Spur Gears Formula Flashcards
Base Circle Diameter
Db= D cos θ
Where:
Db = base circle diameter
D= pitch diameter
θ= pressure angle
Circular Pitch
Pc= πD/N= π/Pd
Where:
N= number of teeth
D=pitch diameter
Pc= circular pitch
Pd= diametral pitch
Diametral Pitch
Pd= N/ D= π/ Pc
Where:
N= number of teeth
D= pitch diameter
Pc= circular pitch
Pd= diametral pitch
Module
M= 1/Pd= Pc/ π= Dp/Np
Where:
Np = number of teeth
Dp= pitch diameter
Pc= circular pitch
Pd= diametral pitch
M= module
Center Distance
C= Dp+ Dg/ 2= Np+ Ng/ 2 Pd
Where:
C= center distance
Dp= pinion diameter
Dg= gear diameter
Ng= number of teeth in gear
Pd-diametral pitch
Outside Diameter
Do= D + 2a
Where:
D= pitch diameter
Do= outside diameter
a= addendum distance
Root Diameter
Dr= D - 2d
Where:
D= pitch diameter
Dr= root diameter or dedendum diameter
d= dedendum diameter
Whole Depth
Wt= W - c = 2a
Where:
W= whole depth
a= addendum
c= clearance
Wt= working depth
Face Width
2.5Pc<b<4Pc
or
8/ Pd<b< 12.5/Pd
Where:
b= face width
Pc= circular pitch
Pd= diametral pitch
Speed Ratio
np/ng= Dg/ Dp= Ng/ Np
Where:
Dp= pinion diameter
Dg= gear diameter
np= rotative speed of pinion
ng= rotative speed of gear
Np= number of teeth in pinion
Ng= number of teeth in gear
Backlash
B= S - T
or
B= 0.03/ Pd to 0.04/Pd
Where:
S= space width
T= tooth thickness
B= backlash
Pd= diametral pitch
Tooth Thickness
T= Pc - B/ 2
Where:
T= tooth thickness
Pc= circular pitch
B= backlash
Tangential or transmitted load
Ft= P/ V
Where:
F= Tangential or transmitted
P= Power
V= Pitch line velocity
Beam Fatigue Strength
Fs= S b Y/ Pd Kf
Where:
Fs= beam fatigue strength
S= endurance stress
b= face width
Y= Lewis form factor
Pd= diametral pitch
Kf= stress reduction factor
= 1.2 to 1.7 when load is applied
= 1.4 to 2.0 when the load is applied near the middle
