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 Title: Leadscrew Author: World Heritage Encyclopedia Language: English Subject: Collection: Screws Publisher: World Heritage Encyclopedia Publication Date:

DVD drive with leadscrew and stepper motor.
Floppy disc drive with leadscrew and stepper motor.

A leadscrew (or lead screw), also known as a power screw[1] or translation screw,[2] is a screw used as a linkage in a machine, to translate turning motion into linear motion. Because of the large area of sliding contact between their male and female members, screw threads have larger frictional energy losses compared to other linkages. They are not typically used to carry high power, but more for intermittent use in low power actuator and positioner mechanisms. Common applications are linear actuators, machine slides (such as in machine tools), vises, presses, and jacks.[3]

Leadscrews are manufactured in the same way as other thread forms (they may be rolled, cut, or ground).

A lead screw is sometimes used with a split nut which allows the nut to be disengaged from the threads and moved axially, independently of the screw's rotation, when needed (such as in single-point threading on a manual lathe).

## Contents

• Types 1
• Alternatives 3
• Mechanics 4
• Running speed 4.1
• References 6
• Bibliography 6.1

## 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, having the least friction, so they are often used for screws that carry high power. But they are also the most difficult to machine, and are 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. These are used where the load force on the screw is only applied in one direction.[6] They are as efficient as square threads in these applications, but are easier to manufacture.

Leadscrews are used to raise and lower the front door of the Boeing 747-8F Freighter aircraft.

• 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 of 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 \pi d_m 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:[7][8]

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{\left(\phi + \lambda\right)}
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{\left(\phi - \lambda\right)}
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\, = angle of friction

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 (\phi > \lambda).[10] When this is not true the screw will back-drive, or lower under the weight of the load.[7]

The efficiency, calculated using the torque equations above, is:[11][12]

\mbox{efficiency} = \frac{T_0}{T_{raise}} = \frac{Fl}{2 \pi T_{raise}} = \frac{\tan{\lambda}}{\tan{\left(\phi + \lambda\right)}}

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:[11][13]

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):[11]

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

where \mu_c 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.[14]

Coefficient of friction for thrust collars[14]
Material combination Starting \mu_c Running \mu_c
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

### Running speed

Safe running speeds for various nut materials and loads on a steel screw[15]
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

The running speed for a leadscrew (or ball screw) is typically limited to, at most, 80% of the calculated critical speed. The critical speed is the speed that excites the natural frequency of the screw. For a steel leadscrew or steel ballscrew, the critical speed is approximately[16]

N = { (4.76 \times 10^6) d_r C \over L^2}

where

• N = critical speed in RPM
• dr = smallest (root) diameter of the leadscrew in inches
• L = length between bearing supports in inches
• C = .36 for one end fixed, one end free
• C = 1.00 for both ends simple
• C = 1.47 for one end fixed, one end simple
• C = 2.23 for both ends fixed

## References

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. ^ a b Shigley, p. 402.
8. ^ Bhandari, pp. 207–208.
9. ^ Shigley, p. 408.
10. ^ Bhandari, p. 208.
11. ^ a b c Shigley, p. 403.
12. ^ Bhandari, p. 209.
13. ^ Bhandari, pp. 211–212.
14. ^ a b Bhandari, p. 213.
15. ^ Shigley, p. 407.
16. ^ Nook Industries, Inc. "Acme & lead screw assembly glossary and technical data"

### Bibliography

• Bhandari, V B (2007), Design of Machine Elements, Tata McGraw-Hill, .
• Martin, Joe (2004), Tabletop Machining: A Basic Approach to Making Small Parts on Miniature Machine Tools, Vista, California, USA: Sherline, Inc., 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, .