Leadscrew

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.[5] 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.[6]

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] Acme threads are generally also stronger than square threads due to their trapezoidal thread profile, which provides greater load-bearing capabilities.

Buttress threads are of a triangular shape. These are used where the load force on the screw is only applied in one direction.[7] They are as efficient as square threads in these applications, but are easier to manufacture.

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

${\displaystyle {\mbox{efficiency}}={\frac {T_{0}}{T_{\text{raise}}}}={\frac {Fl}{2\pi T_{\text{raise}}}}={\frac {\tan {\lambda }}{\tan {\left(\phi +\lambda \right)}}}}$

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 take this into account:[12][14]

${\displaystyle T_{\text{raise}}={\frac {Fd_{\text{m}}}{2}}\left({\frac {l+\pi \mu d_{\text{m}}\sec {\alpha }}{\pi d_{\text{m}}-\mu l\sec {\alpha }}}\right)={\frac {Fd_{\text{m}}}{2}}\left({\frac {\mu \sec {\alpha }+\tan {\lambda }}{1-\mu \sec {\alpha }\tan {\lambda }}}\right)}$

${\displaystyle T_{\text{lower}}={\frac {Fd_{\text{m}}}{2}}\left({\frac {\pi \mu d_{\text{m}}\sec {\alpha }-l}{\pi d_{\text{m}}+\mu l\sec {\alpha }}}\right)={\frac {Fd_{\text{m}}}{2}}\left({\frac {\mu \sec {\alpha }-\tan {\lambda }}{1+\mu \sec {\alpha }\tan {\lambda }}}\right)}$

where ${\displaystyle \alpha \,}$ 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 (${\displaystyle d_{\text{c}}}$):[12]

Plot of square lead screw efficiency against lead angle for different coefficients of friction

${\displaystyle T_{\text{c}}={\frac {F\mu _{\text{c}}d_{\text{c}}}{2}}}$

where ${\displaystyle \mu _{\text{c}}}$ is the coefficient of friction between the collar on the load and ${\displaystyle d_{\text{c}}}$ is the mean collar diameter. For collars that use thrust bearings the frictional loss is negligible and the above equation can be ignored.[15]

Efficiency for non-zero thread angles can be written as follows:[16]

${\displaystyle \eta ={\frac {\cos \alpha \ -\ \mu \tan \lambda }{\cos \alpha \ +\ \mu \cot \lambda }}}$

Coefficient of friction for thrust collars[15]

Material combination	Starting ${\displaystyle \mu _{\text{c}}}$	Running ${\displaystyle \mu _{\text{c}}}$
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

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[18]

${\displaystyle N={(4.76\times 10^{6})d_{\text{r}}C \over L^{2}}}$

where

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

Alternatively using metric units:[19]

${\displaystyle N={\frac {Cd_{\text{r}}\times 10^{7}}{L^{2}}}}$

where the variables are identical to above, but the values are in millimetres and ${\displaystyle C}$ is as follows:

• ${\displaystyle C}$ = 3.9 for fixed-free supports [20]
• ${\displaystyle C}$ = 12.1 for both ends supported
• ${\displaystyle C}$ = 18.7 for fixed-supported structure
• ${\displaystyle C}$ = 27.2 for both ends fixed

• Bhandari, V B (2007), Design of Machine Elements, Tata McGraw-Hill, ISBN 978-0-07-061141-2.
• 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 978-0-07-252036-1.