Menu

Trapezoidal thread

Trapezoidal thread R 1 R 2 h 3 z H 1 a c a c 30° P Nut thread Screw thread H 4 d 2 d 3 d D 1 D 2 D 4
Trapezoidal thread
Type of strut mounting F F F F β = 0.5 β = 0.7 β = 1 β = 2 A B C D
Type of strut mounting

Values for calculation

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

Calculation

Clearance on the crest

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

Height of the overlapping

$$H_1=0.5\cdot P$$
$H_1=0.5\cdot P$
Equations in LaTeX code
H_1=0.5\cdot P

Height of internal threads

$$H_4=H_1+a_c$$
$H_4=H_1+a_c$
Equations in LaTeX code
H_4=H_1+a_c

Height of external threads

$$h_3=H_1+a_c$$
$h_3=H_1+a_c$
Equations in LaTeX code
h_3=H_1+a_c

Minor diameter for internal threads

$$D_1=d-P$$
$D_1=d-P$
Equations in LaTeX code
D_1=d-P

Major diameter for internal threads

$$D_4=d+2\cdot a_c$$
$D_4=d+2\cdot a_c$
Equations in LaTeX code
D_4=d+2\cdot a_c

Minor diameter for external threads

$$d_3=d-2\cdot h_3$$
$d_3=d-2\cdot h_3$
Equations in LaTeX code
d_3=d-2\cdot h_3

Pitch diameter for external threads

$$d_2=d-0.5\cdot P$$
$d_2=d-0.5\cdot P$
Equations in LaTeX code
d_2=d-0.5\cdot P

Dimension $ z $

$$z=0.25\cdot P$$
$z=0.25\cdot P$
Equations in LaTeX code
z=0.25\cdot P

Dimension $ R_{1max} $

$$R_{1max}=0.5\cdot a_c$$
$R_{1max}=0.5\cdot a_c$
Equations in LaTeX code
R_{1max}=0.5\cdot a_c

Dimension $ R_{2max} $

$$R_{2max}=a_c$$
$R_{2max}=a_c$
Equations in LaTeX code
R_{2max}=a_c

Lifting torque

$$M_T=\cfrac{F_A\cdot d_2}{2\cdot 10^3}\cdot\left(\cfrac{P+π\cdot μ\cdot d_2\cdot\sec{30°/2}}{π\cdot d_2-μ\cdot P\cdot\sec{30°/2}}\right)$$
$M_T=\cfrac{F_A\cdot d_2}{2\cdot 10^3}\cdot\left(\cfrac{P+π\cdot μ\cdot d_2\cdot\sec{30°/2}}{π\cdot d_2-μ\cdot P\cdot\sec{30°/2}}\right)$
Equations in LaTeX code
M_T=\cfrac{F_A\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)
$$M_T\le M_T$$
$M_T\le M_T$
Equations in LaTeX code
M_T\le M_T

Allowable combined stress the screw

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

Allowable bearing stress the screw

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

Allowable bearing stress the nut

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

Allowable axial stress the screw

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

Allowable shear stress the screw

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

Screw speed

$$v=\cfrac{n}{60000}\cdot π\cdot d_2$$
$v=\cfrac{n}{60000}\cdot π\cdot d_2$
Equations in LaTeX code
v=\cfrac{n}{60000}\cdot π\cdot d_2
$$v\le 0.25$$
$v\le 0.25$
Equations in LaTeX code
v\le 0.25

Power screw coefficient

$$C_t=2.7093\cdot v^2-1.5937\cdot v+0.25$$
$C_t=2.7093\cdot v^2-1.5937\cdot v+0.25$
Equations in LaTeX code
C_t=2.7093\cdot v^2-1.5937\cdot v+0.25

Axial stress in the screw

$$σ_{A-screw}=\cfrac{F_A}{\cfrac{π}{4}\cdot\left(\cfrac{d_2+d_3}{2}\right)^2}$$
$σ_{A-screw}=\cfrac{F_A}{\cfrac{π}{4}\cdot\left(\cfrac{d_2+d_3}{2}\right)^2}$
Equations in LaTeX code
σ_{A-screw}=\cfrac{F_A}{\cfrac{π}{4}\cdot\left(\cfrac{d_2+d_3}{2}\right)^2}
$$σ_{A-screw}\le σ_{all-A-screw}$$
$σ_{A-screw}\le σ_{all-A-screw}$
Equations in LaTeX code
σ_{A-screw}\le σ_{all-A-screw}

