ME6601 - Design of Transmission System
UNIT 2 & 3 DESIGN OF GEARS (Using Basic Relations/Gear Life) STEP SPUR 1 Calculation of Gear Ratio
2
3
4
5
𝑖=
⁄
=
⁄
Selection of Materials Select Pinion and Gear Materials (Pg.No.: 8.5)
(Pg.No.:8.18) [𝜎 ] = . 𝐻 . 𝐾 [𝜎 ] = . 𝐻 . 𝐾 (Pg.No.:8.16) Calculation of Centre Distance ≥ 𝑖+
√
(Pg.No.: 8.13) Assume Ψ = . 7
𝑖=
⁄
=
⁄
Selection of Materials From PSG data book Pg.no: 1.4,1.25,8.4 Select Pinion and Gear Materials Calculation of Gear Life Calculation of Gear Life If not given, Assume 20,000hrs If not given, Assume 20,000hrs Life Life Calculation Initial Torque Calculation Initial Torque [Mt ] = 𝑘. 𝑘 . [Mt ] = 𝑘. 𝑘 . Assume K.Kd = 1.3 (Pg.No.: Assume K.Kd = 1.3 (Pg.No.: 8.15) 8.15) [𝜎 ],(σ Calculate E, Calculate E, [𝜎 ],(σc) c) E (Pg.No.:8.14) E (Pg.No.:8.14) . . 𝑙 𝑙 [𝜎 ] = [𝜎 ] = . 𝜎− . 𝜎− (Pg.No.:8.18) . . 𝜎
6
HELICAL Calculation of Gear Ratio
.7 [𝜎 ]
𝑞 [𝑀𝑡 ]
𝑖𝜓
Selection of Number of teeth Assume Z1 , Say or Z2 = i Z 1
[𝜎 ] = [𝜎 ] =
𝜎
.𝐻 .𝐾 . 𝐻 . 𝐾 (Pg.No.:8.16)
Calculation of Centre Distance ≥ 𝑖+
√
(Pg.No.: 8.13) Assume Ψ = .
.7 [𝜎 ]
𝑞 [𝑀𝑡 ]
𝑖𝜓
Selection of Number of teeth Assume Z1 , Say or Z2 = i Z 1
BEVEL Calculation of Gear Ratio 𝑖=
⁄
=
WORM Calculation of Gear Ratio ⁄
𝑖=
⁄
=
⁄
Selection of Materials From PSG data book Pg.no: 1.4,1.25,8.4 Select Pinion and Gear Materials
Selection of Materials From PSG data book Pg.no: Select Worm and Worm Gear Materials
Calculation of Gear Life If not given, Assume 20,000hrs Life
Selection of Number of teeth Assume Z1 , Say Z2 = i Z 1 Calculation Initial Torque [Mt ] = 𝑘. 𝑘 . Assume K.Kd = 1 (Pg.No.: 8.15&8.44) Calculate [𝜎 ],(σc) (Pg No.:8.45) Take vs = 3m/s
Calculation Initial Torque [Mt ] = 𝑘. 𝑘 . Assume K.Kd = 1.3 (Pg.No.: 8.15) Calculate E, [𝜎 ],(σc) E (Pg.No.:8.14) . 𝑙 [𝜎 ] = . 𝜎− (Pg.No.:8.18)
[𝜎 ] = [𝜎 ] =
. 𝜎
.𝐻 .𝐾 . 𝐻 . 𝐾 (Pg.No.:8.16)
Calculation of Cone Distance ≥𝜓 √ 𝑖+
(Pg.No.: 8.13) Assume Ψy = 3
.7 ) − . )[𝜎 ] 𝑦
√( (𝜓
Selection of Number of teeth Assume Z1 , Say or Z2 = i Z 1
Calculation of Centre Distance 𝑞 [𝑀𝑡 ]
𝑖
= [
𝑞
+ ] √[
(Pg.No.:8.44) q=11
⁄𝑞 [𝜎 ]
]
[
]
ME6601 - Design of Transmission System
STEP SPUR 8 Calculation of module = (Pg.No.: +
9
10
11
12
13
8.22)Round the "m" Value (Pg.No.:8.2) Revise Centre Distance + (Pg.No.: 8.22) =
Calculation of b,d1, v and Ψp =𝛹 = 𝜋 𝑣= ∗ 𝛹 = ⁄ Selection of quality of gears Using Pitch line velocity and Types, Select IS quality (Pg.No. 8.3) Revise Design Torque [Mt ] Revise K (Pg.No.: 8.15) Revise Kd Value (Pg.No.: 8.16) [Mt ] = 𝑘. 𝑘 .
