What is the efficiency of a self-locking power screw?

Concept:

For self-locking, the maximum efficiency of the screw should be 50%.

If efficiency is more than 50% the condition is known as overhauling.

For a self-locking screw, the coefficient of friction is equal to or greater than the tangent of the helix angle.

In the Power screw, the torque Mt required to lower the load is given by

\({M_t} = \frac{{W{d_m}}}{2}\tan \left( {ϕ - α } \right)\) where, W = load on the screw in N, dm = the mean diameter of screw in m,

ϕ = friction angle and α = helix angle

Case 1.  when ϕ ≥  α 

tan (ϕ - α ) ≥ 0, thus Mt ≥ 0.

i.e. a positive torque is required to lower the load. Thus the load will not turn the screw and will not descend down on its own unless an effort is applied.

Such cases of screws are knowns as 'Self-locking screws'. And the screw will hold the hold without any application of brake.

Also, as ϕ > α 

tan ϕ > tan α 

\(\mu > \frac{l}{{\pi {d_m}}}\)

Case 2. when ϕ < α 

tan (ϕ - α ) < 0, thus Mt < 0.

i.e. negative torque is required to lower the load. The load will turn down the screw and will descend down on its own unless a restoring torque is required to hold the load.

Such cases of screws are known as 'overhauling of the screw' or back drawing of the screw.