Power Screw Torque

#516 / Mechanical Engineering Easy

Consider a square thread power screw can lift a 20 kN load with a 70% efficiency. If the lead is 0.01 m and the thread coefficient of friction is 0.05, how much torque (N∙m) is needed?

Expand Hint
The power screw’s efficiency is:
$$$\eta=\frac{Fl}{2\pi T}$$$
where $$F$$ is the load, $$l$$ is the lead, and $$T$$ is the torque.
Hint 2
The friction coefficient is not needed to solve the problem. It only exists to cause confusion.
The power screw’s efficiency is:
$$$\eta=\frac{Fl}{2\pi T}$$$
where $$F$$ is the load, $$l$$ is the lead, and $$T$$ is the torque.

Notice how the friction coefficient is not needed to solve the problem. It only exists to cause confusion. Solving for torque:
$$$0.7=\frac{(20,000N)(0.01m)}{2\pi \cdot T}$$$
$$$T=\frac{(20,000N)(0.01m)}{2\pi(0.7)}=\frac{200N\cdot m}{4.396}=45.5\:N \cdot m$$$
45.5 N∙m


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