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    PAMUKKALE ÜNİVERSİTESİMAKİNE MÜHENDİSLİĞİ BÖLÜMÜ

    DERS : MAKİNE ELEMANLARIKONU : 2 KADEMELİ REDÜKTÖR

    TASARIMI

    ÖĞR. ADI : MUHAMMEDBOZKURTÖĞR. NUMARASI :08244014 İ.Ö.ÖĞR. ADI : DOÇ.DR. TEZ AN!EKER İOĞLU

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    V"#$%"& B$%'$%"#

    ($#$) (*+* , Pg - / ($#$) D" $# S3 565 , n1 - 1700 d /d

    T 9%3 Ç" #$ O#3&5 , iT - 14K3;" " S3 565 2

    1.K3;" " D$)%$ T$9$ H"%$62.K3;" " D$)%$ T$9$ H"%$61. Kademe ; i 12 4 2. Kademe ; i 34 = 3.5

    1.ÖN HESAPLAMALAR VE MEKANİZMA ÖZELLİKLERİ

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    z1 : ($#$) $%$ 9$& & 5#. z4 : Ç5 5) $%$ *?"#$&;" $ ;@&;*#*%"& 5#.

    β : H"# $ $ 3;" " $ $& 3>63 565 S 1./ 3%5& 5)>5#.

    D$)%$ C>C6C&C& >35#5%3+3 >5#.

    D$)%$%"# 3?;5# 3 @&>" $ %" $ 3% ";$% $) " ;$)%"#$ 93#%3>5% 5)>

    M$%%"# $ $ 3>3 %3& 5) " 6"

    B*>*& " 3&$? 3;3 "#$ 1 3%5& 5)>5#.

    M$% D@&;*# " M "&>%"#$ " D" $# S3 5%3#5

    1 numaralıgiriş mili için; M d 1 =9550 ∗ P

    n1 F//0 G5

    1300 7= 70. = N

    n1 = 1400 d /d

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    2 numaralıaramili için; M d 2 = M d 1∗i12 7= 70. = G 4 14=F27.04

    N n2 = n1 /4 72/ d /d3 numaralıçıkış miliiçin ; M d 3 = M d 2∗i34 14=F27.04G7./ /14270.=4

    N n3 = n2 /3.5 F2.8/ d /d

    1-HELİS Dİ!LİLER İÇİN MODÜL HESABI 3-D$) ;$ $ C 3 " ">$&" '@#" &># %:

    H"%$6 ;$)%$ '#C C $ $& 1 #N$M = 6" "&>36 & "%$ $6" $%;$.

    mn 1 ≥ 3√2∗ M d 1∗ K f ∗ K i∗ K v∗ K m∗ K ε∗cos βφ m∗ z1∗σ em

    M ;*% ;" "#$ mn 1 2./ 3 C% ";$%;$.

    M d 1 7= 70. = N

    K f 2.F , ze 1 = 19.282 J 0 $ $& # 3 >@#*-

    K i 1.20 ,D*?'*& 3%5)3& "%" >#$ > #C " #"& $ $& $)%"> "3 >@#*-

    K v 1.0/42∗π ∗1300 ∗¿

    60 ∗2

    2.5 ∗16

    2= 2.72 msve y ksek kali!e az y k gelendişli için"ız fak!#r

    v1 = ¿¿

    K m= 1.2 , φ∗mn 1 = 12∗2.5 = 30iyi ya!aklanmışaz se"imli mil için y k da$ılım fak!#r -

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    K ε 0.== ,H"%$6 ;$)%$ " ;$) ;$ $&;"& 5#5% 3 3 '@#" &># % $ $& 3 #3 3

    3 >@#* K ε 0.2/0.75

    ε an¿

    H"%$6 ;$)%$%"#;" 3 #3 3 #3&5

    K ε 0.2/0.75

    ε an

    εanε

    acos β%

    2 = 1.611

    cos18.742 = 1.796

    tan β% β∗¿cos a ! = tan 20 ∗cos 21.172 β%= 18.74 °

    tan ¿

    ε= εa +ε β

    εa =√ r a 1

    2 − r %12 +√ r a 2

    2 − r %22 − a d 1∗sin a !

