## Values for calculation

$d$ $\mathrm{mm}$
$P$ $\mathrm{mm}$
$F$ $\mathrm{N}$
$μ$
$M_T$ $\mathrm{Nm}$
$S_{y-screw}$ $\mathrm{MPa}$
$E$ $\mathrm{MPa}$
$S_{y-nut}$ $\mathrm{MPa}$
$l$ $\mathrm{mm}$
$n$ $\mathrm{rpm}$
$C_c$
$S_F$
$β$
$S_{FB}$
$L$ $\mathrm{mm}$
$e$ $\mathrm{mm}$

## Calculation

### Clearance on the crest

$\text{if }\ P=1.5$
$$a_c=0.15$$
$\text{else if }\ P\le 5$
$$a_c=0.25$$
$\text{else if }\ P\le 12$
$$a_c=0.5$$
$\text{else}$
$$a_c=1$$

### Height of the overlapping

$$H_1=0.5\cdot P$$

$$H_4=H_1+a_c$$

$$h_3=H_1+a_c$$

### Minor diameter for internal threads

$$D_1=d-P$$

### Major diameter for internal threads

$$D_4=d+2\cdot a_c$$

### Minor diameter for external threads

$$d_3=d-2\cdot h_3$$

### Pitch diameter for external threads

$$d_2=d-0.5\cdot P$$

### Dimension $z$

$$z=0.25\cdot P$$

### Dimension $R_{1max}$

$$R_{1max}=0.5\cdot a_c$$

### Dimension $R_{2max}$

$$R_{2max}=a_c$$

### Lifting torque

$$M_T=\cfrac{F\cdot d_2}{2\cdot 10^3}\cdot\left(\cfrac{P+π\cdot μ\cdot d_2\cdot\sec{30°/2}}{π\cdot d_2-μ\cdot P\cdot\sec{30°/2}}\right)$$

$$M_T\le M_T$$

### Allowable combined stress the screw

$$σ_{all-C-screw}=\cfrac{S_{y-screw}}{S_F}\cdot C_c$$

### Allowable bearing stress the screw

$$P_{all-B-screw}=\cfrac{0.9\cdot S_{y-screw}}{S_F}\cdot C_c\cdot C_t$$

### Allowable bearing stress the nut

$$P_{all-B-nut}=\cfrac{0.9\cdot S_{y-nut}}{S_F}\cdot C_c\cdot C_t$$

### Allowable axial stress the screw

$$σ_{all-A-screw}=\cfrac{0.45\cdot S_{y-screw}}{S_F}\cdot C_c$$

### Allowable shear stress the screw

$$τ_{all-S-screw}=\cfrac{0.4\cdot S_{y-screw}}{S_F}\cdot C_c$$

### Screw speed

$$v=\cfrac{n}{60000}\cdot π\cdot d_2$$

$$v\le 0.25$$

### Power screw coefficient

$$C_t=2.7093\cdot v^2-1.5937\cdot v+0.25$$

### Axial stress in the screw

$$σ_{A-screw}=\cfrac{F}{\cfrac{π}{4}\cdot\left(\cfrac{d_2+d_3}{2}\right)^2}$$

$$σ_{A-screw}\le σ_{all-A-screw}$$

### Shear stress in the screw

$$τ_{S-screw}=\cfrac{M_T}{\cfrac{π}{16}\cdot\left(\cfrac{d_2+d_3}{2}\right)^3}$$

$$τ_{S-screw}\le τ_{all-S-screw}$$

### Combined stress in the screw

$$σ_{tresca-screw}=\sqrt{σ_{A-screw}^2+4\cdot τ_{S-screw}^2}$$

$$σ_{tresca-screw}\le σ_{all-C-screw}$$

### Bearing stress in the screw and nut

$$P_{B-screw-nut}=\cfrac{4\cdot F}{\cfrac{l}{P}\cdot π\cdot\left(d^2-D_1^2\right)}$$

$$P_{B-screw-nut}\le\min\left(P_{all-B-screw}, P_{all-B-nut}\right)$$

### Profile area

$$S=\cfrac{π}{4}\cdot\left(\cfrac{d_2+d_3}{2}\right)^2$$

### Second moment of area

$$I=\cfrac{π}{64}\cdot\left(\cfrac{d_2+d_3}{2}\right)^4$$

### Extreme fiber distance

$$c=\cfrac{d_2+d_3}{4}$$

$$i=\sqrt{\cfrac{I}{S}}$$

### Slenderness ratio

$$λ=\cfrac{L\cdot β}{i}$$

### Eccentricity parameter

$$η=\cfrac{e\cdot c}{i^2}$$

$$η\geq 0.25$$

### Maximal (critical) force

$\text{if }\ λ>0.282\cdot\sqrt{\cfrac{E\cdot S}{F}}$
$$F_{max}=S_{y-screw}\cdot S/ \left[1+η\cdot\sec\left(\cfrac{λ}{2}\cdot\sqrt{\cfrac{\left|F_{max}\right|}{E\cdot S}}\right)\right]$$
$\text{else}$
$$F_{max}=S_{y-screw}\cdot S/ \left[1+η\right]$$

$$\cfrac{F_{max}}{S_{FB}}\cdot C_c\geq F$$