Presmetka Na Cilindricen Zapcest Par So Kosi Zapci

3UHVPHWNDQDFLOLQGULaHQ]DSaHVWSDUVRNRVL]DSFLYOH]QLSRGDWRFL JHRPHWULMDn m n z 1 z 2 $YWRUMDNRVW 3URI'U

P [kW] n 1 [s -1 ] b Flim Hlim .OLPHQW 7ULPaHY,=%(5,JL6/('1,7(Y )$.725,

Y x Y S Y N Y R Y

,=%(5,JL6/('1,7(Z )$.725,

Z x Z L Z R Z V Z N K A K V .RQWUROQLSUHVPHWNLJHRPHWULMD

(s t +e t )*z = d* pi 2+2 = SRJRQVNL JRQHW SRJRQVNL JRQHWYRA

YRB

YRC

YRD

YRE

QD d a

QD d

QD d f

QD d b

(+ ))z =SRJRQVNL JRQHW a=m n (z 1 +z 2 )/(2cos )=(d b1 +d b2 )/(2cos t )YRA 140.00 140.00 = 140.00YRB

YRC 6WHSHQQDVLJXUQRVWNRQWURODYRC

YRD

S F = RGVYLWNXYDZHYRE

S H = RGSRYU^LQVNLSULWLVRNQD d a

QD d 1$320(1$

QD d f $NR]DGRYROXYDDWVLWHNRQWUROLWRJD^

QD d b VLWHUH]XOWDWLYRSURGROCHQLHVHWRaQL

3UHVPHWNLJHRPHWULMD3RWUHEQLSRGDWRFL]DSUHVPHWNDm t i z inv n tan n

g cos t

p n p t p bt p x

DJROHQaHNRUQD z 1

DJROHQaHNRUQD z 2

t inv t T1T2

a t = PH_XRVNLQRUDVWRMDQLH*ODYQLGLPHQ]LLQD]DSaHVWLRWSDU]DSRJRQVNLRW]DSaHQLNWHPHQSUHaQLN

d a1t =

SRGHOEHQSUHaQLN

d 1t =

SRGQRCHQSUHaQLN

d f1t =

RVQRYHQSUHaQLN

d b1t =

]DJRQHWLRW]DSaHQLNWHPHQSUHaQLN

d a2t =

SRGHOEHQSUHaQLN

d 2t =

SRGQRCHQSUHaQLN

d f2t =

RVQRYHQSUHaQLN

d b2t =

O 2

O 1

4020

010

080

60

at

2

1

t

z 2 = 3 5

z 1 = 1 7

= 21 ,78 7

m n = 5 [m m ]

6O*ODYQLGLPHQ]LLQDJRQHWLRW

]DSaHQLN

d f2

d a 2 db 2

d 2

6O*ODYQLGLPHQ]LLQDSRJRQVNLRW

]DSaHQLN

d f1d a1d b1d 1

.RQVWUXNFLMDQDHYROYHQWLWH

.RQVWUXNFLMDQDGRSLUQLFLWH

l

5

ll l

l

5l l

lll

l l ll

l

5

8 l

O 2db 2

3l

8 l7 l

6 l5 l

4 l

2 ll

1 8 05

2dl 2b pipi**=O 1

55 5

l10 l

10 l9 l8 l7 l6 l5 l4 l3 l2 ll

1 8 0

*5*2

dl 1b=

.RQVWUXNFLMDQDGRSLUQLFLWH]DSR]QDWHYROYHQWHQSURILO

n DD D '

n E

RA

E 'EC C ' E 2

A 1

Bn B D 1

B 1 n A

Rn

AA

A 'B '