    π ∗mn 1∗cos a !

    r a 1d 1 +2∗" a

    2 d 1 = z1∗mn 1

    cos β

    16 ∗2.5

    cos 20 42./=" a = mn1 2./

    r a 1 = 23.78 mm

    r %1d 1∗cos a!

    2 tan a ! =tan 20

    cos20 0.78 a ! 1 = 21.172 °

    r %1 = 19.84 mm

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    d 2 = z2∗mn 1

    cos β z2 = z1∗i12 1=G4 =4

    d 2 = 170.26 mm

    r a 2d 2 +2∗" a

    2 8 .=7

    r %2d 2∗cos a!

    2 F.78

    a d 1 = mn 1∗( z1 + z2 )2∗cos β

    2.5 ∗(16 +64 )2∗cos20 10=.418

    εa =13.109 +37.119 − 38.43

    7.320 1.=11

    ε β=%∗sin β

    Pn

    30 ∗sin 20

    2.5 ∗π 1.70

    ε 2.F11 K ε 0.==

    D$) ;$ $&;"& "6$% " " '@#" " &$ ">%$ '"#$% "

    σ em K %∗ K y∗σ &&

    K ç∗'

    K %= 1 , mn 1 2.5

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    σ && 1000N mm2 ,1 #N$M = 6" "&>36 & "%$ $ "σ )* = σ && $ $& $%'$%$ $?"%'";"& C&3& C 3 " "> ;" "#$

    -

    K ç= 1 ++∗( K ! − 1 )

    0.8/ ,# 0.78G2./ 0.F/ " R 1200 N mm2

    $ $& "&>$

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    K a= 2.36 , β= 20 " J 0 $ $& 3 #3 3 3 565 3 >@#*-

    K i= 1.20 ,D*?'*& 3%5)3& "%" >#$ > #C " #"& $ $&$)%"> " 3 >@#*-

    K v 1.0/42∗π ∗1300 ∗¿

    60 ∗2

    2.5 ∗16

    2= 2.72 msve y ksek kali!e az y k gelendişli için "ız fak!#r

    v1 = ¿¿

    K m= 1.2 , φm∗2.5 = 30ve iyi ya!aklanmışaz se"imlimil için y kda$ılım fak!#r -

    K ε 0.787 ,H"%$6 ;$)%$ *?" 365&+5&3 '@#" &># % "ε β= 1.30 >1 $ $& $%'$%$

    $?"%'";"& 3%5&3& 3 #3 3 3 >@#* # *%*&;"&1 /¿√ ε , = 0.787

    K ε= √ ¿ -

    E 2.1G 105

    N mm2

    i12 = 4

    Pem=σ -lim∗ K #

    '

    σ -lim = ¿ 1/10 N mm2

    K #= 1 , 107 y k !ekrarıiçin -

    Pem=1510 ∗1

    1.5= 1006.66 . /mm2

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    mn 1 ≥ 0.7 ∗cos 203√36730.76 ∗2.36 2∗1.2 ∗1.054 ∗1.2 ∗0.787 ∗2.1 ∗10 5∗512 ∗16 2∗1006.66 2∗4

    mn 1 ≥

    1.8071.807 1.7/1 %;C C $ $& $# *6> ;" "#" C 3#%3>>5 5 5?;3 ;*%;" "#$ $?" C%3)5#5?. mn 1 = 2 ./

    2-HELİS Dİ!LİLER İÇİN MODÜL HESABI3-D$) ;$ $ C 3 " ">$&" '@#" &># %:

    H"%$6 ;$)%$ '#C C $ $& 1 #N$M = 6" "&>36 & "%$ $ 6" $%;$.

    mn ≥ 3√2∗ M d 2∗ K f ∗ K i∗ K v∗ K m∗ K ∈∗cos βφm∗ z3∗σ em

    M d 2 14=F27.04 N

    M ;*% ;" "#$ mn 2 2 3 C% ";$%;$.

    i34 =/ 4/ 3 / 4 /= / 3 1= i34 =

    3.5

    /e 3 = / 3

    (cos β

    )3= 19.282 0 20 ;$)

    K f = 2.87 ( 1= 0 ; /e 3 = 20 )

    K i= 1.25 ( & zg nçalışanelek!rik m(!(ru;kren )

    K v= 1.01 , * 6" 3%$>";" 3? * '"%"& v=π ∗325

    60∗2∗10

    − 3∗16 0./44 6

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    K m= 1.2 , φm∗2 = 24 ve iyi ya!aklanmışaz se"imlimil için y k da$ılım fak!#r -

    εa =√ r a 3

    2 − r %32 +√ r a 4

    2 − r %42 − a d 3∗sin a !

