perhitungan roda gigi transmisi new
DESCRIPTION
cara untukmenghitung rasi kecepatan roda gigiTRANSCRIPT
Perhitungan Roda Gigi Transmisi
RG3 →
Diameter roda : 19″ = 19 x 25,4 = 482, 6 mm
Roda gigi I: z1 = 50 RG2 →
m = 3
Diameter Roda gigi I = m x z1 RG1 →
= 3 x 50
= 150 mm
Keliling roda gigi I = x D roda gigi I
= x 150
= 471, 238 mm
Keliling roda = x D roda
= x 482.6
= 1516 ,132 mm
Jarak pengecatan = 1 meter
Putaran roda = 1000 mm / 1516 ,132 mm
= 0, 659 putaran
Putaran RG I = Putaran Roda ( 1 sumbu )
RG II = z2 = 40
M = 3
Diameter Roda gigi II = m x z2
= 3 x 40
= 120 mm
Keliling roda gigi II = x D roda gigi II
= x 120
= 376 ,991 mm
1000 mm = 0, 659 putaran Roda Gigi I = ……. Putaran Roda Gigi II
Putaran Roda Gigi II = ( Keliling roda gigi I x putaran Roda Gigi I ) / Keliling roda gigi II
= ( 471 ,238 x 0, 659 ) / 376 ,991
= 0, 824 Putaran
Roda Gigi III ( Shaft eksentris) → ( Putaran yang diinginkan = 1)
Putaran Roda Gigi II / Diameter Roda gigi III = Putaran Roda Gigi II ‘/ Diameter Roda gigi III ‘
Diameter Roda gigi III = ( 0, 824 x 120 ) / 1
= 98.85 mm → m = 3
Maka z3 = Diameter Roda gigi III / m
= 98.85 / 3
= 32.95 → 33
Pasangan Roda Gigi 1 dan 2 :
1. Dimensi
Data : m = 3
z1 = 50
z2 = 40
α = 20
β = 0
b = 20 mm
d1 = m x z1 = 3 x 50 = 150 mm
d2 = m x z2 = 3 x 40 = 120 mm
U = z2 / z1 = 40 / 50 = 0, 8
da1 = d1 + 2 ha = 150 + (2 x 3) = 156 mm
da2 = d2 + 2 ha = 120 + (2 x 3) = 126 mm
df1 = d1 - 2 hf = 150 - (2 x 3) = 144 mm
df2 = d2 - 2 hf = 120 - (2 x 3) = 114 mm
db1 = d1 x cos α = 150 x cos 20 ° = 140 ,954 mm
db2 = d2 x cos α = 120 x cos 20 ° = 112 ,763 mm
P = m x = 3 x = 9 ,425 mm
Pe = m x x cos α = 3 x x cos 20 ° = 8 ,856 mm
Ad = r1 + r2 = ( 150 / 2 ) + ( 120 / 2 ) = 135 mm
Inv α = tan 20 ° - ( (20 x ) / 180)
= 0, 0149
K1 = (z2 x α / 180˚) + 0, 5
= (50 x 20˚ / 180˚) + 0, 5
= 6.056 → 6
K2 = (z3 x α / 180˚) + 0, 5
= ( 40 x 20˚ / 180˚) + 0, 5
= 4, 944 → 5
wk1 = m cos α ((K1 – 0, 5) x п + ( inv α x z1 )) + 2m x X1 x sin α
= 3 cos 20˚ ((6 - 0, 5) x п + ( 0, 0149 x 50 )) + 2 x 3 x 0 x sin 20˚
= 50,81 mm
wk2 = m cos α ((K3 – 0, 5) x п + ( inv α x z2 )) + 2m x X3 x sin α
= 3 cos 20˚ ((5- 0, 5) x п + ( 0, 0149 x 40)) + 2 x 3 x 0 x sin 20˚
