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:

ML=Fd22P+πμd2sec30/2πd2-μPsec30/2

ML - lifting torque - [Nm]

F - axial force - [N]

d2 - medium diameter - [mm]

P - thread pitch - [mm]

μ - friction - []


Axial stress the screw:

σ=Fπ4d2+d322

σ - axial stress the screw - [MPa]

F - axial force - [N]

d2 - medium diameter - [mm]

d3 - smaller external thread diameter - [mm]


Shear stress the screw:

τ=Mπ16d2+d323

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:

σtresca=σ2+4τ2σCall

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:

σCall=Rp0,2TSF*Cc

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 - []


Coefficient according to load:

load[]
Static load1
Unidirectional load, non-impact load0,8
Unidirectional load, with a small impact load0,7
Unidirectional load, with a big impact load0,6
Alternating load, with a small impact load0,45
Alternating load, with a big impact load0,25

Bearing stress the thread:

pt=4FLnP*π*d2-D12σall(t)

pt - bearing stress the thread - [MPa]

F - axial force - [N]

Ln - nut length - [mm]

P - thread pitch - [mm]

d - thread - [mm]

D1 - minor diameter - [mm]

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


Allowable bearing stress the thread:

σall(t)=0,9Rp0,2TSF*Cc*Ct

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:

Ct=2,7083v2-1,5937v+0,25; max v=0,25

Ct - power screw coefficient - []

v - screw speed - [m/s]


Screw speed:

v=n60*π*d2

v - screw speed - [m/s]

n - speed - [rpm]

d2 - medium diameter - [mm]


Buckling:

- Columns with eccentric loading:

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

FmaxS=Rp0,2T/ 1+eci2secL*β2iFmaxES

applies under the following conditions:

L*βi>0,282ESF
FmaxSF*CcF

- Struts or short columns with eccentric loading:

FmaxS=Rp0,2T/1+eci2

applies under the following conditions:

L*βi0,282ESF
FmaxSF*CcF

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

MET-Calc: Buckling

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


Download PDF:

Power screws.pdf


Social media:

Twitter Scribd Pinterest