Calculation of closing safety Butterfly valve
Values for calculation
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 disc |
Hydraulic torque |
|---|---|---|
| $ α $ | $ F $ | $ M_H $ |
| $ \mathrm{°} $ | $ \mathrm{kN} $ | $ \mathrm{kNm} $ |
| No data | ||
$ F\ [\mathrm{kN}] $
| No data |
$ α\ [\mathrm{°}] $
$$F=\sqrt{F_x^2+F_y^2}$$
$ M_H\ [\mathrm{kNm}] $
| No data |
$ α\ [\mathrm{°}] $
$$M_H=M+M_{LD}+M_e$$
|
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{°}] $
$$F_{HC-flow-with-frictional}=\cfrac{M_H+M_W-M_{B-flow}-M_{F-HC}-M_S}{L_{HC}}\cdot 10^3$$
$$F_{HC-flow-with-frictional}=\cfrac{M_H+M_W-M_{B-flow}-M_{F-HC}}{L_{HC}}\cdot 10^3$$
$ F_{HC-with-frictional}\ [\mathrm{kN}] $
| No data |
$ α\ [\mathrm{°}] $
$$F_{HC-with-frictional}=\cfrac{M_W-M_B-M_{F-HC}-M_S}{L_{HC}}\cdot 10^3$$
$$F_{HC-with-frictional}=\cfrac{M_W-M_B-M_{F-HC}}{L_{HC}}\cdot 10^3$$
|
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}\ [-] $
| No data |
$ α\ [\mathrm{°}] $
$$S_{f-flow}=\cfrac{M_H+M_W}{M_{F-HC}+M_{B-flow}+M_S}$$
$$S_{f-flow}=\cfrac{M_H+M_W}{M_{F-HC}+M_{B-flow}}$$
$ S_f\ [-] $
| No data |
$ α\ [\mathrm{°}] $
$$S_f=\cfrac{M_W}{M_{F-HC}+M_B+M_S}$$
$$S_f=\cfrac{M_W}{M_{F-HC}+M_B}$$