    π ∗mn 2∗cos a !

    r a 3d 3 +2∗" a

    2 d 3 = z3∗mn 2

    cos β

    16∗2

    cos20 74.0/

    " a = mn 2 2

    r a 3 = 19.025 mm

    r %3d 3∗cos a!

    2 tan a ! =tan 20

    cos 20 0.78 a ! = 21.172 °

    r %3 = 15.875 mm

    d 4 = z4∗mn 2

    cos β

    z4 = z3∗i34 1=G7./ /=

    d 4 = 119.187 mm

    r a 4d 4 +2∗" a

    2 =1./F7/

    r %4d 4∗cos a!

    2 //./ 0

    a d 3 =mn2∗( z3 + z4 )

    2∗cos β

    2∗(72 )2∗cos 20 =.=20

    εa =10.484 +26.56 − 27.672

    π ∗2∗cos21.172 1.=007

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    ε%=%∗sin β

    Pn

    24 ∗sin20

    2∗π 1.70

    ε 2.F0 7 εanε a

    cos β2 1.812

    K ε 0.2/ 0.75

    1.812= 0.663

    D$) ;$ $&;"& "6$% " " '@#" " &$ ">%$ '"#$% "

    σ em K %∗ K y∗σ && K ç∗'

    K %= 1 , mn 2 2

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    σ em 1∗0.928 ∗1000

    1.250 ∗1.5 4F4.F7 N mm2

    mn 2 ≥ 3

    √2∗146923.04 ∗2.87 ∗1.25 ∗1.2 ∗1.01 ∗0.663 ∗cos20

    12∗16∗494.93 1.8F

    2 ¿ 1.8F %;C C $ $& 3 C% ";$%"& ;*% ;$);$ $ C 3 " ">$&" '@#" " &$ ">%$;$#. *?" 365&+5&3'@#" ;" #$ > #C " #"& $ $& $)%"> " 3 >@#*-

    K v= 1.01 , * 6" 3%$>";" 3? * '"%"& v=π ∗325

    60 ∗2∗10−3

    ∗16 0./44 6

    K m= 1.2 , φ∗2 = 24 ve iyi ya!aklanmışaz se"imlimil için y k da$ılım fak!#r-

    K ε=√ 1εa =√ 11.6003 = 0.79

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    E 2.1G 105

    N mm2

    i34 = 3.5

    Pem=σ -lim∗ K #

    '

    σ -lim = ¿ 1/10 N mm2 K #= 1 , 10 7 y k !ekrarıiçin -

    Pem=1510 ∗1

    1.5 = 1006.66 . /mm2

    mn 2 ≥ 0.7 ∗cos203√146923.04 ∗2.36 2∗1.25 ∗1.2 ∗1.01 ∗0.79 ∗2.1 ∗10 5∗4.512∗16 2∗1006.66 2∗3.5 = 1.F

    1.F 1.8F %;C C $ $& $# *6> ;" "#" C 3#%3>>5 5 5?;3;*% ;" "#$ $?" C%3)5#5?. mn 2 = 2

    7-H"%$6 D$)%$%"#$& B C>%3&;5#5% 365

    3-P$& & ;$)%$&$& C>%3&;5#5% 365 , / 1

    -:mn 1 = 2 ./

    m! 1 = mn 1cos 20

    = 2.66

    da 1 = 44.42

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    d 1 =16∗2.5

    cos 20= 42.567

    "a 1 mn 1 = 2 ./

    "f 1 1.2/G2./ 7.12/

    d f 1 d 1 Q 2 G "f 1 42./= Q 2./ G 7.12/ 74. /4

    a ! 1 21.1 2

    d %1 d 1∗cos a ! 1 7F.=F7

    Pn 1 Pn 2 mn 1 G π 2./ G π .8/

    P! 1 P! 2 = m! 1 G π 2.== G π 8.7/2

    " 1 " 2 "a 1 "f 1 2./ 7.12/ /.=2/

    %1 %2 = ¿ φ G mn 1 70

    a d 1 mn 1

    2∗cos β∗(/ 1 +/ 2 )= ¿ 10=.41

    -Ç3# ;$)%$&$& C>%3&;5#5% 365 , / 2 -:

