.4040 +. 45110 +.91440 +,08560 +<!8.1665 +.09102 +14.6172 28 -.70844 +16.9137 +,44872 +,91597 +,08403 •29.2097 +,08904 +15.1269 29 -.76945 +17.4234 +,44646 +,91746 +,08254 +J0.2529 +,087ü9 +15.6366 3C1 -.83047 +17.9329 +,44430 +,91888 +,08112 +.st. 2961 +,08529 +16.1461 31 -.89149 +l.8.4424 +,44226 +,92023 +,07977 +..12.3393 +o08349 +16.6556 3? -.95250 +18.9518 +,44030 +,92152 +,07848 +33.3825 +,08184 +17.1650 33 -1.01352 +19.4611 +,43842 +,92276 •.07724 +34.4257 +.08026 +17.6743 34 -1.0745~ +19.9704 +,43664 +,92.594 +,07606 +35.4689 +,07866 +18.1836 36 -1.19656 +20,9887 +.43329 +,92616 +,07384 +J7.5553 +.0757:3 +19.2019 38 •1. 3185<J +22.0068 +,43020 +,921!21 +,07179 +39.6417 +.07309 +20.2200 4() -1.44063 +23.0248 +,42735 +,93011 +,06989 +41.7281 +.07056 +21.2380 42 -1.56266 +24.0425 +,42471 +,93186 +,06814 +43.8145 +.06820 +22.2558 44 -1.6646\1 +25.0601 +,42225 +,93350 +,06650 +45.9009 +,06607 +23.2733 46 -1.80672 +26.0776 +,41997 +,93,0.5 +,06497 +47.9873 +,06400 +24.2908 48 -1.92875 +27.0949 +,41783 +,93646 +,06354 +50.0737 +.06214 +25~3081 5iJ -2.05078 +28 .1121 +,41584 +,93179 +.06221 +52.1601 +,060.50 +26.3253 52 -2.17281 •29.1292 +,41396 +,93906 +,06094 +54.2465 +,05867 +27.3424 54 -2.29485 +30 .1463 +,41220 +,94024 +,05976 +':>6,3329 +,05702 +28.3595 5(', -2.41688 +31.1632 +,41053 +,94136 +,05864 +58.4193 +,05556 +29,3764 58 -2.53891 +32.1.800 +,40896 +,94242 +,05758 +60.5057 +,05419 +30.3932 6•) -2.66094 +33.1968 +,40748 +,94342 +.05658 +62.5921 +,05278 +31.4100 72 -3.39313 +39.2961 +,40005 +.9484'1 +,05153 +75.1105 +,04600 +37.5093 84 -4.12531 +45.393/ +,39443 +,95231 +,04769 +87.6290 +,04095 +43.6069 96 -4.85750 +51.4904 +,39005 +,9?'::>33 +,04467 +100.1474 +,03680 +49.7037 108 -5.58969 +57.5862 +,38653 +,95777 +,U4223 +112.6658 +,03357 +55,7994 120 -6.32188 +63.6815 +,38364 +,95979 +,04021 +125.1842 +,OJ090 +61.8947 150 -8.1523>:'> +78.9176 +,37824 +.96357 +,03643 +156.4803 +,02620 +77.1308 18U -9.98282 •94.1521 +,37451 +,96620 +,(13380 +187.7763 +,02300 +92.3!>,4 21ll -11.81329 +109.38SQ +.37178 +,961!15 +,03185 +219.0724 +,02066 +107.5991 24t1 -13.64376 •124.6191 +.36969 +,96964 +,03036 +250.3684 +.0188!> +122.832::1 271) -15,47423 •139.8519 +.36804 +.97082 +,(12918 +2!!1.6645 +.01740 +138.06':>1 1û001JOG -61014.6485~ +507703.5656 +,35395 +,9810/ + .IJ1893 +1043201.8577 +12.2652t +50 7701.7789

(24)

