Short Notes: Gears | Short Notes for Mechanical Engineering PDF Download

 Page 1


Gears
Gear can be defined as the mechanical element used for transmitted power and 
rotary motion from one shaft to another by means of progressive engagement of 
projections called teeth.
Classification of Gears
• Spur Gear
• Helical Gear
• Bevel Gear
• Worm Gear
Spur Gear
In spur gears, teeth are cut parallel to axis of the gear.
• Circular pitch •
z
• Diametrical pitch
• Module
d
m = —
z
Page 2


Gears
Gear can be defined as the mechanical element used for transmitted power and 
rotary motion from one shaft to another by means of progressive engagement of 
projections called teeth.
Classification of Gears
• Spur Gear
• Helical Gear
• Bevel Gear
• Worm Gear
Spur Gear
In spur gears, teeth are cut parallel to axis of the gear.
• Circular pitch •
z
• Diametrical pitch
• Module
d
m = —
z
Where z = Number of teeth 
d = Pitch diameter
• Torque transmitted by gear
,, _ 60 x 10s (kJF)
f ^
2 7 T «
Where, Mt = Torque transmitted by gear
n = Speed of rotation
kW = Power transmitted by gear
d P
P xx — — M,Pr — P tanaPv = — —
2 ' C O S Q
• Beam strength of gear tooth
Where, b = Permissible bending stress,
Y = Lewis form factor 
m = Module.
• Dynamic load or incremental dynamic load
p 21 v(ceb+P;)
d Zlv+yjceb— P,
Where, v = Pitch line velocity 
c = Deformation factor 
b = Face width of tooth
Pt = Tangential force due to rated torque, e = Sum of errors between two meshing 
teeth
Estimation of module based on beam strength
Page 3


Gears
Gear can be defined as the mechanical element used for transmitted power and 
rotary motion from one shaft to another by means of progressive engagement of 
projections called teeth.
Classification of Gears
• Spur Gear
• Helical Gear
• Bevel Gear
• Worm Gear
Spur Gear
In spur gears, teeth are cut parallel to axis of the gear.
• Circular pitch •
z
• Diametrical pitch
• Module
d
m = —
z
Where z = Number of teeth 
d = Pitch diameter
• Torque transmitted by gear
,, _ 60 x 10s (kJF)
f ^
2 7 T «
Where, Mt = Torque transmitted by gear
n = Speed of rotation
kW = Power transmitted by gear
d P
P xx — — M,Pr — P tanaPv = — —
2 ' C O S Q
• Beam strength of gear tooth
Where, b = Permissible bending stress,
Y = Lewis form factor 
m = Module.
• Dynamic load or incremental dynamic load
p 21 v(ceb+P;)
d Zlv+yjceb— P,
Where, v = Pitch line velocity 
c = Deformation factor 
b = Face width of tooth
Pt = Tangential force due to rated torque, e = Sum of errors between two meshing 
teeth
Estimation of module based on beam strength
m =
6 0 x 1 0 '
'
( / . )
7Z f b Y s . X
r H m J h r J
Where, cs = Service factor, 
cv = Velocity factor 
fs = Factor of safety, 
n = Speed (rpm)
• Wear strength of gear tooth
Where, K = Load stress factor 
b = Gear width
Q = Ratio factor pitch diameter
• Estimation of module based on wear strength
m =
60 x 10e
71
Helical Gear
The teeth of helical gear cut in the form of helix or an angle on the pitch cylinder.
Where, P„ = Normal diametrical pitch
P = Transverse diametrical pitch
^ = Helix angle
mn = m cos ip
mn = Normal module
m = transverse module
• Axial pitch
tan y
• Pitch circular diameter
d = ----- —
cos
• Tooth proportions
Addendum hg = mn 
Dedendum hf = 1.25 mn 
Clearance c = 0.25 mn
• Addendum circle diameter da = d + 2ha or
Page 4


Gears
Gear can be defined as the mechanical element used for transmitted power and 
rotary motion from one shaft to another by means of progressive engagement of 
projections called teeth.
Classification of Gears
• Spur Gear
• Helical Gear
• Bevel Gear
• Worm Gear
Spur Gear
In spur gears, teeth are cut parallel to axis of the gear.
• Circular pitch •
z
• Diametrical pitch
• Module
d
m = —
z
Where z = Number of teeth 
d = Pitch diameter
• Torque transmitted by gear
,, _ 60 x 10s (kJF)
f ^
2 7 T «
Where, Mt = Torque transmitted by gear
n = Speed of rotation
kW = Power transmitted by gear
d P
P xx — — M,Pr — P tanaPv = — —
2 ' C O S Q
• Beam strength of gear tooth
Where, b = Permissible bending stress,
Y = Lewis form factor 
m = Module.
• Dynamic load or incremental dynamic load
p 21 v(ceb+P;)
d Zlv+yjceb— P,
Where, v = Pitch line velocity 
c = Deformation factor 
b = Face width of tooth
Pt = Tangential force due to rated torque, e = Sum of errors between two meshing 
teeth
Estimation of module based on beam strength
m =
6 0 x 1 0 '
'
( / . )
7Z f b Y s . X
r H m J h r J
Where, cs = Service factor, 
cv = Velocity factor 
fs = Factor of safety, 
n = Speed (rpm)
• Wear strength of gear tooth
Where, K = Load stress factor 
b = Gear width
Q = Ratio factor pitch diameter
• Estimation of module based on wear strength
m =
60 x 10e
71
Helical Gear
The teeth of helical gear cut in the form of helix or an angle on the pitch cylinder.
Where, P„ = Normal diametrical pitch
P = Transverse diametrical pitch
^ = Helix angle
mn = m cos ip
mn = Normal module
m = transverse module
• Axial pitch
tan y
• Pitch circular diameter
d = ----- —
cos
• Tooth proportions
Addendum hg = mn 
Dedendum hf = 1.25 mn 
Clearance c = 0.25 mn
• Addendum circle diameter da = d + 2ha or
d =
zni
2m „
cos^/
Dedendum circle diameter
, ZW- - > <
a f = ----- —+ 2.5m,
cosv'
Force analysis in helical gears is given below
Pitch cylinder
Component of tooth forces
tan or, 
cos y/ 
tan y/
Beam strength of helical gear = mn b a^Y
Where, m = Module,
at, = Permissible bending stress
y = Lawis form factor
Dynamic load or incremental dynamic load Pd
21v (ceb cos' < / / + Pt) cos y /
21v+ yj(ceb cos: y/ + P:)
Where, e = Sum of errors,
C = Deformation factor 
Wear strength of helical gear
b O d K
S* • - ~ ~ T —
cos y/
Herringbone Gear: In order to avoid an axial thrust on the shaft and the bearings, 
the double helical gears or Herringbone gears are used.
Bevel Gears
• Use to transmit power between two intersecting shafts.
• High speed high power transmission.
Classification of Bevel Gear
Mitre Gear: When two bevel gears are mounted on shafts that are intersecting 
at right angle.
Page 5


