Screw Friction:

A screw jack is a device utilized for lifting or lowering heavy loads by applying comparatively smaller efforts at the end of the lever. The thread of a screw jack can be considered as an inclined plane wound round a cylinder and the principles utilized in solving problems on inclined plane may be applied to solve problems involving screw friction. If α is the angle of the inclined plane and φ is the angle of friction, we know that the horizontal force needed to pull the load up is specified by

                                   P = W tan (α + φ)

This force P which drags the load along with the inclined plane is associated to the force P₁ applied at the end of the lever of the screw jack. This may be found out by taking moments of the forces around the centre line of the cylinder. If l is the length of the lever and r is the mean radius of the screw, we have following

P₁ × l = P × r

∴ P₁ =( r/ l) P

∴ P₁ =( r/ l) W tan (α + φ)

= (r/ l ) ( tan α + tan φ/1 - tan α tan φ)

While there is one complete revolution, the load is raised through one pitch, that means centre to centre distance between two consecutive threads.

∴ tan α = p / 2 π r

where, p = pitch. and tan φ = μ

By using these relations, we may work out the horizontal effort P₁ needed to raise the load up.

If the load remains in position even after removal of the effort P1 the screw jack is said to be self-locking. It does not work in reverse direction as the angle of inclination, in such cases, shall be less than the angle of friction

α < φ                             ∴ tan α < tan φ

                                      ∴ tan α < μ,  i.e.  μ > tan α

Thus, if the coefficient of friction is greater than p /2 π r, the screw jack will be self-locking. In order to lower the load, the effort P needed at the thread shall be W tan (φ - α); therefore the effort at the end of the lever shall be specified by

                                               P₂ = (r/ l) × W × tan (φ - α)