HK BO Z1

1.0 .17453 5

l<1 LAMBOA RK1 ZV1 RB1 AA AS ts8

+,ó9492 +,1913<1 +4,04219 +:>. <:>1601 +2,38115 +,35401 +,94089 •.16391

z~ X2 AV AAV EPS PHI lV2 u RK2

6 +,63391 +6.5219 +,63811 •.86191:1 ··13802 •6.2592 +.3911l1 +4,2884 7 +,57289 +7.0074 +.61716 +,87838 +,12162 •7.3024 +,35293 +4. 7740 1:1 +.51187 +7.4902 +.59786 +,89.308 +,10692 +8,3456 +,31687 +5.2567 9 +,45086 +7.9703 +,57992 +,90643 +,09357 +9,3888 +.28344 +5,7368 10 +,38984 +8,4481 +,56317 +.91871 +,08129 +10.4320 +.25236 +6.2146 11 •.3<'883 +8,9236 +.54741 +.93011 +,06989 +11.4752 +.22352 +6,6902 12 +,26781 +9.3971 +,53252 +,94079 +,(.15921 +12.5184 +,19676 +7,1636 13 +,20680 +9.8686 +,51837 +,95U8éi +,04912 •13.5616 +.1i199 +7,6351 14 +,14578 +10.3381 +,50487 +,96048 +,03952 •14.6048 +,14910 •8.1047 15 +,08477 +10.8059 +,49193 •.96966 +,03034 +15.6480 +.12802 +8,'5724 16 +,0237:; +11,2720 +,47949 +.97849 +,02151 +16.6912 +.10868 +9,0385 17 •.03727 +11.7648 +.47227 +,98412 +.01588 +17.7344 +.09976 +9.5314 18 -.09828 +12.2755 +,46841 +,98761 +,01239 +18.7776 +.09686 +10.0420 19 -.1593(1 +12./859 +,46479 +,99067 +,Oû913 •19.8208 ... 09417 +10.5524 2(.1 -.22031 •13,2962 ... 46141 +,99.391 •.00609 +i!0.8640 +.09159 +11. 0627 2t -.2813.:1 +13,8063 +,45823 +,99675 +,00325 +21.9072 +.08920 +11.5728 22 -.34234 +14.3163 +,45525 •.99942 +,00058 +;!2.9504 •.086él9 +12.0828 23 -.40336 +14.8262 •.45244 +1.00193 -.00193 +ii!3.9936 +,08470 +12.5927 24 -.46438 +15.3359 +,44978 •1.00430 •.00430 +:.15.0368 +.08267 •13.1024 25 -.52539 +15.1l456 +.44726 +1.00654 -.00654 +:.16.0800 +,08069 +13.6121 26 -.58641 +16.3552 +,44489 +1.00866 -.00866 +27.1232 +.07886 +14.1217 27 •.64742 +16.8647 +,44264 •1.01067 •.01067 +28.1665 +,07705 +14.6312 28 -.70844 +17,3741 •,44049 +1.01258 -.01258 +29.2097 +.07539 +15.1406 29 -.76945 +17.8834 +,43845 +1.01439 ·.01439 +.30,2529 +,07380 +15.6499 30 -.83041 +18.3927 +,43651 +1.01612 -.01612 +.31.2961 +.07222 +16.1592 31 -.89149 +18.9018 +,43466 +1.01777 -.01777 +32.3393 +,070i7 +16,661:1.3 32 -.95250 •19,4110 +,43289 +1.01934 -.01934 +33.3825 +,06931 +17.1775 33 -1.01352 •19.9200 +.43119 •1,0208~ -.u2085 +.)4.4257 +,06798 +17.6866 34 -1.0745J •20.4290 +,42957 +1.02229 -.02229 +.)5,4689 +,06670 •18,1955 36 -1.19656 +21. 4469 +,42654 +1. 02499 -.u2499 +.37.5553 +,06422 +19.2134 38 -1.31859 +22.464ï •.42374 +1.02748 -.02748 +.)9.6417 +,06192 +20.2312 40 -1.4406.3 +23.4821 +. 42115 •1.02979 -.02979 +41.7281 +.059éi6 +21.2487 42 -1. 5626t• +24.4996 +,41875 +1.0319.) -.03193 +4J,8145 +,05786 +22.2661 44 -1.68469 +25.5169 •.41652 +1.03JII2 -.03392 +45.9009 •·05598 +23.2834 46 ·1.80672 +26.5340 +,41444 •1.03578 -.03578 ->47.9873 +,05431 +24,3005 48 -1.92875 +27.5511 +,41250 +1.03152 -.03752 +50.0737 +.05266 +25.3176 50 -2.05078 +28.5679 +,41067 +1.03916 -.03916 ·~2.1601 +. 05119 +26.3345 52 -2.17281 •29.5847 +,40896 +1.04069 -.04069 +54.2465 +,04982 +27. 3~)13 54 -2.29485 +30.6016 +,40735 +1.04213 -.04213 +')6.3329 +,04841 +21:1.361:11 56 -2.41688 +31.6H!2 +,40584 •1.04350 -.04350 +58.4193 +,04719 +29,3847 58 -2.53891 +32.6349 +,40441 +1.04478 -.04478 +60.5057 +.04592 +30.4014 60 -2.66094 +33.6514 +.40305 +1.04600 -.04600 •62.5921 +,04483 +31. 418ll 72 -3.39313 +39.7497 +,39626 •1.05i!15 -.05215 +75.1105 •.03910 •37,5162 84 -4.1253:1 +45.8465 +. 39:112 •1. 05682 -.05682 +67.6290 +.03484 •43,61~1 96 -4.8575[] +51. 9424 +,38710 •1.06050 •.06050 +100.1474 •.03150 +49.7090 108 -5.58969 +58.0377 +,36387 +1.06346 -.06346 +112.6658 •·02879 •55.8042 120 -6.32188 +64.1325 +,38122 +1. 06591 -.06591 +125.1842 +,02654 +61. 8990 l5U -8.1523~ +79,3681 •.37627 +1,07049 -.07049 +1~6.4803 ... 02238 +77 .1346 18~' -9.98282 +94. 602j +,37285 +1,07J69 -.07369 +1!!7.7763 +,01969 +92.3687 210 -11.81329 +109,835') +,37(134 +1.07604 -.u7604 +1!19.0724 •.01773 •101.6020 240 -13.64376 +125 ,116fHI +,36841 +1.07786 -.07786 +2~0.3684 +. 01663 +122.8345 270 -15.47423 +140.3006 +,36690 +1.07929 -.07929 +281.6645 +,Ol541 +138.0671 1C00000 -61014.64853 +507704. OH1 •.35395 •1. 09168 -.09168 +104.S2ll1.8577 +12.26543 +507701. 7786