E 1

O 1

C

R nA

C 1C 2D 2

A 2B 2

5DGLXVLQDNULYLQLWHYRNDUDNWHULVWLaQLWHWRaNL]DSRJRQVNLRW]DSaHQLNSRaHWQDWRaND 1A

1B NLQHPDWLaNLSRO 1C

1D L]OH]QDWRaND

1E

]DJRQHWLRW]DSaHQLNSRaHWQDWRaND 2A

2B NLQHPDWLaNLSRO 2C

2D L]OH]QDWRaND

2E

3UHaQLFLYRNDUDNWHULVWLaQLWHWRaNLRGVSUHJDWD]DSRJRQVNLRW]DSaHQLNYRA d A1

YRB d B1

YRC d C1

YGD d D1

YRE d E1

]DJRQHWLRW]DSaHQLNYRA d A2

YRB d B2

YRC d C2

YRD d D2

YRE d E2

T 1

T 2

d b1d 1

twC

d a1

d a2

A E

d 2

T 1T 2

1A

1E

2A

1C

2C

2E

D

1 D

2 D

B

2B

1B

6O5DGLXVLQDNULYLQLWH

D

6O3UHaQLFLYRNDUDNWHULVWLaQLWHWRaNLRGVSUHJDWD

d C1BT 1

d A 1

dB1

d 1d a 1

d a2d 2

CA

d E 1d D 1

dA 2

T 2

E

dC2

dD

2

dE

2

dB2

1DSDGQLDJOLQDSRJRQVNLRW]DSaHQLN YRNDUDNWHULVWLaQLWHWRaNLcos sin tan

A B C D E

]DGUXJLWHSUHaQLFLd a

d d f

d b QDJRQHWLRW]DSaHQLN YRNDUDNWHULVWLaQLWHWRaNLcos sin tan

A B C D E

]DGUXJLWHSUHaQLFLd a

d d f

d b 6SUHJQXYDZHYRNDUDNWHULVWLaQLWHWRaNL A, B, C, D LE

O 2

D

6O6SUHJQXYDZHYRWRaNLWHA L D

O 1

C

T 1 A

T 2

C

6O6SUHJQXYDZHYRWRaNLWHB L EO 1

BT 1

E

T 2O 2

C

6O1DSDGQLDJOLYRNDUDNWHULVWLaQLWH

WRaNLRGVSUHJDWD

dB 1d C 1

BA

T 1

dA 1 B 1 A 1 d D 1

O 1 d E 1

D E

C 1

E 1 D 1

6O1DSDGQLDJOLYR

NDUDNWHULVWLaQLWHWRaNLRGVSUHJDWD

d A2

B

d D2d B

2d C

2

d E2

A C

B2

A 2

ED

T 2

E2

C2 D

2

O 2

$JROQLGHEHOLQDQD]DEHFRWL^LURaLQDQDPH_X]DELHWRQDSRJRQVNLRW]DSaHQLNinv 2 2

A B C D E d a

d d f

d b

]DJRQHWLRW]DSaHQLNinv 2 2

A B C D E d a

d d f

d b

6O6SUHJQXYDZHYRNLQHPDWLaNLRWSROC

T 1

O 1

O 2

CT 2

CD

E

2B 12A 1

O 1

2A 12C 1

2D 12E 1

E

CBA

D

2D 1

2B 12C 1

AB

DC

BA

2E 1

E

C

2E 2

A

BA

BC

D DE EE

DC

B

A

2D 22E 2

2C 22B 22A 2

2D 2

2C 2

2B 2

2A 2

O 2

/DaQLGHEHOLQDQD]DEHFRWL^LURaLQDQDPH_X]DELHWR]DSRJRQVNLRW]DSaHQLNs t e tYRA

YRB

YRC

YRD

YRE

da d df db

]DJRQHWLRW]DSaHQLNs t e tYRA

YRB

YRC

YRD

YRE

da d df db

7HWLYQLGHEHOLQDQD]DEHFRWL^LULaLQDQDPH_X]DELHWRaHOQDUDPQLQD]DSRJRQVNLRW]DSaHQLNs t e tYRA

YRB

YRC

YRD

YRE

QD d a

QD d

QD d f

QD d b

e tDstE E

D

s tAstB

s tDs tC

e tAA

e tBe tCC

B

e tEE E

DCBA

ED

CB

A

dE 1

dD

1

d B1

d A1

d 1d f1DD

e tC 2e tD 2

e tB 2

A

CB

e tA 2

dF2

e tE 2E ECs tC 2

As tA 2s tB 2B

C

A

B

dB2

s tE 2s tD 2

ED

dA2

d D2 dE

2

dC2

d B1

B s tC A

dE1

dD 1

As tA

s tB

d b1

d f1 dA1

s tDDE

s tE

e tC

e tA

e tB

e tE

e tD

E

BC

D

d 1

C

]DJRQHWLRW]DSaHQLNs t e tYRA

YRB

YRC

YRD

YRE

QD d a

QD d

QD d f

QD d b 7HWLYQLGHEHOLQDQD]DEHFRWL^LURaLQDQDPH_X]DEMHWRQRUPDOQDUDPQLQD]DSRJRQVNLRW]DSaHQLN ]DJRQHWLRW]DSaHQLN

s tet e tet s tet e tetYRA

YRA

YRB

YRB

YRC

YRC

YRD

YRD

YRE

YRE

QD d a

QD d a

QD d

QD d

QD d f

QD d f

QD d b

QD d b 0HUNDSUHNX]DSFLSRJRQVNL]DSaHQLNz 1 JRQHW]DSaHQLNz2

0HUHQEURM]DSFLk

0HUNDSUHNX]DSFLW

0HUHQNUXJd M

cos b3UHVPHWNLMDNRVWSRJRQVNL]DSaHQLNz 1 JRQHW]DSaHQLNz 2 [Nmm] 9UWHCHQPRPHQW [Nmm]