    mn 1 mn 2 = ¿ 2./ / 2 = / 1∗i12 = 64

    m! 2 = mn 2cos 20

    = 2.66

    d a 2 = d 2 +2∗" a 2 = 175.26 mm

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    d 2 =64 ∗2.5

    cos 20= 170.26

    " a 2 mn 2 = 2 ./

    " f 2 1.2/G mn 2 7.12/

    d f 2 d 2 Q 2 G " f 2 1 0.2= 2 G 7.12/ 1=4.01

    a ! 1 a! 2 21.1 2

    d %2 d 2∗cos a ! 2 = ¿ 1/8.

    2.K3;" "

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    d %3 d 3∗cos a ! 3 71. /1

    Pn 3 Pn 4 mn 3 G π 2 G π =.28

    P! 3 m! 3 G π 2.128 G π =.=81

    " 3 " 4 "a 3 " f 3 2 2./ 4./

    %3 φ G mn 3 24

    a d 2 m

    n3

    2∗cos β∗(/ 3 +/ 4 ) =.=20

    ;-Ç3# ;$)%$&$& C>%3&;5#5% 365 , / 4 -:

    mn 3 2

    m! 4 = mn 4cos 20

    = 2.128 mm

    da 4 = d 4 +2∗" a 4 = 110.41 mm

    d 4 = 56∗2cos 20 = 106.41 mm

    "a 4 mn 4 = 2 mm

    " f 4 1.2/G2 2./

    d f 4 d 4

    Q 2 G " f 4

    101.41

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    a ! 4 21.1 2

    d %4 d 4 G + 6 a! 4 FF.22

    4-MİLLERİN BO UTLANDIRILMASI3-($#$) $%$&$& C>%3&;5#5% 365:M3%?" " 1 #N$M = )" $%;$

    ) ! 1= M d 1

    d 1∗2 2G 36730.7642.56 1 2=.0=F N

    d 1 = z1

    cos 20∗mn 1

    16 ∗2.5

    cos 20 42./=

    ) r 1= ) ! 1∗!an,

    2(sβ 1 2=.0=F G tan20

    cos20 ==8.// N

    ) a 1 = ) ! 1∗!anβ 1 2=.0=F G>3&20 =28.27 N

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    ;*?%" $&;"

    ∑ M 0

    ) 3 y∗135 ) r 1∗35 − ) a 1∗(42.567

    2)

    ) 3 y 4.282 N

    ∑ ) y 0 ) 4 y /F4.2=8 N

    ∑ ) 1= 0 ) 4a − ) a 1 = 0 ) 4a = 628.237 .

    Z ;*?%" $&;"

    ∑ M 4 0 ) 3 z∗135 = ) ! 1∗35

    ) 3 z1726.069 ∗35

    135 44 .4FF N

    ∑ )

    z 0 ) 4 z ) ! 1− ) 3 z

    12 8./ N

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    M e2= √ M e5 2 + M e /

    2

    M e2= √ 20.7992

    +44.7492

    = 49346.44 .mm M d2= 36736 .mm

    D 70 3 C% ";$%;$.

    σ ∗¿T&e¿

    σ T&e∗ K %∗ K y K ç

    σ T&e /80 N mm2

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    K % 0.88 ,; 7/ $ $& C> 3 >@#*-

    K y 0.F8, 6 m= ¿ 1200 N mm2

    " *?" $ 93#%3>5% 5) ;C#C

    $ $& *?" 3>63 565- K ç 1.1/

    77 7 σ ∗¿T&e

    ¿580 ∗0.88 ∗0.98

    1.15 ¿ 474.F4F N mm2

    ;

    σ ∗¿T&e M e2

    ¿¿

    ¿2 + 34∗( M d2 6 e )

    2

    ¿¿

    32 ∗sπ

    ∗√ ¿

    ≥ 3√ ¿

    6 e= 780 . /mm2

    ; ≥ 3√32∗1.5π ∗√(49346.44434.949 )2 + 34 ∗(36736780 )2

    ; ≥ 12.2=0 77 7 D 70 3%5&5#.

