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POWER SCREWS
Torque required to raise load on square threaded screws
Let, l = lead of the screw
d = mean diameter of the screw
a = helix angle
Let,
p = effort applied at the circumference of the screw to lift the load
W = weight of the body to be lifted.
µ = coefficient of friction between the screw and nut ( m = tan f).
So, P = W tan (a + f)
Torque required to overcome friction between the screw and nut,
( α= a, ϕ= f)
where,
R_{1 }and R_{2} = outside and inside radii of collar
R = mean radius of collar
µ_{1} = coefficient of friction for the collar.
Total torque, T = T_{1} + T_{2}
Effort applied at the circumference of the screw to lift the load is
P = W tan (f + a)
It there would have been no friction between the screw and the nut the f will be equal to zero. The value of effort P_{o} necessary to raise the load, will then given by
P_{o} = W tan a
Maximum efficiency of a square threaded screw occurs at
In other words, the load will start moving downward without the application of any torque. Such a condition is known as over hauling of screws. If however, f > a, the torque required to lower the load will be positive, indicating that and effort is applied to lower the load. Such a screw is known as self locking screw.
The efficiency of self locking screws,
So the efficiency of self locking screws is less than 1/2 or 50%. If the efficiency is more than 50%, then the screw is said to be overhauling.
Stresses in Power screws
where,
W = axial load
A_{C} = crosssectional area of screw corresponding to core diameter (d_{c}).
This is only applicable when the axial load is compressive and the unsupported length of the screw between the load and the nut is short. When unsupported length of the screw between the load and the nut is too great, the design is based on the column theory assuming suitable end conditions.
when screw is subjected to both direct stresses and shear stresses than
Shear stress for the screw
Shear stress for the nut
where,
w = axial load on the screw
n = Number of threads in engagement
d_{c} = core or root diameter of the screw
do = outside or major diameter of nut or screw
t = thickness or width of thread, (= p/2)
where,
d = mean diameter of screw
n = Number of threads in contact with nut
t
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