[ s -1 ] =DaHVWHQRVWQDYUWHCLWH 5.489 [ s -1 ] [N] WDQJHQFLMDOQDVLOD [N] [N] QRUPDOQDVLODQDSURILORW [N]Z H Z Y R z n1 Y fa GR

[N/mm2] NULWLaHQQDSRQRGSRYU^LQVNLSULWLVRN [N/mm2] UDERWHQQDSRQRGSRYU^LQVNLSULWLVRN

E s tB

BC

D s tA

s tD

s tC

s tE

E

e tB A

e tA

e tD

e tC

e tE CB

D

dCd

E

dD

d Bd A

A

*(20(75,-$QDERNRWRG]DEHFRW$JOLQD]DNRVXYDZHSRERNRWQD]DEHFRW]DSRJRQVNLRW]DSaHQLN ]DJRQHWLRW]DSaHQLN7DQJHQV 7DQJHQV YRA

YRA

YRB

YRB

YRC

YRC

YRD

YRD

YRE

YRE

QD d a

QD d a

QD d

QD d

QD d f

QD d f

QD d b

QD d b $JOLQD]DYUWXYDZHQDNDUDNWHULVWLaQLWHSURILOL]DSRJRQVNLRW]DSaHQLNz 1 ]DJRQHWLRW]DSaHQLNz 2

i i,A i i,AA 1

A 2

B 1

B 2

C 1

C 2

D 1

D 2

E 1

E 2

E 2A

A 2

C 2B 2

D 2

A 1T 1

E 1D 1

C 1B 1

E 2

E 1A

C 1A

B 1A

D 1A

AB

C 2A

B 2A

D 2A

25 ,0 [mm ]

DC

E

10 ,0

02 ,5

7 ,5

5 ,0

17 ,520 ,0

22 ,5

12 ,515 ,0

T 2

zy - RVNDWDHQRUPDOQDQDaHOQLWHUDPQLQL

NRRUGLQDWQLRWSRaHWRNC OHCLYRSUHGQDWDaHOQDUDPQLQD

3UHGQDaHOQD

SRU^LQD

=DGQDaHOQD

SRU^LQD

x

/DFLQD]DYUWXYDZHQDNDUDNWHULVWLaQLWHSURILOL]DSRJRQVNLRW]DSaHQLNz 1 ]DJRQHWLRW]DSaHQLNz 2i l i,A i l i,A

A 1

A 2

B 1

B 2

C 1

C 2

D 1

D 2

E 1

E 2

.RRUGLQDWLQDGRSLUQLWHWRaNLRGNDUDNWHULVWLaQLWHSURILOL]DSRJRQVNLRW]DSaHQLNz 1 ]DJRQHWLRW]DSaHQLNz 2i x y z i x y zA A B B C C D D E E

5DYHQNDQDSUDYDQL]WRaNLWHA LDUDYHQNDQDSUDYDYRSURVWRUQL]WRaNLWH

A ( x A , y A , z A ) L D ( x D , y D , z D)

SURYHUNDOHCDWOLNDUDNWHULVWLaQLWHGRSLUQLWRaNLQDRYDDSUDYDYRSURVWRU" 0,00,0 ]DWRaNDWDA -1 ]DWRaNDWDB ?? ]DWRaNDWDC 1,01,0 ]DWRaNDWDD1.452356 1.452356 1.452356 = ]DWRaNDWDE=DNOXaRN VLWHNDUDNWHULVWLaQLGRSLUQLWRaNLMD]DGRYROXYDDWGHILQLUDQDWDUDYHQNDQDSUDYDWHGRSLUQDWDOLQLMDSRERNRWQD]DEHFRWHSUDYD