    A%5&3& 39 C%C&3& 39 ;" "#$&;"& * * %;C C $ $&" &$ ">%$;$#.

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    (İRİ! MİLİ İMALAT RESMİ

    -A#3 $%$& C>%3&;5#5% 365:

    d 3 z3∗mn3

    cos β 16∗2

    cos20 74. 0/

    ; ≅ ,1.2 1.4- dmil

    ) ! 2= M d 2d 2∗2 2G

    146923.04

    170.26 1 2=.0=F N

    ) r 2= ) ! 2∗!an,

    2(sβ 1 2=.0=F G tan20

    cos20 ==8.// N

    ) a 2 = ) ! 2∗tan20 =28.27 N

    ) ! 3= M d 2d 3∗2 2G

    146923.04

    34.05 8=2F.84 N

    ) r 3= )

    ! 3∗

    !an,

    2(sβ 8=2F.84 Gtan20

    cos20 7742./8 N

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    ) a 3 = ) ! 3∗tan20 7141 N

    ;*?%" $&;"

    ∑ M 0 ) 2 y∗135 = ) a 3∗17.025 + ) r 3∗100 − ) r 2∗35 − ) a 2∗85.13

    ) 8y∗135 = 3141 ∗17.025 +3342.58 ∗100 − 668.55 ∗35 − 628.237 ∗85.13

    ) 2 y 2702.=1 N

    ∑ ) y 0 ) & y 7742./8 2702.=1 Q ==8.// 7 1.42N

    Z ;*?%" $

    ∑ M 0

    ) 2 z∗135 = ) ! 3∗100 + ) ! 2∗35

    ) 2 z∗135 = 8629.84 ∗100 +1726.069 ∗35

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    ) 2 z =87F.F N

    ∑ ) z 0 ) & z 8629.84 +1726.069 Q=87F.F 7/1/.F7 N

    M e)

    = √ M 2e5

    + M 2e9

    M e) = √ 80.592 +239.39 2 = 252.59 k.mm M %= 207.79 k.mm

    σ ∗¿T&e¿

    σ T&e∗ K %∗ K y K ç

    = 580 ∗0.88 ∗0.981.15

    = 434.94 . /mm2

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    ;

    σ ∗¿T&e M e)

    ¿¿

    ¿2 + 34∗

    ( M %

    6 e )2

    ¿¿

    32 ∗sπ

    ∗√ ¿

    ¿ 3√ ¿

    ; ¿3√32∗1.5π ∗√(252590434.94 )2 + 34∗(207790780 )2 7777777d = 21.218 mm

    ; 40 3 C% ">>$ 40 ¿21.218 %;C C& $ $& " &$ ">%$

    ARA MİL İMALAT RESMİ

    +-Ç5 5) $%$& C>%3&;5#5% 365:

    ) ! 4 = M d 3d 4∗2 2G

    514230.64

    106.41 F==/.08 N

    ) r 4= ) ! 4∗!an,

    2(s, F==/.08Gtan20

    cos20 7 47./= N

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    ) a 4= ) ! 4∗!an, F==/.08G tan 20 7/1 .8 N

    ;*?%" $

    ∑ M 0

    ) * y∗145 = 3743.56 ∗110 − 3517.8 ∗53.205 = 1549.15 .

    ∑ ) y 0

    ) - y= 3743.56 − 1549.15 = 2194.41 .

    Z ;*?%" $

    ∑ M 0

    ) * z∗145 = ) ! 4∗110 F==/.08G110

    ) * z 772.21 N

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    ∑ ) z 0

    ) - z ) ! 4 ) * z F==/.08 Q 772.21 2772.8 N

    M e= √ M 2

    : y❑+ M 2 : z❑

    M e= 352.296 k.mm M %= 524.23 k.mm

    σ ∗¿T&e¿

    σ T&e∗ K %∗ K y K ç

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    σ T&e /80 N mm2

    K % 0.87 ,; /0 $ $& C> 3 >@#*-

    K y 0.F8 , 6 m= ¿ 1200 N mm2

    " *?" $ 93#%3>5% 5) ;C#C$ $& *?" 3>63 565-

    K ç 2.2/ , # A " $% " ;C#C C " 6 m= ¿ 1200 N mm2

    $ $&"&>$ 3>63 565-

    D /0 3%5&;5

    77 7 σ ∗¿T&e¿580 ∗0.83 ∗0.98

    2.25 ¿ 20F.= N mm2

    ;

