Power Screw Lowering Torque and Self-Locking

Turn the screw the other way and friction changes sides. Raising, it fights you and adds to the load; lowering, the load is trying to drive the screw and friction is what holds it back. The bracket flips accordingly — $(\pi\mu d_m - l)$ over $(\pi d_m + \mu l)$ — and the sign of the answer is the whole lesson of the page.

If $\pi\mu d_m > l$, the torque comes out positive: you must apply torque to let the load DOWN, and with the handle released nothing moves. The screw is self-locking. If $\pi\mu d_m < l$, the torque is negative, which is not an error — it is the amount you must apply AGAINST the direction of lowering just to stop the load running away. The screw back-drives, or overhauls, and anything held up by it needs a brake.

Set the torque to zero and the boundary falls out in one line: $\mu = l/(\pi d_m)$, or equivalently $\mu = \tan\lambda$ — the friction angle equals the lead angle. That is the self-locking criterion, and it explains a great deal at a glance. A fine single-start thread has a small lead and locks easily. A coarse or multi-start thread has a large lead and does not. A ball screw has almost no friction at all and never locks, which is exactly why it is fast and exactly why it always needs a holding brake. The same criterion is why a fine-pitch bolt resists loosening better than a coarse one, and why a screw jack under a car is safe while a lead screw on a fast actuator is not.

Work the boundary for a 30 mm mean diameter screw with a 5 mm lead: $\mu_{crit} = 0.005/(\pi \times 0.03) = 0.053$. Almost any dry or greased steel pair sits well above that, so the screw locks comfortably — with µ = 0.15 and a 10 kN load, it takes 14.4 N·m to let it down. Change nothing but the lead, to 10 mm double-start, and the critical coefficient doubles to 0.106; the screw still locks at µ = 0.15, but the margin has halved.

Which brings the real warning. DO NOT DESIGN SELF-LOCKING ON A THIN MARGIN. µ is the least reliable figure in the calculation and it moves the wrong way over a machine's life: fresh grease reduces it, a run-in thread reduces it, and VIBRATION reduces it dramatically — the effective coefficient under vibration can approach zero, which is the mechanism by which bolts back off and by which a screw that passed a static bench test walks down under a vibrating load. Where a dropping load would injure someone, fit a positive holding device — a ratchet, a brake, a worm reducer, a mechanical stop — and treat the self-locking as the second line of defence rather than the first. It is also worth remembering that a thrust collar helps here: its friction torque opposes motion in whichever direction the screw turns, so it adds to the holding in the lowering direction just as it subtracts from the efficiency in the raising one.