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Interference fit

Interference fit l D h D D h D D 0 D 0 = 0 Δ max Δ max
Interference fit

Values for calculation

$ \{M_T\in\mathbb{R}\mid M_T\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ M_T $ $ \mathrm{Nm} $
$ \{D\in\mathbb{R}\mid D>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.
$ D $ $ \mathrm{mm} $
$ \{D_0\in\mathbb{R}\mid D_0\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ D_0 $ $ \mathrm{mm} $
$ \{D_h\in\mathbb{R}\mid D_h>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.
$ D_h $ $ \mathrm{mm} $
$ \{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} $
$ \{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 $
$ \{S_{y-shaft}\in\mathbb{R}\mid S_{y-shaft}>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-shaft} $ $ \mathrm{MPa} $
$ \{E_{shaft}\in\mathbb{R}\mid E_{shaft}>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_{shaft} $ $ \mathrm{MPa} $
$ \{ν_{shaft}\in\mathbb{R}\mid ν_{shaft}>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.
$ ν_{shaft} $
$ \{S_{y-hub}\in\mathbb{R}\mid S_{y-hub}>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-hub} $ $ \mathrm{MPa} $
$ \{E_{hub}\in\mathbb{R}\mid E_{hub}>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_{hub} $ $ \mathrm{MPa} $
$ \{ν_{hub}\in\mathbb{R}\mid ν_{hub}>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.
$ ν_{hub} $
$ 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 $
$ \{F_A\in\mathbb{R}\mid F_A\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ F_A $ $ \mathrm{kN} $
$ \{Δ_{max}\in\mathbb{R}\mid Δ_{max}>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.
$ Δ_{max} $ $ \mathrm{mm} $

Calculation

Allowable combined stress the hub

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

Allowable combined stress the shaft

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

Dimensional characteristics of the connection on diameter $ D_0 $

$$C_{D_0}=\cfrac{D^2+D_0^2}{D^2-D_0^2}$$
$C_{D_0}=\cfrac{D^2+D_0^2}{D^2-D_0^2}$
Equations in LaTeX code
C_{D_0}=\cfrac{D^2+D_0^2}{D^2-D_0^2}

Dimensional characteristics of the connection on diameter $ D $

$$C_{D}=\cfrac{D_h^2+D^2}{D_h^2-D^2}$$
$C_{D}=\cfrac{D_h^2+D^2}{D_h^2-D^2}$
Equations in LaTeX code
C_{D}=\cfrac{D_h^2+D^2}{D_h^2-D^2}

Min. contact pressure

$$p_{min}=\left(\cfrac{2\cdot M_T\cdot 10^3}{π\cdot D^2\cdot l\cdot μ}+\cfrac{F_A\cdot 10^3}{π\cdot D\cdot l\cdot μ}\right)\cdot\cfrac{S_F}{C_c}$$
$p_{min}=\left(\cfrac{2\cdot M_T\cdot 10^3}{π\cdot D^2\cdot l\cdot μ}+\cfrac{F_A\cdot 10^3}{π\cdot D\cdot l\cdot μ}\right)\cdot\cfrac{S_F}{C_c}$
Equations in LaTeX code
p_{min}=\left(\cfrac{2\cdot M_T\cdot 10^3}{π\cdot D^2\cdot l\cdot μ}+\cfrac{F_A\cdot 10^3}{π\cdot D\cdot l\cdot μ}\right)\cdot\cfrac{S_F}{C_c}

Max. contact pressure

$$p_{max}=\cfrac{Δ_{max}}{D\cdot\left(\cfrac{C_{D_0}-ν_{shaft}}{E_{shaft}}+\cfrac{C_{D}+ν_{hub}}{E_{hub}}\right)}$$
$p_{max}=\cfrac{Δ_{max}}{D\cdot\left(\cfrac{C_{D_0}-ν_{shaft}}{E_{shaft}}+\cfrac{C_{D}+ν_{hub}}{E_{hub}}\right)}$
Equations in LaTeX code
p_{max}=\cfrac{Δ_{max}}{D\cdot\left(\cfrac{C_{D_0}-ν_{shaft}}{E_{shaft}}+\cfrac{C_{D}+ν_{hub}}{E_{hub}}\right)}
$$p_{max}\geq p_{min}$$
$p_{max}\geq p_{min}$
Equations in LaTeX code
p_{max}\geq p_{min}

