Mechanical Power Screws

Power screws (also known as translation screws) are mechanical devices used to convert rotary motion into linear motion, transmitting power in applications such as presses, jacks, and lead screws in lathes.

1. Thread Forms and Mechanics

The most common thread forms for power screws are the Square thread, Acme thread, and Buttress thread. Acme threads are frequently used because they are easier to manufacture and can utilize a split nut to compensate for wear.

1.1 Torque Required to Raise a Load

The torque $T_R$ required to raise a load $F$ using a square thread power screw is related to the mean diameter $d_m$, the lead $l$, and the coefficient of friction $f$:

$T_R = \frac{F d_m}{2} \left( \frac{l + \pi f d_m}{\pi d_m - f l} \right) + \frac{F f_c d_c}{2}$

Where:

• $F$ is the axial load.
• $d_m$ is the mean diameter of the thread.
• $l$ is the lead.
• $f$ is the coefficient of thread friction.
• $f_c$ is the coefficient of collar friction.
• $d_c$ is the mean collar diameter.

1.2 Torque Required to Lower a Load

To lower the load, the required torque $T_L$ is:

$T_L = \frac{F d_m}{2} \left( \frac{\pi f d_m - l}{\pi d_m + f l} \right) + \frac{F f_c d_c}{2}$

2. Self-Locking Condition

A power screw is self-locking if it will not lower the load without an external torque applied. This occurs when the thread friction is sufficient to prevent the screw from turning under the axial load. The condition for self-locking is:

$f \ge \tan \lambda$

Where $\lambda$ is the lead angle.

3. Efficiency

The efficiency $e$ of a power screw is the ratio of useful work output to the work input:

$e = \frac{F l}{2 \pi T_R}$

High efficiency is desirable but often conflicts with the requirement for self-locking. Self-locking screws generally have efficiencies below 50%.