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The flow characteristic (hydraulic cylinder)

The flow characteristic (hydraulic cylinder) r a b β α r a b β T L S S a 2 a 1 γ δ α
The flow characteristic (hydraulic cylinder)

Values for calculation

$α$ $\mathrm{°}$
$β$ $\mathrm{°}$
$r$ $\mathrm{mm}$
$a$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$L_d$ $\mathrm{\%}$
$T_c$ $\mathrm{s}$
$T_d$ $\mathrm{s}$
$K_{Q-valve}[1]$
$K_{Q-valve}[2]$
$K_{Q-valve}[3]$
$K_{Q-valve}[4]$
$K_{Q-valve}[5]$
$K_{Q-valve}[6]$
$K_{Q-valve}[7]$
$K_{Q-valve}[8]$
$K_{Q-valve}[9]$
$K_{Q-valve}[10]$

Calculation

Stroke

$$S_{max}=\sqrt{\left(b-r\cdot\sin{\left(α+β\right)}\right)^2+\left(a-r\cdot\cos{\left(α+β\right)}\right)^2}-\sqrt{\left(b-r\cdot\sin{\left(α\right)}\right)^2+\left(a-r\cdot\cos{\left(α\right)}\right)^2}$$
$S_{max}=\sqrt{\left(b-r\cdot\sin{\left(α+β\right)}\right)^2+\left(a-r\cdot\cos{\left(α+β\right)}\right)^2}-\sqrt{\left(b-r\cdot\sin{\left(α\right)}\right)^2+\left(a-r\cdot\cos{\left(α\right)}\right)^2}$
Equations in LaTeX code
S_{max}=\sqrt{\left(b-r\cdot\sin{\left(α+β\right)}\right)^2+\left(a-r\cdot\cos{\left(α+β\right)}\right)^2}-\sqrt{\left(b-r\cdot\sin{\left(α\right)}\right)^2+\left(a-r\cdot\cos{\left(α\right)}\right)^2}

Distance between the axis of rotation of the valve and the axis of the hydraulic cylinder

$$L=\sqrt{a^2+b^2}$$
$L=\sqrt{a^2+b^2}$
Equations in LaTeX code
L=\sqrt{a^2+b^2}

Requirements

$$α\geq\tan^{-1}{\cfrac{b}{a}}\cdot\cfrac{180}{π}$$
$α\geq\tan^{-1}{\cfrac{b}{a}}\cdot\cfrac{180}{π}$
Equations in LaTeX code
α\geq\tan^{-1}{\cfrac{b}{a}}\cdot\cfrac{180}{π}
$$β\le\tan^{-1}{\cfrac{b}{a}}\cdot\cfrac{180}{π}+180-α$$
$β\le\tan^{-1}{\cfrac{b}{a}}\cdot\cfrac{180}{π}+180-α$
Equations in LaTeX code
β\le\tan^{-1}{\cfrac{b}{a}}\cdot\cfrac{180}{π}+180-α
$$0.8\cdot T_c\geq T_d$$
$0.8\cdot T_c\geq T_d$
Equations in LaTeX code
0.8\cdot T_c\geq T_d
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