Check for bending σb i+ σ = .m. .y x[Mt ](Pg.No.: 8.13) y = form Factor (Pg.No.: 8.18) σb ( σb)
HELICAL Calculation of module = 𝑠 (Pg.No.: +
8.22)Round the "m" Value (Pg.No.:8.2) Revise Centre Distance + (Pg.No.: 8.22) = 𝑛 𝛽
Calculation of b,d1, v and Ψp =𝛹 𝑣=
=
𝛹 =
𝜋 ∗
8.13) yv = form Factor (Pg.No.: 8.18) =
σb ( σb)
𝑠
+
Revise Cone Distance (Pg.No.: 8.38) = . √ + Calculation of b,mav, d1, v and Ψy =
⁄
Check for bending σb .7 i+ σ = .m . .y x[Mt ](Pg.No.: v
. √
Round the "m" Value (Pg.No.:8.2)
𝑠
Selection of quality of gears Using Pitch line velocity and Types, Select IS quality (Pg.No. 8.3) Revise Design Torque [Mt ] Revise K (Pg.No.: 8.15) Revise Kd Value (Pg.No.: 8.16) [Mt ] = 𝑘. 𝑘 . n
BEVEL Calculation of transverse module = (Pg.No.: 8.38)
𝑣=
=
=
𝛹 =
𝜓
−
𝜋 ∗
𝑠𝑖
⁄
Selection of quality of gears Using Pitch line velocity and Types, Select IS quality (Pg.No. 8.3) Revise Design Torque [Mt ] Revise K (Pg.No.: 8.15) Revise Kd Value (Pg.No.: 8.16) [Mt ] = 𝑘. 𝑘 . Check for bending σb σ =
R√ i +
R− .
mt . .yv
x[Mt ] (Pg.No.: 8.13)
yv = form Factor (Pg.No.: 8.18) =
σb ( σb)
𝑠
WORM Calculation of axial module = (Pg.No.: 8.43 +
)Round the "m" Value (Pg.No.:8.2) Revise Centre Distance = . 𝑞+ (Pg.No.: 8.43) Calculation of d ,v, γ, and vs =𝑞 (8.43) = 𝜋 𝑣 = 𝑣 =
𝜋
= tan− ( ⁄𝑞 ) 𝑣 𝑣 = ⁄cos (8.44) Recalculation of design contact [𝜎 ] (Ref Pg. No.: 8.45) Revise Design Torque [Mt ] Revise K (Pg.No.: 8.44) Revise Kd Value for v2(Pg.No.: 8. 44) [Mt ] = 𝑘. 𝑘 . Check for bending σb .9[ ] 𝜎 = 𝑞 yv = form Factor (Pg.No.: 8.18) σb ( σb)
=
(8.44)
𝑠
ME6601 - Design of Transmission System
STEP SPUR 14 Check for wear strength σc 𝜎 = .
15
𝑖+
√
𝑖+ 𝑖
[
HELICAL Check for wear strength σc ]
(Pg.No.: 8.13) σc ( σc) Basic Dimensions m, a, c, h, d, da, df (Pg.No.: 8.22)
𝜎 = .
𝑖+
(Pg.No.: 8.13) σc ( σc)
𝑖+ √ 𝑖
[
Basic Dimensions m, a, c, h, d, da, df (Pg.No.: 8.22)
]
BEVEL Check for wear strength σc 𝜎 =
.
− .
(Pg.No.: 8.13) σc ( σc)
√ 𝑖 + [ 𝑖
[
Basic Dimensions m, a, c, h, d, da, df (Pg.No.: 8. 38)
]]
/
WORM Check for wear strength σc 𝜎 =
σc ( σc)
⁄𝑞
√[
⁄𝑞 +
(Pg.No.:8.44)
]
[
]
Basic Dimensions m, a, c, h, d, da, df (Pg.No.: 8.43)
ME6601 - Design of Transmission System
Method: Lewis and Buckingham’s Equation/AGMA/Based on Beam Strength STEP SPUR HELICAL BEVEL WORM Selection of Materials Selection of Materials Selection of Materials Selection of Materials 1 Select Pinion and Gear Select Pinion and Gear Select Pinion and Gear Materials Select Pinion and Gear Materials Materials (Pg.No.: 8.5) Materials (Pg.No.: 8.5) (Pg.No.: 8.5) (Pg.No.: 8.5) Selection of Number of teeth Selection of Number of teeth Selection of Number of teeth Selection of Number of teeth Assume Z1 , Say or Assume Z1 , Say or Assume Z1 , Say or Assume Z1 , Say − Z2 = i Z 1 Z2 = i Z 1 Z2 = i Z1 Z2 = i Z1 = tan =9 °− 2 = (Pg.no.:8.22) 𝛽 = 𝑠 Calculation of Tangential load Calculation of Tangential load Calculation of Tangential load on tooth, Calculation of Tangential load on on tooth, Ft on tooth, Ft Ft tooth, Ft = 𝑘 = 𝑘 = 𝑘 = 𝑘 (Pg.No.:8.50) (Pg.No.:8.50) (Pg.No.:8.50) (Pg.No.:8.50) 3 𝜋 𝜋 𝜋 𝜋 𝑣= 𝑣= 𝑣= 𝑣=