    σ ∗¿T&e M e

    ¿¿

    ¿2 + 34∗

    ( M %

    6 e )2

    ¿¿

    32 ∗sπ

    ∗√ ¿

    ≥ 3√ ¿

    6 e= 780 . /mm2

    ; ≥ 3√32∗1.5π ∗√(352296209.67 )2 + 34∗(524230780 )2

    ; ≥ 70.0= 77 7 D /0 3%5&5#.

    A%5&3& 39 C%C&3& 39 ;" "#$&;"& * * %;C C $ $&" &$ ">%$;$#.

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    /-KAMA BAĞLANTISI APILAN Dİ!LİLERİN KAMAHESAPLARI1-A#3 $% *?"#$&;" $ 3 3%3#5& 565&5& 395%3+3 5 40 ;$#.

    B3 %3&>5;3 %C)3+3 >" ">6"% C ">

    ) ! =2∗ M d 2

    d = 2∗146923.04

    40= 7346.15 .

    D$)%$ $ $ 3;"> 3 3 $%" $%" &>3 395%3+3 >5#.BC *?;"&

    ) ! 1= ) !

    2 7= 7.0 N

    ; 40 14 < F ! 1 /./

    K3 3 3%?" "6$ E77/ '"&"% 395 "%$ $ 6" $%;$.

    K3 3 $%" $% 3#365&;3 $ *?" 365&+5 &># %*

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    P ) ! 1! 1∗

    < P em=ℜ

    '

    3673.07

    5.5 ∗ <

    335

    1.57777

    L ≥ 2.99 mm

    K3 3 $%" '@ " 3#365&;3 *?" 365&+5 &># %*

    L ≥ 2∗s∗ Md

    d (" − ! 1 )∗ℜ∗ z ? 2 , $% *?"#$&;" $ 3 3

    63 565-

    L ≥ 2∗1.5 ∗146923.04

    40 ∗(3.5 )∗355 ∗2 4.=F

    K"6$% " &># %*

    L ≥ 4∗s∗ Mdd∗%∗ℜ∗ z

    L ≥ 4∗1.5 ∗146923.04

    40 ∗14 ∗355 ∗2 2.74

    K3 3 $%" '@ " 3#365&;3 %C)3& *?" 365&+5&3 '@#"395%3& &># % ;" 3 3 C?C&%C C 3J 5 5)>5#.K3 3

    >*#* %3#3 A >$9$ C 'C 3 365 6" $% $)>$#.E);" "# 3 3C?C&%C C

    eş= +% 4.=F 14 18.=F % 3%5;5#.

    TS 14 F A 14GFG20 )" %$&;" 2 3;"> 3 3 6" $%$#.

    2-Ç5 5) $%$ *?"#$&;" $ 3 3%3#5&

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    Ç5 5) $%$ *?"#$&;" 3 3 $%" $%" &>3 395%3+3 >5#.BC *?;"&

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    50 ∗(4 )∗355 ∗2 11./12

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    K"6$% " &># %*

    L ≥ 4∗s∗ Mdd∗%∗ℜ∗ z

    L ≥ 4∗1.5 ∗514230.64

    50 ∗16 ∗355 ∗2 /. /=

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    >*#* %3#3 A >$9$ C 'C 3 365 6" $% $)>$#.E);" "# 3 3C?C&%C C

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    1409.92= 0.44 >e= 0.2 7 9 = 0.92 5 = 0.6

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    ) &r= √ ( ) & y )2 +( ) & z )

    2 = √ 371.42 2 +3515.93 2 = 3535.49 .

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    /7 N /7000 N

    D$&3 $ ");" "# C ">

    ) 8 r= 7217.14 .

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    60∗325 ∗( 53000

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    2 = √ 2194.41 2 +2332.87 2 = 3202.76 .

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    3>3 5& & $&3% @ #* "= 10

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    60∗n3∗( 8 ) - )

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    3.333

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    "= 10

    6

    60∗92.85∗( 345007494.07 )

    3.333

    = 29119.48 >20000 "

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