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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\in\mathbb{R}\mid F>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ F $ $ \mathrm{N} $
$ \{μ\in\mathbb{R}\mid μ>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ μ $
$ \{M_T\in\mathbb{R}\mid M_T>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ M_T $ $ \mathrm{Nm} $
$ \{S_{y-screw}\in\mathbb{R}\mid S_{y-screw}>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ S_{y-screw} $ $ \mathrm{MPa} $
$ \{E\in\mathbb{R}\mid E>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ E $ $ \mathrm{MPa} $
$ \{S_{y-nut}\in\mathbb{R}\mid S_{y-nut}>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ S_{y-nut} $ $ \mathrm{MPa} $
$ \{l\in\mathbb{R}\mid l>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ l $ $ \mathrm{mm} $
$ \{n\in\mathbb{R}\mid n>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ n $ $ \mathrm{rpm} $
$ C_c $
$ \{S_F\in\mathbb{R}\mid S_F>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ S_F $
$ β $
$ \{S_{FB}\in\mathbb{R}\mid S_{FB}>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ S_{FB} $
$ \{L\in\mathbb{R}\mid L>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ L $ $ \mathrm{mm} $
$ \{e\in\mathbb{R}\mid e>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ 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

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

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

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

Slenderness ratio

$$λ=\cfrac{L\cdot β}{i}$$
$λ=\cfrac{L\cdot β}{i}$
Equations in LaTeX code
λ=\cfrac{L\cdot β}{i}

Eccentricity parameter

$$η=\cfrac{e\cdot c}{i^2}$$
$η=\cfrac{e\cdot c}{i^2}$
Equations in LaTeX code
η=\cfrac{e\cdot c}{i^2}
$$η\geq 0.25$$
$η\geq 0.25$
Equations in LaTeX code
η\geq 0.25

Maximal (critical) force

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