9
Worms 105
Chapter and Worm Gears
9.1
A worm having 4 teeth and a lead of 1.0 in drives a worm gear at a velocity ratio of 7.5.
Determine the pitch diameters of the worm and worm gear for a center distance of 1.75
in.
px = l N 2 = 1 in 4 teeth = 0.25 in/tooth
N 3 = ( 2 3 ) N 2 = 7.5 ( 4 teeth ) = 30 teeth
R3 = N 3 px 2 = 1.194 in
9.2
N 3 = ( 2 3 ) N 2 = 60 ( 1 teeth ) = 60 teeth
R2 = 6.500 R3 = 1.725 in
Ans.
A triple-threaded worm drives a worm gear having 40 teeth. The axial pitch is 1.25 in
and the pitch diameter of the worm is 1.75 in. Calculate the lead and lead angle of the
worm. Find the helix angle and pitch diameter of the worm gear.
l = N 2 px = 3 teeth ( 1.25 in/tooth ) = 3.750 in
Ans.
= tan 1 ( l 2 R2 ) = tan 1 ( 3.750 in 1.75 in ) = 34.298
= = 34.298
R3 = N 3 px 2 = 40 teeth ( 1.25 in/tooth ) 2 = 7.957 in
9.4
Ans.
Specify suitable a worm and worm gear combination for a velocity ratio of 60 and a
center distance of 6.50 in using an axial pitch of 0.500 in/tooth.
Use N 2 = 1 tooth ,
R3 = N 3 px 2 = 4.775 in
9.3
R2 = 1.75 R3 = 0.556 in
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A triple threaded worm with a lead angle of 20 and an axial pitch of 0.400 in/tooth
drives a worm gear with a velocity reduction of 15 to 1. Determine for the worm gear:
(a) the number of teeth, ( b) the pitch diameter, and ( c) the helix angle. ( d) Determine
the pitch diameter of the worm. ( e) Compute the center distance.
l = N 2 px = 3 teeth ( 0.400 in/tooth ) = 1.200 in
R2 = l ( 2 tan ) = 1.200 in 2 tan 20 = 0.524 7 in
Ans.
R3 = ( 2 3 ) R2 = 15 ( 0.524 7 in ) = 7.871 in
Ans.
N 3 = 2 R3 px = 123.6 teeth
= = 20.0
R2 + R3 = 0.525 in + 7.871 in = 8.396 in
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