= 41,534 mm
Derajat overlap kontak
ε α = ( (√ ( da12 – db1
2) ) + (√ ( da22 – db2
2) ) – (2 x ad x sin α )) / 2 Pe
= ( (√( 1562 – 140,9542) ) + (√ ( 1262 – 112,7632) ) – (2 x 135 x sin 20˚)) / (2x8,856)
= 1, 734 mm
ε β = ( b x sin β ) / (m x п )
= ( 20 x sin 0 ) / ( 3 x п )
= 0
ε γ = ε α + ε β
= 1, 734 + 0
= 1, 734 mm
Tenaga penggerak Input dan Tenaga Output
na = 125 Rpm
nb = z1 x na / z2
= 50 x 125 / 40
= 156,25 Rpm
ω a = 2п x na
= 2п x ( 125 / 60 s )
= 13, 09 rad/s
ω b = 2п x nb
= 2п x ( 156,25 / 60 s )
= 16,36 rad/s
Gaya Pada Gear
Pb = Pnb x Ki → Ki = 1, 25 ( dari tabel 3 hal 38 )
= 196,2 x 1, 25
= 245.25 W
V ω1 = ( п x d2 x n2 ) / 60
= (п x 150 x 125 ) / 60
= 981,748 Nm/s = 0, 981 m/s
V ω2 = ( п x d2 x n2 ) / 60
= (п x 100 x 156,25 ) / 60
= 818,123 Nm/s = 0, 818 m/s
Ft1 = Pb / V ω1
= 245.25 W / 0, 981 m/s
= 250 N → Asumsi tenaga manusia
Ft2 = Ft1
Momen Puntir
M1 = Ft1 x rm1
= 250 x 75
= 18750 Nmm = 18,75 Nm
M2 = Ft2 x rm2
= 250 x 50
= 12500 Nmm = 12,5 Nm
2. Kelas Pelumas Oli dan Additif
Ks = ( ) . ( )
= ( ) . ( )
= 4,562 m.pa
=
= 0,645 m.pa s/m
- intrpolasi = 160 + ( ) . ( 168 – 160 )
= 163,6 M. Pa s/m
~ Sehingga dipakai ISO VG 150 system celup oli
gf = 0,5 ( - db2 . tan
= 0,5 ( - 126,86 . tan
= 7,684 mm
ga = 0,5 ( - db1 . tan
= 0,5 ( - 84,57 . tan
= 7,324 mm
w1 = 157,07
gi = ga = 0,007324 m
vg = w1 + gi . ( 1 + )
= 157,07 + 0,007324 . ( 1 + )
= 1,9162
V1 = 7,068
Karena : = = 0,271 < 0,3
Maka tidak perlu additive pada pelumas oli.
sf1& sf2
V1 = 7,068 dari table 5 dipilih kualitas 7
Ft = 1642, 61 N
W =
=
= 82,13 N/mm
3. Faktor Dinamik
Roda Gigi difrais halus = kualitas 7
d1 = 135 mm fpe = 11 µm ( Tabel 6 Roda Gigi jilid 1)
m = 3
Dari tabel 10 , untuk pasangan material St.St => Ke = 4µm
w . ki = 82,13 . 1,25
= 102,66 N/mm Cv = 0,028 interpolasi (tabel 9 Roda Gigi jilid 1)
v = 7,02 m/s
β = 0 Cβ = 1 (tabel 9)
Kv = 1 + ( 1 + ( ke . fpe . 0,65) / (w . ki) ) . Cv . Cβ . v
= 1 + ( 1 + ( 4 . 11 . 0,65) / (102,66) ) . 0,028. 1 . 7,02
= 1,253
3. Faktor Distribusi beban dari KFα
Dari table 10
Faktor kontak fE= ke . fpe – 8
= 4 . 11 – 8
= 36
QL = 0,4 + ( fE / w )
= 0,4 + (36/82,13)
= 0,838
=
= 0,591 < QL
Maka factor beban dahi KFα = QL .
