Experiment 11
Gearing
Involute Curve
Forming of gear
http://www.mech.uwa.edu.au/DANotes/gears/meshing/meshing.html#top
Nomenclature and definitions
Also called
base circle
Number of teeth
Diameter pitch,
teeth per length
Module
Circular pitch
Pitch diameter
Pressure angle
rb  r cos 
Example 1
A gear set consists of a 16 tooth pinion driving a
40 tooth gear. The module is 1. the gear are
cut using a pressure angle of 20o.
(a) Compute the circular pitch, the center distance,
and the radii of the base circles.
(b) In mounting these gears, the center distance
was incorrectly made 2 mm larger. Compute
the new values of the pressure angle and
pitch-circle diameters.
Sol.
(a) Circular pitch p   m  3.14mm
pitch diameter of pinion and gear
d P  Nm  16mm, dG  Nm  40mm
d P  dG
the center distance is
 28mm
2
the base circle is rb ( pinion)  16 / 2 cos   7.52mm
rb ( gear )  40 / 2 cos   18.8mm
(b) Designating d P and dG as the new pitch circle diameters, the 2mm increasing
in the center distance require that
d P  dG
d  16
 30mm and P 
2
dG 40
 d P  17.14mm dG  42.86mm
 pressure angle is   cos 1
rb ( pinion)
7.52
 cos 1
 28.66o
d P / 2
8.57
Gear train
n6  
N 2 N3 N 4
n2
N3 N 4 N5
Force analysis
Wt
Strength of Gear Teeth
Max. Stress of a Cantilever beam :
6 F32  h
S
bt 2
Considering similar triangles AVB and VBC:
h .5t
t2

or h 
.5t
x
4x

3t 2
F32
F32
F32
F32
2
x
S



2
2x
2 x bmY
bt
b
bm
3
3m
Lewis
form
factor
AGMA Stress Equations
Bending stress
F23
  Ko Kv K s K H K B
, YJ (J) is the geometric factor of bending
bmYJ
K o = over load factor, K v  dynamic factor, K s = size factor(may set to be 1)
K H = load distribution factor(approximately 1.2), K B = rim-thickness factor
Contact stress
 C  ZE
KH ZR
F23 K o K v K s
d w1b Z I
Z E  elastic factor, Z R  surface condition factor(>1),
Z I  geometric factor d w1  pitch diameter of pinion
Geometric Factor YJ(J)
• Surface strength geometric factor ZI(I)
mN=1, For
spur gear
• Elastic coefficient ZE
Speed ratio
Dynamic coefficient Kv
Over load factor
Example 2
A steel 20o spur pinion with 20 teeth and a module of 2.5 mm
transmits 120 W to a 36 tooth gear. The pinion speed is 100 rpm, the
gears are grade 1, 18 mm face width, manufactured to a No. 6
quality standard, and considered to be of open gearing quality
installation. Find the AGMA bending and contact stresses and
corresponding factors of safety. The allowable strength of the gear
tooth is 654Mpa. Contact strength is 1260MPa.
Sol.
Bending stress
  Ko Kv K s K H K B
F23
,
bmYJ
YJ (J) =0.327
K o = 1,
d p  2.5mm  20  50mm,
v   d p  rpm  3.14  50  100  15700mm / min  52.3 ft / min
K v  1.2, K s = 1, K H = 1.2, K B = 1
1.44  F23
=
18  2.5  0.327
60(10)3 H 60(10)3 0.12
but F23 

 0.46kN
 dn
  50 100
  =45MPa
safety factor is 14.53
Contact stress
 C  Z E F23 K o K v K s
KH ZR
d w1b Z I
Z E  191, Z R  1.1, K H  1.2
ZI 
cos t sin t mG
=0.1, d w1  50mm
2
mG  1
  C  191 460 1.2 
 0.5432 MPa
safety factor=23.7
1.2
1.1
0.05  0.018 0.1
Experiment
Rotating
speed
1750 rpm,
and power
2.5 kW
The structure of a simple transmission is
shown in previous slide. If the power
transfer to lay shaft is 2.5kW at 1750 rpm.
The gear and the pinion is made by a
material of allowable bending strength 650
Mpa, the allowable contact strength is
1200MPa. If the two reduction ratio 0.75
and 0.5 are required, please select the
proper pinion and gear for this system.