Gears
Gear can be defined as the mechanical element used for transmitted power and 
rotary motion from one shaft to another by means of progressive engagement of 
projections called teeth.
Classification of Gears
• Spur Gear
• Helical Gear
• Bevel Gear
• Worm Gear
Spur Gear
In spur gears, teeth are cut parallel to axis of the gear.
• Circular pitch •
z
• Diametrical pitch
• Module
d
m = —
z
Where z = Number of teeth 
d = Pitch diameter
• Torque transmitted by gear
,, _ 60 x 10s (kJF)
f ^
2 7 T «
Where, Mt = Torque transmitted by gear
n = Speed of rotation
kW = Power transmitted by gear
d P
P xx — — M,Pr — P tanaPv = — —
2 ' C O S Q
• Beam strength of gear tooth
Where, b = Permissible bending stress,
Y = Lewis form factor 
m = Module.
• Dynamic load or incremental dynamic load
p 21 v(ceb+P;)
d Zlv+yjceb— P,
Where, v = Pitch line velocity 
c = Deformation factor 
b = Face width of tooth
Pt = Tangential force due to rated torque, e = Sum of errors between two meshing 
teeth
Estimation of module based on beam strength
m =
6 0 x 1 0 '
'
( / . )
7Z f b Y s . X
r H m J h r J
Where, cs = Service factor, 
cv = Velocity factor 
fs = Factor of safety, 
n = Speed (rpm)
• Wear strength of gear tooth
Where, K = Load stress factor 
b = Gear width
Q = Ratio factor pitch diameter
• Estimation of module based on wear strength
m =
60 x 10e
71
Helical Gear
The teeth of helical gear cut in the form of helix or an angle on the pitch cylinder.
Where, P„ = Normal diametrical pitch
P = Transverse diametrical pitch
^ = Helix angle
mn = m cos ip
mn = Normal module
m = transverse module
• Axial pitch
tan y
• Pitch circular diameter
d = ----- —
cos
• Tooth proportions
Addendum hg = mn 
Dedendum hf = 1.25 mn 
Clearance c = 0.25 mn
• Addendum circle diameter da = d + 2ha or
d =
zni
2m „
cos^/
Dedendum circle diameter
, ZW- - > <
a f = ----- —+ 2.5m,
cosv'
Force analysis in helical gears is given below
Pitch cylinder
Component of tooth forces
tan or, 
cos y/ 
tan y/
Beam strength of helical gear = mn b a^Y
Where, m = Module,
at, = Permissible bending stress
y = Lawis form factor
Dynamic load or incremental dynamic load Pd
21v (ceb cos' < / / + Pt) cos y /
21v+ yj(ceb cos: y/ + P:)
Where, e = Sum of errors,
C = Deformation factor 
Wear strength of helical gear
b O d K
S* • - ~ ~ T —
cos y/
Herringbone Gear: In order to avoid an axial thrust on the shaft and the bearings, 
the double helical gears or Herringbone gears are used.
Bevel Gears
• Use to transmit power between two intersecting shafts.
• High speed high power transmission.
Classification of Bevel Gear
Mitre Gear: When two bevel gears are mounted on shafts that are intersecting 
at right angle.
• Crown Gear: In pair of bevel gear, when one of the gear has a pitch angle of 
90°.
• Internal Bevel Gear: When the teeth of bevel gear are cut on the inside of the 
pitch.
• Skew Bevel Gear: Mounted on non-parallel and non-intersecting shafts. It 
constant of straight teeth.
• Hypoid Gear: Similar to skew bevel gear, non-parallel and non-intersecting 
shafts. It consists of curved teeth.
• Zerol Gear: Sprial bevel gear with zero spiral angle.
• Force Gear: Consists of a spur or helical pinion meshing with a conjugate gear 
or disk form.
Terminologies in Bevel Gear
• Pitch circle radius
D
rb —
2 cos y
where, y = Pitch angle
• Formative number of teeth
cosy
tan y = —
z
Where, z = Actual number of teeth
Cone distance in bevel 
gear section
Component o( tooth (ace
• Cone distance
• Mean radius
M .=
60 x 10s (A rJT)
t n.
p , . ±
Pr = P tan a cosy 
Pa = P: tan a cos y