Power Screws
Power Screw Terminology
Learning Objectives:

Recognize and understand advantages and disadvantages of different types of power screws such as Square, Acme, Buttress, etc.

Pitch(p) : The axial distance between successive threads.

Lead (L) : The distance advanced by the screw (or nut) for one rotation. The lead equals the pitch for a single start thread. For a multistart thread the lead equals the pitch multiplied by the number of starts.

Root diameter (d\(_i\)): The root diameter is the inside diameter of the thread, also known as minor diameter.

Pitch diameter (d): The pitch diameter is the diameter of a theoretical thread which had zero thread depth but has the same lead as the actual screw. If there were no clearance, then the pitch diameter would be the mean diameter.
Solved Example: 95101
The effective diameter of an external or internal screw thread, is known as: (ISRO Scientist ME 2011)
A. Minor diameter
B. Major diameter
C. Pitch diameter
D. None of these
Correct Answer: C
Solved Example: 95102
_______ is the bottom surface joining the two sides of the thread. (MP Sub Engg Mech July 2017  Shift II)
A. Root
B. Addendum
C. Dedendum
D. Crest
Correct Answer: A
Power Screw Calculations
Learning Objectives:

Calculate torque required to raise and lower a load in a power screw

Calculate efficiency of a power screw and condition for self locking.
Torque required to raise the load:
\[T_{R}=\dfrac {Fd_m}{2}\left( \dfrac {\pi \mu d_m + l}{\pi d_m\mu l}\right) +\dfrac {F \mu_c d_c}{2}\]
Torque required to lower the load:
\[T_{L}=\dfrac {F d_m}{2}\left( \dfrac {\pi \mu d_m  l}{\pi d_m +\mu l}\right) +\dfrac {F\mu_{c}d_{c}}{2}\]
where,
d\(_c\) = mean collar diameter
d\(_m\) = mean thread diameter
\(l\) = lead
F = load
\(\mu\) = coefficient of friction for thread
\(\mu_c\) = coefficient of friction for collar
Efficiency of a Power Screw:
The efficiency of a power screw may be expressed as:
\[\eta = \dfrac{Fl}{2 \pi T}\]
Solved Example: 95201
A screw will be self locking, if:
A. Friction angle is less than helix angle
B. Friction angle is more than helix angle
C. Friction angle is equal to helix angle
D. Efficiency of screw is 100%
The torque required to lower the screw is given by the relation, \[T = W \tan(\phi  \alpha ) \times \dfrac{d}{2}\]
When friction angle $\phi$ greater than helix angle $\alpha$, frictional forces are greater and that causes the condition called selflocking.
The value of T will be positive, which means torque is required to be applied to move the load down, and load will not come down by itself.
This means that applying a torque to the shaft will cause it to turn, but no amount of axial load force against the shaft will cause it to turn back the other way, even if the applied torque is zero.
Correct Answer: B
Solved Example: 95202
The efficiency of a screw while load is being lowered and angle of friction $\phi$ is greater than angle of plane $\alpha$, is given by:
A. $\dfrac{\tan \phi}{\tan \alpha}$
B. $\dfrac{\tan \alpha}{\tan (\phi  \alpha)}$
C. $\dfrac{\tan \alpha}{\tan (\phi + \alpha)}$
D. $\dfrac{\tan (\phi  \alpha)}{\tan \alpha}$
Correct Answer: D