T-139
16.1 Forces In A Spur Gear Mesh
The spur gear's transmission force
Fn , which is normal to the tooth sur-
face, as in Figure 16-1, can be re-
solved into a tangential component, Fu ,
and a radial component, Fr. Refer to
Equation (16-1).
The direction of the forces ac-
ting on the gears are shown in
Figure 16-2. The tangential compo-
nent of the drive gear, Fu1, is equal
to the driven gear's tangential com-
ponent, Fu2, but the directions are
opposite. Similarly, the same is true
of the radial components.
Fu = Fn cosab
ü
ï
ý (16-1)
ï
Fr = Fn sinab
þ
16.2 Forces In A Helical Gear Mesh
The helical gear's transmission
force, Fn, which is normal to the tooth
surface, can be resolved into a
tangential component, F1, and a
radial component, Fr .
F1 = Fn cosan
ü
ï
ý (16-2)
ï
Fr = Fn sinan
þ
The tangential component, F1,
can be further resolved into circular
subcomponent, Fu, and axial thrust
subcomponent, Fa.
Fu = F1 cosb
ü
ï
ý (16-3)
ï
Fa = F1 sinb
þ
Substituting and manipulating
the above equations result in:
Fa = Fu tanb
ü
ï
ý (16-4)
tanan
ï
Fr = Fu
ï
cosb
þ
ab
Fu
Fn
Fr
Fig. 16-1 Forces Acting on a
Spur Gear Mesh
Fr1
Fr2
Fu2
Fu1
Fr1
Fr2
Fu1
Fu2
Drive Gear
Driven Gear
Fig. 16-2 Directions of Forces Acting
on a Spur Gear Mesh
b
an
Fa
F1
Fu
F1
Fn
Fr
Fig. 16-3 Forces Acting on a
Helical Gear Mesh