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# Encyclopedia

A leadscrew (or lead screw), also known as a power screw[1] or translation screw,[2] is a screw designed to translate radial motion into linear motion. Common applications are machine slides (such as in machine tools), vises, presses, and jacks.[3]

## Types

Power screws are classified by the geometry of their thread. V-threads are less suitable for leadscrews than others such as Acme because they have more friction between the threads. Their threads are designed to induce this friction to keep the fastener from loosening. Leadscrews, on the other hand, are designed to minimize friction.[4] Therefore, in most commercial and industrial use, V-threads are avoided for leadscrew use. Nevertheless, V-threads are sometimes successfully used as leadscrews, for example on microlathes and micromills.[5]

Square threads are named after their square geometry. They are the most efficient power screw, but also the most difficult to machine, thus the most expensive.

An Acme screw

Acme threads have a 29° thread angle, which is easier to machine than square threads. They are not as efficient as square threads, due to the increased friction induced by the thread angle.[3]

Buttress threads are of a triangular shape. It combines the advantages of the square and acme thread forms with only one difference: it only works in one direction.[6]

## Characteristics

A leadscrew nut and screw mate with rubbing surfaces, and consequently they have a relatively high friction and stiction compared to mechanical parts which mate with rolling surfaces and bearings. Leadscrew efficiency is typically between 25 and 70%, with higher pitch screws tending to be more efficient. A higher performing but more expensive alternative is the ball screw.

The high internal friction means that leadscrew systems are not usually capable of continuous operation at high speed, as they will overheat. Due to inherently high stiction, the typical screw is self-locking (i.e. when stopped, a linear force on the nut will not apply a torque to the screw) and are often used in applications where backdriving is unacceptable, like holding vertical loads or in hand cranked machine tools.

Leadscrews are typically used well greased, but, with an appropriate nut, it may be run dry with somewhat higher friction. There is often a choice of nuts, and manufacturers will specify screw and nut combination as a set.

The mechanical advantage of a leadscrew is determined by the screw pitch and lead. For multi-start screws the mechanical advantage is lower, but the traveling speed is better.[7]

Backlash can be reduced with the use of a second nut to create a static loading force known as preload; alternately, the nut can be cut along a radius and preloaded by clamping that cut back together.

A lead screw will back drive, whereby forces on the nut applied parallel with the lead screw will cause a free-moving leadscrew to begin to rotate. A leadscrew's tendency to backdrive depends on its thread helix angle, coefficient of friction of the interface of the components (screw/nut) and the included angle of the thread form. In general, a steel acme thread and bronze nut will back drive when the helix angle of the thread is greater than 20°.

• Compact
• Simple to design
• Easy to manufacture; no specialized machinery is required
• Precise and accurate linear motion
• Smooth, quiet, and low maintenance
• Minimal number of parts
• Most are self-locking

The disadvantages are that most are not very efficient. Due to the low efficiency they cannot be used in continuous power transmission applications. They also have a high degree for friction on the threads, which can wear the threads out quickly. For square threads, the nut must be replaced; for trapezoidal threads, a split nut may be used to compensate for the wear.[4]

## Alternatives

Alternatives to actuation by leadscrew include:

## Mechanics

Diagram of an "unwrapped" screw thread

The torque required to lift or lower a load can be calculated by "unwrapping" one revolution of a thread. This is most easily described for a square or buttress thread as the thread angle is 0 and has no bearing on the calculations. The unwrapped thread forms a right angle triangle where the base is πdm long and the height is the lead (pictured to the right). The force of the load is directed downward, the normal force is perpendicular to the hypotenuse of the triangle, the frictional force is directed in the opposite direction of the direction of motion (perpendicular to the normal force or along the hypotenuse), and an imaginary "effort" force is acting horizontally in the direction opposite the direction of the frictional force. Using this free-body diagram the torque required to lift or lower a load can be calculated:[8][9]

$T_{raise} = \frac{F d_m}{2} \left( \frac{l + \pi \mu d_m}{\pi d_m - \mu l} \right) = \frac{F d_m}{2} \tan{\phi + \lambda}$
$T_{lower} = \frac{F d_m}{2} \left( \frac{\pi \mu d_m - l}{\pi d_m + \mu l} \right) = \frac{F d_m}{2} \tan{\phi - \lambda}$
Screw material Nut material
Steel Bronze Brass Cast iron
Steel, dry 0.15–0.25 0.15–0.23 0.15–0.19 0.15–0.25
Steel, machine oil 0.11–0.17 0.10–0.16 0.10–0.15 0.11–0.17
Bronze 0.08–0.12 0.04–0.06 - 0.06–0.09

where

• T = torque
• F = load on the screw
• dm = mean diameter
• $\mu\,$ = coefficient of friction (common values are found in the table to the right)
• $\phi\,$ = friction angle
• $\lambda\,$ = lead angle

