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 $ |
