Screw Jack - Effort Force vs. Load
Screw jacks and effort forces.
A screw jack is a mechanical device that can increase the magnitude of an effort force.
The effort force for a screw jack when neglecting friction can be expressed as
F = (Q p) / (2 π R) (1)
where
F = effort force at the end of the arm or handle (lb, N)
Q = weight or load (lb, N)
p = pitch - distance or lead of thread in one turn (in, m)
R = lever-arm radius (in, m)
Pitch is the distance between screw grooves and is commonly used with inch sized products and specified as threads per inch. Lead is the linear travel the nut makes per one screw revolution. The pitch and lead are equal.
The torque acting on the screw can be calculated as
T = F R (2)
where
T = torque (lb in, Nm)
Example - Screw jack without friction
If the load on a screw jack is 50000 lb, the lever-arm is 20 inches and the pitch equals 1/8 inches - the effort force can be estimated to
F = ((50000 lb) (1/8 in)) / (2 π (20 in))
= 49.8 lb
The torque acting on the screw can be calculated
T = (49.8 lb) (20 in)
= 995 lb in
= 82.9 lb ft
Example - Metric Screw Lift
A M24 metric screw with pitch 3 mm is used in a mechanical screw lift with load 225 kN. The lever arm is 0.5 m. The effort force required can be calculated as
F = ((225000 N) (0.003 m)) / (2 π (0.5 m))
= 215 N
The torque acting on the screw can be calculated
T = (215 N) (0.5 m)
= 107 Nm
Screw Jack Calculator - without Friction - Imperial Units
Calculate torque and effort force acting on the lever arm.
Screw Jack Calculator - without Friction - Metric Units
Calculate torque and effort force acting on the lever arm.
Note the difference between mass and weight!
Screw Jack with Friction
For motion in the same direction as the load (load assist the screw jack), the effort force can expressed as
F = Q ((2 π μ r - p) / (2 π r + μ p)) (r / R) (2)
where
r = pitch radius of screw (in)
For motion in the opposite direction as the load (load resists the screw jack), the effort force can expressed as
F = Q ((2 π μ r + p) / (2 π r - μ p)) (r / R) (3)