= 0,838 x 1,69
= 1,416
4. Gaya Keliling Spesifik WFt
WFt = w . ki . Kv . KFα . KFβ
= 102,66. 1,253 . 1,416 . 1,336. 1
= 182,144 N/mm
YF1 = 2,6 (tabel 11 Roda Gigi jilid 1)
YF2 = 2,405 (tabel 11 Roda Gigi jilid 1)
Yε =
=
= 0,591
Yβ = 1 (karena β = 0)
σF1 = . YF1 . Yε . Yβ
= . 2,6 . 0,591 . 1
= 93,294 N/mm2
σF2 = . YF2 . Yε . Yβ
= . 2,405 . 0,591 . 1
= 86,297 N/mm2
Material St.60, St 60
Dengan batas patah dinamis ulang , diambil dari tabel 12
Matetrial sementara diambil :
Roda Gigi 1 = St.60 (σFD = 200 N/mm2) (dari tabel 12 Roda Gigi jilid 1)
Roda Gigi 2 = St.60 (σFD2 = 200 N/mm2)
Sf1 = σFD1 / σf1
= 200 / 93,294
= 2,143
Sf2 = σFD2 / σf2
= 200 / 86,294
= 2,317
5. KEKUATAN DINDING GIGI
karena εB = 00 maka menggunakan rumus
Zε =
=
= 0,877
KHα = 1 + 2 (QL – 0,5) (1/Zε2 – 1)
= 1 + 2 (0,838– 0,5) (1/0,8772 – 1)
= 1,202
KHβ = 1 ( roda gigi silindris )
Zm = 272 (tabel 13 Roda Gigi jilid 1)
w = 102,66 N/mm
WHT = w . ki . Kv . KHα . KHβ
= 102,66. 1,253 . 1,202 . 1
= 154,616 N/mm2
ZH =
=
= 1,763
H = . ZH . ZM . Zε
= . 1,763. 272 . 0,877
= 711,62 N/mm2
HD1 = 400 N/mm2
HD2 = 400 N/mm2
Material yang dipilih (dari tabel 12 Roda Gigi jilid 1)
St 60 ( HD =400 N/mm2 ; σFD = 270 N/mm2 )
Baja dikeraskan DIN 17 100 pengerasan bakar atau induksi
(dibakar sambil diputar, gigi dikeraskan terakhir)
Kekerasan RG inti = 180 Hb
Kekerasan RG luar= 180 Hb
SH1 = HD1 / H
= 400 / 711,62
= 0,562
SH2 = HD2 / H
= 400 / 711,62
= 0,562
Material yang dipilih dari table 12 = baja konstruksi umum DIN 17100
Kekerasan pada bagian inti = 180 HB
Kekerasan pada bagian permukaan = 180 HB
6. Life Time
E1E1 = E2 = 210.10= E2 = 210.103 3 N/mm
N1 = ( HD12 . SH1 2
. 3. 106 mm2/ N ) / E1
= ( 4002 . 0.562 2
. 3. 106 mm2/ N ) / 210. 106
= 721929
L1 = H1 / N1 = 721929 / ( 1500 . 60 )
= 8,02 hour
N2 = ( HD22 . SH2 2
. 3. 106 mm2/ N ) / E2
= ( 4002 . 0.562 2
. 3. 106 mm2/ N ) / 210. 106
= 721929
L2 = H2 / N2 = 721929 / ( 1000 . 60 )
= 12,03 hour
Pasangan Roda Gigi 2 dan 3 :
1. Dimensi
Data : m = 3
z2 = 40
z3 = 33
α = 20
β = 0
b = 20 mm
d2 = m x z1 = 3 x 40 = 120 mm
d3 = m x z2 = 3 x 33 = 99 mm
U = z3 / z2 = 33 / 40 = 0.825
da2 = d2 + 2 ha = 120 + (2 x 3) = 126 mm
da3 = d3 + 2 ha = 99 + (2 x 3) = 105 mm
df2 = d2 - 2 hf = 120 - (2 x 3) = 114 mm
