Machine Design - Homework 2 - Ch.8 #1,4,5
Major Diameter d ≔ 25 mm
Pitch
p ≔ 5 mm
Single Thread
n≔1
Part (a)
Thread Depth
Part (b)
p
DTa ≔ ―
2
Thread Depth
DTa = 0.003 m
Thread Width
p
wTa ≔ ―
2
DTb = 0.003 m
Thread Width
wTa = 0.003 m
Mean Diameter
d + ⎛⎝d - DTa⎞⎠
dma ≔ ―――――
2
la ≔ n ⋅ p
la = 0.005 m
p
wTb ≔ ―
2
wTb = 0.003 m
Mean Diameter
dma = 0.024 m
Lead
p
DTb ≔ ―
2
d + ⎛⎝d - DTb⎞⎠
dmb ≔ ――――
2
dmb = 0.024 m
Lead
lb ≔ n ⋅ p
lb = 0.005 m
Given Values:
Major Diameter
Pitch
Collar Friction
Thread Friction
Required Values:
Lead
d ≔ 25 mm
p ≔ 5 mm
fC ≔ 0.06
fT ≔ 0.06
Single Thread
Load
Friction Diameter
l≔n⋅p
l = 0.005 m
Mean Diameter
n≔1
F ≔ 5 kN
dF ≔ 45 mm
p
dm ≔ d - ―
2
dm = 0.023 m
Collar Diameter
dC ≔ dm
Collar Torque
F ⋅ fC ⋅ dC
TC ≔ ―――
2
TC = 3.375 J
Torque to Raise and Lower Load:
F ⋅ dm ⎛ l + π ⋅ fT ⋅ dm ⎞
TR ≔ ―― ⎜――――⎟ + TC
2
⎝ π ⋅ dm - fT ⋅ l ⎠
F ⋅ dm ⎛ π ⋅ fT ⋅ dm - l ⎞
TL ≔ ―― ⎜――――⎟ + TC
2
⎝ π ⋅ dm - fT ⋅ l ⎠
TR = 10.76 N ⋅ m
TL = 2.769 N ⋅ m
Power Screw Efficiency:
Torque to raise
load
F⋅l
TO ≔ ――
2⋅π
TO = 3.979 N ⋅ m
Thread Efficiency
TO
e ≔ ――
TR
e = 0.37
Why only tension testing?
The collar bearing at the bottom of
each threaded rod is not firmly fixed in
the bottom part of the frame. If the
specimen is compressing tested, then
the collar bearing does not loaded and
instead the bottom frame is loaded by
the specimen in compression.
With a tension test, the threaded rod
experiences compression from each
side which firmly fixes the collar
bearing and it absorbs the load.
Can both screws be the same hand?
Yes. Both screws must have the same
hand (the direction the threads wrap
around the screw's shaft) because the
design of the spur gears makes the
screws rotate the same direction.
Therefore, they have to have the same
hand to create the same linear motion
of the bar.
Collar Bearing Diagram