# Calculation of closing safety Spherical valve

## Values for calculation

$a$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$r$ $\mathrm{mm}$
$φ$ $\mathrm{°}$
$W_W$ $\mathrm{kg}$
$W_R$ $\mathrm{kg}$
$W_L$ $\mathrm{kg}$
$L_c$ $\mathrm{mm}$
$α_c$ $\mathrm{°}$
$P_{L-HC}$ $\mathrm{MPa}$
$D_{HC}$ $\mathrm{mm}$
$μ_B$
$r_T$ $\mathrm{mm}$
$f_B$
$e_S$ $\mathrm{mm}$
$P_S$ $\mathrm{MPa}$
$μ_S$

## Calculation

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

$$L=\sqrt{a^2+b^2}$$

### Friction torque in main sealing

$$M_S=D_s^2\cdot e_S\cdot μ_S\cdot P_S\cdot 10^{-6}$$
Angle from open position
Forces on rotating body
Hydraulic torque
$α$ $F$ $M_H$
$\mathrm{°}$ $\mathrm{kN}$ $\mathrm{kNm}$
No data

$F \mathrm{[kN]}$
 No data
$α\mathrm{[°]}$

$M_H \mathrm{[kNm]}$
 No data
$α\mathrm{[°]}$

Angle from open position
The distance between the axis of the hydraulic cylinder and the axis of the eye of the hydraulic cylinder
Height $T$
The angle between the axis of the hydraulic cylinder and the imaginary line between the axis of the closure and the pivot axis of the hydraulic cylinder
Distance between the axis of hydraulic cylinder and the axis of valve rotation
$α$ $S_S$ $T$ $γ$ $L_{HC}$
$\mathrm{°}$ $\mathrm{mm}$ $\mathrm{mm}$ $\mathrm{°}$ $\mathrm{mm}$
No data

$S_S \mathrm{[mm]}$
 No data
$α\mathrm{[°]}$

$$S_S=\sqrt{\left(b-r\cdot\sin{\left(φ-α\right)}\right)^2+\left(a-r\cdot\cos{\left(φ-α\right)}\right)^2}-\sqrt{\left(b-r\cdot\sin{\left(φ-90°\right)}\right)^2+\left(a-r\cdot\cos{\left(φ-90°\right)}\right)^2}+\sqrt{\left(b-r\cdot\sin{\left(φ-90°\right)}\right)^2+\left(a-r\cdot\cos{\left(φ-90°\right)}\right)^2}$$

$T \mathrm{[mm]}$
 No data
$α\mathrm{[°]}$

$$T=\sqrt{S_S^2-\left(\cfrac{L^2-r^2+S_S^2}{2\cdot L}\right)^2}$$

$γ \mathrm{[°]}$
 No data
$α\mathrm{[°]}$

$$γ=\sin^{-1}{\cfrac{T}{S_S}}\cdot\cfrac{180}{π}$$

$L_{HC} \mathrm{[mm]}$
 No data
$α\mathrm{[°]}$

$$L_{HC}=L\cdot\sin{γ}$$
Angle from open position
Static torque
Friction torque from the hydraulic cylinder
Force to the hydraulic cylinder during the closing at flow rate without frictional resistances
Force to the hydraulic cylinder during the closing without flow rate without frictional resistances
Pressure of oil under the hydraulic cylinder piston during the closing at flow rate without frictional resistances
Pressure of oil under the hydraulic cylinder piston during the closing without flow rate without frictional resistances
$α$ $M_W$ $M_{F-HC}$ $F_{HC-flow}$ $F_{HC}$ $P_{HC-flow}$ $P_{HC}$
$\mathrm{°}$ $\mathrm{kNm}$ $\mathrm{kNm}$ $\mathrm{kN}$ $\mathrm{kN}$ $\mathrm{MPa}$ $\mathrm{MPa}$
No data

$M_W \mathrm{[kNm]}$
 No data
$α\mathrm{[°]}$

$$M_W=\left(W_W+W_D+W_L\right)\cdot g\cdot L_c\cdot\sin{\left(α_c-α\right)}\cdot 10^{-6}$$

