# Power screws

The power screws are used to convert the rotary motion into a sliding one (rarely the other way around). They are commonly used as guide screws for machine tools, screws for presses and jacks.

Fig.1 power screws

Lifting torque:

${M}_{L}=\frac{F{d}_{2}}{2}\left[\frac{P+\pi \mu {d}_{2}sec\left(30/2\right)}{\pi {d}_{2}-\mu Psec\left(30/2\right)}\right]$

ML - lifting torque - [Nm]

F - axial force - [N]

d2 - medium diameter - [mm]

P - thread pitch - [mm]

μ - friction - []

Axial stress the screw:

$\sigma =\frac{F}{\frac{\pi }{4}{\left(\frac{{d}_{2}+{d}_{3}}{2}\right)}^{2}}$

σ - axial stress the screw - [MPa]

F - axial force - [N]

d2 - medium diameter - [mm]

d3 - smaller external thread diameter - [mm]

Shear stress the screw:

$\tau =\frac{M}{\frac{\pi }{16}{\left(\frac{{d}_{2}+{d}_{3}}{2}\right)}^{3}}$

τ - shear stress the screw - [MPa]

M - torque - [Nm]

d2 - medium diameter - [mm]

d3 - smaller external thread diameter - [mm]

Maximal shear stress (Tresca) the screw:

${\sigma }_{tresca}=\sqrt{{\sigma }^{2}+4{\tau }^{2}}\le {\sigma }_{Call}$

σtresca - maximal shear stress (Tresca) the screw - [MPa]

σ - axial stress the screw - [MPa]

τ - shear stress the screw - [MPa]

σCall - allowed combined stress - [MPa]

Allowed combined stress:

${\sigma }_{Call}=\frac{{R}_{p0,2T}}{{S}_{F}}*{C}_{c}$

σCall - allowed combined stress - [MPa]

Rp0,2T - the minimum yield strength or 0,2% proof strength at calculation temperature - [MPa]

SF - safety factor - []

Cc - coefficient according to load - []

${p}_{t}=\frac{4F}{\frac{{L}_{n}}{P}*\pi *\left({d}^{2}-{D}_{1}^{2}\right)}\le {\sigma }_{all\left(t\right)}$

pt - bearing stress the thread - [MPa]

F - axial force - [N]

Ln - nut length - [mm]

P - thread pitch - [mm]

D1 - minor diameter - [mm]

σall(t) - allowable bearing stress the thread - [MPa]

${\sigma }_{all\left(t\right)}=\frac{0,9{R}_{p0,2T}}{{S}_{F}}*{C}_{c}*{C}_{t}$

σall(t) - allowable bearing stress the thread - [MPa]

Rp0,2T - the minimum yield strength or 0,2% proof strength at calculation temperature - [MPa]

SF - safety factor - []

Cc - coefficient according to load - []

Ct - power screw coefficient - []

Power screw coefficient:

${C}_{t}=2,7083{v}^{2}-1,5937v+0,25;$ $\mathrm{max}v=0,25$

Ct - power screw coefficient - []

v - screw speed - [m/s]

Screw speed:

$v=\frac{n}{60}*\pi *{d}_{2}$

v - screw speed - [m/s]

n - speed - [rpm]

d2 - medium diameter - [mm]

Buckling:

The Secant equation for the stress calculation in the extreme fiber of a profile.

$\frac{{F}_{max}}{S}={R}_{p0,2T}/$ $\left[1+\frac{ec}{{i}^{2}}sec\left(\frac{L*\beta }{2i}\sqrt{\frac{{F}_{max}}{ES}}\right)\right]$

applies under the following conditions:

$\frac{L*\beta }{i}>0,282\sqrt{\frac{ES}{F}}$
$\frac{{F}_{max}}{{S}_{F}}*{C}_{c}\ge F$

$\frac{{F}_{max}}{S}={R}_{p0,2T}/\left[1+\frac{ec}{{i}^{2}}\right]$

applies under the following conditions:

$\frac{L*\beta }{i}\le 0,282\sqrt{\frac{ES}{F}}$
$\frac{{F}_{max}}{{S}_{F}}*{C}_{c}\ge F$

Fmax - maximal (critical) force - [N]

S - profile area - [mm2]

Rp0,2T - the minimum yield strength or 0,2% proof strength at calculation temperature - [MPa]

e - eccentricity - [mm]

c - extreme fiber distance - [mm]

i - gyration radius - [mm]

L - strut length - [mm]

β - type of strut mounting - []

E - Young’s modulus - [MPa]

F - axial force - [N]

SF - safety factor - []

Cc - coefficient according to load - []

Type of strut mounting:

Fig.2 type of strut mounting

Literature:

MET-Calc: Allowable stress

Joseph E. Shigley, Charles R. Mischke, Richard G. Budynas: Konstruování strojních součástí 2010.

MET-Calc: Buckling