Presmetka Na Cilindricen Zapcest Par So Kosi Zapci
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Transcript of Presmetka Na Cilindricen Zapcest Par So Kosi Zapci
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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
]DSRJRQVNLRW]DSaHQLN z1 ]DJRQHWLRW]DSaHQLN z2
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
=
-
$JRORWQD]DNRVXYDZHQDRVQRYQLRWFLOLQGHUbVSRUHGSR]QDWLRWL]UD]
cos b sin b tan b b0.937208 0.348770 0.372138 20.412
VSRUHGSROHWRQDVSUHJQXYDZH
]DSRJRQVNLRW]DSaHQLN z1 ]DJRQHWLRW]DSaHQLN z2
i tan b b i tan b bB 0.372138 20.412 B 0.37214 20.412C 0.372138 20.412 C 0.37214 20.412D 0.372138 20.412 D 0.37214 20.412E 0.372138 20.412 E 0.37214 20.412
9NXSQDGROCLQDQDGRSLURWYRWHNQDVSUHJDWDRGA GRE
]D]DSaHVWSDUVR = - 1
VSUHJQXYDZHYR$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