df3 = d3 - 2 hf = 99 - (2 x 3) = 93 mm
db2 = d2 x cos α = 120 x cos 20 ° = 112 ,763 mm
db3 = d3 x cos α = 99 x cos 20 ° = 93 ,03 mm
P = m x = 3 x = 9 ,425 mm
Pe = m x x cos α = 3 x x cos 20 ° = 8 ,856 mm
Ad = r1 + r2 = ( 120 / 2 ) + ( 99 / 2 ) = 109 ,5 mm
Inv α = tan 20 ° - ( (20 x ) / 180)
= 0, 0149
K2 = (z3 x α / 180˚) + 0, 5
= ( 40 x 20˚ / 180˚) + 0, 5
= 4, 944 → 5
K3 = (z3 x α / 180˚) + 0, 5
= (33 x 20˚ / 180˚) + 0, 5
= 4.167 → 4
wk2 = m cos α ((K3 – 0, 5) x п + ( inv α x z2 )) + 2m x X3 x sin α
= 3 cos 20˚ ((5- 0, 5) x п + ( 0, 0149 x 40)) + 2 x 3 x 0 x sin 20˚
= 41,534 mm
wk3 = m cos α ((K1 – 0, 5) x п + ( inv α x z1 )) + 2m x X1 x sin α
= 3 cos 20˚ ((4 - 0, 5) x п + ( 0, 0149 x 33 )) + 2 x 3 x 0 x sin 20˚
= 32,384 mm
Derajat overlap kontak
ε α = ( (√ ( da22 – db2
2) ) + (√ ( da32 – db3
2) ) – (2 x ad x sin α )) / 2 Pe
= ( (√(1262 – 112,7632) ) + (√ (1052 – 93,032) ) – (2 x 109,5 x sin 20˚)) / (2x8,856)
= 1, 694 mm
ε β = ( b x sin β ) / (m x п )
= ( 20 x sin 0 ) / ( 3 x п )
= 0
ε γ = ε α + ε β
= 1, 694 + 0
= 1, 694 mm
Tenaga penggerak Input dan Tenaga Output
nb = 156,25 Rpm
nc = z2 x nb / z3
= 40 x 156,25 / 33
= 189,394 Rpm
ω b = 2п x nb
= 2п x ( 156,25 / 60 s )
= 16,36 rad/s
ω c = 2п x nc
= 2п x ( 189,394 / 60 s )
= 19,83 rad/s
Gaya Pada Gear
Pb = Pnb x Ki → Ki = 1, 25 ( dari tabel 3 hal 38 )
= 196,2 x 1, 25
= 245,25 W
V ω2 = ( п x d2 x n2 ) / 60
= (п x 100 x 156,25 ) / 60
= 818,123 Nm/ = 0, 818 m/s
V ω3 = ( п x d3 x n3 ) / 60
= (п x 99 x 189,394 ) / 60
= 981,748 Nm/s = 0, 981 m/s
Ft2 = Pb / V ω2
= 245,25 / 0, 818 m/s
= 200.615 N
Ft3 = Ft2
Momen Puntir
M2 = Ft2 x rm2
= 200,615 x 50
= 10030,75 Nmm = 10,03 Nm
M3 = Ft3 x rm3
= 200,615 x 16.5
= 3310,148 Nmm = 3,31 Nm
2. Kelas Pelumas Oli dan Additif
Ks = ( ) . ( )
= ( ) . ( )
= 4,562 m.pa
=
= 0,645 m.pa s/m
- intrpolasi = 160 + ( ) . ( 168 – 160 )
= 163,6 M. Pa s/m
~ Sehingga dipakai ISO VG 150 system celup oli
gf = 0,5 ( - db2 . tan
= 0,5 ( - 126,86 . tan
= 7,684 mm
ga = 0,5 ( - db1 . tan
= 0,5 ( - 84,57 . tan
= 7,324 mm
w1 = 157,07
gi = ga = 0,007324 m
vg = w1 + gi . ( 1 + )
= 157,07 + 0,007324 . ( 1 + )
= 1,9162
V1 = 7,068
Karena : = = 0,271 < 0,3
Maka tidak perlu additive pada pelumas oli.