$M_{F-HC} \mathrm{[kNm]}$
 No data
$α\mathrm{[°]}$

$$M_{F-HC}=P_{L-HC}\cdot\cfrac{π\cdot D_{HC}^2}{4}\cdot L_{HC}\cdot 10^{-6}$$

$F_{HC-flow} \mathrm{[kN]}$
 No data
$α\mathrm{[°]}$

$$F_{HC-flow}=\cfrac{M_H+M_W}{L_{HC}}\cdot 10^3$$

$F_{HC} \mathrm{[kN]}$
 No data
$α\mathrm{[°]}$

$$F_{HC}=\cfrac{M_W}{L_{HC}}\cdot 10^3$$

$P_{HC-flow} \mathrm{[MPa]}$
 No data
$α\mathrm{[°]}$

$$P_{HC-flow}=\cfrac{4\cdot F_{HC-flow}\cdot 10^3}{π\cdot D_{HC}^2}$$

$P_{HC} \mathrm{[MPa]}$
 No data
$α\mathrm{[°]}$

$$P_{HC}=\cfrac{4\cdot F_{HC}\cdot 10^3}{π\cdot D_{HC}^2}$$
Angle from open position
Friction torque bearing during the closing at flow rate
Friction torque bearing during the closing without flow rate
Force to the hydraulic cylinder during the closing at flow rate with frictional resistances
Force to the hydraulic cylinder during the closing without flow rate with frictional resistances
$α$ $M_{B-flow}$ $M_B$ $F_{HC-flow-with-frictional}$ $F_{HC-with-frictional}$
$\mathrm{°}$ $\mathrm{kNm}$ $\mathrm{kNm}$ $\mathrm{kN}$ $\mathrm{kN}$
No data

$M_{B-flow} \mathrm{[kNm]}$
 No data
$α\mathrm{[°]}$

$$M_{B-flow}=\left(F+F_{HC-flow}+\left(W_W+W_D+W_L\right)\cdot g\cdot 10^{-3}\right)\cdot μ_B\cdot f_B\cdot r_T\cdot 10^{-3}$$

$M_B \mathrm{[kNm]}$
 No data
$α\mathrm{[°]}$

$$M_B=\left(F_{HC}+\left(W_W+W_D+W_L\right)\cdot g\cdot 10^{-3}\right)\cdot μ_B\cdot f_B\cdot r_T\cdot 10^{-3}$$

$F_{HC-flow-with-frictional} \mathrm{[kN]}$
 No data
$α\mathrm{[°]}$

$\text{if }\ α= 90$
$$F_{HC-flow-with-frictional}=\cfrac{M_H+M_W-M_{B-flow}-M_{F-HC}-M_S}{L_{HC}}\cdot 10^3$$
$\text{else}$
$$F_{HC-flow-with-frictional}=\cfrac{M_H+M_W-M_{B-flow}-M_{F-HC}}{L_{HC}}\cdot 10^3$$

$F_{HC-with-frictional} \mathrm{[kN]}$
 No data
$α\mathrm{[°]}$

$\text{if }\ α= 90$
$$F_{HC-with-frictional}=\cfrac{M_W-M_B-M_{F-HC}-M_S}{L_{HC}}\cdot 10^3$$
$\text{else}$
$$F_{HC-with-frictional}=\cfrac{M_W-M_B-M_{F-HC}}{L_{HC}}\cdot 10^3$$
Angle from open position
Pressure of oil under the hydraulic cylinder piston during the closing at flow rate with frictional resistances
Pressure of oil under the hydraulic cylinder piston during the closing without flow rate with frictional resistances
Safety factor during the closing at flow rate
Safety factor during the closing without flow rate
$α$ $P_{HC-flow-with-frictional}$ $P_{HC-with-frictional}$ $S_{f-flow}$ $S_f$
$\mathrm{°}$ $\mathrm{MPa}$ $\mathrm{MPa}$ $\mathrm{ }$ $\mathrm{ }$
No data

$P_{HC-flow-with-frictional} \mathrm{[MPa]}$
 No data
$α\mathrm{[°]}$

$$P_{HC-flow-with-frictional}=\cfrac{4\cdot F_{HC-flow-with-frictional}\cdot 10^3}{π\cdot D_{HC}^2}$$

$P_{HC-with-frictional} \mathrm{[MPa]}$
 No data
$α\mathrm{[°]}$

$$P_{HC-with-frictional}=\cfrac{4\cdot F_{HC-with-frictional}\cdot 10^3}{π\cdot D_{HC}^2}$$

$S_{f-flow} \mathrm{[-]}$
 No data
$α\mathrm{[°]}$

$\text{if }\ α= 90$
$$S_{f-flow}=\cfrac{M_H+M_W}{M_{F-HC}+M_{B-flow}+M_S}$$
$\text{else}$
$$S_{f-flow}=\cfrac{M_H+M_W}{M_{F-HC}+M_{B-flow}}$$

$S_f \mathrm{[-]}$
 No data
$α\mathrm{[°]}$

$\text{if }\ α= 90$
$$S_f=\cfrac{M_W}{M_{F-HC}+M_B+M_S}$$
$\text{else}$
$$S_f=\cfrac{M_W}{M_{F-HC}+M_B}$$