Shear stress in the screw

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

Combined stress in the screw

$$σ_{tresca-screw}=\sqrt{σ_{A-screw}^2+4\cdot τ_{S-screw}^2}$$
$σ_{tresca-screw}=\sqrt{σ_{A-screw}^2+4\cdot τ_{S-screw}^2}$
Equations in LaTeX code
σ_{tresca-screw}=\sqrt{σ_{A-screw}^2+4\cdot τ_{S-screw}^2}
$$σ_{tresca-screw}\le σ_{all-C-screw}$$
$σ_{tresca-screw}\le σ_{all-C-screw}$
Equations in LaTeX code
σ_{tresca-screw}\le σ_{all-C-screw}

Bearing stress in the screw and nut

$$P_{B-screw-nut}=\cfrac{4\cdot F_A}{\cfrac{l}{P}\cdot π\cdot\left(d^2-D_1^2\right)}$$
$P_{B-screw-nut}=\cfrac{4\cdot F_A}{\cfrac{l}{P}\cdot π\cdot\left(d^2-D_1^2\right)}$
Equations in LaTeX code
P_{B-screw-nut}=\cfrac{4\cdot F_A}{\cfrac{l}{P}\cdot π\cdot\left(d^2-D_1^2\right)}
$$P_{B-screw-nut}\le\min\left(P_{all-B-screw}, P_{all-B-nut}\right)$$
$P_{B-screw-nut}\le\min\left(P_{all-B-screw}, P_{all-B-nut}\right)$
Equations in LaTeX code
P_{B-screw-nut}\le\min\left(P_{all-B-screw}, P_{all-B-nut}\right)

Profile area

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

Second moment of area

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

Extreme fiber distance

$$c=\cfrac{d_2+d_3}{4}$$
$c=\cfrac{d_2+d_3}{4}$
Equations in LaTeX code
c=\cfrac{d_2+d_3}{4}

Gyration radius

$$i=\sqrt{\cfrac{I}{S}}$$
$i=\sqrt{\cfrac{I}{S}}$
Equations in LaTeX code
i=\sqrt{\cfrac{I}{S}}

Maximal (critical) force

$\text{if }\ \cfrac{L\cdot β}{i}>0.282\cdot\sqrt{\cfrac{E\cdot S}{F_A}}$
$\text{if }\ \cfrac{L\cdot β}{i}>0.282\cdot\sqrt{\cfrac{E\cdot S}{F_A}}$
Equations in LaTeX code
\text{if }\ \cfrac{L\cdot β}{i}>0.282\cdot\sqrt{\cfrac{E\cdot S}{F_A}}
$$F_{max}=S_{y-screw}\cdot S/ \left[1+\cfrac{e\cdot c}{i^2}\cdot\sec\left(\cfrac{L\cdot β}{2\cdot i}\cdot\sqrt{\cfrac{F_{max}}{E\cdot S}}\right)\right]$$
$F_{max}=S_{y-screw}\cdot S/ \left[1+\cfrac{e\cdot c}{i^2}\cdot\sec\left(\cfrac{L\cdot β}{2\cdot i}\cdot\sqrt{\cfrac{F_{max}}{E\cdot S}}\right)\right]$
Equations in LaTeX code
F_{max}=S_{y-screw}\cdot S/ \left[1+\cfrac{e\cdot c}{i^2}\cdot\sec\left(\cfrac{L\cdot β}{2\cdot i}\cdot\sqrt{\cfrac{F_{max}}{E\cdot S}}\right)\right]
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$F_{max}=S_{y-screw}\cdot S/ \left[1+\cfrac{e\cdot c}{i^2}\right]$$
$F_{max}=S_{y-screw}\cdot S/ \left[1+\cfrac{e\cdot c}{i^2}\right]$
Equations in LaTeX code
F_{max}=S_{y-screw}\cdot S/ \left[1+\cfrac{e\cdot c}{i^2}\right]

Requirements

$$\cfrac{e\cdot c}{i^2}\geq 0.25$$
$\cfrac{e\cdot c}{i^2}\geq 0.25$
Equations in LaTeX code
\cfrac{e\cdot c}{i^2}\geq 0.25
$$\cfrac{F_{max}}{S_{FB}}\cdot C_c\geq F_A$$
$\cfrac{F_{max}}{S_{FB}}\cdot C_c\geq F_A$
Equations in LaTeX code
\cfrac{F_{max}}{S_{FB}}\cdot C_c\geq F_A
On this page