sf1& sf2
V1 = 7,068 dari table 5 dipilih kualitas 7
Ft = 1642, 61 N
W =
=
= 82,13 N/mm
3. Faktor Dinamik
Roda Gigi difrais halus = kualitas 7
d1 = 135 mm fpe = 11 µm ( Tabel 6 Roda Gigi jilid 1)
m = 3
Dari tabel 10 , untuk pasangan material St.St => Ke = 4µm
w . ki = 82,13 . 1,25
= 102,66 N/mm Cv = 0,028 interpolasi (tabel 9 Roda Gigi jilid 1)
v = 7,02 m/s
β = 0 Cβ = 1 (tabel 9)
Kv = 1 + ( 1 + ( ke . fpe . 0,65) / (w . ki) ) . Cv . Cβ . v
= 1 + ( 1 + ( 4 . 11 . 0,65) / (102,66) ) . 0,028. 1 . 7,02
= 1,253
3. Faktor Distribusi beban dari KFα
Dari table 10
Faktor kontak fE= ke . fpe – 8
= 4 . 11 – 8
= 36
QL = 0,4 + ( fE / w )
= 0,4 + (36/82,13)
= 0,838
=
= 0,591 < QL
Maka factor beban dahi KFα = QL .
= 0,838 x 1,69
= 1,416
4. Gaya Keliling Spesifik WFt
WFt = w . ki . Kv . KFα . KFβ
= 102,66. 1,253 . 1,416 . 1,336. 1
= 182,144 N/mm
YF1 = 2,6 (tabel 11 Roda Gigi jilid 1)
YF2 = 2,405 (tabel 11 Roda Gigi jilid 1)
Yε =
=
= 0,591
Yβ = 1 (karena β = 0)
σF1 = . YF1 . Yε . Yβ
= . 2,6 . 0,591 . 1
= 93,294 N/mm2
σF2 = . YF2 . Yε . Yβ
= . 2,405 . 0,591 . 1
= 86,297 N/mm2
Material St.60, St 60
Dengan batas patah dinamis ulang , diambil dari tabel 12
Matetrial sementara diambil :
Roda Gigi 1 = St.60 (σFD = 200 N/mm2) (dari tabel 12 Roda Gigi jilid 1)
Roda Gigi 2 = St.60 (σFD2 = 200 N/mm2)
Sf1 = σFD1 / σf1
= 200 / 93,294
= 2,143
Sf2 = σFD2 / σf2
= 200 / 86,294
= 2,317
5. KEKUATAN DINDING GIGI
karena εB = 00 maka menggunakan rumus
Zε =
=
= 0,877
KHα = 1 + 2 (QL – 0,5) (1/Zε2 – 1)
= 1 + 2 (0,838– 0,5) (1/0,8772 – 1)
= 1,202
KHβ = 1 ( roda gigi silindris )
Zm = 272 (tabel 13 Roda Gigi jilid 1)
w = 102,66 N/mm
WHT = w . ki . Kv . KHα . KHβ
= 102,66. 1,253 . 1,202 . 1
= 154,616 N/mm2
ZH =
=
= 1,763
H = . ZH . ZM . Zε
= . 1,763. 272 . 0,877
= 711,62 N/mm2
HD1 = 400 N/mm2
HD2 = 400 N/mm2
Material yang dipilih (dari tabel 12 Roda Gigi jilid 1)
St 60 ( HD =400 N/mm2 ; σFD = 270 N/mm2 )
Baja dikeraskan DIN 17 100 pengerasan bakar atau induksi
(dibakar sambil diputar, gigi dikeraskan terakhir)
Kekerasan RG inti = 180 Hb
Kekerasan RG luar= 180 Hb
SH1 = HD1 / H
= 400 / 711,62
= 0,562
SH2 = HD2 / H
= 400 / 711,62
= 0,562
Material yang dipilih dari table 12 = baja konstruksi umum DIN 17100
Kekerasan pada bagian inti = 180 HB
Kekerasan pada bagian permukaan = 180 HB
6. Life Time
E1E1 = E2 = 210.10= E2 = 210.103 3 N/mm
N1 = ( HD12 . SH1 2
. 3. 106 mm2/ N ) / E1
= ( 4002 . 0.562 2
. 3. 106 mm2/ N ) / 210. 106
= 721929
L1 = H1 / N1 = 721929 / ( 1500 . 60 )
= 8,02 hour
N2 = ( HD22 . SH2 2
. 3. 106 mm2/ N ) / E2
= ( 4002 . 0.562 2
. 3. 106 mm2/ N ) / 210. 106
= 721929
L2 = H2 / N2 = 721929 / ( 1000 . 60 )
= 12,03 hour