Ball screw calculation

2021/04/27 categories:Mechanical design| tags:Mechanical design|

Buckling load

Item Formula Value Unit
Distance between installations $ l_a = $ $ mm $
Young’s modulus $ E = $ $ N/mm^2 $
Thread shaft root diameter $ d_1 = $ $ mm $
Coefficient depending on the mounting method $ \eta = $
Moment of inertia of area $ I=\frac{\pi}{64}{d_1}^4 = $ $ mm^4 $
Buckling load $ P_1 = $ $ N $

Allowable tensile compressive load

Item Formula Value Unit
Allowable tensile compressive stress $ \sigma = $ $ N $
Allowable tensile compressive load $ P_2 = \sigma \frac{\pi}{4} {d_1}^2 = $ $ N $

Efficiency calculation

Item Formula Value Unit
Lead $ Ph = $ $ mm $
Ball center diameter $ dP = $ $ mm $
Coefficient of friction $ \mu = $
Contact angle $ \alpha = $ $ \deg $
Lead angle $ \beta = tan^{-1} \frac{Ph}{\pi d_P} = $ $ \deg $
Positive efficiency $ \eta_1 = \frac{(sin \alpha - \mu \cdot tan \beta)}{sin \alpha + \frac{\mu}{tan \beta}} = $
Reverse efficiency $ \eta_2 = \frac{sin \alpha - \frac{\mu}{tan \beta} }{sin \alpha + \mu \cdot tan \beta} = $

Calculate thrust from torque

Item Formula Value Unit
Torque $ T_1 = $ $ Nm $
Thrust $ F_1 = \frac{2 \pi \cdot \ \eta_1 \cdot T_1}{Ph \times 10^{-3}} = $ $ Nm $

Calculate torque from thrust

Item Formula Value Unit
Thrust $ F_2 = $ $ Nm $
Torque $ T_2 = \frac{Ph \cdot \eta_2 \cdot F_2}{2 \pi} = $ $ Nm $

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