Based on the Tlower equation it can be found that the screw is self-locking when the coefficient of friction is greater than the tangent of the lead angle. An equivalent comparison is when the friction angle is greater than the lead angle (φ > λ).[11] When this is not true the screw will back-drive, or lower under the weight of the load.[8]

The efficiency, calculated using the torque equations above, is:[12][13]

$\mbox{efficiency} = \frac{T_0}{T_{raise}} = \frac{Fl}{2 \pi T_{raise}} = \frac{\tan{\lambda}}{\tan{\phi + \lambda}}$

For screws that have a thread angle other than zero, such as a trapezoidal thread, this must be compensated as it increases the frictional forces. The equations below takes this into account:[12][14]

$T_{raise} = \frac{F d_m}{2} \left( \frac{l + \pi \mu d_m \sec{\alpha}}{\pi d_m - \mu l \sec{\alpha}} \right) = \frac{F d_m}{2} \left( \frac{\mu \sec{\alpha} + \tan{\lambda}}{1 - \mu \sec{\alpha} \tan{\lambda}} \right)$
$T_{lower} = \frac{F d_m}{2} \left( \frac{\pi \mu d_m \sec{\alpha} - l}{\pi d_m + \mu l \sec{\alpha}} \right) = \frac{F d_m}{2} \left( \frac{\mu \sec{\alpha} - \tan{\lambda}}{1 + \mu \sec{\alpha} \tan{\lambda}} \right)$

where $\alpha\,$ is one half the thread angle.

If the leadscrew has a collar in which the load rides on then the frictional forces between the interface must be accounted for in the torque calculations as well. For the following equation the load is assumed to be concentrated at the mean collar diameter (dc):[12]

$T_c = \frac{F \mu_c d_c}{2}$

where μc is the coefficient of friction between the collar on the load and dc is the mean collar diameter. For collars that use thrust bearings the frictional loss is negligible and the above equation can be ignored.[15]

Coefficient of friction for thrust collars[15]
Material combination Starting μc Running μc
Soft steel / cast iron 0.17 0.12
Hardened steel / cast iron 0.15 0.09
Soft steel / bronze 0.10 0.08
Hardened steel / bronze 0.08 0.06
Safe running speeds for various nut materials and loads on a steel screw[16]
Nut material Safe loads [psi] Speed
Bronze 2500–3500 Low speed
Bronze 1600–2500 10 fpm
Cast iron 1800–2500 8 fpm
Bronze 800–1400 20–40 fpm
Cast iron 600–1000 20–40 fpm
Bronze 150–240 50 fpm

## References

### Notes

1. ^ Ball Screws & Lead screws, retrieved 2008-12-16 .
2. ^ a b Bhandari, p. 202.
3. ^ a b Shigley, p. 400.
4. ^ a b Bhandari, p. 203.
5. ^ Martin 2004, p. 266.
6. ^ Bhandari, p. 204.
7. ^ Bhandari, pp. 205–206.
8. ^ a b Shigley, p. 402.
9. ^ Bhandari, pp. 207–208.
10. ^ Shigley, p. 408.
11. ^ Bhandari, p. 208.
12. ^ a b c Shigley, p. 403.
13. ^ Bhandari, p. 209.
14. ^ Bhandari, pp. 211–212.
15. ^ a b Bhandari, p. 213.
16. ^ Shigley, p. 407.

### Bibliography

• Bhandari, V B (2007), Design of Machine Elements, Tata McGraw-Hill, ISBN 9780070611412 .
• Martin, Joe (2004), Tabletop Machining: A Basic Approach to Making Small Parts on Miniature Machine Tools, Vista, California, USA: Sherline, Inc., ISBN 978-0-9665433-0-8 . Originally published in 1998; content updated with each print run, similar to a "revised edition". Currently in the fourth print run.
• Shigley, Joseph E.; Mischke, Charles R.; Budynas, Richard Gordon (2003), Mechanical Engineering Design (7th ed.), McGraw Hill, ISBN 9780072520361 .