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Disc compression springs (given the force on spring)

Disc compression springs D 0 D f δ
Disc compression springs

Values for calculation

$ \{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>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_0 $ $ \mathrm{mm} $
$ \{δ\in\mathbb{R}\mid δ>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 $ $ \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{GPa} $
$ \{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} $
$ \{σ_{adm}\in\mathbb{R}\mid σ_{adm}>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.
$ σ_{adm} $ $ \mathrm{MPa} $

Calculation

Tensile stress

$$σ=\cfrac{F\cdot\left(1-2/3\cdot D_0/D\right)}{δ^2}$$
$σ=\cfrac{F\cdot\left(1-2/3\cdot D_0/D\right)}{δ^2}$
Equations in LaTeX code
σ=\cfrac{F\cdot\left(1-2/3\cdot D_0/D\right)}{δ^2}
$$σ\le σ_{adm}$$
$σ\le σ_{adm}$
Equations in LaTeX code
σ\le σ_{adm}

Spring deflection

$$f=\cfrac{0.65\cdot\left(\cfrac{D}{2}\right)^2}{E\cdot 10^3\cdot δ\cdot\left(1-2/3\cdot D_0/D\right)}\cdot σ$$
$f=\cfrac{0.65\cdot\left(\cfrac{D}{2}\right)^2}{E\cdot 10^3\cdot δ\cdot\left(1-2/3\cdot D_0/D\right)}\cdot σ$
Equations in LaTeX code
f=\cfrac{0.65\cdot\left(\cfrac{D}{2}\right)^2}{E\cdot 10^3\cdot δ\cdot\left(1-2/3\cdot D_0/D\right)}\cdot σ

Spring stiffness

$$k=\cfrac{F}{f\cdot 10^{-3}}$$
$k=\cfrac{F}{f\cdot 10^{-3}}$
Equations in LaTeX code
k=\cfrac{F}{f\cdot 10^{-3}}
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