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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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