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The flow characteristic (crank mechanism)

The flow characteristic (crank mechanism) e l r α β 0% 100%
The flow characteristic (crank mechanism)

Values for calculation

$ \{α\in\mathbb{R}\mid α>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.
$ α $ $ \mathrm{°} $
$ \{β\in\mathbb{R}\mid β>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.
$ β $ $ \mathrm{°} $
$ \{r\in\mathbb{R}\mid r>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.
$ r $ $ \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} $
$ \{e\in\mathbb{R}\mid e\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.
$ e $ $ \mathrm{mm} $
$ \{K_{Q-valve}\in\mathbb{R}\mid K_{Q-valve}>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.
$ K_{Q-valve} $

Calculation

Stroke

$$S_{max}=\sqrt{l^2-\left(r\cdot\sin{α}-e\right)^2}+r\cdot\cos{α}-\sqrt{l^2-\left(r\cdot\sin{\left(α+β\right)}-e\right)^2}-r\cdot\cos{\left(α+β\right)}$$
$S_{max}=\sqrt{l^2-\left(r\cdot\sin{α}-e\right)^2}+r\cdot\cos{α}-\sqrt{l^2-\left(r\cdot\sin{\left(α+β\right)}-e\right)^2}-r\cdot\cos{\left(α+β\right)}$
Equations in LaTeX code
S_{max}=\sqrt{l^2-\left(r\cdot\sin{α}-e\right)^2}+r\cdot\cos{α}-\sqrt{l^2-\left(r\cdot\sin{\left(α+β\right)}-e\right)^2}-r\cdot\cos{\left(α+β\right)}
Stroke from open position
Angle rotation of the rocking motion
Stroke in the pivot position
Stroke percentage
Flow coefficient $ K_{Q-valve} $
Flow coefficient
$ s $ $ β_S $ $ S_S $ $ S_{S\%} $ $ K_{Q-valve} $ $ K_Q $
$ \mathrm{\%} $ $ \mathrm{°} $ $ \mathrm{mm} $ $ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Stroke from open position Angle rotation of the rocking motion Stroke in the pivot position Stroke percentage Flow coefficient $ K_{Q-valve} $ Flow coefficient
$ s $ $ β_S $ $ S_S $ $ S_{S\%} $ $ K_{Q-valve} $ $ K_Q $
$ \mathrm{\%} $ $ \mathrm{°} $ $ \mathrm{mm} $ $ \mathrm{\%} $ $ \mathrm{\ } $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position;Angle rotation of the rocking motion;Stroke in the pivot position;Stroke percentage;Flow coefficient $ K_{Q-valve} $ ;Flow coefficient;
s;β_S;S_S;S_{S\%};K_{Q-valve};K_Q;
\%;°;mm;\%; ; ;

$ β_S\ [\mathrm{°}] $
No data
$ s\ [\mathrm{\%}] $
Angle rotation of the rocking motion

Stroke from open position Angle rotation of the rocking motion
$ s $ $ β_S $
$ \mathrm{\%} $ $ \mathrm{°} $
No data
Unrounded data
Stroke from open position; Angle rotation of the rocking motion;
s; β_S;
\%; °;
$$β_S=\cfrac{β}{100}\cdot s$$
$β_S=\cfrac{β}{100}\cdot s$
Equations in LaTeX code
β_S=\cfrac{β}{100}\cdot s

$ S_S\ [\mathrm{mm}] $
No data
$ s\ [\mathrm{\%}] $
Stroke in the pivot position

Stroke from open position Stroke in the pivot position
$ s $ $ S_S $
$ \mathrm{\%} $ $ \mathrm{mm} $
No data
Unrounded data
Stroke from open position; Stroke in the pivot position;
s; S_S;
\%; mm;
$$S_S=S_{max}-\sqrt{l^2-\left(r\cdot\sin{α}-e\right)^2}-r\cdot\cos{α}+\sqrt{l^2-\left(r\cdot\sin{\left(α+β-β_S\right)}-e\right)^2}+r\cdot\cos{\left(α+β-β_S\right)}$$
$S_S=S_{max}-\sqrt{l^2-\left(r\cdot\sin{α}-e\right)^2}-r\cdot\cos{α}+\sqrt{l^2-\left(r\cdot\sin{\left(α+β-β_S\right)}-e\right)^2}+r\cdot\cos{\left(α+β-β_S\right)}$
Equations in LaTeX code
S_S=S_{max}-\sqrt{l^2-\left(r\cdot\sin{α}-e\right)^2}-r\cdot\cos{α}+\sqrt{l^2-\left(r\cdot\sin{\left(α+β-β_S\right)}-e\right)^2}+r\cdot\cos{\left(α+β-β_S\right)}

$ S_{S\%}\ [\mathrm{\%}] $
No data
$ s\ [\mathrm{\%}] $
Stroke percentage

Stroke from open position Stroke percentage
$ s $ $ S_{S\%} $
$ \mathrm{\%} $ $ \mathrm{\%} $
No data
Unrounded data
Stroke from open position; Stroke percentage;
s; S_{S\%};
\%; \%;
$$S_{S\%}=\cfrac{100}{S_{max}}\cdot S_S$$
$S_{S\%}=\cfrac{100}{S_{max}}\cdot S_S$
Equations in LaTeX code
S_{S\%}=\cfrac{100}{S_{max}}\cdot S_S

$ K_{Q-valve}\ [-] $
No data
$ s\ [\mathrm{\%}] $
Flow coefficient $ K_{Q-valve} $

Stroke from open position Flow coefficient $ K_{Q-valve} $
$ s $ $ K_{Q-valve} $
$ \mathrm{\%} $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position; Flow coefficient $ K_{Q-valve} $ ;
s; K_{Q-valve};
\%; ;

$ K_Q\ [-] $
No data
$ s\ [\mathrm{\%}] $
Flow coefficient

Stroke from open position Flow coefficient
$ s $ $ K_Q $
$ \mathrm{\%} $ $ \mathrm{\ } $
No data
Unrounded data
Stroke from open position; Flow coefficient;
s; K_Q;
\%; ;
$\text{if }\ s= 0$
$\text{if }\ s= 0$
Equations in LaTeX code
\text{if }\ s= 0
$$K_Q=K_{Q-valve}$$
$K_Q=K_{Q-valve}$
Equations in LaTeX code
K_Q=K_{Q-valve}
$\text{else if }\ s= 100$
$\text{else if }\ s= 100$
Equations in LaTeX code
\text{else if }\ s= 100
$$K_Q=K_{Q-valve}$$
$K_Q=K_{Q-valve}$
Equations in LaTeX code
K_Q=K_{Q-valve}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$K_Q=K_{Q-valve}-\cfrac{K_{Q-valve}-K_{Q-valve}[i+1]}{10}\cdot\left(S_{S\%}-s\right)$$
$K_Q=K_{Q-valve}-\cfrac{K_{Q-valve}-K_{Q-valve}[i+1]}{10}\cdot\left(S_{S\%}-s\right)$
Equations in LaTeX code
K_Q=K_{Q-valve}-\cfrac{K_{Q-valve}-K_{Q-valve}[i+1]}{10}\cdot\left(S_{S\%}-s\right)
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