4
5
6
Calculation of initial dynamic load,Fd = (Pg.No.:8.50) Cv= Velocity factor, initially taken for vm10 to 15m/s
Calculation of initial dynamic load, Fd = (Pg.No.:8.50) Cv= Velocity factor, initially taken for vm 10 to 15m/s
Calculation of beam strength, Fs = [𝜎 ] (Pg.No.:8.50) 𝜋 =
Calculation of beam strength, Fs = [𝜎 ] (Pg.No.:8.50) 𝜋 =
=
= [𝜎 ]
𝜋
Calculation of module m ≥ (Pg.No.:8.51) Round the "m" Value (Pg.No.:8.2)
=
= [𝜎 ] 𝜋 Use Zv instead of z in the equation of y to get yv Calculation of normal module, mn ≥ (Pg.No.:8.51) Round the "m" Value (Pg.No.:8.2)
=
− 𝑠𝑖
=
−
𝑠𝑖
Calculation of initial dynamic load, Fd = (Pg.No.:8.50)
Calculation of initial dynamic load, Fd = (Pg.No.:8.50)
Cv= Velocity factor, initially taken for vm 5m/s Cv= Velocity factor, initially taken for vm 5m/s Calculation of beam strength, Fs Calculation of beam strength, Fs [𝜎 ] 𝑉 𝑛 [𝜎 ] 𝑉 − = (Pg.No.:8.50) 𝑅 = (Pg.No.:8.50) 𝜋 𝜋 𝜋 𝜋 = = = = = = = 𝜋 = 𝜋 = . =𝑞 √ = . + = [𝜎 ] 𝜋 Use Zv instead of z in the equation = [𝜎 ] 𝜋 ( − ) of y to get yv Use Zv instead of z in the equation of y Assume q=11 to get yv Calculation of transverse module,mt Calculation of module, mx ≥ (Pg.No.:8.51) ≥ (Pg.No.:8.51) Round the "m" Value (Pg.No.:8.2) Round the "m" Value (Pg.No.:8.2)
ME6601 - Design of Transmission System
STEP
7
8
9
SPUR Calculation of b, d, and v = = 𝜋 𝑣=
11
12 13
=
𝑣=
Recalculation of beam strength, Fs = [𝜎 ] 𝜋 Calculation of accurate dynamic load, Fd + 𝑡 = + +
(Pg.No.:8.51)
10
HELICAL Calculation of b, d, and v =
+√
𝑡
(Pg.No.:8.51)
𝑣 Check for beam strength ≥ Calculation of the maximum wear load, Fw = 𝑘 (Pg.No.:8.51) 𝑖 = 𝑖+
𝑘=
.
[
+
𝑠
Recalculation of beam strength, Recalculation of beam strength, Fs Fs = [𝜎 ] 𝜋 ( − ) = [𝜎 ] 𝜋 Calculation of accurate Calculation of accurate dynamic load, dynamic load, Fd Fd + 𝑡 ( 𝛽+ 𝑡 ) 𝛽 (Pg.No.:8.51) = + = +
=
[𝜎 ]𝑠𝑖
𝜋
BEVEL Calculation of b, d, and v = = − 𝑠𝑖 𝜋 𝑣=
]
Check for wear ≥ Basic Dimensions m, a, c, h, d, da, df (Pg.No.: 8.22)
+√
+√
𝛽+ 𝑡
=
𝑣 Check for beam strength ≥ Calculation of the maximum wear load, Fw = (Pg.No.:8.51) 𝛽 𝑖 = 𝑖+
𝑘=
[𝜎 ]𝑠𝑖
.
[
+
+ 𝑡
=
𝑣
Check for beam strength ≥ Calculation of the maximum wear load, Fw .7 = (Pg.No.:8.51) 𝛿
]
Check for wear ≥ Basic Dimensions mn, a, c, h, d, da, df (Pg.No.: 8.22)
=
𝑘=
[𝜎 ]𝑠𝑖
Check for wear
+
.
[
+
]
≥ Basic Dimensions mt, a, c, h, d, da, df (Pg.No.: 8. 38)
WORM Calculation of b, d, and v = . (Pg.No.:8.43) = (Pg.No.:8.44) 𝜋 𝑣=
Recalculation of beam strength, Fs = [𝜎 ] 𝜋 (Pg.No.:8.50) Calculation of accurate dynamic load, Fd = (Pg.No.:8.50) Cv= Velocity factor, Take 𝑣 from Step7.
Check for beam strength ≥ Calculation of the maximum wear load, Fw = 𝑘 (Pg.No.:8.51) Take 𝑘 value from table 43
(pg.No.:8.54)
Check for wear ≥ Basic Dimensions mx, a, c, h, d, da, df (Pg.No.: 8.43)
