Page 110 - Mechanical Engineer's Data Handbook

APPLIED MECHANICS 99

2.10.6 Worm gears
The worm gear is basically a screw (the worm)
engaging with a nut (the gear). The gear is, in effect, a
partial nut whose length is wrapped around in a circle.
Let :
b,, = normal pressure angle
u =worm helix angle
n, = number of threads or starts on worm
n, = number of teeth in gear
D, = worm pitch circle diameter
D, = gear pitch circle diameter
L = lead of worm
p=pitch of worm threads and gear teeth
p =coefficient of friction
q =efficiency
T, = worm torque
u = velocity of gear teeth
N, = speed of worm
N, = speed of gear

Worm
\

Tangential force on worm ,F,=axial force on gear$,=- 2TW
DW
cos 4,, -p tan u
Tangential force on gear ,F, = axial force on worm = ,F,
cos 4" tan u + p
sin 4"
Separating force on each component F,= ,F,
cos 4, sin u + p cos u
L
tanu=-; L=pn,; D,=pn,Jn
nDW
cos b,,-/* tan LY
Efficiency q= 1
( cos 4" + p cot a
Input power P, = 2nN,T,
Gear tooth velocity u = nD,N,