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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

$α$ $\mathrm{°}$
$β$ $\mathrm{°}$
$r$ $\mathrm{mm}$
$l$ $\mathrm{mm}$
$e$ $\mathrm{mm}$
$K_{Q-valve}[1]$
$K_{Q-valve}[2]$
$K_{Q-valve}[3]$
$K_{Q-valve}[4]$
$K_{Q-valve}[5]$
$K_{Q-valve}[6]$
$K_{Q-valve}[7]$
$K_{Q-valve}[8]$
$K_{Q-valve}[9]$
$K_{Q-valve}[10]$

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

$K_{Q-valve} \mathrm{[-]}$
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};
\%; ;

$K_Q \mathrm{[-]}$
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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