OLQLMDYRSURVWRU^WROHCLYRUDPQLQDWDQDGRSLUQLFDWDLHGHORG

SROHWRQDVSUHJQXYDZH

AD

A

AD

A

AD

A

zz

zz

yyyy

xx

xx

=

=

5DPQLQDLSROHQDVSUHJQXYDZH

1

y i

y C = 32 ,1 88

4,7 24

11 ,8 49

16 ,7 03

20 ,4 74

27 ,5 99T 2

23 ,4 93

30 ,6 17

34 ,3 88

39 ,2 42

46 ,3 67

01 02 03 04 05 06 07 0

9 010 0

8 0

T 1(+1) p x = 103 ,3 27

2p x = 84 ,5 98

74 ,4 64

51 ,0 91

A B EC D

20 ,413

(3 -) p x = 65 ,4 99

y D = px = 42 ,3 22

y B = (-1 ) p x = 19 ,1 44(2 -) p x = 23 ,1 77

y E = p x = 61 ,4 52

T 2T 1 A B EC D

a

134,10tg

ab

C1D1=

=

6WHSHQLQDSUHNULYDZHQDNDUDNWHULVWLaQLWHSURILOLSRERNRWQD]DEHFRWVSRUHGSR]QDWLRWL]UD]

]DSRJRQVNLRW]DSaHQLN z1 ]DJRQHWLRW]DSaHQLN z2

i NRQVWDWDF i NRQVWDWDFA A B 11 B 11C C D D E E VSRUHGUDGLXVLWHQDNULYLQD

]DSRJRQVNLRW]DSaHQLN z 1 ]DJRQHWLRW]DSaHQLN z 2

i NRQVWDWDF i NRQVWDWDFA A B 11 B 11C C D D E E VSRUHGNRRUGLQDWLWHQDGRSLUQLWHNDUDNWHULVWLaQLWRaNL


i NRQVWDWDF i NRQVWDWDFA A B 11 B 11C C D D E E A A B 11 B 11C C D D E E A A B 11 B 11C C D D E E

pipi

*

sin*n

iA

m

y=

A1D1

A1i1

=

AD

A

xx

xx i

=

Dyy i

=

AD

A

zz

zz i

=

$JRORWQD]DNRVXYDZHQDRVQRYQLRWFLOLQGHUbVSRUHGSR]QDWLRWL]UD]

cos b sin b tan b b0.937208 0.348770 0.372138 20.412

VSRUHGSROHWRQDVSUHJQXYDZH


i tan b b i tan b bB 0.372138 20.412 B 0.37214 20.412C 0.372138 20.412 C 0.37214 20.412D 0.372138 20.412 D 0.37214 20.412E 0.372138 20.412 E 0.37214 20.412

