T-138
Table 15-7 Allowable Values of Running Errors, mm
SECTION 16 GEAR FORCES
In designing a gear, it is important to analyze the magnitude and direction of the
forces acting upon the gear teeth, shaft, bearings, etc. In analyzing these forces, an
idealized assumption is made that the tooth forces are acting upon the central part of the
tooth flank.
Table 16-1 Forces Acting Upon a Gear
Grade
0
1
2
3
4
5
6
7
8
1.12m + 3.55
1.6m + 5.0
2.24m + 7.1
3.15m + 10.0
4.5m + 14.0
6.3m + 20.0
9.0m + 28.0
12.5m + 40.0
18.0m + 56.0
(1.4W + 4.0) + 0.5 (1.12m + 3.55)
(2.0W + 5.6) + 0.5 (1.6m + 5.0)
(2.8W + 8.0) + 0.5 (2.24m + 7.1)
(4.0W + 11.2) + 0.5 (3.15m + 10.0)
(5.6W + 16.0) + 0.5 (4.5m + 14.0)
(8.0W + 22.4) + 0.5 (6.3m + 20.0)
(11.2W + 31.5) + 0.5 (9.0m + 28.0)
(22.4W + 63.0) + 0.5 (12.5m + 40.0)
(45.0W + 125.0) + 0.5 (18.0m + 56.0)
Tooth-to-Tooth Composite Error
Total Composite Error
Types of Gears
Axial Force, Fa
Tangential Force, Fu
Radial Force, Fr
Spur Gear
Helical Gear
Straight Bevel Gear
Spiral Bevel Gear
2000 T
Fu = ––––––
d
2000 T
Fu = ––––––
dm
dm is the central
pitch diameter
dm = d – b sind
2000 T1
Fu = ––––––
d1
cosancosg – m sing
Fu –––––––––––––––––
cosansing + m cosg
2000 T1
Fu = ––––––
d1
cosansinb – m cosb
Fu –––––––––––––––––
cosancosb + m sinb
Worm
Drive
Screw
Gear
S = 90°
( )
b = 45°
Worm
(Driver)
Wheel
(Driven)
Driver
Gear
Driven
Gear
–––––––
Fu tanb
Fu tana
sind
When convex surface is working:
Fu
––––– (tanan sind
– sinbm cosd)
cosbm
When concave surface is working:
Fu
––––– (tanan sind
+ sinbm cosd
)
cosbm
cosan cosg
– m
sing
Fu –––––––––––––––––––––
cosan sing
+ m
cosg
Fu
cosansinb – m cosb
Fu ––––––––––––––––––
cosancosb + m sinb
Fu
Fu tana
tanan
Fu –––––
cosb
Fu tana
cosd
Fu
––––– (tanan cosd
+ sinbm sind)
cosbm
Fu
––––– (tanan cosd
– sinbm sind
)
cosbm
sinan
Fu ––––––––––––––––––
cosan sing
+ m
cosg
sinan
Fu ––––––––––––––––––
cosancosb + m sinb
__
where:
W = Tolerance unit =
3
Ö
d + 0.65m (mm)
d = Pitch diameter (mm)
m = Module
