Which of the following is true with regard to self-locking screw?

Explanation:

Self-locking screw:

The power screw in which an effort is required to lower a load is known as a self-locking screw.

Eg. Screw jack

P = Force require to lower a body, W = Weight of the body to be lowered, N = Normal force

μN = Friction force between body and screw, d_m = Mean diameter of a screw, α = Lead angle

l = Lead i.e. distance travelled by screw along the axis in one rotation, πd_m = Distance travelled by a point in screw in one rotation.

∴ The effort required to lower a body is given by ⇒ P = W × tan (ϕ - α )

where ϕ = friction angle and μ = tan ϕ is co-efficient of friction.

The tangent of the helix angle is given by ⇒ \(\tan \alpha = \frac{l}{{\pi {d_m}}}\)

The Torque required to lower the body is given by –

M_t = Force × perpendicular distance

\({M_t} = P \times \frac{{{d_m}}}{2}\)

\({M_t} = \frac{{W{d_m}}}{2}\tan \left( {\phi - \alpha } \right)\)

When ϕ ≥ α, the torque required is positive and the condition is known as “Self-locking”.

∴ tan ϕ ≥ tan α

∴ A screw will be self-locking if the coefficient of friction is equal to or greater than the lead angle.