The torque T_r required to raise a load F with a square-threaded power screw (pitch diameter d_m, lead l, friction mu) is:

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Mechanical Engineering QUESTION #2456

Question 1

The torque \(T_r\) required to raise a load \(F\) with a square-threaded power screw (pitch diameter \(d_m\), lead \(l\), friction \(\mu\)) is:

\(T_r = \frac{Fd_m}{2}\left(\frac{l - \pi\mu d_m}{\pi d_m + \mu l}\right)\)
\(T_r = \frac{Fd_m}{2}\left(\frac{l + \pi\mu d_m}{\pi d_m - \mu l}\right)\)✔️
\(T_r = \frac{F l}{2\pi}\)
\(T_r = \mu F d_m\)

Correct Answer Explanation

From force equilibrium on the unrolled thread diagram for raising: \(T_r = \frac{Fd_m}{2}\cdot\frac{l+\pi\mu d_m}{\pi d_m - \mu l}\). The ideal torque (no friction, \(\mu=0\)) is \(T_0=Fl/(2\pi)\), and screw efficiency \(e=T_0/T_r=Fl/(2\pi T_r)\).

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