Screw (simple Machine) - Actual Mechanical Advantage and Efficiency

Actual Mechanical Advantage and Efficiency

Because of the large area of sliding contact between the moving and stationary threads, screws typically have large frictional energy losses. Even well-lubricated jack screws have efficiencies of only 15% - 20%, the rest of the work applied in turning them is lost to friction. When friction is included, the mechanical advantage is no longer equal to the distance ratio but also depends on the screw's efficiency. From conservation of energy, the work W_in done on the screw by the input force turning it is equal to the sum of the work done moving the load W_out, and the work dissipated as heat by friction W_fric in the screw

The efficiency η is a dimensionless number between 0 and 1 defined as the ratio of output work to input work

Work is defined as the force multiplied by the distance moved, so and and therefore

or in terms of torque :

So the mechanical advantage of an actual screw is reduced from what it would be in an ideal, frictionless screw by the efficiency . Because of their low efficiency, in powered machinery screws are not often used as linkages to transfer large amounts of power (except in lead screws) but are more often used in positioners that operate intermittently.