Calculation of screw action forces

When we apply a torque on a screw the torque is converted (through balance of moments) to a peripheral force F_u acting on the screw pitch diameter d₂. A coaxial (with screw axis) force F vertical to the peripheral force F_u is created. Neglecting friction forces between screw and nut, the relation between the forces F_u and F is given from equation (1) where a is the lead angle and pitch the lead of thread. When we don’t neglect the friction between the nut and the screw then we use: formula (3) in case the force F has the same direction with the screw linear motion (force assists motion), and formula (4) when it has opposite direction (force resists motion). Formula (5) gives the relation between the friction coefficient and the friction angle which is used in formulas (3) and (4). Formulas (3) and (4) are applied when the thread is straight (Straight Thread: A straight thread is a screw thread projecting from cylindrical surface-MACHINERY’S HANDBOOK page 1478). Usually threads are tapered (Taper Thread: A taper thread is a screw thread projecting from a conical surface-MACHINERY’S HANDBOOK page 1478). Due to tapered geometry the force and friction coefficient are modified (divided with the cosine of the flank angle- see formulas (6) and (7)). Use formula (6) in case the force F has the same direction with the screw linear motion (force assists motion) and with a minus sign in opposite case. Formula (8) gives the relation between the actuating torque and the peripheral force acting on the pitch diameter. In case of lubricate instead of dry sliding the friction coefficients are lower.