Min. Interference

$$Δ_{min}=p_{min}\cdot D\cdot\left(\cfrac{C_{D_0}-ν_{shaft}}{E_{shaft}}+\cfrac{C_{D}+ν_{hub}}{E_{hub}}\right)$$
$Δ_{min}=p_{min}\cdot D\cdot\left(\cfrac{C_{D_0}-ν_{shaft}}{E_{shaft}}+\cfrac{C_{D}+ν_{hub}}{E_{hub}}\right)$
Equations in LaTeX code
Δ_{min}=p_{min}\cdot D\cdot\left(\cfrac{C_{D_0}-ν_{shaft}}{E_{shaft}}+\cfrac{C_{D}+ν_{hub}}{E_{hub}}\right)

Radial stress in the hub on diameter $ D $

$$σ_{R-hub-D}=-p_{max}$$
$σ_{R-hub-D}=-p_{max}$
Equations in LaTeX code
σ_{R-hub-D}=-p_{max}

Tangential stress in the hub on diameter $ D $

$$σ_{T-hub-D}=p_{max}\cdot C_{D}$$
$σ_{T-hub-D}=p_{max}\cdot C_{D}$
Equations in LaTeX code
σ_{T-hub-D}=p_{max}\cdot C_{D}

Torsion stress in the hub on diameter $ D $

$$τ_{T-hub-D}=\cfrac{10^3\cdot M_T}{\cfrac{π}{16}\cdot\cfrac{D_h^4-D^4}{D}}$$
$τ_{T-hub-D}=\cfrac{10^3\cdot M_T}{\cfrac{π}{16}\cdot\cfrac{D_h^4-D^4}{D}}$
Equations in LaTeX code
τ_{T-hub-D}=\cfrac{10^3\cdot M_T}{\cfrac{π}{16}\cdot\cfrac{D_h^4-D^4}{D}}

Shear stress in the hub on diameter $ D $

$$τ_{S-hub-D}=\cfrac{10^3\cdot F_A}{π\cdot D\cdot l}$$
$τ_{S-hub-D}=\cfrac{10^3\cdot F_A}{π\cdot D\cdot l}$
Equations in LaTeX code
τ_{S-hub-D}=\cfrac{10^3\cdot F_A}{π\cdot D\cdot l}

Combined stress in the hub on diameter $ D $

$$σ_{tresca-hub-D}=\sqrt{σ_{T-hub-D}^2+σ_{R-hub-D}^2-\left(σ_{T-hub-D}\cdot σ_{R-hub-D}\right)+4\cdot(τ_{T-hub-D}^2+τ_{S-hub-D}^2)}$$
$σ_{tresca-hub-D}=\sqrt{σ_{T-hub-D}^2+σ_{R-hub-D}^2-\left(σ_{T-hub-D}\cdot σ_{R-hub-D}\right)+4\cdot(τ_{T-hub-D}^2+τ_{S-hub-D}^2)}$
Equations in LaTeX code
σ_{tresca-hub-D}=\sqrt{σ_{T-hub-D}^2+σ_{R-hub-D}^2-\left(σ_{T-hub-D}\cdot σ_{R-hub-D}\right)+4\cdot(τ_{T-hub-D}^2+τ_{S-hub-D}^2)}
$$σ_{tresca-hub-D}\le σ_{all-C-hub}$$
$σ_{tresca-hub-D}\le σ_{all-C-hub}$
Equations in LaTeX code
σ_{tresca-hub-D}\le σ_{all-C-hub}

Radial stress in the shaft on diameter $ D $

$$σ_{R-shaft-D}=-p_{max}$$
$σ_{R-shaft-D}=-p_{max}$
Equations in LaTeX code
σ_{R-shaft-D}=-p_{max}

Tangential stress in the shaft on diameter $ D $

$$σ_{T-shaft-D}=-p_{max}\cdot C_{D_0}$$
$σ_{T-shaft-D}=-p_{max}\cdot C_{D_0}$
Equations in LaTeX code
σ_{T-shaft-D}=-p_{max}\cdot C_{D_0}

Torsion stress in the shaft on diameter $ D $

$$τ_{T-shaft-D}=\cfrac{10^3\cdot M_T}{\cfrac{π}{16}\cdot\cfrac{D^4-D_0^4}{D}}$$
$τ_{T-shaft-D}=\cfrac{10^3\cdot M_T}{\cfrac{π}{16}\cdot\cfrac{D^4-D_0^4}{D}}$
Equations in LaTeX code
τ_{T-shaft-D}=\cfrac{10^3\cdot M_T}{\cfrac{π}{16}\cdot\cfrac{D^4-D_0^4}{D}}

Shear stress in the shaft on diameter $ D $

$$τ_{S-shaft-D}=τ_{S-hub-D}$$
$τ_{S-shaft-D}=τ_{S-hub-D}$
Equations in LaTeX code
τ_{S-shaft-D}=τ_{S-hub-D}

