Mechanical Design
Selected Topics
Dr. Amr
Shaaban
Assistant Professor at
Ain Shams University, Egypt.
Founder of
Design Online
https://www.facebook.com/designonlineacademy
Academy.
Power transmission elements
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Dr.Amr Shaaban- Shaft Analysis
1/20/2019
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Dr.Amr Shaaban- Shaft Analysis
1/20/2019
Gear Units
Geometry
GEARS
Tangential, radial, and axial loads
Margin of safety
Material
Power transmitted
Geometry
SHAFTS
Material
NFD,SFD,BMD,TD
Bearing reactions
Tangential, radial, and axial loads
Bearing reactions
BEARINGS
Bearing types
Dynamic capacity
Bearing life
Power transmitted
Key type and dimensions
KEYS
Safety factor for key, hub, and shaft
Power transmitted
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Dr.Amr Shaaban- Shaft Analysis
1/20/2019
Gear Design
Gear Geometry
Module
Number of teeth
Center distance
Gear width
Helix angle
Pressure angle
Gear ratio
Gear Material
Gear Loading
Power
Torque
Velocity
Gear Results
Tangential, radial, and axial loads
Margin of safety
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Dr.Amr Shaaban- Gear Analysis
1/20/2019
Gear geometry
m: Module (mm)
D: Pitch circle diameter (=m.Z)
a: Addendum (≈m)
d: Dedendum (≈1.25m)
b: Gear width (≈12.5m-20m)
Pc: Circular pitch.
U: Gear ratio
Dp: Pinion pitch circle diameter (mm)
Np : Pinion rpm.
Zp : Pinion tooth number.
Dg: Gear pitch circle diameter (mm)
Ng : Gear rpm.
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Zg : Gear tooth number.
V: Linear velocity (m/s).
P: Motor power (KW or HP).
T: Torque (N.m).
ω: Angular velocity (rad/sec).
Dr.Amr Shaaban- Gear Analysis
1/20/2019
Gear geometry
Zg
C= (m.Zp + m.Zg)/2
Given
Assume
Get
U, m, Np
Zp
C, Zg
U, C, Np
Zp
m, Zg
C: center distance
m: module
Zp : Pinion tooth number
Zg : Gear tooth number
U: Gear ratio
C
Both pinion and gear have same (m), (V), and (P).
Gear kinetics
• Direction of tangential Load is assigned so that it forms a resisting torque for the
driver gear (opposite to rotating direction), and simultaneously, a driving torque
(with rotating direction) for the driven one.
•Radial load is assigned so that it woks on the line connecting the centers of the
two meshed gears, normal to tooth face.
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Dr.Amr Shaaban- Gear Analysis
1/20/2019
ZP
Spur Gear kinetics
Given
Get
Motor (rpm)
Linear velocity (V)
Motor (HP),V
Tangential force (Ft)
Ft, Dp
Resisting torque (Tp)
Ft, Dg
Driving torque (Tg)
Spur
Helical
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Using
Ft,α
Radial force (Fr)
Ft,α,ϒ
Radial force (Fr)
Ft , ϒ
Axial force (Fa)
Dr.Amr Shaaban- Gear Analysis
1/20/2019
Helical Gear kinetics
R.H
Driver
Thrust
• The tangential and radial loads directions in helical are as same as spur.
• Thrust load direction can be detected as shown in figure to the right.
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Dr.Amr Shaaban- Gear Analysis
Ft
Thrust
Ft
1/20/2019
C.C.W C.W
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Dr.Amr Shaaban- Gear Analysis
1/20/2019
m: Module (mm)
a: Addendum (≈m)
d: Dedendum (≈1.25m)
b: Gear width (≈1/3L)
Bevel gear geometry
a
b
L
Dp: Pinion pitch circle diameter
Dg: Gear pitch circle diameter
δp: Pinion half cone angle
δg: Gear half cone angle
L: front cone length
δp
Dp
δg
Dg
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d
Dr.Amr Shaaban- Gear Analysis
1/20/2019
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Dr.Amr Shaaban- Gear Analysis
1/20/2019
Bevel gear kinetics
Fr
Fy
Given
Using
Get
Zp, Zg
U= Zp/Zg
Gear ratio
U
Tanδp =1/U
Pinion half cone angle
m, Zp, δp
L=m.Zp/2sinδp
Cone length
Ft,α
Fr= Ft tanα
Radial force (Fr)
Fr, δp
Fx=Fr.sinδp
Force parallel to axis
Fr, δp
Fy=Fr.cosδp
Force normal to axis
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Dr.Amr Shaaban- Gear Analysis
Ft
Fx
C.W
Driver
1/20/2019
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Dr.Amr Shaaban- Gear Analysis
1/20/2019
Gear tooth design
Given
Using
Get
Empirical formulas or tables
Modified form factor
Spur: Kyp ,Kyg
Helical: Kyp̀ ,Kyg̀
V
Empirical formulas
Kv
m, Zp,Zg
D=m.Z
Dp, Dg
Spur: Zp ,Zg
Helical: Zp̀ ,Zg̀, ϒ(helix angle)
Where Zp̀/g=Zp/g/cos3 ϒ
Bevel: Zp̀ ,Zg̀, δp(Half cone angle)
Where Zp̀/g=Zp/g/cos δp/g
σbp ,Ft, (Ky or Kỳ) ,Kv ,Ks ,KL ,b,
Lewis Equation(spur/helical)
m (module)
L (in case of bevel)
Pinion material
σbp ,σbg ,Kyb
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Material properties tables
σbp (pinion allowable bending stress)
σbg (Gear allowable bending stress)
Dr.Amr Shaaban- Gear Analysis
1/20/2019
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Dr.Amr Shaaban- Gear Analysis
1/20/2019
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Dr.Amr Shaaban- Gear Analysis
1/20/2019
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Dr.Amr Shaaban- Gear Analysis
1/20/2019
Dynamic analysis for gear tooth
Given
Using
Get
Tables
permissible error
e (Probable error)
m,V
(or mn for helical gears)
& manufacturing grade
(K=0.111),e ,Ep,Eg
Deformation factor Kd
(Young’s modulus for pinion and gear)
Kd,b, ϒ,Ft
2
A
V, A, ϒ, Ft
Fd: Acting dynamic load
σen/p, (Kyp or Kyp̀) , b, m
Fen/p: Allowable dynamic load
Fd ,Fen/p
σen/p, Kyp, Kyg
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Fen/p larger than Fd
Dr.Amr Shaaban- Gear Analysis
Check (safe or upgrade)
σen/g
1/20/2019
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Dr.Amr Shaaban- Gear Analysis
1/20/2019
Wear analysis
Given
Using
Zp, Zg
for bevel: Zp̀ ,Zg̀
Get
Kn
Kw
B.H.Np/g
Tables
(Kg/cm2)Load
stress factor
Kw, Kn, Dp, b, ϒ
Fw ,Fd
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Dr.Amr Shaaban- Gear Analysis
Fw (Kg)
Spur/helical
Fw larger than Fd
1/20/2019
Check (safe
or upgrade)