9NXSQDGROCLQDQDGRSLURWYRWHNQDVSUHJDWDRGA GRE

]D]DSaHVWSDUVR = - 1

VSUHJQXYDZHYR$RGQRVQRD

UDY . 1.54YRVSUHJD]DSFLVRmax l z = 40.855

]DEHF YR GROCLQD

n A n+1 D YNXSQR

]DEHF YR GROCLQD

n A n+1 D YNXSQR

t

nb

cos

coscoscos =

i

A1i1b

y =tan

i

i2A2b

y =tan

B EC D

yi

T 1

19,1

4432

7

T 2

B

A

T 2

0

1 0

2 0ET 1

51 ,0 910 5

n - WLSDU]DEFL

n + 1- YLSDU]DEFL

b

x)z

co s

p)(IN T(2lm a x

=

VSUHJQXYDZHYRB RGQRVQR E

UDY . 1.55YRVSUHJD]DEHFVRmin l z = 20.427

]DEHF YR GROCLQD

n B n+1 E YNXSQR

]DEHF YR GROCLQD

n B n+1 E YNXSQR

VSUHJQXYDZHYRC YRVSUHJD]DSFLVR l z = 30.042

]DEHF YR GROCLQD

n-1 n C YNXSQR

]DEHF YR GROCLQD

n-1 n B YNXSQR

B EC D

y i

T 1

19,1

4432

7

T 2

B

A

T 2

0

1 0

2 0ET 1

51 ,0 910 5

n - WLSDU]DEFL

n + 1- YLSDU]DEFL

B EC D

y i

T 1 T 2

B

A

T 2

0

10

20ET 1n - WLSDU]DSFL

n -1 - YLSDU]DSFL

51 ,0 9 1

19,1

44

10,1

34

b

x

zc os

p)1()(I N T(lm in

+=

b

C1D1

tga

=

=D]DSaHVWSDUVR = 2 - VSUHJQXYDZHYRA RGQRVQRD

UDY . 1.57 YRVSUHJD]DSFLVR l z = 45.158

]DEHF YR GROCLQD

n A n+1 D YNXSQR

YRVSUHJD ]DSFL

]DEHF YR GROCLQD

n A n+1 D YNXSQR

VSUHJQXYDZHYRB RGQRVQRE

UDY . 1.58 YRVSUHJD]DEHFVR l z = 24.730

]DEHF YR GROCLQD

n B n+1 E YNXSQR

YRVSUHJD ]DEHF

]DEHF YR GROCLQD

n B n+1 E YNXSQR

VSUHJQXYDZHYRC

]DEHF YR GROCLQD

n C n-1 YNXSQR

YRVSUHJD ]DEHF

]DEHF YR GROCLQD

n C n-1 YNXSQR

B EC DT 1 T 2

B

A

T 2

0

10

20E

n - WLSDU]DEFL

n + 1 - YLSDU]DEFL

23,1

5433

6

30T 1

B EC DT 1 T 2

B

A

T 2

0

10

20E

23,1

5433

6

30T 1

n - WLSDU]DSFL

b

xz

p1INTl cos)))(((min +=

b

xz

pINT11l cos)))()(((max +=

B EC DT 1 T 2

B

A

T 2

0

1 0

2 0E

n - WLSDU]DSFL

23,1

5433

6

3 0T 1

n -1 - YLSDU]DSFLb

C1D1

tga

=

=D]DSaHVWSDUVR = 1VSUHJQXYDZHYRA RGQRVQRD VSUHJQXYDZHYRB RGQRVQRE]DEHF YR GROCLQD ]DEHF YR GROCLQD

n A YRVSUHJD ]DSFL n B n+1 D n-1 YNXSQR YNXSQR

VSUHJQXYDZHYRC]DEHF YR GROCLQD

n C n-1 YNXSQR

01 02 03 04 05 0

T 2T 1 A B EC D

T 2T 1 A B EC D42

,322

7DEHODUHQSUHJOHGQD]ELUQDWDGROCLQDQDGRSLURW

]D [ INT ]

]D [ INT ] !

]D [ INT ]

]D [ INT ] !

7DEHODUHQSULND]]DGROCLQDWDQDGRSLURWYRWHNQDVSUHJDWDRGA GRE

INT IRUPXOD max lz IRUPXOD min lz

*UDILaNLSULND]]DGROCLQDWDQDGRSLURWYRWHNQDVSUHJDWDRGA GRE

)1(cos

p)]2()(INT2[lmaxb

xz =

)2(cos

p)]}(INT1[)1({lmaxb

xz ++=

)3(cos

p)]1()(INT[lminb

xz +=

)4(cos

p)]}(INT1[)2(2{lminb

xz +=

$JOLWH L YR]DYLVQRVWRG

01 02 0

B EC DT 1 T 2Ab

3 04 05 06 07 08 0

23,1

77

19,1

44

42,3

229 0

10 011 012 013 0

65,4

9961

,466

84,6

43

T 1

-1

2-

1

3-

2

65,4

99

9,57

2

32,7

49

51,8

94

1

2

m n = 5 ;z 1 =17 ; z 2 = 35 ; = 21 ,7 87B

EC

DA

T 2

b

4 0,85 4

2 0,42 72 4,73 0

10 6,43 9

8 6,01 2

4 5,15 8

6 5,53 8

9 0,31 5

11 0,74 2

13 1,23 1 l

b2

cos

1tg =

b1

cos

2tg =

o1 8 9 2 1 8 4,6 4=

o2 85651,46=

t b 1 2 cos b sin b tg b 1.000000 0.999462 0.997849 0.995164 0.991411 0.986597 0.980729 0.973817 0.965873 0.956911 0.946946 0.935994 0.924077 0.911214 0.897429 0.882748 0.867199 0.937208

UHODWLYHQUDGLXVQDNULYLQLWH

1122

l

SRJRQVNLRW]DSaHQLN z 1WRaND 1 T 1

A B

T 1 T 2 /4

C D

T 1 T 2 /2

E 3T1T2/4

T 2 JRQHWLRW]DSaHQLN z2WRaND 2

T 2

T 1 T 2 /4

E T 1 T 2 /2

D C

3T1T2/4 B A T 1

T 1

A CBT 2

ED3T

1T2/4

T 1T 2

/4

T 1T 2

/2

2

Presmetka Na Cilindricen Zapcest Par So Kosi Zapci

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Transcript of Presmetka Na Cilindricen Zapcest Par So Kosi Zapci