Combined stress in the shaft on diameter $ D $

$$σ_{tresca-shaft-D}=\sqrt{σ_{T-shaft-D}^2+σ_{R-shaft-D}^2-\left(σ_{T-shaft-D}\cdot σ_{R-shaft-D}\right)+4\cdot(τ_{T-shaft-D}^2+τ_{S-shaft-D}^2)}$$
$σ_{tresca-shaft-D}=\sqrt{σ_{T-shaft-D}^2+σ_{R-shaft-D}^2-\left(σ_{T-shaft-D}\cdot σ_{R-shaft-D}\right)+4\cdot(τ_{T-shaft-D}^2+τ_{S-shaft-D}^2)}$
Equations in LaTeX code
σ_{tresca-shaft-D}=\sqrt{σ_{T-shaft-D}^2+σ_{R-shaft-D}^2-\left(σ_{T-shaft-D}\cdot σ_{R-shaft-D}\right)+4\cdot(τ_{T-shaft-D}^2+τ_{S-shaft-D}^2)}
$$σ_{tresca-shaft-D}\le σ_{all-C-shaft}$$
$σ_{tresca-shaft-D}\le σ_{all-C-shaft}$
Equations in LaTeX code
σ_{tresca-shaft-D}\le σ_{all-C-shaft}

Radial stress in the shaft on diameter $ D_0 $

$\text{if }\ D_0=0$
$\text{if }\ D_0=0$
Equations in LaTeX code
\text{if }\ D_0=0
$$σ_{R-shaft-D_0}=-p_{max}$$
$σ_{R-shaft-D_0}=-p_{max}$
Equations in LaTeX code
σ_{R-shaft-D_0}=-p_{max}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$σ_{R-shaft-D_0}=0$$
$σ_{R-shaft-D_0}=0$
Equations in LaTeX code
σ_{R-shaft-D_0}=0

Tangential stress in the shaft on diameter $ D_0 $

$\text{if }\ D_0=0$
$\text{if }\ D_0=0$
Equations in LaTeX code
\text{if }\ D_0=0
$$σ_{T-shaft-D_0}=-p_{max}$$
$σ_{T-shaft-D_0}=-p_{max}$
Equations in LaTeX code
σ_{T-shaft-D_0}=-p_{max}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$σ_{T-shaft-D_0}=-p_{max}\cdot\left(C_{D_0}+1\right)$$
$σ_{T-shaft-D_0}=-p_{max}\cdot\left(C_{D_0}+1\right)$
Equations in LaTeX code
σ_{T-shaft-D_0}=-p_{max}\cdot\left(C_{D_0}+1\right)

Torsion stress in the shaft on diameter $ D_0 $

$\text{if }\ D_0=0$
$\text{if }\ D_0=0$
Equations in LaTeX code
\text{if }\ D_0=0
$$τ_{T-shaft-D_0}=0$$
$τ_{T-shaft-D_0}=0$
Equations in LaTeX code
τ_{T-shaft-D_0}=0
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$τ_{T-shaft-D_0}=\cfrac{10^3\cdot M_T}{\cfrac{π}{16}\cdot\cfrac{D^4-D_0^4}{D_0}}$$
$τ_{T-shaft-D_0}=\cfrac{10^3\cdot M_T}{\cfrac{π}{16}\cdot\cfrac{D^4-D_0^4}{D_0}}$
Equations in LaTeX code
τ_{T-shaft-D_0}=\cfrac{10^3\cdot M_T}{\cfrac{π}{16}\cdot\cfrac{D^4-D_0^4}{D_0}}

Combined stress in the shaft on diameter $ D_0 $

$$σ_{tresca-shaft-D_0}=\sqrt{σ_{T-shaft-D_0}^2+σ_{R-shaft-D_0}^2-\left(σ_{T-shaft-D_0}\cdot σ_{R-shaft-D_0}\right)+4\cdot τ_{T-shaft-D_0}^2}$$
$σ_{tresca-shaft-D_0}=\sqrt{σ_{T-shaft-D_0}^2+σ_{R-shaft-D_0}^2-\left(σ_{T-shaft-D_0}\cdot σ_{R-shaft-D_0}\right)+4\cdot τ_{T-shaft-D_0}^2}$
Equations in LaTeX code
σ_{tresca-shaft-D_0}=\sqrt{σ_{T-shaft-D_0}^2+σ_{R-shaft-D_0}^2-\left(σ_{T-shaft-D_0}\cdot σ_{R-shaft-D_0}\right)+4\cdot τ_{T-shaft-D_0}^2}
$$σ_{tresca-shaft-D_0}\le σ_{all-C-shaft}$$
$σ_{tresca-shaft-D_0}\le σ_{all-C-shaft}$
Equations in LaTeX code
σ_{tresca-shaft-D_0}\le σ_{all-C-shaft}
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