Power screws convert rotary motion into linear motion, so they are used in vises, jacks, clamps, presses, and actuators. This cheat sheet helps students connect screw geometry to motion, force, torque, and efficiency. It is useful for solving engineering mechanics problems where friction and thread shape strongly affect performance.
The core ideas are pitch, lead, lead angle, friction angle, torque to raise or lower a load, and mechanical advantage. For a single-start screw, lead equals pitch, while multi-start screws move farther per revolution. Self-locking occurs when friction is high enough that the load cannot back-drive the screw without applied torque.
Key Facts
- Lead is the axial distance a screw advances in one full turn, so lead L = pitch p x number of starts.
- For a single-start screw, lead L = pitch p because there is only one thread helix.
- The lead angle is found from tan lambda = L / (pi dm), where lambda is the lead angle and dm is the mean thread diameter.
- For a square thread raising a load, torque Tr = W dm / 2 x tan(lambda + phi), where W is load and phi is the friction angle.
- The friction angle is defined by tan phi = mu, where mu is the coefficient of friction.
- For a square thread lowering a load, torque Tl = W dm / 2 x tan(phi - lambda) when the screw is self-locking.
- A power screw is self-locking when phi > lambda, which is approximately the same as mu > tan lambda.
- Ideal screw efficiency without collar friction can be estimated by efficiency e = tan lambda / tan(lambda + phi).
Vocabulary
- Power screw
- A screw mechanism designed to convert rotational input torque into linear force or motion.
- Pitch
- The axial distance from one thread to the next matching point on an adjacent thread.
- Lead
- The axial distance a nut or screw advances during one complete revolution.
- Lead angle
- The angle between the thread helix and a plane perpendicular to the screw axis at the mean diameter.
- Friction angle
- The angle phi whose tangent equals the coefficient of friction, so tan phi = mu.
- Self-locking
- A condition where the load cannot cause the screw to rotate backward without an external torque.
Common Mistakes to Avoid
- Confusing pitch and lead is wrong because they are equal only for a single-start screw. For a multi-start screw, lead = pitch x number of starts.
- Using the outside diameter instead of the mean diameter is wrong because torque and lead angle formulas use dm, the approximate diameter where thread force acts.
- Ignoring units in tan lambda = L / (pi dm) is wrong because lead and diameter must use the same length unit before calculating the ratio.
- Assuming every power screw is self-locking is wrong because self-locking requires phi > lambda, or approximately mu > tan lambda.
- Forgetting collar friction is wrong in real designs because a thrust collar can add significant torque beyond the thread torque.
Practice Questions
- 1 A single-start screw has a pitch of 4 mm. What is its lead?
- 2 A four-start screw has a pitch of 2.5 mm. What distance does the nut move in 6 revolutions?
- 3 A square-thread power screw has L = 6 mm, dm = 30 mm, and mu = 0.15. Find the lead angle and decide whether it is self-locking.
- 4 Explain why increasing the number of starts can make a screw faster but less likely to be self-locking.
Understanding Power Screws & Lead Reference
A screw thread can be understood by imagining that one turn of its helix has been cut and laid flat. It becomes an inclined ramp wrapped around a cylinder. The ramp rises by the lead during one trip around the mean diameter.
The mean diameter matters because it represents the approximate location where the thread contact force acts. A larger lead makes the ramp steeper. This gives faster linear travel per turn, but it usually requires more turning force to lift the same load.
A smaller lead acts like a gentler ramp. It gives more mechanical advantage, though the nut travels more slowly.
The turning torque must overcome more than the weight of the load. At the thread surfaces, the load creates a normal contact force. Friction acts along the thread surface and opposes the relative motion between screw and nut.
When lifting, gravity and friction both resist motion. When lowering, gravity tends to drive the motion while friction resists it. This difference explains why raising and lowering torque calculations use different angle relationships.
Real assemblies often have collar friction under the screw head or at a thrust bearing. Collar friction can be a major part of the required torque, especially when the collar diameter is large or lubrication is poor. Square threads are often used in basic calculations because their force directions are simpler than those of common trapezoidal threads.
Efficiency describes how much input work becomes useful lifting work. The rest becomes heat from friction. A screw with a high efficiency needs less input torque for a given load and travel distance.
Yet high efficiency is not always desirable. A bench vise, car jack, or lifting support may need to hold a load safely when the handle is released. In that case, self-locking prevents the load from rotating the screw backward.
A low-friction, steep-lead screw can back-drive under load. Ball screws are designed to reduce friction and are common in machine tools, 3D printers, and precision actuators. They move efficiently, but they often need a brake or motor holding torque when a vertical load is present.
When solving a problem, begin by drawing the load path. Identify whether the screw is raising, lowering, or simply holding a load. Check the number of thread starts before choosing the lead.
Use consistent units for force, diameter, pitch, and torque. The coefficient of friction is often an estimate, not a fixed material property. It changes with lubrication, surface finish, wear, contamination, and temperature.
Pay attention to whether the stated friction applies only to threads or includes the collar. Students often confuse pitch with lead, use the outside diameter instead of the mean diameter, or apply a raising torque result to a lowering case.
A final reasonableness check helps. More friction should require more effort during lifting, while a larger lead should increase travel per turn and reduce the tendency to self-lock.