(25)

204ó8 - 10 0006

HK 80 Z1

1.0 .17453 6

X1 L.AMBOA RK1 ZV1 R81 AA AS BB

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X2 AV AAV EPS PHI lV'i u RK2

6 +,63391 +7.00i4 +.61716 +,924'ii3 +,07507 +b.2592 +,3!::>293 +4,3273 7 +,57269 +7.4902 +,5976(1 +.94401 +,05599 +7,3024 +.31687 +4,!:1100 8 + .51187 +7.97(13 +,57992 +,96118 +,03882 +8,3456 +,28344 +5.2901 9 +,45086 +8.448l +,56317 +.97684 +.02316 +9,3888 +,25236 +5,7679 10 +,38984 +8,92;:.6 +.54741 +,99129 +,00871 +10.4320 +.22352 +6,2435 11 +,3288~ +9.3971 +,53252 +1,00475 -.00475 +11.4752 +.19676 +6. 7169 12 +.26781 +9,8686 +,51837 +1. 01740 -.01740 +12.5184 +,17199 +7.1884 1.3 +,20680 +10.3381 +,50467 +1.02938 -.02938 +13.5616 +,14910 +7,6580 14 +,14578 +10.8059 +,49193 +1.04079 -,04079 +14.6046 +.12602 +6.1257 15 +,08477 +11.2720 +,47949 +1.05174 -.05174 +15.6460 + .10868 •8.5918 16 +,02375 +11,7363 +.46749 +1. 06229 -.06229 +16.6912 +.0911J2 +9.0561 17 -.03727 +12.2282 +,46071 +1. 06894 -.06694 +17.7344 +.08307 +9.5480 18 •.09828 +12.7363 +,45729 +1.07J01 -.07301 +18. 7776 +,08067 +10.0582 19 •,1593U +13.2483 +,45409 +1.07680 -.07680 +19.8208 +.07846 +10.5661 20 -.22031 +13.7581 •• 45to9 +1,08033 -.08033 +20.8640 +,07632 +11.0779 21 -.28133 +14,?678 +,44626 +1.08365 -.06365 +21.9072 +,07435 +11.5876 22 -.34234 +14.7774 +,44561 +1.08676 -.08676 +22.9504 +,07243 +12,0973 23 -.40336 +15.2869 +,44310 +1. 089ó9 -.08969 +23,9936 +.07067 +12.601>7 24 -.46438 +15.7964 +.44073 +1. 09245 -.09245 +25.0368 +.06893 +13.1162 25 -.52539 +16.3057 +,43848 +1.09!::>06 -.1)9506 +26.0800 •·06734 +13.6255 26 -.58641 +16.8150 +,43636 +1. 09753 -.09753 +27.1232 +,06577 +14.1348 27 -.64742 +17.3241 +,43434 +1. 09986 -.09988 +28.1665 +,06433 +14.6439 28 -.7u844 +17.8333 +,43:?42 +1.10210 -.10210 +<:!9.2097 +,06288 +15.1531 29 -.76945 +18,3423 +,43059 +1.10422 -.10422 +30.2529 +.06157 +15.6621 30 -.83047 +18.8513 +,42885 +1,10623 -.10623 +.51.2961 +,06025 +16.1711 31 -.89149 +19. 36'02 +,42718 +1.10816 -.10816 +..S</.3393 +,05905 +16.6801 32 -.95250 +19.8691 +,42559 +1.11000

-.uooo

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(26)

HK 80 Z1

1.0 .17453 7

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Z2 X2 AV AAV EPS PHI ZV2 u RK2

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Z2 X2 All AAV EPS PHI lV2 u RK2

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